KPZ equation with realistic short-range-correlated noise

We study a realistic simulation model for the propagation of slow-combustion fronts in paper. In the simulations the deterministic part of the dynamics is that of the KPZ equation. The stochastic part, including in particular the short-range noise correlations, is taken from images of the structure of real paper samples. The parameters of the simulations are determined by using an inverse method applied to the experimental front data and by comparing the simulated and the experimental effective-noise distributions. Our model predicts well the shape of the spatial and temporal correlation functions, including the location of the crossovers from short-range (SR) to long-range (LR) behavior. T…

Spreading dynamics of three-dimensional droplets by the lattice-Boltzmann method

Abstract We have simulated spreading of small droplets on smooth and rough solid surfaces using the three-dimensional lattice-Boltzmann method. We present results for the influence of the initial distance and shape of the drop from the surface on scaling of droplet radius R as a function of time. For relatively flat initial drop shapes our observations are consistent with Tanner's law R ∼ t q , where q =1/10. For increasingly spherical initial shapes, the exponent q increases rapidly being above one half for spherical droplets initially just above the surface. As expected, surface roughness slows down spreading, decreases the final drop radius, and results in irregular droplet shape due to …

Stochastic Kinetics with Wave Nature

We consider stochastic second-order partial differential equations. We indroduce a noisy non-linear wave equation and discuss its connections, in particular via the Lorentz transformation, with known stochastic models.

Polymer dynamics in time-dependent periodic potentials.

Dynamics of a discrete polymer in time-dependent external potentials is studied with the master equation approach. We consider both stochastic and deterministic switching mechanisms for the potential states and give the essential equations for computing the stationary state properties of molecules with internal structure in time-dependent periodic potentials on a lattice. As an example, we consider standard and modified Rubinstein-Duke polymers and calculate their mean drift and effective diffusion coefficient in the two-state non-symmetric flashing potential and symmetric traveling potential. Rich non-linear behavior of these observables is found. By varying the polymer length, we find cur…

Adatom dynamics and diffusion in a model of O/W(110)

We consider adatom dynamics and diffusion in a lattice-gas model of the O/W(110) system under conditions where the adatom interaction effects are important. In particular, we study the behavior of the tracer and collective diffusion coefficients as a function of temperature when crossing over from the high-temperature disordered phase to a low-temperature symmetry broken phase. To this end, we utilize a combined analytical and numerical approach based on the recently developed dynamical mean field theory (DMF) in addition to conventional Monte Carlo simulations. In the case studied here, the origin of the strong temperature dependence of the effective activation barrier ${E}_{A}^{D}$ close …

Accelerated transport and growth with symmetrized dynamics

In this paper we consider a model of accelerated dynamics with the rules modified from those of the recently proposed [Dong et al., Phys. Rev. Lett. 109, 130602 (2012)] accelerated exclusion process (AEP) such that particle-vacancy symmetry is restored to facilitate a mapping to a solid-on-solid growth model in $1+1$ dimensions. In addition to kicking a particle ahead of the moving particle, as in the AEP, in our model another particle from behind is drawn, provided it is within the ``distance of interaction'' denoted by ${\ensuremath{\ell}}_{\mathrm{max}}$. We call our model the doubly accelerated exclusion process (DAEP). We observe accelerated transport and interface growth and widening …

Dynamical mean field theory: an efficient method to study surface diffusion coefficients

Abstract We test the accuracy of the dynamical mean field theory (DMF) developed recently for the collective and tracer diffusion coefficients D C and D T , respectively, by Monte Carlo simulations of two very strongly interacting model systems. The deviation of the DMF results from the true hydrodynamic diffusion coefficients is a measure of memory effects, which are not fully accounted for in DMF. In the cases studied here, DMF predicts the behavior of both D C and D T accurately, while the memory effects are found to be most pronounced at low temperatures, and at high coverages and stronger interactions. Nevertheless, the computational cost of DMF is just a fraction of what is needed for…

Totally asymmetric exclusion process fed by using a non-Poissonian clock

In this article we consider the one-dimensional totally asymmetric open-boundary exclusion process fed by a process with power-law-distributed waiting times. More specifically, we use a modified Pareto distribution to define the jump rate for jumps into the system. We then characterize the propagation of fluctuations through the system by kinetic Monte Carlo simulations and by numerical evaluation of the steady-state partition function. peerReviewed

Temporal and spatial persistence of combustion fronts in paper

The spatial and temporal persistence, or first-return distributions are measured for slow-combustion fronts in paper. The stationary temporal and (perhaps less convincingly) spatial persistence exponents agree with the predictions based on the front dynamics, which asymptotically belongs to the Kardar-Parisi-Zhang universality class. The stationary short-range and the transient behavior of the fronts are non-Markovian, and the observed persistence properties thus do not agree with the predictions based on Markovian theory. This deviation is a consequence of additional time and length scales, related to the crossovers to the asymptotic coarse-grained behavior. Peer reviewed

Ferromagnetism in small clusters.

Magnetization of small ferromagnetic clusters at finite temperatures has been studied using the Ising model and Monte Carlo techniques. The magnetization of finite clusters is reduced from the bulk value, and increases with the external magnetic field and with the cluster size. The results explain qualitatively the recent observations by de Heer, Milani, and Chatelain of the reduction with decreasing cluster size of the average magnetic moment in small iron clusters.

Cluster size distributions in particle systems with asymmetric dynamics

We present exact and asymptotic results for clusters in the one-dimensional totally asymmetric exclusion process (TASEP) with two different dynamics. The expected length of the largest cluster is shown to diverge logarithmically with increasing system size for ordinary TASEP dynamics and as a logarithm divided by a double logarithm for generalized dynamics, where the hopping probability of a particle depends on the size of the cluster it belongs to. The connection with the asymptotic theory of extreme order statistics is discussed in detail. We also consider a related model of interface growth, where the deposited particles are allowed to relax to the local gravitational minimum.

Superparamagnetism in Ising Clusters

Recent experiments on small ferromagnetic clusters have inspired introduction of a number of seemingly quite different theoretical models. We shall argue that all these models show superparamagnetic behaviour above the blocking temperature but below the Curie temperature. In particular, we shall show that Ising clusters display superparamagnetism and introduce a simple correction to the usual tank behaviour of magnetisation which has to be included for very small clusters. We also discuss the dependence of magnetisation on coordination number.

Non-Arrhenius Behavior of Surface Diffusion Near a Phase Transition Boundary

We study the non-Arrhenius behavior of surface diffusion near the second-order phase transition boundary of an adsorbate layer. In contrast to expectations based on macroscopic thermodynamic effects, we show that this behavior can be related to the average microscopic jump rate which in turn is determined by the waiting-time distribution W(t) of single-particle jumps at short times. At long times, W(t) yields a barrier that corresponds to the rate-limiting step in diffusion. The microscopic information in W(t) should be accessible by STM measurements.

Adsorption on a stepped substrate.

Properties of small antiferromagnetic Ising clusters

Magnetic properties of small antiferromagnetic clusters have been studied by using the Ising model with nearest-neighbour interactions. The number of atoms in the clusters varied between 6 and 30. Several cluster geometries were analysed in detail with the result that there is no generic phase diagram. In an external magnetic field magnetisation can increase with increasing temperature in a considerable temperature range. Magnetisation was found to strongly depend on both the overall geometry of the cluster and on the symmetry of the underlaying lattice structure.

Kinetic Roughening in Slow Combustion of Paper

Results of experiments on the dynamics and kinetic roughening of one-dimensional slow-combustion fronts in three grades of paper are reported. Extensive averaging of the data allows a detailed analysis of the spatial and temporal development of the interface fluctuations. The asymptotic scaling properties, on long length and time scales, are well described by the Kardar-Parisi-Zhang (KPZ) equation with short-range, uncorrelated noise. To obtain a more detailed picture of the strong-coupling fixed point, characteristic of the KPZ universality class, universal amplitude ratios, and the universal coupling constant are computed from the data and found to be in good agreement with theory. Below …

Effect of a columnar defect on the shape of slow-combustion fronts

We report experimental results for the behavior of slow-combustion fronts in the presence of a columnar defect with excess or reduced driving, and compare them with those of mean-field theory. We also compare them with simulation results for an analogous problem of driven flow of particles with hard-core repulsion (ASEP) and a single defect bond with a different hopping probability. The difference in the shape of the front profiles for excess vs. reduced driving in the defect, clearly demonstrates the existence of a KPZ-type of nonlinear term in the effective evolution equation for the slow-combustion fronts. We also find that slow-combustion fronts display a faceted form for large enough e…

DISORDERING MECHANISMS OF THE Cu(110) SURFACE

We review recent theoretical work on the various disordering mechanisms of the Cu(110) surface. In these studies the properties of the surface, from the onset of enhanced anharmonicity in surface vibrations up to bulk melting point T M , have been studied using molecular dynamics and lattice-gas Monte Carlo methods with many-body interactions derived from the effective medium theory. Well after the onset of enhanced out-of-plane surface vibrations, clustering of surface defects is found to induce a roughening transition at T≈0.81T M , and surface premelting is found to occur at T≈0.97T M . These results suggest, that these transitions can both appear at Cu(110). The general picture of diso…

Diffusion between evolving interfaces

Diffusion in an evolving environment is studied by continuos-time Monte Carlo simulations. Diffusion is modelled by continuos-time random walkers on a lattice, in a dynamic environment provided by bubbles between two one-dimensional interfaces driven symmetrically towards each other. For one-dimensional random walkers constrained by the interfaces, the bubble size distribution domi- nates diffusion. For two-dimensional random walkers, it is also controlled by the topography and dynamics of the interfaces. The results of the one-dimensional case are recovered in the limit where the interfaces are strongly driven. Even with simple hard-core repulsion between the interfaces and the particles, …

Comment on “Finite-size scaling behavior of the tracer surface diffusion coefficient near a second-order phase transition” by F. Nieto et al.

Single-layer metal-on-metal islands driven by strong time-dependent forces

Non-linear transport properties of single-layer metal-on-metal islands driven with strong static and time-dependent forces are studied. We apply a semi-empirical lattice model and use master equation and kinetic Monte Carlo simulation methods to compute observables such as the velocity and the diffusion coefficient. Two types of time-dependent driving are considered: a pulsed rotated field and an alternating field with a zero net force (electrophoretic ratchet). Small islands up to 12 atoms were studied in detail with the master equation method and larger ones with simulations. Results are presented mainly for a parametrization of Cu on Cu(001) surface, which has been the main system of int…

Determination of the stochastic evolution equation from noisy experimental data

We have determined the coefficients of the Kardar-Parisi-Zhang equation as functions of coarse graining, which best describe the time evolution and spatial behavior observed for slow-combustion fronts in sheets of paper and magnetic flux fronts in a thin-film high-Tc superconductor. Reconstruction of the relevant equation of motion and its coefficients was mainly based on the inverse method proposed by Lam and Sander [Phys. Rev. Lett. 71, 561 (1993)]. The coefficient of the nonlinear term was also determined from the local slope-dependence of the front velocity.

Antiferromagnetic order and frustration in small clusters

Dependence of thermal conductivity on structural parameters in porous samples

The in-plane thermal conductivity of porous sintered bronze plates was studied both experimentally and numerically. We developed and validated an experimental setup, where the sample was placed in vacuum and heated while its time-dependent temperature field was measured with an infrared camera. The porosity and detailed three-dimensional structure of the samples were determined by X-ray microtomography. Lattice-Boltzmann simulations of thermal conductivity in the tomographic reconstructions of the samples were used to correct the contact area between bronze particles as determined by image analysis from the tomographic reconstructions. Small openings in the apparent contacts could not be de…

Roughening of the Cu(110) surface

The structure of the Cu(110) surface is studied at high temperatures using a combination of lattice-gas Monte Carlo and molecular dynamics methods with identical many-atom interactions derived from the effective medium theory. The anisotropic six-vertex model is used in the interpretation of the lattice-gas results. We find a clear roughening transition around T_R=1000K and T_R/T_M=0.81. Molecular dynamics reveals the clustering of surface defects as the atomistic mechanism of the transition and allows us to estimate characteristic time scales. For the system of size 50x50, the time scale of the local roughening at 1150 K of an initially smooth surface is of the order of 100 ps.

Memory effects and coverage dependence of surface diffusion in a model adsorption system

We study the coverage dependence of surface diffusion coefficients for a strongly interacting adsorption system O/W(110) via Monte Carlo simulations of a lattice-gas model. In particular, we consider the nature and emergence of memory effects as contained in the corresponding correlation factors in tracer and collective diffusion. We show that memory effects can be very pronounced deep inside the ordered phases and in regions close to first and second order phase transition boundaries. Particular attention is paid to the details of the time dependence of memory effects. The memory effect in tracer diffusion is found to decay following a power law after an initial transient period. This beha…

Comment on “Surface diffusion near the points corresponding to continuous phase transitions” [J. Chem. Phys. 109, 3197 (1998)]

It is well known that unlike static equilibrium properties, kinetic quantities in Monte Carlo simulations are very sensitive to the details of the algorithm used for the microscopic transition rates. This is particularly true near the critical region where fluctuations are pronounced. We demonstrate that when diffusion of oxygen adatoms near the order–disorder transition of a lattice-gas model of the O/W(110) model system is studied, the transition rates must be chosen carefully. In particular, we show that the choice by Uebing and Zhdanov [J. Chem. Phys. 109, 3197 (1998)] is inappropriate for the study of critical effects in diffusion.

Roughness of two nonintersecting one-dimensional interfaces.

The dynamics of two spatially discrete one-dimensional single-step model interfaces with a noncrossing constraint is studied in both nonsymmetric propagating and symmetric relaxing cases. We consider possible scaling scenarios and study a few special cases by using continuous-time Monte Carlo simulations. The roughness of the interfaces is observed to be nonmonotonic as a function of time, and in the stationary state it is nonmonotonic also as a function of the strength of the effective force driving the interfaces against each other. This is related on the one hand to the reduction of the available configuration space and on the other hand to the ability of the interfaces to conform to eac…

Characteristics of the polymer transport in ratchet systems

Molecules with complex internal structure in time-dependent periodic potentials are studied by using short Rubinstein-Duke model polymers as an example. We extend our earlier work on transport in stochastically varying potentials to cover also deterministic potential switching mechanisms, energetic efficiency and non-uniform charge distributions. We also use currents in the non-equilibrium steady state to identify the dominating mechanisms that lead to polymer transportation and analyze the evolution of the macroscopic state (e.g., total and head-to-head lengths) of the polymers. Several numerical methods are used to solve the master equations and nonlinear optimization problems. The domina…

Memory expansion for diffusion coefficients

We present a memory expansion for macroscopic transport coefficients such as the collective and tracer diffusion coefficients ${D}_{C}$ and ${D}_{T},$ respectively. The successive terms in this expansion for ${D}_{C}$ describe rapidly decaying memory effects of the center-of-mass motion, leading to fast convergence when evaluated numerically. For ${D}_{T},$ one obtains an expansion of similar form that contains terms describing memory effects in single-particle motion. As an example we evaluate ${D}_{C}$ and ${D}_{T}$ for three strongly interacting surface systems through Monte Carlo simulations, and for a simple model diffusion system via molecular dynamics calculations. We show that the n…

A dynamical mean field theory for the study of surface diffusion constants

We present a combined analytical and numerical approach based on the Mori projection operator formalism and Monte Carlo simulations to study surface diffusion within the lattice-gas model. In the present theory, the average jump rate and the susceptibility factor appearing are evaluated through Monte Carlo simulations, while the memory functions are approximated by the known results for a Langmuir gas model. This leads to a dynamical mean field theory (DMF) for collective diffusion, while approximate correlation effects beyond DMF are included for tracer diffusion. We apply our formalism to three very different strongly interacting systems and compare the results of the new approach with th…

Effect of kinks and concerted diffusion mechanisms on mass transport and growth on stepped metal surfaces

Abstract We study the effect of kinks and concerted atomic mechanisms on diffusion processes relevant to metal-on-metal homoepitaxy on fcc metal surfaces vicinal to the fcc (100) direction. First, we carry out extensive finite-temperature molecular dynamics simulations based on the effective medium theory to search for diffusion mechanisms that dominate the mass transport perpendicular and parallel to step edges. Then, the energetics of these processes are studied by ground state calculations. Our results show that kinks play an important role for diffusion both across and along step edges. In particular, the combined effect of kinks and concerted exchange is found to be able to remove loca…

Finite-size effects in dynamics of zero-range processes

The finite-size effects prominent in zero-range processes exhibiting a condensation transition are studied by using continuous-time Monte Carlo simulations. We observe that, well above the thermodynamic critical point, both static and dynamic properties display fluid-like behavior up to a density {\rho}c (L), which is the finite-size counterpart of the critical density {\rho}c = {\rho}c (L \rightarrow \infty). We determine this density from the cross-over behavior of the average size of the largest cluster. We then show that several dynamical characteristics undergo a qualitative change at this density. In particular, the size distribution of the largest cluster at the moment of relocation,…

Island Diffusion on Metal fcc (100) Surfaces

We present Monte Carlo simulations for the size and temperature dependence of the diffusion coefficient of adatom islands on the Cu(100) surface. We show that the scaling exponent for the size dependence is not a constant but a decreasing function of the island size and approaches unity for very large islands. This is due to a crossover from periphery dominated mass transport to a regime where vacancies diffuse inside the island. The effective scaling exponents are in good agreement with theory and experiments.

Adatom Island Diffusion on Metal Fcc(100) Surfaces

We study the energetics and atomic mechanisms of diffusion of adatom islands on fcc(100) metal surfaces. For small islands, we perform detailed microscopic calculations using semi-empirical embedded-atom model and glue potentials in the case of Cu and Al, respectively. Combining systematic saddle-point search methods and molecular statics simulations allows us to find all the relevant transition paths for island motion. In particular, we demonstrate that there are novel many-body mechanisms such as internal row shearing which can, in some cases, control the island dynamics. Next, we show how using the master equation formalism, diffusion coefficients for small islands up to about five atoms…