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For quicker formation of ice, before inserting inside a refrigerator, heating up of a body of water can be beneficial. We report first observation of a counterpart of this intriguing fact, referred to as the Mpemba effect (ME), during ordering in ferromagnets. By performing Monte Carlo simulations of a generic model, we have obtained results on relaxation of systems that are quenched to sub-critical state points from various temperatures above the critical point. For a fixed final temperature, a system with higher starting temperature equilibrates faster than the one prepared at a lower temperature, implying the presence of ME. The observation is extremely counter-intuitive, particularly because of the fact that the model has no in-built frustration or metastability that typically is thought to provide ME. Via the calculations of nonequilibrium properties concerning structure and energy, we quantify the role of critical fluctuations behind this fundamental as well as technologically relevant observation., This five-page article on Mpemba Effect contains 5 Figures

We analyse the spread of COVID-19, a disease caused by a novel coronavirus, in various countries by proposing a model that exploits the scaling and other important concepts of statistical physics. Quite expectedly, for each of the considered countries, we observe that the spread at early times occurs exponentially fast. We show how the countries can be classified into groups, likeuniversality classesin the literature of phase transitions, based on the rates of infections during late times. This method brings a new angle to the understanding of disease spread and is useful in obtaining a country-wise comparative picture of the effectiveness of lockdown-like social measures. Strong similarity, during both natural and lockdown periods, emerges in the spreads within countries having varying geographical locations, climatic conditions, population densities and economic parameters. We derive accurate mathematical forms for the corresponding scaling functions and show how the model can be used as a predictive tool, with instruction even for future waves, and, thus, as a guide for optimizing social measures and medical facilities. The model is expected to be of general relevance in the studies of epidemics.

Via computer simulations we study kinetics of pattern formation in a two-dimensional active matter system. Self-propulsion in our model is incorporated via the Vicsek-like activity, i.e., particles have the tendency of aligning their velocities with the average directions of motion of their neighbors. In addition to this dynamic or active interaction, there exists passive inter-particle interaction in the model for which we have chosen the standard Lennard-Jones form. Following quenches of homogeneous configurations to a point deep inside the region of coexistence between high and low density phases, as the systems exhibit formation and evolution of particle-rich clusters, we investigate properties related to the morphology, growth and aging. A focus of our study is on the understanding of the effects of structure on growth and aging. To quantify the latter we use the two-time order-parameter autocorrelation function. This correlation, as well as the growth, is observed to follow power-law time dependence, qualitatively similar to the scaling behavior reported for passive systems. The values of the exponents have been estimated and discussed by comparing with the previously obtained numbers for other dimensions as well as with the new results for the passive limit of the considered model. We have also presented results on the effects of temperature on the activity mediated phase separation., Comment: 10 pages, 10 figures

Following quenches from random initial configurations to zero temperature, we study aging during evolution of the ferromagnetic (nonconserved) Ising model towards equilibrium, via Monte Carlo simulations of very large systems, in space dimensions $d=2$ and $3$. Results for the two-time autocorrelations, obtained by using different acceptance probabilities for the spin-flip trial moves, are in agreement with each other. We demonstrate the scaling of this quantity with respect to $\ell/\ell_w$, where $\ell$ and $\ell_w$ are the average domain sizes at $t$ and $t_w$ $(\leqslant t)$, the observation and waiting times, respectively. The scaling functions are shown to be of power-law type for $\ell/\ell_{w} \rightarrow \infty$. The exponents of these power-laws have been estimated via the finite-size scaling analyses and discussed with reference to the available results from non-zero temperatures. While in $d=2$ we do not observe any temperature dependence, in the case of $d=3$ the outcome for quench to zero temperature is very different from the available results for high temperature and violates a lower bound, which we explain via structural consideration. We also present results on the freezing phenomena that this model exhibits at zero temperature. Furthermore, from simulations of extremely large system, thereby avoiding the freezing effect, it has been confirmed that the growth of average domain size in $d=3$, that remained a puzzle in the literature, follows the Lifshitz-Allen-Cahn law in the asymptotic limit.

Via molecular dynamics simulations, we study kinetics in a Vicsek-like phase-separating active matter model. Quantitative results, for isotropic bicontinuous pattern, are presented on the structure, growth, and aging. These are obtained via the two-point equal-time density-density correlation function, the average domain length, and the two-time density autocorrelation function. Both the correlation functions exhibit basic scaling properties, implying self-similarity in the pattern dynamics, for which the average domain size exhibits a power-law growth in time. The equal-time correlation has a short distance behavior that provides reasonable agreement between the corresponding structure factor tail and the Porod law. The autocorrelation decay is a power-law in the average domain size. Apart from these basic similarities, the overall quantitative behavior of the above-mentioned observables is found to be vastly different from those of the corresponding passive limit of the model which also undergoes phase separation. The functional forms of these have been quantified. An exceptionally rapid growth in the active system occurs due to fast coherent motion of the particles, mean-squared-displacements of which exhibit multiple scaling regimes, including a long time ballistic one.

Via a combination of molecular dynamics (MD) simulations and finite-size scaling (FSS) analysis, we study dynamic critical phenomena for the vapor-liquid transition in a three dimensional Lennard-Jones system. The phase behavior of the model, including the critical point, have been obtained via the Monte Carlo simulations. The transport properties, viz., the bulk viscosity and the thermal conductivity, are calculated via the Green-Kubo relations, by taking inputs from the MD simulations in the microcanonical ensemble. The critical singularities of these quantities are estimated via the FSS method. The results thus obtained are in nice agreement with the predictions of the dynamic renormalization group and mode-coupling theories., 9 pages, 11 figures

We present results from molecular dynamics simulations for the non-equilibrium evolution of a binary fluid in the presence of a wetting surface. We study the pattern dynamics which results when a homogeneous fluid mixture is quenched to temperatures both above and below the critical temperature. Our extensive computer simulation results are in agreement with arguments based on Ginzburg-Landau theory.

Kinetics of separation between the low and high density phases in a single component Lennard-Jones model has been studied via molecular dynamics simulations, at a very low temperature, in the space dimension $d=2$. For densities close to the vapor (low density) branch of the coexistence curve, disconnected clusters of the high density phase exhibit ballistic motion, the kinetic energy distribution of the clusters being closely Maxwellian. Starting from nearly circular shapes, at the time of nucleation, these clusters grow via sticky collisions, gaining filament-like nonequilibrium structure at late times, with a very low fractal dimensionality. The origin of the latter is shown to lie in the low mobility of the constituent particles, in the corresponding cluster reference frame, due to the (quasi-long-range) crystalline order. Standard self-similarity in the domain pattern, typically observed in kinetics of phase transitions, is found to be absent in this growth process. This invalidates the common method, that provides a growth law same as in immiscible solid mixtures, of quantifying growth. An appropriate alternative approach, involving the fractality in the structure, quantifies the growth of the characteristic "length" to be a power-law with time, the exponent being surprisingly high. The observed growth law has been derived via a nonequilibrium kinetic theory., Comment: 5 pages, 4 figures

We study phase ordering dynamics in the three-dimensional nearest-neighbor Ising model, following rapid quenches from infinite to zero temperature. Results on various aspects, viz., domain growth, persistence, aging and pattern, have been obtained via the Glauber Monte Carlo simulations of the model on simple cubic lattice. These are analyzed via state-of-the-art methods, including the finite-size scaling, and compared with those for quenches to a temperature above the roughening transition. Each of these properties exhibit remarkably different behavior at the above mentioned final temperatures. Such a temperature dependence is absent in the two-dimensional case for which there is no roughening transition.

We study equilibrium dynamics of a symmetrical binary Lennard-Jones fluid mixture near its consolute criticality. Molecular dynamics simulation results for shear viscosity, $\eta$, from microcanonical ensemble are compared with those from canonical ensemble with various thermostats. It is observed that Nos\'{e}-Hoover thermostat is a good candidate for this purpose and so, is adopted for the quantification of critical singularity of $\eta$, to avoid temperature fluctuation (or even drift) that is often encountered in microcanonical simulations. Via finite-size scaling analysis of our simulation data, thus obtained, we have been able to quantify even the weakest anomaly, of all transport properties, that shear viscosity exhibits and confirm the corresponding theoretical prediction., Comment: 6 pages, 6 figures

Via Monte Carlo simulations we study pattern and aging during coarsening in nonconserved nearest neighbor Ising model, following quenches from infinite to zero temperature, in space dimension $d=3$. The decay of the order-parameter autocorrelation function is observed to obey a power-law behavior in the long time limit. However, the exponent of the power-law, estimated accurately via a state-of-art method, violates a well-known lower bound. This surprising fact has been discussed in connection with a quantitative picture of the structural anomaly that the 3D Ising model exhibits during coarsening at zero temperature. These results are compared with those for quenches to a temperature above that of the roughening transition., Comment: 15 pages, 6 figures

Results for the kinetics of vapor-liquid phase transition have been presented from the molecular dynamics simulations of a single component two-dimensional Lennard-Jones fluid. The phase diagram for the model, primary prerequisite for this purpose, has been obtained via the Monte Carlo simulations. Our focus is on the region very close to the vapor branch of the coexistence curve. Quenches to such region provide morphology that consists of disconnected circular liquid clusters in the vapor background. We identified that these clusters exhibit diffusive motion and grow via sticky collisions among them. The growth follows power-law behavior with time, exponent of which is found to be in nice agreement with a theoretical prediction., Comment: 7 pages, 8 figures

Using a hydrodynamics preserving thermostat, we present extensive molecular dynamics simulation results for the kinetics of phase separation in a model binary fluid confined inside a cylindrical nanopore with neutral wall. We observe the formation of a striped pattern, where A -rich and B -rich domains appear alternately along the axis of the cylinder. For a wide range of diameters of the cylinders, the growth of the pattern freezes and does not lead to complete phase separation. Prior to freezing, the growth of these stripes passes through two power-law regimes. The early-time regime is related to the Lifshitz-Slyozov diffusive mechanism and the estimated value of the exponent for the later-time regime matches well with that for the inertial hydrodynamic growth in three-dimensional fluid systems. Appropriate arguments have been provided to justify the observations. Furthermore, our results show that the length of the cylinder does not seem to affect the average axial length of the frozen patterns. However, the latter exhibits a linear dependence on the diameter of the cylinder.

The bubble model is widely used for the analysis of the decay characteristics of the positronium atom in liquids. However, according to some authors this description is inappropriate in the case of polar liquids with high surface tension. It has been advocated that for such media, rather than employing the value of the bulk surface tension (which appears as a parameter in the model), one should incorporate the notion of a transition layer between the liquid phase and the cavity that encloses the positronium. Accordingly, the usual bubble model with sharp boundaries is modified in the present work through the introduction of a diffusivity in the bubble surface, thus developing the proper setting (without involving any extra free parameters) such that liquids with high surface tension may also be meaningfully discussed in this context and confronted with experimental data.

Aging in kinetics of three different phase transitions, viz., magnetic, binary solid and single component fluid, have been studied via Monte Carlo and molecular dynamics simulations in three space dimensions with the objective of identifying the effects of order-parameter conservation and hydrodynamics. We observe that the relevant autocorrelations exhibit power-law decay in ferromagnet and binary solid but with different exponents. At early time fluid autocorrelation function nicely follows that of binary solid, the order parameter being conserved for both of them, as opposed to a ferromagnet. At late time the fluid data crosses over to an exponential decay which we identify as a hydrodynamic effect and provide analytical justification for this behavior., 4 pages, 4 figures

Finite-size effects in systems with diverging characteristic lengthscale have been addressed via state-of-the-art Monte Carlo and molecular dynamics simulations of various models exhibiting solid-solid, liquid-liquid and vapor-liquid transitions. Our simulations, combined with the appropriate application of finite-size scaling theory, confirm various non-trivial singularities in equilibrium dynamic critical phenomena and non-equilibrium domain coarsening phenomena, as predicted by analytical theories. We convincingly demonstrate that the finite-size effects in the domain growth problems, with conserved order parameter dynamics, is weak and universal, irrespective of the transport mechanism. This result is strikingly different from the corresponding effects in critical dynamics. In critical phenomena, difference in finite-size effects between statics and dynamics is also discussed., Comment: 6 pages, 5 figures

Kinetics of phase separation in a three dimensional single-component Lennard-Jones fluid, that exhibits vapor-liquid transition, is studied via molecular dynamics simulations after quenching homogeneous systems, of different overall densities, inside the coexistence region. For densities close to the vapor branch of the coexistence curve, phase separation progresses via nucleation of liquid droplets and collisions among them. This is different from the evaporation-condensation mechanism proposed by Lifshitz and Slyozov, even though both lead to power-law growth of average domain size, as a function of time, with an exponent $\alpha=1/3$. Beyond a certain threshold value of the overall density, we observe elongated, percolating domain morphology which suddenly enhances the value of $\alpha$. These results are consistent with some existing theoretical expectations., Comment: 10 pages, 13 figures

We present results for structure and dynamics of mixtures of active and passive particles, from molecular dynamics (MD) simulations and integral equation theory (IET) calculations, for a physically motivated model. The perfectly passive limit of the model corresponds to the phase-separating Asakura-Oosawa model for colloid-polymer mixtures in which, for the present study, the colloids are made self-propelling by introducing activity in accordance with the well known Vicsek model. Such activity facilitates phase separation further, as confirmed by our MD simulations and IET calculations. Depending upon the composition of active and passive particles, the diffusive motion of the active species can only be realized at large time scales. Despite this, we have been able to construct an equilibrium approach to obtain the structural properties of such inherently out-of-equilibrium systems. In this method, effective inter-particle potentials were constructed via IET by taking structural inputs from the MD simulations of the active system. These potentials in turn were used in passive MD simulations, results from which are observed to be in fair agreement with the original ones.

Perfect screening of all charges characterizes a conductor, a fact embodied in the Stillinger-Lovett sum rule: namely, the charge-charge correlation or structure factor, ${S}_{ZZ}(k)$, varies with momentum transfer $k\ensuremath{\rightarrow}0$ as ${\ensuremath{\xi}}_{D}^{2}{k}^{2}$ where the Debye length ${\ensuremath{\xi}}_{D}$ is a universal function, $\sqrt{{k}_{B}T/\ensuremath{\rho}{q}_{D}^{2}}$, of $T$ and the ion density $\ensuremath{\rho}$, with a scaled charge ${q}_{D}$. For a charge-symmetric hard-sphere electrolyte our grand canonical simulations, with a new finite-size scaling device, confirm the Stillinger-Lovett rule except, contrary to current theory, for its failure at criticality. Furthermore, the ${k}^{4}$ term in the ${S}_{ZZ}(k)$ expansion is found to diverge like the compressibility when $T\ensuremath{\rightarrow}{T}_{c}$ at ${\ensuremath{\rho}}_{c}$.

From the analysis of Monte Carlo simulations of a binary Lennard-Jones mixture in the coexistence region, we provide evidence that the curvature dependence of the interfacial tension can be described by a simple theoretical function σ(R)ξ(2)=C(1)/[1+C(2)(ξ/R)(2)], where ξ is the correlation length and R is the droplet radius. The universal constants C(1) and C(2) are estimated. In the model, a Tolman length is strictly absent, but, since its critical behavior is believed to be much weaker than ξ, we argue that it only provides a correction to scaling and does not affect the leading critical behavior, which should be described by the above function for any system in the Ising universality class. The large value of C(2)≃32 implies that conventional nucleation theory becomes inaccurate even for a significantly large droplet radius.

We present comprehensive molecular dynamics (MD) results for the kinetics of surface-directed spinodal decomposition (SDSD) and surface enrichment (SE) in binary mixtures at wetting surfaces. We study the surface morphology and the growth dynamics of the wetting and enrichment layers. The growth law for the thickness of these layers shows a crossover from a diffusive regime to a hydrodynamic regime. We provide phenomenological arguments to understand this crossover., 14 pages, 4 figures

Results for transport properties, in conjunction with phase behavior and thermodynamics, are presented at the criticality of a binary Lennard-Jones fluid from Monte Carlo and molecular dynamics simulations. Evidence for much stronger finite-size effects in dynamics compared to statics has been demonstrated. Results for bulk viscosity are the first in the literature that quantifies critical divergence via appropriate finite-size scaling analysis. Our results are in accordance with the predictions of mode-coupling and dynamic renormalization group theoretical calculations., 4 pages, 4 figures

We study the excess free energy due to phase coexistence of fluids by Monte Carlo simulations using successive umbrella sampling in finite LxLxL boxes with periodic boundary conditions. Both the vapor-liquid phase coexistence of a simple Lennard-Jones fluid and the coexistence between A-rich and B-rich phases of a symmetric binary (AB) Lennard-Jones mixture are studied, varying the density rho in the simple fluid or the relative concentration x_A of A in the binary mixture, respectively. The character of phase coexistence changes from a spherical droplet (or bubble) of the minority phase (near the coexistence curve) to a cylindrical droplet (or bubble) and finally (in the center of the miscibility gap) to a slab-like configuration of two parallel flat interfaces. Extending the analysis of M. Schrader, P. Virnau, and K. Binder [Phys. Rev. E 79, 061104 (2009)], we extract the surface free energy gamma (R) of both spherical and cylindrical droplets and bubbles in the vapor-liquid case, and present evidence that for R -> Infinity the leading order (Tolman) correction for droplets has sign opposite to the case of bubbles, consistent with the Tolman length being independent on the sign of curvature. For the symmetric binary mixture the expected non-existence of the Tolman length is confirmed. In all cases {and for a range of radii} R relevant for nucleation theory, gamma(R) deviates strongly from gamma (Infinity) which can be accounted for by a term of order gamma(Infinity)/gamma(R)-1 ~ 1/R^2. Our results for the simple Lennard-Jones fluid are also compared to results from density functional theory and we find qualitative agreement in the behavior of gamma(R) as well as in the sign and magnitude of the Tolman length., 25 pages, submitted to J. Chem. Phys

We use molecular dynamics (MD) to study the kinetics of surface enrichment (SE) in a stable homogeneous mixture (AB), placed in contact with a surface which preferentially attracts A. The SE profiles show a characteristic double-exponential behavior with two length scales: \xi_-, which rapidly saturates to its equilibrium value, and \xi_+, which diverges as a power-law with time (\xi_+ \sim t^\theta). We find that hydrodynamic effects result in a crossover of the growth exponent from \theta \simeq 0.5 to \theta \simeq 1.0. There is also a corresponding crossover in the growth dynamics of the SE-layer thickness., Comment: 20 pages, 6 figures, Published in J. Chem. Phys. (Research Highlights)

When a phase-separated binary ($A+B$) mixture is exposed to a wall, that preferentially attracts one of the components, interfaces between A-rich and B-rich domains in general meet the wall making a contact angle $\theta$. Young's equation describes this angle in terms of a balance between the $A-B$ interfacial tension $\gamma_{AB}$ and the surface tensions $\gamma_{wA}$, $\gamma_{wB}$ between, respectively, the $A$- and $B$-rich phases and the wall, $\gamma _{AB} \cos \theta =\gamma_{wA}-\gamma_{wB}$. By Monte Carlo simulations of bridges, formed by one of the components in a binary Lennard-Jones liquid, connecting the two walls of a nanoscopic slit pore, $\theta$ is estimated from the inclination of the interfaces, as a function of the wall-fluid interaction strength. The information on the surface tensions $\gamma_{wA}$, $\gamma_{wB}$ are obtained independently from a new thermodynamic integration method, while $\gamma_{AB}$ is found from the finite-size scaling analysis of the concentration distribution function. We show that Young's equation describes the contact angles of the actual nanoscale interfaces for this model rather accurately and location of the (first order) wetting transition is estimated., Comment: 6 pages, 6 figures

The phase separation kinetics of binary fluids in constrained geometry is a challenge for computer simulation, since nontrivial structure formation occurs extending from the atomic scale up to mesoscopic scales, and a very large range of time needs to be considered. One line of attack to this problem is to try nevertheless standard Molecular Dynamics (MD), another approach is to coarse-grain the model to apply a time-dependent nonlinear Ginzburg–Landau equation that is numerically integrated. For a symmetric binary mixture confined between two parallel walls that prefer one species, both approaches are applied and compared to each other. There occurs a nontrivial interplay between the formation of a stratified structure due to enrichment layers of the component preferred by the walls, and lateral phase separation. While the former process already occurs during the initial stages, the latter dominates during intermediate and late stages. The extent to which the two methods are equivalent when one suitably translates the time scales is critically discussed.

We report comprehensive simulations of the critical dynamics of a symmetric binary Lennard-Jones mixture near its consolute point. The self-diffusion coefficient exhibits no detectable anomaly. The data for the shear viscosity and the mutual-diffusion coefficient are fully consistent with the asymptotic power laws and amplitudes predicted by renormalization-group and mode-coupling theories {\it provided} finite-size effects and the background contribution to the relevant Onsager coefficient are suitably accounted for. This resolves a controversy raised by recent molecular simulations., 4 pages, 4 figures

A symmetrical binary, A+B Lennard-Jones mixture is studied by a combination of semi-grandcanonical Monte Carlo (SGMC) and Molecular Dynamics (MD) methods near a liquid-liquid critical temperature $T_c$. Choosing equal chemical potentials for the two species, the SGMC switches identities (${\rm A} \to {\rm B} \to {\rm A}$) to generate well-equilibrated configurations of the system on the coexistence curve for $TT_c$. A finite-size scaling analysis of the concentration susceptibility above $T_c$ and of the order parameter below $T_c$ is performed, varying the number of particles from N=400 to 12800. The data are fully compatible with the expected critical exponents of the three-dimensional Ising universality class. The equilibrium configurations from the SGMC runs are used as initial states for microcanonical MD runs, from which transport coefficients are extracted. Self-diffusion coefficients are obtained from the Einstein relation, while the interdiffusion coefficient and the shear viscosity are estimated from Green-Kubo expressions. As expected, the self-diffusion constant does not display a detectable critical anomaly. With appropriate finite-size scaling analysis, we show that the simulation data for the shear viscosity and the mutual diffusion constant are quite consistent both with the theoretically predicted behavior, including the critical exponents and amplitudes, and with the most accurate experimental evidence., Comment: 35 pages, 13 figures

Via the event-driven molecular-dynamics simulations, we have studied the structure and dynamics in a model granular fluid of hard discs in space dimension d = 2. Inelastic collisions among these discs lead to clustering, resembling the kinetics in a vapor-liquid phase transition. The structural growth of these clusters are quantified via an application of finite-size scaling theory. We also present results for the decay of the kinetic energy. Discussion on the validity of a scaling argument, connecting the latter with the time dependence of clustering, is provided. Further, a striking difference in the finite-size effects of the kinetics with those of the phase transition dynamics is pointed out.

We use molecular dynamics to simulate experiments where a symmetric binary fluid mixture (AB), confined between walls that preferentially attract one component (A), is quenched from the one-phase region into the miscibility gap. Surface enrichment occurs during the early stages, yielding a B-rich mixture in the film center with well-defined A-rich droplets. The droplet size grows with time as l(t) proportional t(2/3) after a transient regime. The present atomistic model is also compared to mesoscopic coarse-grained models for this problem.

Static and dynamic structure factors and various transport coefficients are computed for a Lennard-Jones model of a binary fluid (A,B) with a symmetrical miscibility gap, varying both temperature and relative concentration of the mixture. The model is first equilibrated by a semi-grandcanonical Monte Carlo method, choosing the temperature and chemical potential difference $\Delta \mu$ between the two species as the given independent variables. Varying for $\Delta \mu=0$ the temperature and particle number $N$ over a wide range, the location of the coexistence curve in the thermodynamic limit is estimated. Well-equilibrated configurations from these Monte Carlo runs are used as initial states for microcanonical Molecular Dynamics runs, in order to study the microscopic structure and the behavior of transport coefficients as well as dynamic correlation functions along the coexistence curve. Dynamic structure factors $S_{\alpha \beta} (q,t)$ (and the corresponding static functions $S_{\alpha \beta} (q)$) are recorded ($\alpha, \beta, \in$ A,B), $q$ being the wavenumber and $t$ the time, as well as the mean square displacements of the particles (to obtain the self-diffusion constants $D_{\rm A}$, $D_{\rm B}$) and transport coefficients describing collective transport, such as the interdiffusion constant and the shear viscosity. The minority species is found to diffuse a bit faster than the majority species. Despite the presence of strong concentration fluctuations in the system the Stokes-Einstein relation is a reasonable approximation., Comment: 33 pages, 14 figures

We present results from comprehensive event-driven (ED) simulations of nonlinear pattern formation in freely-evolving granular gases. In particular, we focus on the the morphologies of density and velocity fields in the inhomogeneous cooling state (ICS). We emphasize the strong analogy between the ICS morphologies and pattern formation in phase ordering systems with a globally conserved order parameter., Comment: 11 pages, 4 figures. to appear in Europhys. Lett

We use Monte Carlo and molecular dynamics simulations to study phase behavior and transport properties in a symmetric binary fluid where particles interact via Lennard-Jones potential. Our results for the critical behavior of collective transport properties, with particular emphasis on bulk viscosity, is understood via appropriate application of finite-size scaling technique. It appears that the critical enhancements in these quantities are visible far above the critical point. This result is consistent with an earlier report from computer simulations where, however, the authors do not quantify the critical singularity., Comment: 10 pages, 11 figures

We present results for the kinetics of phase separation in solid binary mixtures ($A_1+A_2$) from Monte Carlo simulations of the Ising model in two dimensions. The simulation results are understood via appropriate application of the finite-size scaling theory. At moderately high temperatures, for symmetric $(50:50)$ compositions of $A_1$ and $A_2$ particles the average size of the domains exhibit power-law growth with the exponent having the Lifshitz-Slyozov value of 1/3 from very early time. However, our analysis shows that for low enough temperatures, the growth exponent at early time is smaller than the Lifshitz-Slyozov value. For composition dependence, we find that at moderate temperature, even for extreme off-critical composition, curvature dependent correction to the growth law is weak which is counterintuitive in this case that gives rise to droplet morphology. This is however consistent with the recent understanding on curvature dependence of surface tension. Results from rather general studies on the finite-size effects with the variations of temperature and composition have also been presented., Comment: 11pages, 15 figures

Results for the nonequilibrium dynamics in the complex Ginzburg-Landau equation are presented from Euler-discretization numerical solutions, for both single-spiral as well as multi-spiral morphologies. Single-spiral dynamics has been studied with a specially prepared vortex initial configurations. For random initial conditions, multi-spiral morphologies are observed to be frozen at late time. This frozen dynamics, however, is found to be unlocked in a disordered environment. For the latter, the late-time growth of the average spiral size is seen to be unusually fast. Various possible scenarios leading to this completely counterintuitive result are discussed, for which Hagan's single-spiral solution has been used as a reference.

Domain growth during the kinetics of phase separation is studied following vapor-liquid transition in a single component Lennard-Jones fluid. Results are analyzed after appropriately mapping the continuum snapshots obtained from extensive molecular dynamics simulations to a simple cubic lattice. For near critical quench interconnected domain morphology is observed. A brief period of slow diffusive growth is followed by a linear viscous hydrodynamic growth that lasts for an extended period of time. This result is in contradiction with earlier inclusive reports of late time growth exponent 1/2 that questions the uniqueness of the non-equilibrium universality for liquid-liquid and vapor-liquid transitions., 6 pages, 5 figures

Recently, Das et al. [J. Chem. Phys. 125, 024506 (2006)] established that computer simulations of critical dynamics in a binary Lennard-Jones mixture are consistent with the predicted Stokes-Einstein behavior of the asymptotic decay rate of the order-parameter fluctuations near criticality. Here, we show that the noncritical or "background" contributions to the computed diffusion coefficient are also in agreement with both theory and experiment, thus further validating the feasibility of molecular dynamics simulations for studying dynamic critical behavior.