[Show abstract][Hide abstract] ABSTRACT: We consider an individual-based two-dimensional spatial model with nearest-neighbor preemptive competition to study front propagation between an invader and a resident species. In particular, we investigate the asymptotic front velocity and compare it with mean-field predictions.
Computer Simulation Studies in Condensed Matter Physics XIX, Springer Proceedings in Physics Vol. 123, Edited by D.P. Landau, S.P. Lewis, H.-B. Schüttler, 12/2007: chapter 11. Fisher Waves and the Velocity of Front Propagation in a Two-Species Invasion Model with Preemptive Competition: pages 73-78; Springer-Verlag, Berlin, Heidelberg, 2007.
[Show abstract][Hide abstract] ABSTRACT: We report on the morphological instabilities of the liquid-liquid interface in a liquid crystal at a nematic-smectic transition. Upon increasing the undercooling of the nematic phase, the following sequence of distinct structures was observed: dense branching fingers, dendrites, and dense branching fronts. We have determined the characteristic length scales and growth velocities of these patterns.
[Show abstract][Hide abstract] ABSTRACT: We study front propagation when an invading species competes with a resident; we assume nearest-neighbor preemptive competition for resources in an individual-based, two-dimensional lattice model. The asymptotic front velocity exhibits an effective power-law dependence on the difference between the two species' clonal propagation rates (key ecological parameters). The mean-field approximation behaves similarly, but the power law's exponent slightly differs from the individual-based model's result. We also study roughening of the front, using the framework of nonequilibrium interface growth. Our analysis indicates that initially flat, linear invading fronts exhibit Kardar-Parisi-Zhang (KPZ) roughening in one transverse dimension. Further, this finding implies, and is also confirmed by simulations, that the temporal correction to the asymptotic front velocity is of O(t(-2/3)).
[Show abstract][Hide abstract] ABSTRACT: The zero-temperature XX chain is studied with emphasis on the properties of a block of $L$ spins inside the chain. We investigate the quantum fluctuations resulting from the entanglement of the block with the rest of the chain using analytical as well as numerical (density matrix renormalization group) methods. It is found that the rest of the chain acts as a thermal environment and an effective temperature can be introduced to describe the fluctuations. We show that the effective temperature description is robust in the sense that several independent definitions (through fluctuation dissipation theorem, comparing with a finite temperature system) yield the same functional form in the limit of large block size ($L\to\infty$). The effective temperature can also be shown to satisfy the basic requirements on how it changes when two bodies of equal or unequal temperatures are brought into contact. Comment: 19 pages, 7 figures
Journal of Statistical Mechanics Theory and Experiment 09/2006; · 2.06 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Motivated by a synchronization problem in distributed computing we studied a simple growth model on regular and small-world networks, embedded in one and two dimensions. We find that the synchronization landscape (corresponding to the progress of the individual processors) exhibits Kardar-Parisi-Zhang-like kinetic roughening on regular networks with short-range communication links. Although the processors, on average, progress at a nonzero rate, their spread (the width of the synchronization landscape) diverges with the number of nodes (desynchronized state) hindering efficient data management. When random communication links are added on top of the one and two-dimensional regular networks (resulting in a small-world network), large fluctuations in the synchronization landscape are suppressed and the width approaches a finite value in the large system-size limit (synchronized state). In the resulting synchronization scheme, the processors make close-to-uniform progress with a nonzero rate without global intervention. We obtain our results by "simulating the simulations," based on the exact algorithmic rules, supported by coarse-grained arguments.
Physical Review E 06/2006; 73:066115. · 2.31 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Nonequilibrium phase transitions are discussed with emphasis on general features such as the role of detailed balance violation in generating effective (long-range) interactions, the importance of dynamical anisotropies, the connection between various mechanisms generating power-law correlations, and the emergence of universal distribution functions for macroscopic quantities. Quantum spin chains are also discussed in order to demonstrate how to construct steady-states carrying fluxes in quantum systems, and to explain how the fluxes may generate power-law correlations.
[Show abstract][Hide abstract] ABSTRACT: Simulations of restricted solid-on-solid growth models are used to build the width distributions of d=2-5 dimensional Kardar-Parisi-Zhang (KPZ) interfaces. We find that the universal scaling function associated with the steady-state width distribution changes smoothly as d is increased, thus strongly suggesting that d=4 is not an upper critical dimension for the KPZ equation. The dimensional trends observed in the scaling functions indicate that the upper critical dimension is at infinity.
[Show abstract][Hide abstract] ABSTRACT: Monte Carlo simulations are presented for Ising dipoles on body centred cubic and tetragonal lattices. A finite size scaling form that includes logarithmic corrections is proposed and found to significantly improve the data collapse. With lattice parameters appropriate to LiHoF4 the authors obtain a ferromagnetic transition temperature Tc=1.51 K in good agreement with experiment.
[Show abstract][Hide abstract] ABSTRACT: The ordering properties of Ising dipoles are studied in mean field theory, and by Monte Carlo simulations. The boundary conditions are such that there is no net depolarizing field and both regular lattices and various random arrangements are considered. In the mean field approach the authors employ the replica method with a Gaussian approximation for the distribution of dipole-dipole interactions, while a Kirkwood approximation is used for the spatial distribution of dipoles. The low-temperature phase for a system of randomly parked dipoles and diluted face centred cubic and body centred cubic lattices is found to be ferro-electric above a critical concentration. Below this concentration the mean field theory predicts a spin glass. The simulations are only carried out for the body centred cubic lattice. The transition temperature to the ferroelectric state is determined from finite size scaling of the mean square polarization. The critical concentration for the occurrence of a spin glass phase is estimated by zero temperature Monte Carlo simulations using the simulated annealing method. The results are found to be in qualitative agreement with those of the mean field theory described above.
[Show abstract][Hide abstract] ABSTRACT: Edwards--Wilkinson type models are studied in 1+1 dimensions and the time-dependent distribution, P_L(w^2,t), of the square of the width of an interface, w^2, is calculated for systems of size L. We find that, using a flat interface as an initial condition, P_L(w^2,t) can be calculated exactly and it obeys scaling in the form <w^2>_\infty P_L(w^2,t) = Phi(w^2 / <w^2>_\infty, t/L^2) where <w^2>_\infty is the stationary value of w^2. For more complicated initial states, scaling is observed only in the large- time limit and the scaling function depends on the initial amplitude of the longest wavelength mode. The short-time limit is also interesting since P_L(w^2,t) is found to closely approximate the log-normal distribution. These results are confirmed by Monte Carlo simulations on a `roof-top' model of surface evolution. Comment: 5 pages, latex, 3 ps figures in a separate files, submitted to Phys.Rev.E
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 10/1996; 54(3):2256-2260. · 2.33 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Two-spin correlations generated by interactions that decay with distance r as r-1-sigma with -10 that can be observed by introducing magnified correlations LC(r,L)-tsumrC(r,L). The magnified correlations are shown to have a scaling form Phi(r/L), and the singular structure of Phi(x) for x-->0 is found to be the same at all temperatures, including the critical point. These conclusions are supported by the results of Monte Carlo simulations for systems with sigma=-0.50 and -0.25 both at the critical temperature T=Tc and at T=2Tc. (c) 1995 The American Physical Society
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 01/1996; 52(6):6031-6036. · 2.33 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: One-dimensional interfaces with curvature-driven growth kinetics are investigated. We calculate the steady-state distribution P(w2) of the square of the width of the interface w2 and show that, as in the case for random-walk interfaces, the result can be written in a scaling form P(w2)=Phi(w2/), where is the average of w2. The scaling function Phi(x) is found to be distinct from that of random-walk interfaces, but, as our Monte Carlo simulations indicate, this function is universal for curvature-driven growth. It is argued that comparison of scaling functions can be a useful method for distinguishing between universality classes of growth processes.
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 12/1994; 50(5):3589-3593. · 2.33 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Nonequilibrium growth processes are frequently characterized by the width w(L,t) of the active zone, where t is the time elapsed since the start of the process and L is the spatial interval over which the measurement is carried out. Quite generally, w(L,t) obeys a scaling form w(L,t)~Lzetaf(tL-z), and many workers have attempted to determine the dynamic universality class of such processes by a measurement of the exponents zeta and z. In this paper, we calculate the steady-state width distribution P(w2) for several three-dimensional growth processes and show that, expressed in a suitable form, P(w2) can be used to distinguish between different possible universality classes. We also reanalyze experimental data obtained by scanning-tunneling or atomic-force microscopy and show that P(w2) provides valuable information on the nature of a growth process.
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 12/1994; 50(5):3530-3537. · 2.33 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The phase diagram of a two-temperature kinetic Ising model which evolves by Kawasaki dynamics is studied using Monte Carlo simulations in dimension d=2 and solving mean-spherical approximation in general d. We show that the equal-temperature (equilibrium) Ising critical point is a bicritical point where two nonequilibrium critical lines meet a first-order line separating two distinct ordered phases. The shape of the nonequilibrium critical lines is described by a crossover exponent, phi, which we find to be equal to the susceptibility exponent, gamma, of the Ising model.
[Show abstract][Hide abstract] ABSTRACT: Roughening of a one-dimensional interface is studied under the assumption that the interface configurations are continuous, periodic random walks. The distribution of the square of the width of interface, [ital w][sup 2], is found to scale as [ital P]([ital w][sup 2])=[l angle][ital w][sup 2][r angle][sup [minus]1][Phi]([ital w][sup 2]/[l angle][ital w][sup 2][r angle]) where [l angle][ital w][sup 2][r angle] is the average of [ital w][sup 2]. We calculate the scaling function [Phi]([ital x]) exactly and compare it both to exact enumerations for a discrete-slope surface evolution model and to [Phi]'s obtained in Monte Carlo simulations of equilibrium and driven interfaces of chemically reacting systems.
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 09/1994; 50(2):R639-R642. · 2.33 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We study the nonequilibrium properties of a one-dimensional kinetic Ising model in which spins interact by nearest-neighbor ferromagnetic interactions and a spin-flip dynamics is generated by contact with heat baths that are at different temperatures on even and odd lattice sites. The average energy (ɛ) and the energy flux between the two sublattices (jɛ) are calculated exactly and the two-spin steady-state correlations are expressed through ɛ and jɛ. It is found that the correlations can be classified as ferromagnetic (for ɛ<0 and jɛ small), antiferromagnetic (ɛ>0, jɛ small), oscillating ferromagnetic (ɛ<0, jɛ large), and oscillating antiferromagnetic (ɛ>0, jɛ large). We also find a disorder line (ɛ=0, jɛ arbitrary) on which all correlations are zero. The character of spatial correlations is shown to be reflected in the time evolution of sublattice magnetizations: The dynamics is purely relaxational in the ferromagnetic and antiferromagnetic regime while it is damped oscillatory in the oscillating ferromagnetic and antiferromagnetic regions.
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 02/1994; 49(1):139-144. · 2.33 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: A d=2 dimensional kinetic Ising model that evolves by a combination of spin flips and spin exchanges is investigated. The spin flips satisfy detailed balance for the equilibrium state of the Ising model at temperature T while the spin exchanges are random Lévy flights of dimension sigma=1.5. Our Monte Carlo (MC) simulations show that the steady state of this system displays a second-order phase transition as T is lowered. Comparing the critical fluctuations of the magnetization to those of an Ising model in which the interaction decays with distance as r-3.5, we find that, within the resolution of the MC data, the critical exponents and the scaling functions of the two systems coincide. We argue that this coincidence indicates that a recent conjecture about the random Lévy flights generating long-range interaction of the form Veff(r)~r-d-sigma is valid not only in the spherical limit and in d=1 but also in d=2.
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 04/1993; 47(3):1520-1524. · 2.33 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The growth kinetics following a quench from high temperatures to zero temperature is studied using the time-dependent Ginzburg-Landau model. We investigate d-dimensional systems with n-component order parameter and assume that the interactions decay with distance r as V^(r)~r-d-sigma with 0
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 04/1993; 47(3):1499-1505. · 2.33 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: It is shown that dimensional analysis can be used (i) to calculate the energy levels in a one-dimensional potentialV(x) ≈ |k, and (ii) to estimate the value of the gravitational constantG.