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Active matter systems[1–3] are made of self-propelling particles and make ideal ground for studies of out-of-equilibrium phenomena. The self-propulsion is fueled by continuous drawing of energy fro...

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

Via Monte Carlo simulations we study nonequilibrium dynamics in the nearest-neighbor Ising model, following quenches to points inside the ordered region of the phase diagram. With the broad objective of quantifying the nonequilibrium universality classes corresponding to spatially correlated and uncorrelated initial configurations, in this paper we present results for the decay of the order-parameter autocorrelation function for quenches from the critical point. This autocorrelation is an important probe for the aging dynamics in far-from-equilibrium systems and typically exhibits power-law scaling. From the state-of-the-art analysis of the simulation results we quantify the corresponding exponents ($\mathbf{\lambda}$) for both conserved and nonconserved (order parameter) dynamics of the model, in space dimension $d=3$. Via structural analysis we demonstrate that the exponents satisfy a bound. We also revisit the $d=2$ case to obtain more accurate results. It appears that irrespective of the dimension, $\lambda$ is same for both conserved and nonconserved dynamics., Comment: 9 pages, 12 figures

We performed molecular dynamics simulations to study relaxation phenomena during vapor-liquid transitions in a single component Lennard-Jones system. Results from two different overall densities are presented; one in the neighborhood of the vapor branch of the coexistence curve and the other being close to the critical density. The nonequilibrium morphologies, growth mechanisms and growth laws in the two cases are vastly different. In the low density case growth occurs via diffusive coalescence of droplets in a disconnected morphology. On the other hand, the elongated structure in the higher density case grows via advective transport of particles inside the tube-like liquid domains. The objective in this work has been to identify how the decay of the order-parameter autocorrelation, an important quantity to understand aging dynamics, differs in the two cases. In the case of the disconnected morphology, we observe a very robust power-law decay, as a function of the ratio of the characteristic lengths at the observation time and at the age of the system, whereas the results for the percolating structure appear rather complex. To quantify the decay in the latter case, unlike standard method followed in a previous study, here we have performed a finite-size scaling analysis. Outcome of this analysis shows the presence of a strong preasymptotic correction, while revealing that in this case also, albeit in the asymptotic limit, the decay follows a power-law. Even though the corresponding exponents in the two cases differ drastically, this study, combined with a few recent ones, suggests that power-law behavior of this correlation function is rather universal in coarsening dynamics., Comment: 8 pages, 5 figures

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

From Kawasaki-exchange Monte Carlo simulations of the $q$-state Potts model, we present results for the kinetics of phase separation in multicomponent mixtures, for $q\ensuremath{\le}10$, in space dimension $d=2$. A particular focus has been on the quantification of finite-size scaling functions for various values of $q$ and quench depths. For a range of final quench temperatures, our analyses, via finite-size scaling and other state-of-the-art methods, show that the growth follows the Lifshitz-Slyozov behavior, expected for a diffusive mechanism, irrespective of the number of components. We show that the growth for different $q$ values and quench temperatures, in finite systems, can be described by a universal scaling function with a nonuniversal metric factor, originating from the differences in the amplitudes. We also demonstrate the morphological and kinetic equivalence between a $q$-component equal proportion mixture and an off-critical binary mixture, in the framework of the Ising model, with relative concentration of the minority component in the latter being ${x}_{c}=1/q$.

Via event-driven molecular dynamics simulations we study kinetics of clustering in assemblies of inelastic particles in various space dimensions. We consider two models, viz., the ballistic aggregation model (BAM) and the freely cooling granular gas model (GGM), for each of which we quantify the time dependence of kinetic energy and average mass of clusters (that form due to inelastic collisions). These quantities, for both the models, exhibit power-law behavior, at least in the long time limit. For the BAM, corresponding exponents exhibit strong dimension dependence and follow a hyperscaling relation. In addition, in the high packing fraction limit the behavior of these quantities become consistent with a scaling theory that predicts an inverse relation between energy and mass. On the other hand, in the case of the GGM we do not find any evidence for such a picture. In this case, even though the energy decay, irrespective of packing fraction, matches quantitatively with that for the high packing fraction picture of the BAM, it is inversely proportional to the growth of mass only in one dimension, and the growth appears to be rather insensitive to the choice of the dimension, unlike the BAM.

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 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 study far-from-equilibrium dynamics in models of freely cooling granular gas and ballistically aggregating compact clusters. For both the cases, from event-driven molecular dynamics simulations, we have presented detailed results on structure and dynamics in space dimensions d=1 and 2. Via appropriate analyses it has been confirmed that the ballistic aggregation mechanism applies in d=1 granular gases as well. Aging phenomena for this mechanism, in both the dimensions, have been studied via the two-time density autocorrelation function. This quantity is demonstrated to exhibit scaling property similar to that in the standard phase transition kinetics. The corresponding functional forms have been quantified and the outcomes have been discussed in connection with the structural properties. Our results on aging establish a more complete equivalence between the granular gas and the ballistic aggregation models in d=1.

Dynamics of ordering in Ising model, following quench to zero temperature, have been studied via Glauber spin-flip Monte Carlo simulations in space dimensions $d=2$ and $3$. One of the primary objectives has been to understand phenomena associated with the persistent spins, viz., time decay in the number of unaffected spins, growth of the corresponding pattern and its fractal dimensionality, for varying correlation length in the initial configurations, prepared at different temperatures, at and above the critical value. It is observed that the fractal dimensionality and the exponent describing the power-law decay of persistence probability are strongly dependent upon the relative values of nonequilibrium domain size and the initial equilibrium correlation length. Via appropriate scaling analyses, these quantities have been estimated for quenches from infinite and critical temperatures. The above mentioned dependence is observed to be less pronounced in higher dimension. In addition to these findings for the local persistence, we present results for the global persistence as well. Further, important observations on the standard domain growth problem are reported. For the latter, a controversy in $d=3$, related to the value of the exponent for the power-law growth of the average domain size with time, has been resolved., 10 pages, 16 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 the dynamics of ordering in ferromagnets via Monte Carlo simulations of the Ising model, employing the Glauber spin-flip mechanism, in space dimensions d = 2 and 3, on square and simple cubic lattices. Results for the persistence probability and the domain growth are discussed for quenches to various temperatures (T f ) below the critical one (T c ), from different initial temperatures T i ≥ T c . In long time limit, for T i >T c , the persistence probability exhibits power-law decay with exponents θ ≃ 0.22 and ≃ 0.18 in d = 2 and 3, respectively. For finite T i , the early time behavior is a different power-law whose life-time diverges and exponent decreases as T i → T c . The two steps are connected via power-law as a function of domain length and the crossover to the second step occurs when this characteristic length exceeds the equilibrium correlation length at T = T i . T i = T c is expected to provide a new universality class for which we obtain θ ≡ θ c ≃ 0.035 in d = 2 and ≃0.105 in d = 3. The time dependence of the average domain size l, however, is observed to be rather insensitive to the choice of T i .

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

We present results from a granular dynamics study of the nonequilibrium behavior of a freely evolving inelastic granular gas. The velocity and density fields exhibit complex pattern formation, which is reminiscent of phase-ordering systems. At early times, the density field stays approximately uniform and the system is said to be in a homogeneous cooling state. However, at later times, the density field undergoes clustering, and evolves into an inhomogeneous cooling state (ICS). We characterize the nonlinear evolution of the density and velocity fields in the ICS by invoking analogies from studies of phase ordering dynamics.

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

Nonequilibrium dynamics in Ising and Ginzburg-Landau models were studied for a nonconserved order parameter that mimics ordering in ferromagnets. The focus was on the understanding of the decay of the two time (t, t(w); ttw) order-parameter correlation function. For this quantity, a full form has been obtained empirically which, for t ≫ t(w), provides a power-law ∼ (ℓ/ℓ(w))(-λ), ℓ and ℓ(w) being the characteristic lengths at t and tw, respectively. This empirical form was used for a finite-size scaling analysis to obtain the exponent λ in space dimensions d = 2 and 3. Our estimates of λ and understanding of the finite-size effects, for the models considered, provide useful information on the relevance of thermal noise. The values of λ obtained are in good agreement with the predictions of a theory based on Gaussian auxiliary field ansatz.

Results from the state-of-the-art molecular dynamics simulations are presented for both equilibrium and nonequilibrium dynamics following vapor-liquid transition in a single component Lennard-Jones system. We have fixed the overall density close to the vapor-branch of the coexistence curve so that the liquid phase forms droplet structure in the background of vapor phase. In the equilibrium case, the motion of a single droplet is studied in both microcanonical and canonical ensembles, in the latter case a hydrodynamics preserving Nos\'{e}-Hoover thermostat was used to control the temperature. The droplet nucleation, motion, collision and coalescence dynamics in the nonequilibrium case were studied in the canonical ensemble with Nos\'{e}-Hoover thermostat. There it was observed that the average droplet volume grows linearly with time. Between two successive collisions, the size of the droplets remain same even though all the constituent particles do not move with the droplets \textminus some leave, others join. It is seen that the number of original particles in a droplet decays exponentially fast. Results from a liquid-liquid transition are also presented in the equilibrium context. Dynamics of droplets in equilibrium appears to be at variant with the nonequilibrium case., Comment: 14 figures, 10 pages

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

With the objective of demonstrating usefulness of thermostats in the study of dynamic critical phenomena in fluids, we present results for transport properties in a binary Lennard-Jones fluid that exhibits liquid-liquid phase transition. Results from the molecular dynamics simulations in canonical ensemble, with various thermostats, are compared with those from microcanonical ensemble. It is observed that the Nos\'{e}-Hoover and dissipative particle dynamics thermostats are useful for the calculations of mutual diffusivity and shear viscosity. The Nos\'{e}-Hoover thermostat, however, appears inadequate for the study of bulk viscosity., Comment: 5 pages, 4 figures in European Physical Journal E 2015

We present results for pattern formation and related dynamics in the two-dimensional complex Ginzburg-Landau equation. Both single and multispiral morphologies have been considered. For the former, Hagan's solution has been tested. In case of the multispiral morphology, at a late time, depending upon certain parameter values, the dynamics is found to be frozen. However, upon introduction of disorder in these parameters the frozen dynamics is observed to be unlocked. This latter result is counterintuitive considering our current knowledge of dynamics in disorder systems. We also present results for the role of shocks (the regions where Hagan's solution is violated) in the multispiral dynamics. It is observed that the suppression of the order-parameter amplitude, in this region, to the value allowed by Hagan's single-spiral solution, also unlocks the dynamical freezing. In this case, both the pattern and dynamics are observed to be very similar to the the dynamical XY model.

We use molecular dynamics (MD) simulations to study surface-directed spinodal decomposition (SDSD) in unstable binary ($AB$) fluid mixtures at wetting surfaces. The thickness of the wetting layer $R_1$ grows with time $t$ as a power-law ($R_1 \sim t^\theta$). We find that hydrodynamic effects result in a crossover of the growth exponent from $\theta\simeq 1/3$ to $\theta\simeq1$. We also present results for the layer-wise correlation functions and domain length scales., Comment: 29 pages, 13 figures, submitted to PRE

We use state-of-the-art molecular dynamics simulations to study hydrodynamic effects on aging during kinetics of phase separation in a fluid mixture. The domain growth law shows a crossover from a diffusive regime to a viscous hydrodynamic regime. There is a corresponding crossover in the autocorrelation function from a power-law behavior to an exponential decay. While the former is consistent with theories for diffusive domain growth, the latter results as a consequence of faster advective transport in fluids for which an analytical justification has been provided., Comment: 6 pages, 4 figures

A three-dimensional symmetric binary fluid is studied, as a function of temperature, in the two-phase (liquid-liquid) coexistence region via Monte Carlo simulations. Particular focus has been in the understanding of curvature-dependent interfacial tension, which is observed to vary as {sigma}(R)={sigma}({infinity})/[1+2((l/R)){sup 2}], implying that a Tolman length is zero in the limit R{yields}{infinity}. The length l is found to have a critical divergence the same as the correlation length, but its amplitude is significantly larger (l{approx_equal}4{xi}). Our findings hence imply that the barrier against homogeneous nucleation is significantly reduced (in comparison with the classical nucleation theory) in the critical region. We also report results for the critical behavior of the flat interfacial tension {sigma}({infinity}) and the concentration susceptibility, as well as the amplitude ratios involving these thermodynamic quantities. Noting that the interatomic potential in our model is described by the Lennard-Jones form that decays faster that 1/r{sup 3}, all of our results for critical phenomena are expectedly consistent with the Ising universality class of three spatial dimensions.

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 study diffusive dynamics of phase separation in a binary mixture, following critical quench, both in spatial dimensions $d=2$ and $d=3$. Particular focus in this work is to obtain information about effects of system size and correction to the growth law via appropriate application of finite-size scaling method to the results obtained from Kawasaki exchange Monte Carlo simulation of Ising model. Observations of only weak size effects and very small correction to scaling in the growth law are significant. The methods used in this work and information thus gathered will be of paramount importance in the study of kinetics of phase separation in fluids and other problems of growing length scale. We also provide detailed discussion on standard methods of understanding simulation results which may lead to inappropriate conclusions., 11 pages, 12 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)

We present results from a study of finite-size effect in the kinetics of domain growth with conserved order parameter for a critical quench. Our observation of a weak size effect is a significant and surprising result. For diffusive dynamics, appropriate scaling analysis of Monte Carlo results obtained for small systems using a two-dimensional Ising model also shows that the correction to the expected Lifshitz-Slyozov law for the domain growth is very small. The methods used in this work to understand the growth dynamics should find application in other nonequilibrium systems with increasing length scales.

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

A brief review of the application of Monte Carlo and Molecular Dynamics methods to the study of the phase behavior of condensed‐matter systems is given, focusing on the binary symmetric Lennard‐Jones mixture as an example. Phase transitions of fluids are conveniently studied by Monte Carlo simulation, applying a statistical ensemble which allows the sampling of the order parameter distribution, analysis of which is done by finite‐size scaling methods. Having located the critical point with very good accuracy by the cumulant intersection method, the expected Ising critical behavior is confirmed. Analysis of the order parameter distribution in the two‐phase coexistence region allows to extract the interface tension of both flat interfaces and of spherical droplets. Using well equilibrated configurations from the Monte Carlo runs as initial states for microcanonical Molecular Dynamics runs, also the dynamic critical behavior can be successfully analyzed.

When a binary mixture is quenched into the unstable region of the phase diagram, phase separation starts by spontaneous growth of long-wavelength concentration fluctuations ("spinodal decomposition"). In the presence of surfaces, the latter provide nontrivial boundary conditions for this growth. These boundary conditions can be derived from lattice models by suitable continuum approximations. But the lattice models can also be simulated directly, and thus used to clarify the conditions under which the Ginzburg–Landau type theory is valid. This comparison shows that the latter is accurate only in the immediate vicinity of the bulk critical point, if thermal fluctuations can also be neglected (true for the late stages of phase separation). In contrast, a local kinetic molecular field theory can take full account of nonlinearities and of rapid concentration variations, and thus has a much wider validity. This enables the detailed study of phase separation processes in thin films of solid binary alloys. However, the extension to spinodal decomposition in fluid binary systems (which can be simulated by brute force large scale molecular dynamics methods, of course) remains an unsolved challenge.

Molecular dynamics computer simulations are performed to study structure and structural relaxation in the glassforming metallic alloy ${\text{Al}}_{80}{\text{Ni}}_{20}$. The interactions between the particles are modeled by an effective potential of the embedded atom type. Our model of ${\text{Al}}_{80}{\text{Ni}}_{20}$ exhibits chemical short-range order (CSRO) that is reflected in a broad prepeak around a wave number of $1.8\text{ }{\text{\AA{}}}^{\ensuremath{-}1}$ in the partial static structure factor for the Ni-Ni correlations. The CSRO is due to the preference of Ni atoms to have Al rather than Ni atoms as nearest neighbors. By analyzing incoherent and coherent intermediate scattering functions as well as self-diffusion constants and shear viscosity, we discuss how the chemical ordering is reflected in the dynamics of the deeply undercooled melt. The $q$ dependence of the $\ensuremath{\alpha}$ relaxation time as well as the Debye-Waller factor for the Al-Al correlations show oscillations at the location of the prepeak in the partial static structure factor for the Ni-Ni correlations. The latter feature of the Debye-Waller factor is well reproduced by a calculation in the framework of the mode coupling theory (MCT) of the glass transition, using the partial static structure factors from the simulation as input. We also check the validity of the Stokes-Einstein-Sutherland formula that relates the self-diffusion coefficients with the shear viscosity. We show that it breaks down already far above the mode coupling critical temperature ${T}_{c}$. The failure of the Stokes-Einstein-Sutherland relation is not related to the specific chemical ordering in ${\text{Al}}_{80}{\text{Ni}}_{20}$.

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 present results from Monte Carlo simulations of hysteresis in the zero-temperature $(T=0)$ dynamics of the Sherrington-Kirkpatrick spin glass model. We study the statistics of magnetization-jumps (denoted as $\ensuremath{\Delta}m$) in response to a time-dependent magnetic field $H(t)$, which increases or decreases with constant increments $\ensuremath{\Delta}$ as $H(t)\ensuremath{\rightarrow}H(t)\ifmmode\pm\else\textpm\fi{}\ensuremath{\Delta}$. In particular, we focus on the field dependence of the $\ensuremath{\Delta}m$-distribution function $P(\ensuremath{\Delta}m,H)$. We formulate arguments to understand the variation of $P(\ensuremath{\Delta}m,H)$ along the hysteresis loop in the weak-disorder limit.

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 study the dynamical behavior of a freely evolving granular gas, where the particles undergo inelastic collisions. The velocity and density fields exhibit complex pattern dynamics, which is reminiscent of phase ordering systems. For example, in the initial time regime, the density field stays (approximately) uniform, and the system is said to be in a homogeneous cooling state (HCS). At later times, the density field undergoes nonlinear clustering, and the system continues to lose energy in an inhomogeneous cooling state (ICS). We quantitatively characterize the HC$\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}$ICS crossover as a function of system parameters. Furthermore, we study nonlinear growth processes in the ICS by invoking analogies from studies of phase ordering dynamics.

This paper is the second of a two-stage exposition, in which we study the nonequilibrium dynamics of the complex Ginzburg-Landau (CGL) equation. We use spiral defects to characterize the system evolution and morphologies. In the first paper of this exposition [S.K. Das, S. Puri, and M.C. Cross, Phys. Rev E 64, 046206 (2001)], we presented analytical results for the correlation function of a single spiral defect, and its short-distance singular behavior. We had also examined the utility of the Gaussian auxiliary field ansatz for characterizing multispiral morphologies. In this paper, we present results from an extensive numerical study of nonequilibrium dynamics in the CGL equation with dimensionality d=2,3. We discuss the behavior of domain growth laws; real-space correlation functions; and momentum-space structure factors. We also compare numerical results for the correlation functions and structure factors with analytical results presented in our first paper.

We study the dynamics of phase separation in multicomponent mixtures through Monte Carlo simulations of the q-state Potts model with conserved kinetics. We use the Monte Carlo renormalization-group method to investigate the asymptotic regime. The domain growth law is found to be consistent with the Lifshitz-Slyozov law, L(t) equivalent to t(1/3) (where t is time), regardless of the value of q. We also present results for the scaled correlation functions and domain-size distribution functions for a range of q values.

We present results from a comprehensive analytical and numerical study of nonequilibrium dynamics in the 2-dimensional complex Ginzburg-Landau (CGL) equation. In particular, we use spiral defects to characterize the domain growth law and the evolution morphology. An asymptotic analysis of the single-spiral correlation function shows a sequence of singularities -- analogous to those seen for time-dependent Ginzburg-Landau (TDGL) models with O(n) symmetry, where $n$ is even., 11 pages, 5 figures

We present a detailed analytical and numerical study of nonequilibrium dynamics for the complex Ginzburg-Landau (CGL) equation. In particular, we characterize evolution morphologies using spiral defects. This paper (referred to as $\rm I$) is the first in a two-stage exposition. Here, we present analytical results for the correlation function arising from a single-spiral morphology. We also critically examine the utility of the Gaussian auxiliary field (GAF) ansatz in characterizing a multi-spiral morphology. In the next paper of this exposition (referred to as $\rm II$), we will present detailed numerical results., Comment: 21 pages, 7 figures

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

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