Publications

close

close

close

close

close

close

close

close

close

close

close

close

close

close

close

close

close

close

close

close

close

close

close

close

close

close

close

close

close

close

close

close

close

close

close

close

close

close

close

close

close

A fully parallel version of the contact dynamics (CD) method is presented in this paper. For large enough systems, 100% efficiency has been demonstrated for up to 256 processors using a hierarchical domain decomposition with dynamic load balancing. The iterative scheme to calculate the contact forces is left domain-wise sequential, with data exchange after each iteration step, which ensures its stability. The number of additional iterations required for convergence by the partially parallel updates at the domain boundaries becomes negligible with increasing number of particles, which allows for an effective parallelization. Compared to the sequential implementation, we found no influence of the parallelization on simulation results. (C) 2011 Elsevier Inc. All rights reserved.

close

We developed a three-dimensional, atomistic model based on the kinetic Monte Carlo method to investigate how voids penetrating a monocrystalline silver film are affected by electromigration. The simulations show a clear dependency between the nonequilibrium shape of the voids and the crystallographic orientation of the film. The simulation results are in accordance with experimental results on bicrystalline silver wires.

close

We study the effect of polydispersity on the macroscopic physical properties of granular packings in two and three dimensions. A mean-field approach is developed to approximate the macroscale quantities as functions of the microscopic ones. We show that the trace of the fabric and stress tensors are proportional to the mean packing properties (e.g., packing fraction, average coordination number, and average normal force) and dimensionless correction factors, which depend only on the moments of the particle-size distribution. Similar results are obtained for the elements of the stiffness tensor of isotropic packings in the linear affine response regime. Our theoretical predictions are in good agreement with the simulation results.

close

A recently proposed statistical model for the effects of decoherence on electron transport manifests a decoherence-driven transition from quantum-coherent localized to Ohmic behavior when applied to the one-dimensional Anderson model. Here we derive the resistivity in the Ohmic case and show that the transition to localized behavior occurs when the coherence length surpasses a value which only depends on the second-order generalized Lyapunov exponent xi(-1). We determine the exact value of xi(-1) of an infinite system for arbitrary uncorrelated disorder and electron energy. Likewise all higher even-order generalized Lyapunov exponents can be calculated, as exemplified for fourth order. An approximation for the localization length (inverse standard Lyapunov exponent) is presented, by assuming a log-normal limiting distribution for the dimensionless conductance T. This approximation works well in the limit of weak disorder, with the exception of the band edges and the band center.

close

close

We investigate the effective long-range interactions between intruder particles immersed in a randomly driven granular fluid. The effective Casimir-like force between two intruders, induced by the fluctuations of the hydrodynamic fields, can change its sign when varying the control parameters: the volume fraction, the distance between the intruders, and the restitution coefficient. More interestingly, by inserting more intruders, we verify that the fluctuation-induced interaction is not pairwise additive. The simulation results are qualitatively consistent with the theoretical predictions based on mode coupling calculations. These results shed new light on the underlying mechanisms of collective behaviors in fluidized granular media.

close

Unilateral interparticle interactions have an effect on the elastic response of granular materials due to the opening and closing of contacts during quasi-static shear deformations. A simplified model is presented, for which constitutive relations can be derived. For biaxial deformations the elastic behavior in this model involves three independent elastic moduli: bulk, shear, and anisotropy modulus. The bulk and the shear modulus, when scaled by the contact density, are independent of the deformation. However, the magnitude of the anisotropy modulus is proportional to the ratio between shear and volumetric strain. Sufficiently far from the jamming transition, when corrections due to non-affine motion become weak, the theoretical predictions are qualitatively in agreement with simulation results.

close

The nonequilibrium phase transition in driven two-dimensional Ising models with two different geometries is investigated using Monte Carlo methods as well as analytical calculations. The models show dissipation through fluctuation induced friction near the critical point. We first consider high driving velocities and demonstrate that both systems are in the same universality class and undergo a strongly anisotropic nonequilibrium phase transition, with anisotropy exponent theta = 3. Within a field theoretical ansatz the simulation results are confirmed. The crossover from Ising to mean field behavior in dependency of system size and driving velocity is analyzed using crossover scaling. It turns out that for all finite velocities the phase transition becomes strongly anisotropic in the thermodynamic limit.

close

We study a two-dimensional kinetic Ising model with Swendsen-Wang dynamics, replacing the usual percolation on top of Ising clusters by explosive percolation. The model exhibits a reversible first-order phase transition with hysteresis. Surprisingly, at one of the transition flanks the global bond density seems to be equal to the percolation threshold.

close

We report on a numerical study of the shear flow of a simple two-dimensional model of a granular material under controlled normal stress between two parallel smooth frictional walls moving with opposite velocities +/- V. Discrete simulations, which are carried out with the contact dynamics method in dense assemblies of disks, reveal that, unlike rough walls made of strands of particles, smooth ones can lead to shear strain localization in the boundary layer. Specifically, we observe, for decreasing V, first a fluidlike regime (A), in which the whole granular layer is sheared, with a homogeneous strain rate except near the walls, then (B) a symmetric velocity profile with a solid block in the middle and strain localized near the walls, and finally (C) a state with broken symmetry in which the shear rate is confined to one boundary layer, while the bulk of the material moves together with the opposite wall. Both transitions are independent of system size and occur for specific values of V. Transient times are discussed. We show that the first transition, between regimes A and B, can be deduced from constitutive laws identified for the bulk material and the boundary layer, while the second one could be associated with an instability in the behavior of the boundary layer. The boundary zone constitutive law, however, is observed to depend on the state of the bulk material nearby.

close

The role of rotational degrees of freedom and of microscopic contact properties at smooth walls in two dimensional planar shear has been investigated by contact dynamics simulations of round hard frictional particles. Our default system setup consists of smooth frictional walls, giving rise to slip. We show that there exists a critical microscopic friction coefficient at the walls, above which they are able to shear the granular medium. We observe distinctive features at this critical point, which to our knowledge have not been reported before. Activating rolling friction at smooth walls reduces slip, leading to similar shear behavior as for rough walls (with particles glued on their surface). Our simulations with rough walls are in agreement with previous results, provided the roughness is strong enough. In the limit of small roughness amplitude, however, the distinctive features of shearing with smooth walls are confirmed.

close

close

close

close

close

close

Nanocrystalline bulk materials are desirable for many applications as they combine mechanical strength and specific electronic transport properties. Our bottom-up approach starts with tailored nanoparticles. Compaction and thermal treatment are crucial, but usually the final stage sintering is accompanied by rapid grain growth which spoils nanocrystallinity. For electrically conducting nanoparticles, field activated sintering techniques overcome this problem. Small grain sizes have been maintained in spite of consolidation. Nevertheless, the underlying principles, which are of high practical importance, have not been fully elucidated yet. In this combined experimental and theoretical work, we show how the developing microstructure during sintering correlates with the percolation paths of the current through the powder using highly doped silicon nanoparticles as a model system. It is possible to achieve a nanocrystalline bulk material and a homogeneous microstructure. For this, not only the generation of current paths due to compaction, but also the disintegration due to Joule heating is required. The observed density fluctuations on the micrometer scale are attributed to the heat profile of the simulated powder networks.

close

Energy dissipation is studied for a hard magnetic tip that scans a soft magnetic substrate. The dynamics of the atomic moments are simulated by solving the Landau-Lifshitz-Gilbert (LLG) equation numerically. The local energy currents are analysed for the case of a Heisenberg spin chain taken as substrate. This leads to an explanation for the velocity dependence of the friction force: The non-linear contribution for high velocities can be attributed to a spin wave front pushed by the tip along the substrate. Copyright (C) EPLA, 2011

close

We demonstrate that in a ferromagnetic substrate which is continuously driven out of equilibrium by a field moving with constant velocity v, at least two types of friction may occur when v goes to zero. The substrate may feel a friction force proportional to v (Stokes friction) if the field changes on a time scale which is larger than the intrinsic relaxation time. On the other hand, the friction force may become independent of v in the opposite case (Coulomb friction). These observations are analogous to, e.g., solid friction. The effect is demonstrated in both the Ising (one spin dimension) and the Heisenberg (three spin dimensions) models, irrespective of which kind of dynamics (Metropolis spin-flip dynamics or Landau-Lifshitz-Gilbert precessional dynamics) is used. For both models the limiting case of Coulomb friction can be treated analytically. Furthermore we present an empiric expression reflecting the correct Stokes behavior and therefore yielding the correct crossover velocity and dissipation.

close

We present a visco-elastic coupling model between caked spheres, suitable for Distinct Element Method simulations, which incorporates the different loading mechanisms (tension, shear, bending, torsion) in a combined manner and allows for a derivation of elastic and failure properties on a common basis. In pull, shear, and torsion failure tests with agglomerates of up to 10.000 particles, we compare the failure criterion to different approximative variants of it, with respect to accuracy and computational cost. The failure of the agglomerates, which behave according to elastic parameters derived from the contact elasticity, gives also insight into the relative relevance of the different load modes.

close

In this paper we present a novel experimental setup created to measure the strength of solid bridges between double-particle systems in the millimeter range. Beside the tensile strength, shear and torsional strength can be measured as well. Urea particles are used which are known for creating solid bridges under well defined climatic conditions. The measurements indicate that unlike to isotropic materials the bridge between two particles has higher shear than tensile strength. Moreover, the strengthening of the bridges with storage time is very inhomogeneous, suggesting the use of wide distribution for bridge strength instead of mean values in modelling.

close

In this paper we present a novel experimental setup created to measure the strength of solid bridges between double-particle systems in the millimeter range. Beside the tensile strength, shear and torsional strength can be measured as well. Urea particles are used which are known for creating solid bridges under well defined climatic conditions. The measurements indicate that unlike to isotropic materials the bridge between two particles has higher shear than tensile strength. Moreover, the strengthening of the bridges with storage time is very inhomogeneous, suggesting the use of wide distribution for bridge strength instead of mean values in modelling.

close

True biaxial tests of granular materials are investigated by applying the principle of minimal dissipation and comparing to two dimensional contact dynamics simulations. It is shown that the macroscopic steady state manifested by constant stress ratio and constant volume is the result of the ever changing microscopic structure which minimizes the dissipation rate. The shear band angle in the varying shear band structures is found to be constant. We also show that introducing friction on the walls reduces the degeneracy of the optimal shear band structures to one for a wide range of parameters which gives a non-constant stress ratio curve with varying aspect ratio that can be calculated.

close

close

close

The influence of decoherence and bonding on the linear conductance of single double-stranded DNA molecules is examined by fitting a phenomenological statistical model developed recently [M. Zilly, O. Ujsaghy, and D. E. Wolf, Eur. Phys. J. B 68, 237 (2009)] to experimental results. The DNA molecule itself is described by a tight-binding ladder model with parameters obtained from published ab initio calculations [K. Senthilkumar, F. C. Grozema, C. F. Guerra, F. M. Bickelhaupt, F. D. Lewis, Y. A. Berlin, M. A. Ratner, and L. D. A. Siebbeles, J. Am. Chem. Soc. 127, 14894 (2005)]. The good agreement with the experiments on sequence and length dependence gives a hint on the nature of conduction in DNA and at the same time provides a crucial test of the model.

close

close

close

We present a statistical model for the effects of dephasing on the transport properties of large devices. The physical picture is different from earlier models which assume that dephasing happens continuously throughout the sample, whereas we model the dephasing in a statistical sense, assuming a distribution of completely phase randomizing regions between which the transport is coherent and described by the nonequilibrium Green's function method. Thus the sample is effectively divided into smaller parts making the numerical treatment more efficient. As a first application the conductances of ordered and disordered linear tight-binding chains are calculated and compared to the results of other phenomenological models in the literature.

close

Energy dissipation via spin excitations is investigated for a hard ferromagnetic tip scanning a soft magnetic monolayer. We use the classical Heisenberg model with Landau-Lifshitz-Gilbert (LLG) dynamics including a stochastic field representing finite temperatures. The friction force depends linearly on the velocity ( provided it is small enough) for all temperatures. For low temperatures, the corresponding friction coefficient is proportional to the phenomenological damping constant of the LLG equation. This dependence is lost at high temperatures, where the friction coefficient decreases exponentially. These findings can be explained by properties of the spin polarisation cloud dragged along with the tip. Copyright (C) EPLA, 2009

close

A magnetic dipole moving parallel to a ferromagnetically interacting surface is subject to a friction force due to the conversion of kinetic energy into spin excitations. This phenomenon is studied in the framework of the classical anisotropic Heisenberg-model, using the stochastic Landau-Lifshitz-Gilbert equation. The friction force is calculated from dissipation rates, which are obtained directly from energy functions. For small velocities, magnetic friction increases linearly (like Stokes' law for laminar flow). The characteristic low-and high-temperature behavior is analyzed and explained by a relaxation time ansatz.

close

Static packings of frictional rigid particles are investigated by means of discrete element simulations. We explore the ensemble of allowed force realizations in the space of contact forces for a given packing structure. We estimate the extent of force indeterminacy with different methods. The indeterminacy exhibits a nonmonotonic dependence on the interparticle friction coefficient. We verify directly that larger force indeterminacy is accompanied by a more robust behavior against local perturbations. We also investigate the local indeterminacy of individual contact forces. The probability distribution of local indeterminacy changes its shape depending on friction. We find that local indeterminacy tends to be larger on force chains for intermediate friction. This correlation disappears in the large friction limit.

close

The contact dynamics (CD) method is an efficient simulation technique of dense granular media where unilateral and frictional contact problems for a large number of rigid bodies have to be solved. In this paper, we present a modified version of the CD to generate homogeneous random packings of rigid grains. CD simulations are performed at constant external pressure, which allows the variation of the size of a periodically repeated cell. We follow the concept of the Andersen dynamics and show how it can be applied within the framework of the CD method. The main challenge here is to handle the interparticle interactions properly, which are based on constraint forces in CD. We implement the proposed algorithm, perform test simulations, and investigate the properties of the final packings.

close

close

close

close

We study a simplified model for pulsed laser deposition [Hinnemann , Phys. Rev. Lett. 87, 135701 (2001)] by rate equations. We consider a set of equations where islands are assumed to be pointlike, as well as an improved one that takes the size of the islands into account. The first set of equations is solved exactly but its predictive power is restricted to a few pulses. The improved set of equations is integrated numerically, is in excellent agreement with simulations, and fully accounts for the crossover from continuous to pulsed deposition. Moreover, we analyze the scaling of the nucleation density and show numerical results indicating that a previously observed logarithmic scaling does not apply.

close

We theoretically study the occurrence of magnetic friction of a nanometer-sized tip scanning a magnetic surface by studying the dynamics of a model of classical spins interacting through dipolar and exchange interactions, neglecting thermal effects. We find that for small scanning velocities, the friction force linearly scales with the velocity, with a slope proportional to the phenomenological damping parameter of the Landau-Lifshitz-Gilbert equation. At higher velocities, the friction vs velocity relationship becomes rather complex with the presence of a maximum that is explained by the excitations of spin-wave resonances in the sample.

close

The structural evolution of a nanopowder by repeated dispersion and settling can lead to characteristic fractal substructures. This is shown by numerical simulations of a two-dimensional model agglomerate of adhesive rigid particles. The agglomerate is cut into fragments of a characteristic size l, which then are settling under gravity. Repeating this procedure converges to a loosely packed structure, the properties of which are investigated: ( a) The final packing density is independent of the initialization, (b) the short-range correlation function is independent of the fragment size, ( c) the structure is fractal up to the fragmentation scale l with a fractal dimension close to 1.7, and (d) the relaxation time increases linearly with l.

close

Steady state flow of powders is a crucial concept to investigate the powders' strength and flow properties. This state is defined as a continuous deformation of the material without volume change while the stresses at the specimen's boundaries remain constant. Recent investigations have shown that this state, especially for cohesive powders, is not always as constant as it should be by definition. This paper presents experimental and numerical work, both for cohesive and non-cohesive powders. The experimental part focuses on the use of different control strategies, leading to steady state flow of different quality. Differences between steady state flow for cohesive and non-cohesive powders are shown.

close

Steady-state flow of powders is defined as a continuous deformation of the material without volume change while the stresses at the specimen's boundaries remain constant. Recent investigations have shown that this state, especially for cohesive powders, is not always as steady as it should be by definition. In this article a recent extension of the true biaxial shear tester is introduced that allows a view of the shear motion of the brick-shaped powder specimen inside the tester. By applying a dark-colored powder pattern onto a light powder sample, the movement of the powder can be captured using a CCD camera. Development of shear bands and inhomogeneities of the sample can be visualized. Experiments with a cohesive powder with purely strain-controlled, volume-preserving shear cycles, as well as mixed stress-strain controlled experiments, are presented. The recorded images as well as stress-strain data from discrete elements simulations are compared to the experimental results.

close

The relationship between an external stress applied to a bulk and its resulting porosity-i.e. its compaction behavior-is studied in this work, varying the median particle diameter by using different batches of carbonyl iron powder (CIP) as well as by mixing them. Firstly, compaction equations of other authors and an algebraic relation suggested by us are presented. Secondly, these descriptions are compared to data obtained by compacting CIP. Last, for powder mixtures, the role of the particles' median and mean diameters is studied in experiments and DEM-simulations, respectively. We show that they take on the role of the relevant length scale appearing in the algebraic compaction law.

close

A new contribution to friction is predicted to occur in systems with magnetic correlations: Tangential relative motion of two Ising spin systems pumps energy into the magnetic degrees of freedom. This leads to a friction force proportional to the area of contact. The velocity and temperature dependence of this force are investigated. Magnetic friction is strongest near the critical temperature, below which the spin systems order spontaneously. Antiferromagnetic coupling leads to stronger friction than ferromagnetic coupling with the same exchange constant. The basic dissipation mechanism is explained. A surprising effect is observed in the ferromagnetically ordered phase: The relative motion can act like a heat pump cooling the spins in the vicinity of the friction surface.

close

In suspensions with charged particles, electrostatic forces and hydrodynamic interactions are both important to describe the system. We study different models of hydrodynamic interaction for monopolarly charged particles in a non-polar liquid. In this case, there is no screening of the Coulomb repulsion, so the repulsion between all pairs must be taken into account. The particles are expected to drift away from each other, however at a lower rate when hydrodynamic interaction between the particles is taken into account. Existing, frequently used models of hydrodynamic interactions tend to overestimate the slowing down of the charged particles, even to the extent that the particles effectively attract each other. This is demonstrated for some selected particle setups. We find that these anomalies even occur in dilute systems, if they contain sufficiently many particles. We explain why these anomalies can be avoided by an approach, in which the superposition of interactions is done in the friction tensor instead of the mobility tensor.

close

Complementary experimental and theoretical results on the coalescence of nanoparticles demonstrate the importance of the crystallographic orientation on the coalescence process. In situ hot-stage transmission electron microscopy studies on self-supporting films consisting of indium tin oxide nanoparticles clearly show rotations of neighboring particles preceding their coalescence. Both rotation and coalescence are observed well below half the melting temperature. The coalescence of two adjacent nanoparticles is simulated by means of a combination of the kinetic Monte Carlo method for atomic diffusion with an integration of the equations of motion for the rigid body degrees of freedom of the two particles. This allows analyzing the reorientation of the two crystal lattices prior to the merging process. Thus, nanoparticle coalescence has theoretically as well as experimentally been shown to be a two-step process: first a reorientation of adjacent nanoparticles, and second their complete or incomplete coalescence depending on the matching of the crystallographic orientations.

close

The sintering of Ni nanoparticle agglomerates in the gas phase is studied. The partially or completely sintered agglomerates are characterized in flight by in situ electrical mobility measurement and after their deposition by transmission electron microscopy. The mobility diameter, the mean primary particle diameter, and the total surface area of the agglomerates are determined as functions of the sintering temperature. The experimental results are analyzed using an empirical law for the primary particle coarsening as well as by means of a modified Koch-Friedlander theory. It turns out that the activation energy for the dominating diffusion process is E-a=0.6 eV/atom, which is characteristic for surface diffusion in Ni. Our analysis provides a consistent picture with respect to both the temperature dependence of the characteristic sintering time and the mean diffusion length.

close

We introduce a model to describe the wide shear zones observed in modified Couette cell experiments with granular material. The model is a generalization of the recently proposed approach based on a variational principle. The instantaneous shear band is identified with the surface that minimizes the dissipation in a random potential that is biased by the local velocity difference and pressure. The apparent shear zone is the ensemble average of the instantaneous shear bands. The numerical simulation of this model matches excellently with experiments and has measurable predictions.

close

The properties of shear zones forming in slow three-dimensional granular flow are investigated. We simulate a straight version of the split-bottom shear cell. It is shown that the same type of wide shear zones is obtained in the presence as well as in the absence of gravity. We investigate the relaxation of the material toward stationary flow and analyze the stress and the velocity fields. A functional form of the widening of the shear zone inside the bulk is given. We discuss the growth of the region where the material is in the critical state. The growth of this critical zone turns out to be responsible for the initial transient of the shear zone.

close

Cemented granular materials (CGMs) consist of densely packed solid particles and a pore-filling solid matrix sticking to the particles. We use a sub-particle lattice discretization method to investigate the particle-scale origins of strength and failure properties of CGMs. We show that jamming of the particles leads to highly inhomogeneous stress fields. The stress probability density functions are increasingly wider for a decreasing matrix volume fraction, the stresses being more and more concentrated in the interparticle contact zones with an exponential distribution as in cohesionless granular media. Under uniaxial loading, pronounced asymmetry can occur between tension and compression both in strength and in the initial stiffness as a result of the presence of bare contacts (with no matrix interposed) between the particles. Damage growth is analyzed by considering the evolution of stiffness degradation and the number of broken bonds in the particle phase. A brutal degradation appears in tension as a consequence of brittle fracture in contrast to the more progressive nature of damage growth in compression. We also carry out a detailed parametric study in order to assess the combined influence of the matrix volume fraction and particle-matrix adherence. Three regimes of crack propagation can be distinguished corresponding to no particle damage, particle abrasion and particle fragmentation, respectively. We find that particle damage scales well with the relative toughness of the particle-matrix interface with respect to the particle toughness. This relative toughness is a function of both matrix volume fraction and particle-matrix adherence and it appears therefore to be the unique control parameter governing transition from soft to hard behavior.

close

The majority of experimental and theoretical friction studies considers translational motion, where all coarse-grained interface elements are displaced alike. An additional rotation of the slider introduces a well controlled displacement inhomogeneity across the interface. The friction response now consists of a force and a torque that are generally coupled. Recent results for a cylindrical slider are reviewed and applied to rigid objects with rotational symmetry about an axis. It is predicted that the difference between static and dynamic friction force can be suppressed, if a certain torque is applied. Moreover, we study the dynamics of the transition from sticking to sliding.

close

We present a Monte Carlo algorithm that facilitates efficient parallel tempering simulations of the density of states g(E). We show that the algorithm eliminates the supercritical slowing down in the case of the Q=20 and Q=256 Potts models in two dimensions, typical examples for systems with extreme first-order phase transitions. As recently predicted, and shown here, the microcanonical heat capacity along the calorimetric curve has negative values for finite systems.

close

close

This report discusses the use of the discrete element method (DEM) to the porosity distribution of spherical particles in narrow pipes as a function of the pipe-to-particle diameter ratio. It was found that the packing structure depends mainly on the pipe-to-particle ratio and the particle friction. The numerical results with respect to the radial porosity distribution are in agreement with experimental data from the literature. Radial porosity distributions were calculated using algorithms developed by Mueller. The packing structure of the particles shows channeling for small pipe to particle diameter ratios. The simulated height averaged porosity distribution agrees with models from the literature. Moreover, DEM provides the possibility to include particle properties which reflect on the porosity distribution. (c) 2006 Elsevier B.V. All rights reserved.

close

Two dimensional simulations of non-cohesive granular matter in a biaxial shear tester are discussed. The effect of particle elasticity on the mechanical behavior is investigated using two complementary distinct element methods (DEM): Soft particle molecular dynamics simulations (Particle Flow Code, PFC) for elastic particles and contact dynamics simulations (CD) for the limit of perfectly rigid particles. As soon as the system dilates to form shear bands, it relaxes the elastic strains so that one finds the same stresses for rigid respectively elastic particles in steady state flow. The principal stresses in steady state flow are determined. They are proportional to each other, giving rise to an effective macroscopic friction coefficient which is about 10% smaller than the microscopic friction coefficient between the grains.

close

In this study we discuss methods for solving random resistor networks and similar problems. We discuss the node elimination method and we demonstrate its equivalence to the Gaussian elimination scheme, finding a good elimination order, which makes the method highly efficient. The transfer matrix method is shown to be a special case of the node elimination method with an ordering that is far from optimal. We compare the performance of these exact methods with a state of the art conjugate gradient solver. In general, the node elimination method is the faster method. (c) 2005 Elsevier Inc. All rights reserved.

close

We present numerical results on spontaneous symmetry breaking strain localization in axisymmetric triaxial shear tests of granular materials. We simulated shear band formation using the three-dimensional distinct element method with spherical particles. We demonstrate that the local shear intensity, the angular velocity of the grains, the coordination number, and the local void ratio are correlated and any of them can be used to identify shear bands; however, the latter two are less sensitive. The calculated shear band morphologies are in good agreement with those found experimentally. We show that boundary conditions play an important role. We discuss the formation mechanism of shear bands in the light of our observations and compare the results with experiments. At large strains, with enforced symmetry, we found strain hardening.

close

We study the aggregation of insulating electrically charged spheres suspended in a nonpolar liquid. Regarding the van der Waals interaction as an irreversible sticking force, we are especially interested in the charge distribution after aggregation. Solving the special case of two oppositely charged particles exactly, it is shown that the surface charges either recombine or form a residual dipole, depending on the initial condition. The theoretical findings are compared to numerical results from Monte Carlo simulations.

close

We investigate the rheology of dense cohesive granular media outside the quasistatic regime using molecular dynamic simulations of homogeneous plane shear flow in the steady state. Friction as well as dilatancy are governed by two dimensionless numbers, the inertial number and the cohesion number. The internal friction coefficient and the solid fraction depend linearly on the inertial number, as in the cohesionless case. Weak cohesion leads to an expansion of the material, while the friction remains unchanged. Above a characteristic cohesion strength, a strong increase of friction combined with a decrease of solid fraction is observed. We relate this behavior to the growing space-time heterogeneities and to the increase of the cohesion-enhanced microscopic friction between the grains.

close

This paper describes the modeling of the toner behavior in the development nip of the Oce Direct Imaging print process. The discrete element method (DEM) is used as the simulation tool for a quantitative description of the system. The interaction rules and the associated parameters are determined for the toner particles and the surfaces of the development rollers. The model is validated with print quality results. It is shown that it is possible to achieve quantitative agreement between DEM simulations and experimental print quality results.

close

In order to control the aggregation phenomena in suspensions of nanoparticles, one often charges the particles electrically in order to delay or even suppress the aggregation process. The resulting cumulative size distribution of agglomerates of monopolarly charged nanoparticles suspended in liquid nitrogen is measured experimentally. The distribution is compared to results obtained by mean field theory. The relative width of the distribution obeys the lower bound predicted by theory. The results are discussed with respect to technical applications, e.g. stabilization of suspensions against aggregation. (c) 2006 Elsevier B.V. All rights reserved.

close

close

close

close

close

close

close

The porosity of uniaxially compacted cohesive powders depends on the applied stress (including gravity). The case, where these stresses are weak, is considered. The compaction results in a porosity which is a function of sliding, rolling and torsion friction. By contact dynamics simulations it is shown that the influences of contact torques (static rolling and torsion friction) on the porosity are significant and approximately additive. The relevance for nano-powder pressure sintering is discussed.

close

A simple model for solid friction is analysed. It is based on tangential springs representing interlocked asperities of the surfaces in contact. Each spring is given a maximal strain according to a probability distribution. At their maximal strain the springs break irreversibly. Initially all springs are assumed to have zero strain, because at static contact local elastic stresses are expected to relax. Relative tangential motion of the two solids leads to a loss of coherence of the initial state: the springs get out of phase due to differences in their sizes. This mechanism alone is shown to lead to a difference between static and dynamic friction forces already. We find that in this case the ratio of the static and dynamic coefficients decreases with increasing relative width of the probability distribution, and has a lower bound of 1 and an upper bound of 2.

close

We show that the static friction force which must be overcome to render a sticking contact sliding is reduced if an external torque is also exerted. As a test system we study a planar disk lying on a horizontal flat surface. We perform experiments and compare with analytical results to find that the coupling between static friction force and torque is nontrivial: It is not determined by the Coulomb friction laws alone, instead it depends on the microscopic details of friction. Hence, we conclude that the macroscopic experiment presented here reveals details about the microscopic processes lying behind friction.

close

Granular packings of hard disks are investigated by means of contact dynamics which is an appropriate technique to explore the allowed force realizations in the space of contact forces. Configurations are generated for given friction coefficients, and then an ensemble of equilibrium forces is found for fixed contacts. We study the force fluctuations within this ensemble. In the limit of zero friction, the fluctuations vanish in accordance with the isostaticity of the packing. The magnitude of the fluctuations has a nonmonotonous friction dependence. The increase for small friction can be attributed to the opening of the angle of the Coulomb cone, while the decrease as friction increases is due to the reduction of connectivity of the contact network, leading to local, independent clusters of indeterminacy. We discuss the relevance of indeterminacy to packings of deformable particles and to the mechanical response properties.

close

If a body is resting on a. at surface, the maximal static friction force before motion sets in is reduced if an external torque is also applied. The coupling between the static friction force and static friction torque is nontrivial as our studies for a tripod lying on a horizontal. at surface show. In this paper we report on a series of experiments that we performed on a tripod and compare our findings with analytical and numerical solutions. It turns out that the coupling between force and torque reveals information about the microscopic properties at the onset of sliding.

close

We performed computer simulations based on a two-dimensional distinct element method to study granular systems of magnetized spherical particles. We measured the angle of repose and the surface roughness of particle piles, and we studied the effect of magnetization on avalanching. We report linear dependence of both angle of repose and surface roughness on the ratio f of the magnetic dipole interaction and the gravitational force (interparticle force ratio). There is a difference in avalanche formation at small and at large interparticle force ratios. The transition is at f(c)approximate to 7. For f < f(c) small vertical chains follow each other at short times (granular regime), while for f > f(c) the avalanches are typically formed by one single large particle- cluster (correlated regime). The transition is not sharp. We give plausible estimates for f(c) based on stability criteria.

close

close

close

close

close

close

close

close

close

close

close

We investigate the growth of a film of some element B on a substrate made of another substance A in a model of molecular beam epitaxy. A vertical exchange mechanism (partial surfactant behavior) allows the A atoms to stay on the growing surface with a certain probability. Using kinetic Monte Carlo simulations as well as scaling arguments, the incorporation of the A's into the growing B layer is investigated. Moreover, we develop a rate equation theory for this process. The concentration of A impurities decays in the B-film like (distance from the interface)(-1-beta), where betaapproximate to0.5 for two-dimensional surfaces, approximate to0.8 in the one-dimensional case, and 1 in mean-field approximation. The power law is cut off exponentially at a characteristic thickness of the interdiffusion zone that depends on the rate of exchange of a B adatom with an A atom in the surface and on the diffusion length. Under certain conditions the interdiffusion zone is predicted to become narrower, if the growth temperature is increased.

close

We report on generic relations between fractional flow and pressure in steady two-phase flow in porous media. The main result is a differential equation for fractional flow as a function of phase saturation. We infer this result from two underlying observations of steady-flow simulations in two and three dimensions using biperiodic boundary conditions. The resulting equation is solved generally, and the result is tested against simulations and experimental relative permeability results found in the literature.

close

We report on molecular-dynamics (MD) simulations of tensile loading of nano-crystalline Al modeled by an embedded-atom method (EAM) potential. Usage of two different sample preparation methods of the nano-crystalline material allows us to compare mechanical properties for different sample qualities. A Voronoi-constructed polycrystal exhibits nearly no pores and has different mechanical properties compared to a material that is sintered under pressure and temperature from spherical nanoparticles, resulting in a lower-density sample. We found an inverse Hall-Petch relation for the flow stress for grain sizes smaller than 10 nm. Intergranular fracture was observed for the larger Al grain sizes, but not for nano-crystalline Cu.

close

Strain in sheared dense granular material is often localized in a narrow region called the shear band. Recent experiments in a modified Couette cell provided localized shear flow in the bulk away from the confining walls. The nontrivial shape of the shear band was measured as the function of the cell geometry. First, we present a geometric argument for narrow shear bands that connects the function of their surface position with the shape in the bulk. Assuming a simple dissipation mechanism, we show that the principle of minimum dissipation of energy provides a good description of the shape function. Furthermore, we discuss the possibility and behavior of shear bands that are detached from the free surface and are entirely covered in the bulk.

close

The Smoluchowski equation for irreversible aggregation in suspensions of equally charged particles is studied. Accumulation of charges during the aggregation process leads to a crossover from power-law to sublogarithmic cluster growth at a characteristic time and cluster size. For larger times the suspension is usually called stable, although aggregation still proceeds slowly. In this regime the size distribution evolves towards a universal scaling form, independent of any parameter included in the theory. The relative width falls off to a universal value sigma(r)(infinity)approximate to0.2017 that is much smaller than in the uncharged case. We conjecture that sigma(r)(infinity) is a lower bound for the asymptotic relative width for all physical systems with irreversible aggregation.

close

Strain in sheared dense granular material is often localized in a narrow region called the shear band. Recent experiments in a modified Couette cell provided localized shear flow in the bulk away from the confining walls. The nontrivial shape of the shear band was measured as the function of the cell geometry. First, we present a geometric argument for narrow shear bands that connects the function of their surface position with the shape in the bulk. Assuming a simple dissipation mechanism, we show that the principle of minimum dissipation of energy provides a good description of the shape function. Furthermore, we discuss the possibility and behavior of shear bands that are detached from the free surface and are entirely covered in the bulk.

close

close

Cohesive powders tend to form porous aggregates which can be compacted by applying an external pressure. This process is modelled using the Contact Dynamics method supplemented with a cohesion law and rolling friction. Starting with ballistic deposits of varying density, we investigate how the porosity of the compacted sample depends on the cohesion strength and the friction coefficients. This allows to explain different pore stabilization mechanisms. The final porosity depends on the cohesion force scaled by the external pressure and on the lateral distance between branches of the ballistic deposit. Even if cohesion is switched off, pores can be stabilized by Coulomb friction alone. This effect is weak for round particles, as long as the friction coefficient is smaller than 1. However, for non-spherical particles the effect is much stronger.

close

It has been observed experimentally that under certain conditions, pulsed laser deposition (PLD) produces smoother surfaces than ordinary molecular beam epitaxy (MBE). So far, the mechanism leading to the improved quality of surfaces in PLD is not yet fully understood. In the present work, we investigate the physical properties of a simple model for PLD, in which the transient mobility of adatoms and diffusion along edges is neglected. Analyzing the crossover from MBE to PLD, the scaling properties of the time-dependent nucleation density as well as the influence of Ehrlich-Schwoebel barriers, we find that there is indeed a range of parameters, where the surface quality in PLD is better than in MBE. However, since the improvement is weak and occurs only in a small range of parameters we conclude that deposition in pulses alone cannot explain the experimentally observed smoothness of PLD-grown surfaces.

close

The aim of this work is to understand the agglomeration of charged powders suspended in nonpolar fluids. The concerted influence of electromagnetic, hydrodynamic and van der Waals forces as well as Brownian motion leads to a complex agglomeration behavior that depends on several parameters, e.g., the ratios of electric charges, particle sizes, temperatures and concentrations of the particles. Both experimental and theoretical considerations are presented. Hydrodynamic forces, especially the Brownian motion, effectively reduce the Coulomb repulsion. It is predicted that a suspension can only be stabilized at sufficiently low temperatures compared to the Coulomb barrier. Therefore, the aggregation of charged nanoparticles proceeds until a characteristic flake size is reached for which the effective Coulomb barrier equals the attraction forces and the suspension can be regarded as stable. The experimental verification of this result showed that the real agglomeration process starts with presintered aggregates-not primary particles-which agglomerate to larger flakes. (C) 2003 Elsevier B.V. All rights reserved.

close

The tangential motion at the contact of two solid objects is studied. It consists of a sliding and a spinning degree of freedom (no rolling). We show that the friction force and torque are inherently coupled. As a simple test system, a sliding and spinning disk on a horizontal flat surface is considered. We calculate, and also measure, how the disk slows down and find that it always stops its sliding and spinning motion at the same moment. We discuss the impact of this coupling between friction force and torque on the physics of granular materials.

close

Based on theoretical results and simulations, in two-dimensional arrangements of a dense dipolar particle system, there are two relevant local dipole arrangements: (1) a ferromagnetic state with dipoles organized in a triangular lattice and (2) an antiferromagnetic state with dipoles organized in a square lattice. In order to accelerate simulation algorithms, we search for the possibility of cutting off the interaction potential. Simulations on a dipolar two-line system lead to the observation that the ferromagnetic state is much more sensitive to the interaction cutoff R than the corresponding antiferromagnetic state. For Rgreater than or similar to8 (measured in particle diameters) there is no substantial change in the energetical balance of the ferromagnetic and antiferromagnetic state and the ferromagnetic state slightly dominates over the antiferromagnetic state, while the situation is changed rapidly for lower interaction cutoff values, leading to the disappearance of the ferromagnetic ground state. We studied the effect of bending ferromagnetic and antiferromagnetic two-line systems and observed that the cutoff has a major impact on the energetical balance of the ferromagnetic and the antiferromagnetic state for Rless than or similar to4. Based on our results we argue that Rapproximate to5 is a reasonable choice for dipole-dipole interaction cutoff in two-dimensional dipolar hard sphere systems, if one is interested in local ordering.

close

We study the statical indeterminacy of contact, forces in 2D random frictional packings of perfectly rigid disks. Based on contact dynamics simulations we perform a random walk in the force space in order to explore the equilibrium force-states for a fixed packing structure. Our measurement is in agreement with the isostaticity of frictionless hard particles, in that case forces are fully determined. For non-zeio friction coefficient the problem gets undetermined, the possible force fluctuations. are growing with increasing friction up to a maximum at friction coefficient around 0.1. Further increase of friction reduces the force fluctuations on the average.

close

Cohesive powders tend to form porous aggregates which can be compacted by applying an external pressure. This process is modelled using the Contact Dynamics method supplemented with a cohesion law and rolling friction. Starting with ballistic deposits of varying density, we investigate how the porosity of the compacted sample depends on the cohesion strength and the friction coefficients. This allows to explain different pore stabilization mechanisms. The final porosity depends on the cohesion force scaled by the external pressure and on the lateral distance between branches of the ballistic deposit. Even if cohesion is switched off, pores can be stabilized by Coulomb friction alone. This effect is weak for round particles, as long as the friction coefficient is smaller than 1. However, for non-spherical particles the effect is much stronger.

close

The growth temperature dependence of Si adatom diffusion on Si (100) surface was systematically investigated in a cold wall ultrahigh vacuum chemical vapor deposition system. Si epitaxial layers were selectively grown on local oxidation of silicon patterned Si substrates. By cross-sectional transmission electron microscopy analysis, the increase in Si growth rate on the Si (100) surface near the edge of (311) facet was observed at various growth temperatures. This can be understood as a consequence of the mass transport from the sidewall (311) facet to the top.(100), surface. Based on a simple diffusion model, the surface diffusion lengths of Si adatoms along the [110] direction were estimated to be about 70, 140, and 200 nm at 550, 600, and 650degreesC, respectively. The calculated activation energy of 1.4 eV for diffusion of Si adatoms from the temperature dependence of the diffusion length was relatively higher than those in previous reports obtained under ultrahigh vacuum environment. This difference was discussed in terms of the discrepancy in the surface states by hydrogen adsorption on the Si surface. (C) 2003 American Vacuum Society.

close

close

close

close

The modelling of cohesion on the particle scale in granular matter [Vermeer et al., 2001] [1] has recently received increasing attention, because various important applications call for a microscopic foundation for the existing phenomenological continuum theories. Specifically for understanding the different behaviour of nano-powders and ordinary granular matter cohesion has to be taken into account. An example in this context is the so-called sinter-forging of nano-powders, i.e. pressure sintering at relatively low temperatures [Skandan et al., 1994] [2]. We model the corresponding compaction by the rearrangement of a large number of grains by means of contact-dynamics. For this purpose we introduce an attractive force (cohesion) as well as rolling friction between the (round) grains. The latter turns out to be crucial for the stabilization of force chains. (C) 2002 Elsevier Science B.V. All rights reserved.

close

The systematic errors due to the practical implementation of the contact dynamics method for simulation of dense granular media are examined. It is shown that, using the usual iterative solver to simulate a chain of rigid particles, effective elasticity and sound propagation with a finite velocity occur. The characteristics of these phenomena are investigated analytically and numerically in order to assess the limits of applicability of this simulation method and to compare it with soft particle molecular dynamics.

close

The dissipation rate due to inelastic collisions between equally charged, insulating particles in a granular gas is calculated. It is equal to the known dissipation rate for uncharged granular media multiplied by a Boltzmann-like factor, that originates from Coulomb repulsion. Particle correlations lead to an effective potential that replaces the bare Coulomb potential in the Boltzmann factor. Collisional cooling in a granular gas proceeds with the known t(-2)-law, until the kinetic energy of the grains becomes smaller than the Coulomb barrier. Then the granular temperature approaches a time dependence proportional to 1/ln t. If the particles have different charges of equal sign, the collision rate can always be lowered by redistributing the charge, until all particles carry the same charge. Finally granular flow through a vertical pipe is briefly discussed. All results are confirmed by computer simulations.

close

Simulation results for (a) interfacial alloying and (b) the Villain instability are presented. Both phenomena are important for the interface structure of epitaxial heterolayers and involve new scaling laws. For (a) a mechanism is discussed, which in a limiting case leads to a concentration profile decaying like (distance from the interface)(-2). In (b) the critical film thickness is estimated, at which the Villain instability becomes important. Its scaling with the diffusion constant and the Schwoebel length can be combined with results on the strain dependence of these parameters in order to predict what kind of strains enhance or suppress the instability. (C) 2002 Elsevier Science B.V. All rights reserved.

close

The aim of our work is to understand agglomeration of charged powders suspended in nonpolar fluids. The concerted influence of electromagnetic, hydrodynamic, thermal and van der Waals forces as well as Brownian forces leads to complex agglomeration behavior which depends on several parameters, e.g., the ratios of charges, sizes, temperature and concentrations of the particles. The present theoretical investigation of the problem is based on molecular dynamics simulations. The surrounding liquid is not simulated explicitly. Instead, the long-range hydrodynamic interactions between the particles are taken into account in Stokeslet approximation. In order to simulate larger systems, we parallelized the numerical integration, using a hypersystolic algorithm. (C) 2002 Elsevier Science B.V. All rights reserved.

close

We report on a segregation scheme for granular binary mixtures, where the segregation is per-formed by a ratchet mechanism realized by a vertically shaken asymmetric sawtooth-shaped base in a quasi-two-dimensional box. We have studied this system by computer simulations and found that most binary mixtures can be segregated using an appropriately chosen ratchet, even when the particles in the two components have the same size and differ only in their normal restitution coefficient or friction coefficient. These results suggest that the components of otherwise nonsegregating granular mixtures may be separated using our method.

close

The cellular automata (CA) approach to traffic modelling is extended to allow for spatially homogeneous steady state solutions that cover a two-dimensional region in the flow-density plane. Hence these models fulfil a basic postulate of a three-phase traffic theory proposed by Kerner. This is achieved by a synchronization distance, within which a vehicle always tries to adjust its speed to that of the vehicle in front. In the CA models presented, the modelling of the free and safe speeds, the slow-to-start rules as well as some contributions to noise are based on the ideas of the Nagel-Schreckenberg-type modelling. It is shown that the proposed CA models can be very transparent and still reproduce the two main types of congested patterns (the general pattern and the synchronized flow pattern) as well as their dependence on the flows near an on-ramp, in-qualitative agreement with the recently developed continuum version of the three-phase traffic theory (Kerner B S and Klenov S L 2002 J. Phys. A: Math. Gen. 35 L31). These features are qualitatively different from those in previously considered CA traffic models. The probability of the breakdown phenomenon (i.e. of the phase transition from free flow to synchronized flow) as function of the flow rate to the on-ramp and of the flow rate on the road upstream of the on-ramp is investigated. The capacity drops at the on-ramp which occur due to the formation of different congested patterns are calculated.

close

We introduce two simple stochastic growth models which describe the motion of the interfaces driven through random media in two and three dimensions. One model describes the motion of the interface driven through isotropic random media, where the dynamics of the interface can be described by the quenched Edwards-Wilkinson (QEW) equation. The other model describes the motion of the interface driven through anisotropic random media, where the dynamics of the interface can be described by the quenched Kardar-Parisi-Zhang (QKPZ) equation, We show via computer simulations that two models belong to the QEW and QKPZ universality class in two and three dimensions, respectively.

close

We introduce a simple growth model which exhibits a first-order pinning-depinning (PD) transition in disordered media. In our model, a first-order PD transition is triggered by the local inertia force F-l=pL (nu) over bar, where p denotes a constant between 0 and 1, L is the system size, and (nu) over bar is the average velocity in a local region of the growing interface. If p<p(c), our model shows a continuous PD transition. However, if p>p(c), our model shows a first-order PD transition. We measure the critical exponents characterizing the dynamical behavior of our model and explain how a first-order PD transition can occur if p>p(c). Besides the PD transitions, our model exhibits another phase transition from a fluctuating to a nonfluctuating interface with a constant velocity.

close

We introduce a simple stochastic growth model where particles of two different species are deposited and evaporated. In the model, a randomly chosen particle of two species is deposited at a rate p and a particle on the edge of the plateau of the interface is evaporated at a rate 1-p. When p<p(c1)=0.4985(2) and p>p(c2)=0.5015(5), the velocity of the interface is zero. When p(c1)less than or equal topless than or equal top(c2), however, the interface grows with a constant velocity. At both p(c1) and p(c2), the velocity of the interface changes from zero to a constant value discontinuously. The first-order transitions in our model are related to a nonequilibrium phase transition from an active to an inactive phase at the bottom layer of the interface. Interestingly, the first-order transition at p(c1) is triggered by the combination of the parity conserving and the directed percolation dynamics. We explain why the transitions in our model are of first order. Moreover, our model shows two nonequilibrium roughening transitions at p(c1) as well as at p(r)[=0.444(2)].

close

We argue that the reaction-diffusion process 3A-->4A,3A-->2A exhibits a different type of continuous phase transition from an active into an absorbing phase. Because of the upper critical dimension d(c)greater than or equal to4/3 we expect the phase transition in 1+1 dimensions to be characterized by nontrivial fluctuation effects.

close

Recently it was suggested that a pair contact process with diffusion (PCPD) might represent an independent new universality class different from the directed percolation (DP) and the parity conservation (PC) class. The dynamics in the PCPD are usually controlled by two independent parameters. The critical exponents for the PCPD are known to have different values for varying values of the two independent parameters. However, once the diffusion and annihilation (or coagulation) rate in the PCPD is tuned in a way that the process without offspring production is exactly solvable, a well-defined set of the exponents for the PCPD is obtained. Then dynamics are controlled by only one independent parameter. The obtained critical exponents are different than those of DP and PC. The critical exponents satisfy the generalized hyperscaling relation within numerical errors.

close

Pulsed laser deposition (PLD) is a popular growth method, which has been successfully used for fabricating thin films. Compared to continuous deposition (like molecular beam epitaxy) the pulse intensity can be used as an additional parameter for tuning the growth behavior, so that under certain circumstances PLD improves layer-by-layer growth. We present kinetic Monte-Carlo simulations for PLD in the submonolayer regime and give a description of the island distance versus intensity. Furthermore we discuss a theory for second layer nucleation and the impact of Ehrlich-Schwoebet barriers on the growth behavior. We find an exact analytical expression for the probability of second layer nucleation during one pulse for high Ehrlich-Schwoebel barriers.

close

close

Recently there has been a debate concerning the universal properties of the phase transition in the pair contact process with diffusion (PCPD) 2A --> 3A, 2A -->0. Although some of the critical exponents seem to coincide with those of the so-called parity-conserving universality class, it was suggested that the PCPD might represent an independent class of phase transitions. This point of view is motivated by the argument that the PCPD does not conserve parity of the particle number. In the present work we question what happens if the parity conservation law is restored. To this end, we consider the reaction-diffusion process 2A --> 4A, 2A -->0. Surprisingly, this process displays the same type of critical behavior, leading to the conclusion that the most important characteristics of the PCPD is the use of binary reactions for spreading, regardless of whether parity is conserved or not.

close

We introduce a simple Volume conserving stochastic model undergoing a nonequilibrium roughening transition (NRT) in 1 + 1 dimensions. In our model, there is no deposition and evaporation of a particle breaking the volume conserving condition. The degree of roughness of the fluctuating interface in our model is determined by whether or not the hopping of a particle depends on the local slope of the interface. The hopping process of a particle is controlled by the probability 0 less than or equal to p less than or equal to 1. For p < 1/2, a moving particle tends to hop in the downhill direction of the local slope of the interface, and so the interface is in a smooth phase with a zero roughness exponent. For p > 1/2, a particle tends to hop in the uphill direction, and so the interface cannot reach a saturated phase. When p = 1/2, the hopping of a particle does not depend on the local slope of the interface. Then the interface can reach a saturated phase. The saturated interface at p = 1/2 is in a rough phase with a nonzero roughness exponent. Our model, therefore, exhibits the NRT at the critical parameter p(c) = 1/2.

close

We introduce a stochastic growth model where the growth is controlled by a temperature-like parameter T. The model shows various types of dynamical behavior as T changes from 0 to infinity. For T=0 the growth process belongs to the quenched Kardar-Parisi-Zhang (KPZ) universality class, whereas it belongs to the Edwards-Wilkinson (EW) universality class for T= infinity. In the intermediate range 0 < T< infinity, the model shows an anomalous crossover behavior from the quenched KPZ to the thermal KPZ class. The KPZ nonlinearity is generated by an anisotropic effect of the quenched noise which exists only for T<<infinity> in our model. We also study crossovers between different types of scaling behavior of the interface width for various T's.

close

We show that a simple model for pulsed laser deposition exhibits an unusual type of scaling behavior for the island density in the submonolayer regime. This quantity is studied as a function of pulse intensity and deposition time. We find a data collapse for the ratios of the logarithms of these quantities, whereas conventional scaling as observed in molecular beam epitaxy involves ratios of powers.

close

Time-resolved in situ-applied scanning tunnelling microscopy (STM) has been used to study the homoepitaxial growth of Fe on Fe(110). Sequences of STM images taken during growth directly show the atomistics of the growth processes on the surface. These data are statistically analysed and compared with kinetic Monte Carlo simulations which include the correct symmetry of the bcc (110) surface. Two sets of activation barriers were used in the simulation. Applying simple bond-counting energetics the influence of the probabilities of different hopping events on the growth has been studied. Material-specific barriers calculated using a Finnis-Sinclair potential reproduce most of the real growth behaviour. A strongly anisotropic growth is found with islands elongated in [001] which is kinetically stabilized by a hindered diffusion at step edges along [001]. At room temperature, the presence of a step edge barrier prevents the interlayer mass transport nearly completely and leads to kinetic roughening and complete facetting of the surface.

close

Time-resolved in situ STM has been applied to the system Fe on Fe(110) to study the characteristics of homoepitaxial growth on bcc surfaces. Additionally the growth of W on W(110) has been investigated which shows the same behaviour at 500 degrees C as iron at room temperature. The resulting data are compared with kinetic Monte Carlo simulation which include the correct symmetry of the bcc(110) surface. It is found that islands grow strongly anisotropically elongated in [100] which is due to a hindered diffusion at step edges along [001]. At room temperature the inter-layer diffusion is suppressed by a step edge barrier which leads at higher coverages to a kinetic roughening and a complete faceting of the surface. The developing stable facets were investigated by SPA-LEED. (C) 2000 Elsevier Science B.V. All rights reserved.

close

The Bak-Tang-Wiesenfeld (BTW) sandpile model is a cellular automaton which has been intensively studied during the last years as a paradigm for self-organized criticality. In this paper, we reconsider a deterministic version of the BTW model introduced by Wiesenfeld, Theiler and McNamara, where sand grains are added always to one fixed site on the square lattice. Using the Abelian sandpile formalism we discuss the static properties of the system. We present numerical evidence that the deterministic model is only in the BTW universality class if the initial conditions and the geometric form of the boundaries do not respect the full symmetry of the square lattice.

close

We investigated the inelastic hard-disk gas sheared by two parallel bumpy walls (Couette flow). In our molecular dynamic simulations we found a sensitivity to the asymmetries of the initial particle positions and velocities and an asymmetric stationary state, where the deviation from (anti)symmetric hydrodynamic fields is stronger as the normal restitution coefficient decreases. For better understanding of this sensitivity we carried out a linear stability analysis of the former kinetic theoretical solution [J. T. Jenkins and M. W. Richman, J. Fluid. Mech. 171, 53 (1986)] and found it to be unstable. The effect of this asymmetry on the self-diffusion coefficient is also discussed.

close

close

close

close

close

close

close

Traffic phenomena such as the transition from free to congested flow, lane inversion and platoon formation can be accurately reproduced using cellular automata, Being computationally extremely efficient, they simulate large traffic systems many times faster than real time so that predictions become feasible. A review of recent results is given. The presence of metastable states at the jamming transition is discussed in detail. A simple new cellular automaton is introduced, in which the interaction between cars is Galilei-invariant. It is shown that this type of interaction accounts for metastable states in a very natural way.

close

Molecular dynamics (MD) simulations are now widely used to study both dense and dilute granular flows, which often coexist in the same system. However, this simulation technique has to be used with care when the forces are non-conservative. We briefly discuss the artifacts which then may arise. The example of granular chute flow illustrates how MD simulations may help to understand the microscopic processes underlying the macroscopic flow properties. In particular, it is shown how sterical constraints in the flow can lead to an insensitivity of the mean quantities to material properties like the coefficient of restitution. (C) 1999 Elsevier Science B.V. All rights reserved.

close

Molecular dynamics (MD) simulations are now widely used to study both dense and dilute granular flows, which often coexist in the same system. However, this simulation technique has to be used with care when the forces are non-conservative. We briefly discuss the artifacts which then may arise. The example of granular chute flow illustrates how MD simulations may help to understand the microscopic processes underlying the macroscopic flow properties. In particular, it is shown how sterical constraints in the flow can lead to an insensitivity of the mean quantities to material properties like the coefficient of restitution. (C) 1999 Elsevier Science B.V. All rights reserved.

close

We propose a generalization of the cellular automaton model introduced recently by Lai, Jia and Chan [Phys. Rev. Lett. 79 (1997) 4994] for simulating friction induced segregation in a rotating drum. We use our model to investigate geometrical properties of mixing and segregation. Simulations of the model reproduce recent experimental results on mixing efficiency and spontaneous stratification. We also make two predictions - for the dependence of the mixing rate on the speed of rotation and for the stratification of granular system in the drum which is less than half filled. (C) 1999 Elsevier Science B.V. All rights reserved.

close

The non-Newtonian character of granular flow in a vertical pipe is analyzed. The time evolution of the flow velocity and the velocity fluctuations (or granular temperature) is derived. The steady-state velocity has a power law dependence on the pipe width with an exponent between 3/4 and 3/2. The flow becomes faster the more efficient the collisional cooling is, provided the density remains low enough. The dependence of collisional cooling on the solid fraction, the restitution coefficient and a possible electric charge of all grains is discussed in detail. (C) 1999 Elsevier Science B.V. All rights reserved.

close

close

For two simple set-ups, we discuss how dissipative grain-grain interactions give rise to unexpected properties on large scales. In the first example, a spherical particle rolling along a rough surface experiences an effective viscous friction on large time scales. It is due to temporal correlations among collisions with incomplete normal restitution. The second example is a sheared granular packing. There, spatial correlations among non-sliding and sliding contacts with Coulomb friction suggest that the deviatoric stress, although responsible for the dissipation, is localized on bonds that are non-sliding and hence nondissipative.

close

For several discrete growth models, the damping lime of layer-by-layer growth, manifesting itself in oscillations of the surface width, will be related to parameters appearing in the corresponding continuum equations. The control parameter in all cases is the so called noise-reduction parameter m. The damping time depends on m with power laws determined by the continuum equations. The Eden model (versions A and B), and models related to molecular beam epitaxy are considered.

close

Microscopic modeling of multilane traffic is usually done by applying heuristic lane changing rules and often with unsatisfying results. Recently, a cellular automaton model for two-lane traffic was able to overcome some of these problems and to generate the density inversion found in many European countries at densities somewhat below the maximum flow density. In this paper we summarize different approaches to lane changing and their results and propose a general scheme, according to which realistic lane changing rules can be developed. We test this scheme by applying it to several different lane changing rules, which, in spite of their differences, generate similar and realistic results. We thus conclude that, for producing realistic results, the logical structure of the lane changing rules, as proposed here, is at least as important as the microscopic details of the rules.

close

The correlation between contact forces and the texture of a packing of rigid particles subject to biaxial compression is analyzed by means of numerical simulations. Four different aspects are investigated: stress tensor, dissipation due to friction, angular distribution of forces, and fabric tensor characterizing the anisotropy of the texture. All of them provide evidence that the contact network can be decomposed unambiguously into two subnetworks with complementary mechanical properties.

close

Reflection high-energy electron diffraction (RHEED) intensity studies were performed during the growth of thin Fe layers on vicinal Cr(001)/Nb(001)/Al2O3(1 (1) over bar 02) substrates. The results are compared with those of recent molecular-beam epitaxy (MBE) growth models. General agreement is found as concerns the linear relationship between the logarithm of the number of RHEED oscillations and the inverse growth temperature. In agreement with theory the RHEED oscillation damping time is found to depend algebraically on the growth rate. However, contrary to expectations, the RHEED oscillations vanish faster at higher growth temperatures and lower growth rates. This behavior can be explained by a change in the growth mode from layer-by-layer to step flow. Numerical simulations in which step bunch melting during the Fe growth on the Cr buffer is assumed reproduce well the present experimental results. [S0163-1829(98)02708-8].

close

The typical island distance l in submonolayer epitaxial growth depends on the growth conditions via an exponent gamma. This exponent is known to depend on the substrate dimensionality, the dimension of the islands, and the size i* of the critical nucleus for island formation. In this paper we study the dependence of gamma on i* in one-dimensional epitaxial growth. We derive that gamma = i*/(2i* + 3) for i* greater than or equal to 2 and confirm this result by computer simulations.

close

close

close

close

close

close

close

close

Using different simulation techniques, we study the influence of the friction law governing interparticle and particle-plane contacts on the dynamics of a regular array of rigid parallel cylinders moving on a plane. We find that the evolution of the system depends strongly on the simulation method. But both in simulations with a Contact Dynamics algorithm, which prescribes the basic Coulomb's law of friction, and in simulations with molecular dynamics, which prescribes a regularized form of Coulomb's law, a steady state with very similar collective rotation modes is reached. As long as the static and dynamic friction coefficients are equal, the rotation modes are independent of the initial conditions. We show that in all cases, the global steady-state coefficient of friction between the array and the plane is a function of the driving force and the system size, and hence is not Coulombian.

close

The conserved Sine-Gordon equation with nonconserved shot noise is used to model homoepitaxial crystal growth. With increasing coverage the renormalized pinning potential changes from strong to weak. This is interpreted as a transition from layer-by-layer to rough growth. The associated length and time scales are identified, and found to agree with recent scaling arguments. A heuristically postulated nonlinear term del(2)(del h)(2) is created under renormalization.

close

We present a theory for the damping of layer-by-layer growth oscillations in molecular beam epitaxy. The surface becomes rough on distances larger than a layer coherence length which is substantially larger than the diffusion length. The damping time can be calculated by a comparison of the competing roughening and smoothening mechanisms. The dependence on the growth conditions, temperature and deposition rate, is characterized to be a power law. The theoretical results are confirmed by computer simulations.

close

A set of lane changing rules for cellular automata simulating multi-lane traffic is proposed, It reproduces qualitatively that the passing lane becomes more crowded than the one for slower cars if the flux is high enough, which is true for motorways in countries like Germany where passing should be done on a specified lane as a rule. The rules have two parameters allowing to adjust the inversion point of the lane-usage distribution and to calibrate the model.

close

We develop particle-hopping models of two-lane traffic with two different types of vehicles (characterized by two different values of the maximum allowed speed V-max) generalizing the Nagel-Schreckenberg stochastic cellular-automata model for single-lane traffic with a single V-max. The simplest of the two models is symmetric with respect to the two lanes as well as with respect to the two types of vehicles. In the asymmetric model, different rules govern the changing from the ''fast'' lane to the ''slow'' one and the reverse process. Moreover, in the asymmetric model, the drivers of fast vehicles can anticipate, often well in advance, the possibility of getting trapped behind a slow vehicle and tend to avoid such possibilities.

close

We present a new analytical description of the cellular automaton model for single-lane traffic. In contrast to previous approaches we do not use the occupation number of sites as dynamical variable but rather the distance between consecutive cars. Therefore certain longer-ranged correlations are taken into account and even a mean-field approach yields non-trivial results. In fact for the model with upsilon(max) = 1 the exact solution is reproduced. For upsilon(max) = 2 the fundamental diagram shows a good agreement with results from simulations.

close

We extend the Nagel-Schreckenberg stochastic cellular automata model for single-lane vehicular traffic to incorporate quenched random deceleration probabilities. We show, by computer simulations, that at low densities this model displays queueing of cars with a power-law probability distribution of gaps between the cars while at high densities the behaviour of the model is similar to the jammed phase of the standard Nagel-Schreckenberg model. The approach to the steady state is characterized by the same critical exponents as for the coarsening process in the simple exclusion processes with random rates, recently investigated independently by Krug and Ferrari, and Evans. The numerical values of the exponents for gap distributions are in agreement with the analytical conjecture of Krug and Ferrari, which implies that the models belong to the same universality class.

close

A simple two-parameter model with a novel nearest-neighbor bond-counting scheme is developed that closely reproduces energy barriers obtained from microscopic calculations using a directional Lennard-Jones potential. We discuss the physical interpretation of our bond-counting scheme as well as results obtained with the model.

close

The change of diffusion kinetics when elastic fields are present is discussed for diffusion on (001) surfaces of simple cubic, fee and bcc lattices. All particles interact pairwise with a Lennard-Jones potential. The simple cubic lattice was stabilized by an anisotropic prefactor. It is found that generically compressive strain enhances diffusion whereas tensile strain increases the activation barrier. An approximately linear dependence of the barrier in a wide range of misfits is found. In heteroepitaxy, diffusion on top of large clusters is inhomogeneous and anisotropic. The kinetics close to edges and centers of islands are remarkably different. In many cases changes of binding energies are small compared to those of saddle point energies. Thermodynamic arguments (minimization of free energy) are not appropriate to describe diffusion on strained surfaces in these cases. (C) 1997 Elsevier Science B.V.

close

Synchronization of molecular reactions in a macroscopic volume may cause the volume's physical properties to change dynamically and thus reveal much about the reactions. As an example, experimental time series for so-called microtubule oscillations are analyzed in terms of a minimal model for this complex polymerization-depolymerization cycle. The model reproduces well the qualitatively different time series that result from different experimental conditions, and illuminates the role and importance of individual processes in the cycle. Simple experiments are suggested that can further test and define the model and the polymer's reaction cycle.

close

At least, for human and medfly populations, the death rates for females are lower than the male ones. By studying a sexual variant of the bit-string model for biological ageing, we can reproduce this feature. Our hypotheses are supported (and inspired) by some recent cancer statistics.

close

Using different simulation techniques, we study the influence of the friction law governing interparticle and particle-plane contacts on the dynamics of a regular array of rigid parallel cylinders moving on a plane. We find that the evolution of the system depends strongly on the simulation method. But both in simulations with a Contact Dynamics algorithm, which prescribes the basic Coulomb's law of friction, and in simulations with molecular dynamics, which prescribes a regularized form of Coulomb's law, a steady state with very similar collective rotation modes is reached. As long as the static and dynamic friction coefficients are equal, the rotation modes are independent of the initial conditions. We show that in all cases, the global steady-state coefficient of friction between the array and the plane is a function of the driving force and the system size, and hence is not Coulombian.

close

We present molecular-dynamics simulations of a sphere moving down an inclined plane consisting of similar spheres of smaller size. For a certain range of inclinations, the sphere moves down the plane with a mean velocity (v) over bar(x) not equal 0. We investigate the properties of the motion in this steady state and the limits for its existence for a certain set of parameters. It is found that the steady-state velocity of the particle is independent of material properties and depends only on the geometry of the system. This means that the particle experiences an effective velocity-dependent friction force, with an effective ''viscosity'' determined only by the geometry. The fluctuations of the motion, however, can depend on the coefficient of restitution e(n). For example, the diffusion coefficient D-x is influenced by e(n), but hardly depends on the roughness of the plane, while for D-y the reverse is true. The range of the inclination angle and the roughness for which a steady state exists also depends on e(n). We discuss how these results can be understood by considering the details of the motion.

close

During epitaxial crystal growth a pattern that has initially been imprinted on a surface approximately reproduces itself after the deposition of an integer number of monolayers. Computer simulations of the one-dimensional case show that the quality of reproduction decays exponentially with a characteristic time which is linear in the activation energy of surface diffusion. We argue that this lifetime of a pattern is optimized if the characteristic feature size of the pattern is larger than (D/F)(1/(d+2)), where D is the surface diffusion constant, F the deposition rate, and d the surface dimension.

close

It is well known, that the dynamics of small particles moving in a viscous fluid is strongly influenced by the long-range hydrodynamical interaction between them. Motion at high viscosity is usually treated by means of the Stokes equations, which are linear and instantaneous. Nevertheless, the hydrodynamical interaction mediated by the liquid is nonlinear; therefore the dynamics of more than two particles can be rather complex. Here we present a high resolution numerical analysis of the classical three-particle Stokeslet problem in a vertical plane. We show that a chaotic saddle in the phase space is responsible for the extreme sensitivity to initial configurations, which has been mentioned several times in the literature without an explanation. A detailed analysis of the transiently chaotic dynamics and the underlying fractal patterns is given.

close

Scanning tunneling microscopy measurements during growth at high substrate temperatures (500-800 K) an used to study the transition from two-dimensional island growth to step-flow growth of Si on Si(100). The presence of surface reconstructions leads to complex behavior in the transition region. In particular, the theoretically predicted transient growth mode, with an oscillatory behavior of the fractional coverages of each of the nonequivalent (1 x 2) and (2 x 1) reconstruction domains, is found Comparisons of experimental results with kinetic Monte Carlo simulations show that the speed of biatomic step formation is related to the growth rate-dependent sticking coefficients at the step edges.

close

We reexamine the density of two dimensional islands in the submonolayer regime of a homoepitaxially growing surface using the coarse grained Monte Carlo simulation with random sequential updating rather than parallel updating. It turns out that the power law dependence of the density of islands on the deposition rate agrees much better with the theoretical prediction than previous data obtained by other methods if random sequential instead of parallel updating is used.

close

close

close

close

close

close

close

In computer simulations of granular flow, one widely used technique is classical soft-sphere Molecular Dynamics, where the equations of motion of the particles are numerically integrated. This requires specification of the forces acting between grains. In this paper, we systematically study the properties of the force laws most commonly used and compare them with recent experiments on the impact of spheres. We point out possible problems and give criteria for the right choice of parameters. Finally, two generic problems of soft-sphere simulations are discussed.

close

One of the generic scenarios in molecular beam epitaxy is the growth of three-dimensional structures such as mounds and pyramids. These structures are a nonequilibrium effect thought to be due to a combination of the microscopic Ehrlich-Schwoebel barriers and the breaking of detailed balance by the deposition process. We propose and investigate by computer simulation a simple microscopic model that displays (i) slope selection, (ii) pyramid and moundlike structures, and (iii) coarsening. The characteristic length scale of our three-dimensional features grows as R(t) similar to t(n) with n between 0.17 and 0.26. We discuss these results in the light of recent experiments and continuum models of molecular beam epitaxy.

close

For a model of a slowly rotating two-dimensional drum the statistics of the potential energy dissipation in avalanches is studied. Self-organized criticality occurs only for the small disks in bidisperse fillings. The large disks in bidisperse fillings as well as monodisperse fillings show a stretched exponential distribution. This is due to the absence of niches on the surface which are able to trap these disks.

close

By means of molecular-dynamics simulations, we investigate the elementary process of avalanches and size segregation by surface flow in two dimensions: a single ball confined to moving along an inclined line consisting of balls. The global characteristics of the motion depend strongly on the size of the moving ball relative to the size of the balls on the line, as well as the distribution of the balls on the line. We find that in the steady state the friction force acting on the ball is independent of material properties such as the Coulomb friction coefficient and the coefficient of restitution. Contrary to previous notions about the details of the motion, we find that it is very regular and consists of many small bounces on each ball on the line. As a result of this regularity, introducing a random spacing between the balls on the line has mainly the same influence as a regular spacing of adequate length. The insensitivity of the steady-state velocity to material properties and to the detailed arrangement of the balls on the line allows for an analytical estimation of the mean velocity that fits the simulation results very well. We find that results from the two-dimensional case can probably not be transferred to the three-dimensional case of a ball moving on a rough inclined plane as easily as has been suggested previously.

close

One of the central objectives when simulating models of kinetic surface roughening is the calculation of the scaling exponents that describe the roughness of the surface and its temporal evolution. This can generally be done by studying various correlation functions. In this paper it is shown that in models that exhibit a crossover at large length scales the choice of the correlation function is crucial: Using the two-dimensional Wolf-Villain model as an example, it is shown that the exponents obtained from the scaling behavior of the width or the height-height correlation function can be almost twice as large as the correct values. Reliable estimates are obtained using the structure factor or the time-time autocorrelation function.

close

Temporal correlations of nucleation events in layer-by-layer growth are studied by simulating a one dimensional model. In order to focus on fluctuations due to the nucleation process, deposition and diffusion are treated deterministically. The correlations decay algebraically with effective exponents depending on the order of the nucleations in a layer. The autocorrelation function of all nucleation events decays as t(-1.35) with time t. In spite of these correlations, the corresponding randomness in the growth process does not lead to a roughening of the surface. The reason is that stochastic nucleation implies only conserved current fluctuations.

close

We examine a simple two-lane cellular automaton based upon the single-lane CA introduced by Nagel and Schreckenberg. We point out important parameters defining the shape of the fundamental diagram. Moreover we investigate the importance of stochastic elements with respect to real life traffic.

close

We propose a bridge between the theory of exactly solvable models and the investigation of traffic flow. By choosing the activities in an appropriate way, the dimer configurations of the Kasteleyn model on a hexagonal lattice can be interpreted as spacetime trajectories of cars. This then allows for a calculation of the Row-density relationship (fundamental diagram). We further introduce a closely related cellular automaton model. This model can be viewed as a variant of the Nagel-Schreckenberg model in which the cars do not have a velocity memory. It is also exactly solvable and the fundamental diagram is calculated.

close

close

close

close

close

close

close

close

close

close

We discuss a number of solid-on-solid models that contain the two most important features of molecular-beam epitaxy: a flux of particles and relaxation of the growing film by surface diffusion. Evaporation of particles is not allowed and surface diffusion is driven by a Hamiltonian containing short-range interactions. In the absence of deposition, the correct equilibrium phase is recovered. We find that there are two generic situations depending on whether or not diffusing particles are repelled from step edges by so-called Schwoebel barriers: (i) Positive Schwoebel barriers lead to unstable growth and the formation of pyramidlike structures. (ii) Negative Schwoebel barriers result in surface roughness that scales only logarithmically with separation or system size. This class is described at large length scales by the Edwards-Wilkinson equation. The atypical case of no Schwoebel barrier occurs only if there is a special symmetry in the diffusion process. This scenario is present regardless of whether surface diffusion is implemented through an Arrhenius process or through Metropolis-type hopping rates. We conclude that, at least in the context of solid-on-solid models, there are only two generic universality classes. These results are discussed in terms of a general Langevin equation and related to recent experiments.

close

We propose a simple Langevin equation that describes the growth of pyramidlike structures on a surface under conditions typical of molecular beam epitaxy. The slope of these pyramids is selected by the crystalline symmetries of the growing film. By analogy with the problem of domain growth of systems with a conserved order parameter we show that the dynamic exponent that controls the growth of the pyramids is z congruent-to 4. There is no mechanism that limits the size of the growing structures. This implies that the roughness exponent is alpha = 1, in agreement with recent experiments.

close

The size segregation phenomenon of granular materials in a two-dimensional rotating drum is simulated very efficiently using a simplified deterministic model. We demonstrate ergodicity in the sense that the statistical properties of a particle trajectory reflect the behaviour of the whole assembly. Segregation is shown to occur in a bidisperse system even if the radii of the particles are very similar (ratio as big as 0.9).

close

The Kardar-Parisi-Zhang (KPZ) equation describing kinetic roughening is solved numerically for (3 + 1)-dimensional systems in the strong-coupling phase. By massive use of supercomputing tools we calculate for the first time the exponent beta (= 0.181 +/- 0.007) with an accuracy comparable with that of lattice growth model simulations. A possible source of errors in parallel Monte Carlo calculations is pointed out.

close

close

The Wolf-Villain model for growing surfaces is investigated using the height-height correlation function and the structure factor. Both functions show an unusual scaling behaviour that can be attributed to the time dependence of the average step size and is characterized by a new exponent. A modified scaling law is introduced which may describe quite generally the crossover behaviour in models of this kind. It leads to a very different classification of the model than has been inferred from the exponents obtained by measuring the width of the surface as a function of time and system size.

close

We investigate a solid-on-solid model in which the interface of the deposit relaxes through a surface-diffusion process controlled by a local energy function and obeys detailed balance. We find that in the steady state the dynamic structure factor of the interface obeys scaling with exponents which, remarkably, are equal to those of the Edwards-Wilkinson model for sedimentation. Thus the interface fluctuations in two dimensions diverge only logarithmically and are therefore much smaller than those of all previously proposed models. We discuss the relevance of these results to molecular beam epitaxy.

close

close

MBE growth on high symmetry surfaces depends to some extent on the shape of the terraces which form the embryos of each new atomic layer. The conditions for formation of compact or fractal terraces are discussed in two limits: large terraces, to which a continuous description applies, and small terraces, which require that the discrete nature of matter be taken into account. In both cases it is found that terraces are fractal if and only if diffusion of adatoms along steps is much slower than on the flat surface at the same temperature. Precise conditions are given which should be accessible to experiment.

close

The time tau necessary for the formation of bumps due to thermal fluctuations on steps of vicinal surfaces is evaluated in various relevant cases. Formulae already derived by Mullins and Bales and Zangwill and other expressions recently published by Bartelt et al., are found as special cases. For Si(111) at 900-degrees-C we predict that tau is proportional to the step-step separation l and to the square of the fluctuation wavelength L. This prediction is found to be in reasonable agreement with direct experimental observations of equilibrium step fluctuations.

close

Experimental evidence is given that the sublimation rate of vicinal silicon (001) surfaces depends on the misorientation. Three regimes are studied: step flow without and with Lochkeim-formation on the terraces, as well as the high temperature regime, where the surface becomes atomically rough. Qualitatively these observations are in agreement with theoretical predictions of the anisotropic KPZ-theory.

close

close

close

We simulate ballistic deposition with long-range temporal correlated noise of bounded amplitude in 1 + 1 dimensions. Good agreement with the dynamical renormalization-group calculation of Medina et al. [Phys. Rev. A 39, 3053 (1989)] is obtained for the scaling exponents when the noise is generated by a version of Mandelbrot's fast fractional Gaussian noise (FFGN) generator. However, using the original FFGN, other exponents axe obtained. We suggest that this error is due to an extraordinarily slow crossover caused by the existence of an anomalous growth mode incompatible with the KPZ equation. This may have implications on similar model-dependent results for recent simulations on growth with power-law noise and spatially correlated noise.

close

The order of magnitude of the typical distance l between steps in MBE-grown crystal surfaces is calculated from simple scaling assumptions in the absence of evaporation. This distance is measurable by diffraction methods and yields access to the surface diffusion constant D. At the lowest non trivial temperatures the characteristic distance is of order (D/F)1/6 where F is the beam flux. At slightly higher temperature, l is given by an algebraic formula which depends on the lifetime tau2 of a bound pair of adatoms at the surface, as well as of the diffusion constant D2 Of these pairs. In certain ranges, l varies as F-1/4 or F-1/5. At higher temperatures yet, l is given by a formula which depends on a larger number of parameters. In special cases, our results are in agreement with the classical formulae, of Stoyanov and Kashchiev, but disagree with certain recents works. l is found to increase with temperature more rapidly than an Arrhenius exponential. Monte-Carlo simulations are reported and the discrepancy with certain other authors is clarified.

close

close

A new method for measuring the width of an interface in the presence of overhangs and holes is presented, using a local Gibbs dividing surface. It is compared with the conventional method based on the order-parameter profile. Dynamics and size dependence of an interface are studied numerically in the two dimensional Q2R cellular automaton. Two types of interface fluctuations can be distinguished: the capillary waves dominate on length scales larger than the bulk correlation length, whereas order parameter fluctuations on small scales give rise to an intrinsic interface width. The scaling behavior of the capillary waves is shown to be the same as for the Ising model. The divergence of the intrinsic width at the critical point and its critical slowing down are investigated.

close

The roughening behavior of a moving surface under a deposition and evaporation dynamics is explored within the hypercube-stacking model. One limiting case of the model is an equilibrium surface, which exhibits thermal roughening for surface dimension d less-than-or-equal-to 2. Another limiting case is nonequilibrium irreversible growth, where the model is shown to map exactly to zero-temperature directed polymers on a hypercubic lattice with a random energy distribution. Results of exact calculations for d = 1 and of large-scale Monte Carlo simulations [N = 2(20), 11520(2), and 2 x 192(3) surface sites for d = 1, 2, and 3, respectively] are presented that establish the Kardar-Parisi-Zhang equation as the correct continuum description of the growth process. For pure deposition (i.e., irreversible growth), careful analysis of surface width data yields the exponents beta(2) = 0.240 +/- 0.001 and beta(3) = 0.180 +/- 0.005, which violate a number of recent conjectures. By allowing for evaporation, we observe a less rapid increase of the surface roughness as a function of time. This phenomenon is consistently explained by a crossover scenario for d = 1 and 2 but a nonequilibrium roughening transition for d = 3, as predicted by a perturbative renormalization-group analysis of the Kardar-Parisi-Zhang equation. Detailed predictions on crossover scaling from the renormalization-group analysis are also confirmed by simulation data. In the d = 1 case, some of the continuum parameters characterizing the renormalization-group flow are obtained explicitly in terms of the lattice parameters via the exact calculation of steady-state properties of the model.

close

close

close

close

We introduce a surface growth model where the elementary events are characterized by a waiting time distribution P(tau). Exact relations to directed polymer statistics and to continuous time random walk problems are established. For P(tau) approximately 1/tau-mu + 1 the behaviour is similar to that of the Zhang model where rare-event-dominated kinetic roughening occurs due to a power-law noise in the surface increments. A careful correction to scaling analysis of our numerical results in 1 + 1 dimensions indicates universality with the Zhang model for fixed values of mu.

close

Large scale simulations of stochastic growth of 2 + 1 dimensional surfaces were carried out on a 16K processor Connection Machine. We introduce a family of models for which we could reproduce the known scaling behavior of kinetic roughening in the presence of bounded noise. For noise amplitudes eta distributed according to P(eta) approximately eta-mu-1, the growth exponents depend on mu and they are well described by the recently proposed formula based on the scaling of rare events.

close

On a course-grained level a family of microscopic growth processes may be described by a stochastic differential equation, which is solved numerically for surface dimensions d = 1, 2 and 3. Dimensional analysis shows that the spatial discretization parameter has the meaning of an effective coupling constant. The numerical stability of the Euler integration scheme is discussed. For the strong coupling exponents-beta defined by surface width approximately time-beta the following effective values were obtained: beta(d = 1) = 0.330 +/- 0.004 and beta(d = 2) = 0.24 +/- 0.005. Considering the width and its ensemble fluctuations at constant dimensionless time the transition between strong and weak coupling phases is located in d = 3. For the largest coupling for which reliable data are available we obtain an effective exponent-beta close to the best estimates on discrete models, beta(d = 3) approximately 0.17.

close

Two models of the wetting dynamics of a non-volatile liquid are introduced. Both models exhibit a transition between partial and complete wetting regimes. The first model, which can also be viewed as an inhomogeneous surface growth model, is studied in a two-dimensional capillary geometry. For complete wetting the profile of the fluid surface, apart from a precursor film, then assumes a stationary shape, which scales with the system size. A precursor film forms even at the transition, which one can locate analytically, although here it moves only as t(x), where X congruent-to 1/2. This first model permits only fluctuations parallel to the wall over which the fluid spreads. Monte Carlo simulations of the second model show that the inclusion of fluctuations perpendicular to the wall can lead to qualitatively new phenomena.

close

The description of growth at vicinal surfaces leads to an anisotropic generalization of the Kardar-Parisi-Zhang equation [Phys. Rev. Lett. 56, 889 (1986)] which is investigated by a dynamical renormalization calculation. If the nonlinear terms have opposite signs parallel and perpendicular to the average step direction, the roughness is only logarithmic. This should be the case, e.g., for step-flow growth. As the temperature is lowered so that island formation on the terraces becomes significant, a sharp morphological transition to algebraic roughness is predicted.

close

close

close

close

close

close

close

close

close

close

close

close

close

close

close

close

close

close

close

close

close

close

close

close

close

close