Search

We present results from the molecular dynamics (MD) simulation of surface-directed spinodal decomposition (SDSD) in binary fluid mixtures ($A+B$) with off-critical compositions. The aim is to elucidate the role of composition ratio in the early-time wetting kinetics under the influence of long-range surface potential. In our simulations, the attractive part of surface potential varies as $V(z)= -\epsilon_a/z^{n}$, with $\epsilon_{a}$ being the surface-potential strength. The surface prefers `$A$' species to form the wetting layer. Its thickness [$R_1(t)$] for the majority wetting (number of $A$-type particles [$N_A$] > number of $B$-type particles [$N_B$]), grows as a power-law with an exponent $1/(n+2)$. This is consistent with the early-time kinetics in the form of potential-dependent growth present in the Puri-Binder model. However, for minority wetting ($N_A$ < $N_B$), the growth exponent in $R_1(t)$ is less than $1/(n+2)$. Furthermore, on decreasing the field strength $\epsilon_{a}$, we recover $1/(n+2)$ for a minority wetting case. We provide phenomenological arguments to explain the early-time wetting kinetics for both cases., Comment: 11 pages, 7 figures

In the domain growth process, small structures gradually vanish, leaving behind larger ones. We investigate spectral energy transfers in two standard models for domain growth: (a) the {\it Cahn-Hilliard} (CH) equation with conserved dynamics, and (b) the {\it time-dependent Ginzburg-Landau} (TDGL) equation with non-conserved dynamics. The nonlinear terms in these equations dissipate fluctuations and facilitate energy transfers among Fourier modes. In the TDGL equation, only the $\phi(\mathbf{k} = 0, t)$ mode survives, and the order parameter $\phi(\mathbf{r},t)$ approaches a uniform state with $\phi = +1$ or $-1$. On the other hand, there is no dynamics of the $\phi(\mathbf{k} = 0, t)$ mode in the CH equation due to the conservation law, highlighting the different dynamics of these equations.

We study the phase separation kinetics of miktoarm star polymer (MSP) melts and blends with diverse architectures using dissipative particle dynamics simulations. Our study focuses on symmetric and asymmetric miktoarm star polymer (SMSP/AMSP) mixtures based on arm composition and number. For a fixed MSP chain size, the characteristic microphase-separated domains initially show diffusive growth with a growth exponent $\phi \sim 1/3$ for both melts that gradually crossover to saturation at late times. The simulation results demonstrate that the evolution morphology of SMSP melts exhibits perfect dynamic scaling with varying arm numbers; the time scale follows a power-law decay with an exponent $\theta \simeq 1$ as the number of arms increases. The structural constraints on AMSP melts cause the domain growth rate to decrease as the number of one type of arms increases while their length remains fixed. This increase in the number of arms for AMSP corresponds to increased off-criticality. The saturation length in AMSP follows a power law increase with an exponent $\lambda \simeq 2/3$ as off-criticality decreases. Additionally, macrophase separation kinetics in SMSP/AMSP blends show a transition from viscous ($\phi \sim 1$) to inertial ($\phi \sim 2/3$) hydrodynamic growth regimes at late times; this exhibits the same dynamical universality class as linear polymer blends, with slight deviations at early stages.

We use molecular dynamics simulations to study coarsening dynamics in achiral banana-shaped bent-core liquid crystals following a quench from the high concentration polar smectic (SmX) phase to lower concentrations that favor the exotic twist-bend (TB) phase. Our novel result is the identification of an intermediate splay-bend state emerging prior to the eventual TB phase. The latter coarsens via the annihilation of {\it beta lines} which are analogous to string defects in nematic liquid crystals. Our findings are relevant for a large class of chiral systems assembled from achiral entities.

We perform a comprehensive study on the role of thermal noise on the ordering kinetics of a collection of active Brownian particles modeled using coarse-grained conserved active model B (AMB). The ordering kinetics of the system is studied for the critical mixture when quenched from high to a low temperature. The structure of the growing domains changes from isolated droplet type for AMB without noise to bi-continuous type for active model B with noise (AMBN). Unlike the passive counterpart of the AMB, the noise is relevant for the growth kinetics of the AMB. We use extensive numerical study, as well as dynamic scaling hypothesis to characterize the kinetics of the system. We find that the asymptotic growth law for AMBN is diffusive Lifshitz-Slyozov (LS) type, whereas it was reported previously that the asymptotic growth law for the AMB without noise is slower, with a growth exponent 4. Moreover, the kinetics of the growing domains show a strong time dependent growth for AMBN. The growth law shows a crossover from early time 1/3 value to intermediate time 1/4 value, and it again traverses from 1/4 to 1/3 asymptotically. The two different scaling functions are found for intermediate time and late time with growth law 1/4 and 1/3 respectively., Comment: 9 Pages, 7 figures

We study living liquid crystals (LLCs), which are an amalgam of nematic liquid crystals (LCs) and active matter (AM). These LLCs are placed in contact with surfaces which impose planar/homeotropic boundary conditions on the director field of the LC and the polarization field of the AM. The interplay of LC-AM interactions and the surface-directed conditions yield controlled pattern dynamics in the LLC, which has important technological implications. We discuss two representative examples of this pattern dynamics.

We present results for phase ordering kinetics in the {\it Coulomb glass} (CG) model, which describes electrons on a lattice with unscreened Coulombic repulsion. The filling factor is denoted by $K \in [0,1]$. For a square lattice with $K=0.5$ (symmetric CG), the ground state is a checkerboard with alternating electrons and holes. In this paper, we focus on the asymmetric CG where $K \lesssim 0.5$, i.e., the ground state is checkerboard-like with excess holes distributed uniformly. There is no explicit quenched disorder in our system, though the Coulombic interaction gives rise to frustration. We find that the evolution morphology is in the same dynamical universality class as the ordering ferromagnet. Further, the domain growth law is slightly slower than the {\it Lifshitz-Cahn-Allen} law, $L(t) \sim t^{1/2}$, i.e., the growth exponent is underestimated. We speculate that this could be a signature of logarithmic growth in the asymptotic regime., Comment: 21 pages, 6 figures

We investigate the influence of long-range (LR) interactions on the phase ordering dynamics of the one-dimensional random field Ising model (RFIM). Unlike the usual RFIM, a spin interacts with all other spins through a ferromagnetic coupling that decays as $r^{-(1+\sigma)}$, where $r$ is the distance between two spins. In the absence of LR interactions, the size of coarsening domains $R(t)$ exhibits a crossover from pure system behavior $R(t) \sim t^{1/2}$ to an asymptotic regime characterized by logarithmic growth: $R(t) \sim (\ln t)^2$. The LR interactions affect the pre-asymptotic regime, which now exhibits ballistic growth $R(t) \sim t$, followed by $\sigma$-dependent growth $R(t) \sim t^{1/(1+\sigma)}$. Additionally, the LR interactions also affect the asymptotic logarithmic growth, which becomes $R(t) \sim (\ln t)^{\alpha(\sigma)}$ with $\alpha(\sigma) < 2$. Thus, LR interactions lead to faster growth than for the nearest-neighbor system at short times. Unexpectedly, this driving force causes a slowing-down of the dynamics ($\alpha < 2$) in the asymptotic logarithmic regime. This is explained in terms of a non-trivial competition between the pinning force caused by the random field and the driving force introduced by LR interactions. We also study the spatial correlation function and the autocorrelation function of the magnetization field. The former exhibits superuniversality for all $\sigma$, i.e., a scaling function that is independent of the disorder strength. The same holds for the autocorrelation function when $\sigma<1$, whereas a signature of the violation of superuniversality is seen for $\sigma>1$., Comment: 27 pages, 12 figures

An amalgamate of nematic liquid crystals and active matter, referred to as living liquid crystals, is a promising self-healing material with futuristic applications for targeted delivery of information and micro-cargo. We provide a phenomenological model to study the symbiotic pattern dynamics in this contemporary system using the Toner-Tu model for active matter (AM), the Landau-de Gennes free energy for liquid crystals (LCs), and an experimentally motivated coupling term that favours co-alignment of the active and nematic components. Our extensive theoretical studies unfold two novel steady states, chimeras and solitons, with sharp regions of distinct orientational order that sweep through the coupled system in synchrony. The induced dynamics in the passive nematic is unprecedented. We show that the symbiotic dynamics of the AM and LC components can be exploited to induce and manipulate order in an otherwise disordered system.

The dynamic critical behavior at the paramagnetic-antiferromagnetic (PM-AFM) transition in manganites has recently been studied experimentally [Niermann et al., Phys. Rev. Lett. {\bf 114}, 037204 (2015)]. We extend the Hamiltonian of Paper I by incorporating an energy field, and study the corresponding Model C of critical dynamics. We use the dynamic renormalization group (RG) approach and calculate the dynamic critical exponents $z$, $\nu z$ and the line-width exponent $\Delta$ to leading order in the small expansion parameters $\epsilon=4-d+2\sigma$ and $\epsilon'=4-d$. Here, $d$ is the space dimension and $\sigma$ is the long-range exponent. Using $\sigma$ as an adjustable parameter, the theory gives us a good match to the experimentally available static and dynamic critical exponents at the PM-AFM transition., Comment: "To appear in JSTAT: Theory and Experiment"

We use a model Hamiltonian to study critical phenomena in manganites. This Hamiltonian includes long-range strain interactions, and a coupling between the magnetic order parameter and the strain field. We perform a perturbative renormalization group (RG) analysis and calculate the static critical exponents, correct to the one-loop level. We compare our RG results with many experiments on doped manganite critical systems. Our theory is in excellent agreement with the experimental values for the critical exponents.

The biaxial phase in nematic liquid crystals has been elusive for several decades after its prediction in the 1970s. A recent experimental breakthrough was achieved by Liu et al. [PNAS 113, 10479 (2016)] in a liquid crystalline medium with magnetic nanoparticles (MNPs). They exploited the different length scales of dipolar and magneto-nematic interactions to obtain an equilibrium state where the magnetic moments are at an angle to the nematic director. This tilt introduces a second distinguished direction for orientational ordering or biaxiality in the two-component system. Using coarse-grained Ginzburg-Landau free energy models for the nematic and magnetic fields, we provide a theoretical framework which allows for the manipulation of morphologies and quantitative estimates of biaxial order.

We present simulation results from a comprehensive molecular dynamics (MD) study of surface-directed spinodal decomposition (SDSD) in unstable symmetric binary mixtures at wetting surfaces. We consider long-ranged and short-ranged surface fields to investigate the early-stage wetting kinetics. The attractive part of the long-ranged potential is of the form $V(z) \sim z^{-n}$, where $z$ is the distance from the surface and $n$ is the power-law exponent. We find that the wetting-layer thickness $R_1(t)$ at very early times exhibits a power-law growth with an exponent $\alpha = 1/(n+2)$. It then crosses over to a universal fast-mode regime with $\alpha=3/2$. In contrast, for the short-ranged surface potential, a logarithmic behavior in $R_1(t)$ is observed at initial times. Remarkably, similar rapid growth is seen in this case too. We provide phenomenological arguments to understand these growth laws. Our MD results firmly establish the existence of universal fast-mode kinetics and settle the related controversy., Comment: 6 pages, 4 figures

Enormous advances have been made in the past 20 years in our understanding of the random-field Ising model, and there is now consensus on many aspects of its behavior at least in thermal equilibrium. In contrast, little is known about its generalization to the random-field Potts model which has wide-ranging applications. Here we start filling this gap with an investigation of the three-state random-field Potts model in three dimensions. Building on the success of ground-state calculations for the Ising system, we use a recently developed approximate scheme based on graph-cut methods to study the properties of the zero-temperature random fixed point of the system that determines the zero and non-zero temperature transition behavior. We find compelling evidence for a continuous phase transition. Implementing an extensive finite-size scaling (FSS) analysis, we determine the critical exponents and compare them to those of the random-field Ising model., Comment: RevTeX, 6+5 pages, 4+5 figures, 3+1 tables, version accepted for publication

The anisotropic shape of calamitic LC particles results in distinct energy values when nematogens are placed side-by-side or end-to-end. The energy anisotropy governed by parameter K' has deep consequences on equilibrium & non-equilibrium properties. Using GB model, which shows Nm & low temperature Sm order, we undertake large-scale MC & MD simulations to probe effect of K' on the equilibrium phase diagram & the non-equilibrium domain growth following a quench in the temperature T (coarsening). There are 2 transitions in the model, I->Nm at Tc1 & Nm->Sm at Tc2Tc1->T

It is known that, after a quench to zero temperature ($T=0$), two-dimensional ($d=2$) Ising ferromagnets with short-range interactions do not always relax to the ordered state. They can also fall in infinitely long-lived striped metastable states with a finite probability. In this paper, we study how the abundance of striped states is affected by long-range interactions. We investigate the relaxation of $d=2$ Ising ferromagnets with power-law interactions by means of Monte Carlo simulations at both $T=0$ and $T \ne 0$. For $T=0$ and the finite system size, the striped metastable states are suppressed by long-range interactions. In the thermodynamic limit, their occurrence probabilities are consistent with the short-range case. For $T \ne 0$, the final state is always ordered. Further, the equilibration occurs at earlier times with an increase in the strength of the interactions.

We study the breaking of time-reversal invariance (TRI) by the application of a magnetic field in the quantum kicked rotor (QKR), using Izrailev's finite-dimensional model. There is a continuous crossover from TRI to time-reversal non-invariance (TRNI) in the spectral and eigenvector fluctuations of the QKR. We show that the properties of this TRI $\rightarrow$ TRNI transition depend on $\alpha^2/N$, where $\alpha$ is the chaos parameter of the QKR and $N$ is the dimensionality of the evolution operator matrix. For $\alpha^2/N \gtrsim N$, the transition coincides with that in random matrix theory. For $\alpha^2/N < N$, the transition shows a marked deviation from random matrix theory. Further, the speed of this transition as a function of the magnetic field is significantly enhanced as $\alpha^2/N$ decreases.

We use large-scale Monte Carlo simulations to obtain comprehensive results for domain growth and aging in the random field XY model in dimensions $d=2,3$. After a deep quench from the paramagnetic phase, the system orders locally via annihilation of topological defects, i.e., vortices and anti-vortices. The evolution morphology of the system is characterized by the correlation function and the structure factor of the magnetization field. We find that these quantities obey dynamical scaling, and their scaling function is independent of the disorder strength $\Delta$. However, the scaling form of the autocorrelation function is found to be dependent on $\Delta$, i.e., superuniversality is violated. The large-$t$ behavior of the autocorrelation function is explored by studying aging and autocorrelation exponents. We also investigate the characteristic growth law $L(t,\Delta)$ in $d=2,3$, which shows an asymptotic logarithmic behavior: $L(t,\Delta) \sim \Delta^{-\varphi} (\ln t)^{1/\psi}$, with exponents $\varphi, \psi > 0$.

The behavior of many magnetic and dielectric solids, and the more contemporary magnetic super-lattices, is governed by dipolar interactions. They are anisotropic and long-ranged, having varied consequences ranging from ground states with complicated magnetic order to the presence of glassy dynamics characterised by a plethora of relaxation times.These systems are well-captured by the dipolar Ising model (DIM) with nearest-neighbor exchange interactions (J) and long-range dipolar interactions (D). Depending on the relative interaction strength {\Gamma} =J/D, there are four phases of distinct magnetic order and symmetry. Using Monte Carlo simulations, we perform deep quenches to study domain growth or coarsening in the d= 3 DIM. This important non-equilibrium phenomenon has not been addressed as dipolar interactions are notoriously difficult to handle theoretically. Our study reveals that, in spite of the anisotropy in interactions and diversity in ground state configurations, we observe universality in the ordering dynamics of all phases.

We study the ordering kinetics of an assembly of {\it active Brownian particles} (ABPs) on a two-dimensional substrate. We use a coarse-grained equation for the composition order parameter $\psi ({\bf r},t)$, where ${\bf r}$ and $t$ denote space and time, respectively. The model is similar to the {\it Cahn-Hilliard equation} or {\it Model B} (MB) for a conserved order parameter with an additional activity term of strength $\lambda$. This model has been introduced by Wittkowski et al., Nature Comm. {\bf 5}, 4351 (2014), and is termed {\it Active Model B} (AMB). We study domain growth kinetics and dynamical scaling of the correlation function for the AMB with critical and off-critical compositions. The quantity $P = \mbox{sign}(\lambda \times \psi_0)$ governs the asymptotic growth kinetics for the off-critical AMB, where $\psi_0$ denotes the average order parameter. For negative $P$, the domain growth law is the usual Lifshitz-Slyozov growth law with $L(t,\lambda) \sim t^{1/3}$. For positive $P$, the growth law shows a crossover to a novel growth law $L(t,\lambda) \sim t^{1/4}$. Further, the correlation function shows good dynamical scaling for the off-critical AMB but the scaling function has a dependency on $\psi_0$ and $\lambda$. We also study the effects of both additive and multiplicative noise on the AMB.

We undertake a detailed numerical study of the {\it Active Model B} proposed by Wittkowski et al. [Nature Comm. {\bf 5}, 4351 (2014)]. We find that the introduction of activity has a drastic effect on the ordering kinetics. First, the domain growth law shows a crossover from the usual Lifshitz-Slyozov growth law for phase separation ($L \sim t^{1/3}$, where $t$ is the time) to a novel growth law ($L \sim t^{1/4}$) at late times. Second, the correlation function exhibits dynamical scaling for a given activity strength $\lambda$, but the scaling function depends on $\lambda$.

We undertake a comprehensive Monte Carlo (MC) study of the ordering kinetics in nematic liquid crystals (NLCs) in 3-dimensions $(d=3)$ by performing deep quenches from the isotropic $(T>T_c)$ to the nematic $(T

Using dissipative particle dynamics (DPD) simulation method, we study the phase separation dynamics in block copolymer (BCP) melt in $d=3$, subjected to external stimuli such as light. An initial homogeneous BCP melt is rapidly quenched to a temperature $T < T_c$, where $T_c$ is the critical temperature. We then let the system go through alternate light "on" and "off" cycles. An on-cycle breaks the stimuli-sensitive bonds connecting both the blocks A and B in BCP melt, and during the off-cycle, broken bonds reconnect. By simulating the effect of light, we isolate scenarios where phase separation begins with the light off (set 1); the cooperative interactions within the system allow it to undergo microphase separation. When the phase separation starts with the light on (set 2), the system undergoes macrophase separation due to the bond breaking. Here, we report the role of alternate cycles on domain morphology by varying bond-breaking probability for both the sets 1 and 2, respectively. We observe that the scaling functions depend upon the conditions mentioned above that change the time scale of the evolving morphologies in various cycles. However, in all the cases, the average domain size respects the power-law growth: $R(t)\sim t^{\phi}$ at late times, here $\phi$ is the dynamic growth exponent. After a short-lived diffusive growth ($\phi \sim 1/3$) at early times, $\phi$ illustrates a crossover from the viscous hydrodynamic ($\phi \sim 1$) to the inertial hydrodynamic ($\phi \sim 2/3$) regimes at late times., Comment: 36 pages, 9 main figures, 7 SI figures

We study the low-temperature domain growth kinetics of the two-dimensional Ising model with long-range coupling: $J(r) \sim r^{-(d+\sigma)}$, where $d=2$ is the dimensionality. According to the Bray-Rutenberg predictions, the exponent $\sigma$ controls the algebraic growth in time of the characteristic domain size $L(t)$, $L(t) \sim t^{1/z}$, with growth exponent $z=1+\sigma$ for $\sigma <1$ and $z=2$ for $\sigma >1$. These results hold for quenches to a non-zero temperature $T>0$ below the critical temperature $T_c$. We show that, in the case of quenches to $T=0$, due to the long-range interactions, the interfaces experience a drift which makes the dynamics of the system peculiar. More precisely we find that in this case the growth exponent takes the value $z=4/3$, independent of $\sigma$, showing that it is a universal quantity. We support our claim by means of extended Monte Carlo simulations and analytical arguments for simplified models., Comment: 22 pages, 12 figures. Accepted by Phys. Rev. E

Ferronematics (FNs) are suspensions of magnetic nanoparticles in nematic liquid crystals (NLCs). They have attracted much experimental attention, and are of great interest both scientifically and technologically. There are very few theoretical studies of FNs, even in equilibrium. In this paper, we study the non-equilibrium phenomenon of domain growth after a thermal quench (or coarsening) in this coupled system. Our modeling is based on coupled time-dependent Ginzburg-Landau (TDGL) equations for two order parameters: the LC tensor order parameter ${\bf Q}$, and the magnetization ${\bf M}$. We consider both shallow and deep quenches from a high-temperature disordered phase. The system coarsens by the collision and annihilation of topological defects. We focus on slaved coarsening, where a disordered ${\bf Q}$ (or ${\bf M}$) field is driven to coarsen by an ordered ${\bf M}$ (or ${\bf Q}$) field. We present detailed results for the morphologies and growth laws, which exhibit unusual features purely due to the magneto-nematic coupling. To the best of our knowledge, this is the first study of non-equilibrium phenomena in FNs.

We study the dynamics of an intruder moving through a fluidized granular medium in three dimensions ($d=3$). The intruder and grains have both translational and rotational degrees of freedom. The energy-dissipation mechanism is solid friction between all pairs of particles. We keep the granular system fluidized even at rather high densities by randomly perturbing the linear and angular velocities of the grains. We apply a constant external force of magnitude $F$ to the intruder, and obtain its steady state velocity $V_s$ in the center-of-mass frame of the grains. The $F$-$V_s$ relation is of great interest in the industrial processing of granular matter, and has been the subject of most experiments on this problem. We also obtain the mobility, which is proportional to the inverse viscosity, as a function of the volume fraction $\phi$. This is shown to diverge at the jamming volume fraction. For $\phi$ below the jamming fraction, we find that $V_s \sim F$ for small $F$ and $V_s \sim F^{1/2}$ for large $F$. The intruder shows diffusive motion in the plane perpendicular to the direction of the external force., Comment: 14 Pages, 5 Figs, and 1 Table, Accepted to Phys. Rev. E

This paper is the second in a two-part exposition on {\it surface-directed spinodal decomposition} (SDSD), i.e., the interplay of kinetics of wetting and phase separation at a surface which is wetted by one of the components of a binary mixture. In our first paper [P. Das, P.K. Jaiswal and S. Puri, Phys. Rev. E {\bf 102}, 012803 (2020)], we studied SDSD on chemically heterogeneous and physically flat substrates. In this paper, we study SDSD on a chemically homogeneous but morphologically patterned substrate. Such substrates arise in a vast variety of technological applications. Our goal is to provide a theoretical understanding of SDSD in this context. We present detailed numerical results for domain growth both inside and above the grooves in the substrate. The morphological evolution can be understood in terms of the interference of SDSD waves originating from the different surfaces comprising the substrate., Comment: 17Pages, 9 Figures, Accepted to Physical Review E

{\it Surface-directed spinodal decomposition} (SDSD) is the kinetic interplay of phase separation and wetting at a surface. This process is of great scientific and technological importance. In this paper, we report results from a numerical study of SDSD on a chemically patterned substrate. We consider simple surface patterns for our simulations, but most of the results apply for arbitrary patterns. In layers near the surface, we observe a dynamical crossover from a {\it surface-registry regime} to a {\it phase-separation regime}. We study this crossover using layer-wise correlation functions and structure factors, and domain length scales., Comment: 19 Pages, 11 Figs, Accepted to Physical Review E

We study numerically the ordering kinetics in a two-dimensional Ising model with random coupling where the fraction of antiferromagnetic links $a$ can be gradually tuned. We show that, upon increasing such fraction, the behavior changes in a radical way. Small $a$ does not prevent the system from a complete ordering, but this occurs in an extremely (logarithmically) slow manner. However, larger values of this parameter destroy complete ordering, due to frustration, and the evolution is comparatively faster (algebraic). Our study shows a precise correspondence between the kind of developing order, ferromagnetic versus frustrated, and the speed of evolution. The aging properties of the system are studied by focusing on the scaling properties of two-time quantities, the autocorrelation and linear response functions. We find that the contribution of equilibrium and an aging part to these functions occurs differently in the various regions of the phase diagram of the model. When quenching inside the ferromagnetic phase, the two-time quantities are obtained by the addition of these parts. Instead, in the paramagnetic phase, these two contributions enter multiplicatively. Both of the scaling forms are shown with excellent accuracy, and the corresponding scaling functions and exponents have been determined and discussed.

In this article, we present a Monte Carlo study of phase transition and coarsening dynamics in the non-conserved two-dimensional random-bond $q$-state clock model (RBCM) deriving from a pure clock model [Phys. Rev. E 98, 032109 (2018)]. Akin to the pure clock model, RBCM also passes through two different phases when quenched from a disordered initial configuration representing at infinite temperature. Our investigation of the equilibrium phase transition affirms that both upper ($T_c^1$) and lower ($T_c^2$) phase transition temperatures decrease with bond randomness strength $\epsilon$. Effect of $\epsilon$ on the non-equilibrium coarsening dynamics is investigated following independent rapid quenches in the quasi-long range ordered (QLRO, $T_c^2 < T < T_c^1$) regime and long-range ordered (LRO, $T

We study the flocking model introduced by Vicsek in the "coarsening" regime. At standard self-propulsion speeds, we find two distinct growth laws for the coupled density and velocity fields. The characteristic length scale of the density domains grows as $L_{\rho}(t) \sim t^{\theta_\rho}$ (with $\theta_\rho \simeq 0.25$), while the velocity length scale grows much faster, $viz.$, $L_{v}(t) \sim t^{\theta_v}$ (with $\theta_v \simeq 0.83$). The spatial fluctuations in the density and velocity fields are studied by calculating the two-point correlation function and the structure factor, which show deviations from the well-known Porod's law. This is a natural consequence of scattering from irregular morphologies that dynamically arise in the system. At large values of the scaled wave-vector, the scaled structure factors for the density and velocity fields decay with powers $-2.6$ and $-1.52$, respectively., Comment: 15 pages, 4 figures

We focus on understanding the influence of the two-component coupling in ferronematics, a colloidal suspension of magnetic nanoparticles in nematic liquid crystals. Using coarse-grained Landau-de Gennes free energies, we study the ordering dynamics of this complex fluid and present a range of analytical and numerical results. Our main observations are: (i) slaved coarsening for quench temperatures $T$ intermediate to the critical temperatures of the uncoupled components, (ii) slower growth similar to the Lifshitz-Slyozov law ($L \sim t^{1/3}$) for symmetric magneto-nematic coupling, (iii) sub-domain morphologies dominated by interfacial defects for asymmetric coupling strengths. These novel results will serve to guide future experiments on this technologically important system., Comment: 17 pages, 3 figures

This article is an introductory review of random matrix theory (RMT) and its applications, with special focus on quantum chaos. Random matrices were first used by Wigner to understand the spectra of complex nuclei from a statistical perspective. Subsequently there have been novel applications to diverse areas, e.g., atomic and molecular physics, mesoscopic and nanoscopic systems, microwave cavities, econophysics, biological sciences, communication theory. This article is designed to be accessible at the graduate and post-doctoral level.

Dyson has shown an equivalence between infinite-range Coulomb gas models and classical random matrix ensembles for the study of eigenvalue statistics. In this paper, we introduce finite-range Coulomb gas (FRCG) models as a generalization of the Dyson models with a finite range of eigenvalue interactions. As the range of interaction increases, there is a transition from Poisson statistics to classical random matrix statistics. These models yield new universality classes of random matrix ensembles. They also provide a theoretical framework to study banded random matrices, and dynamical systems whose matrix representation can be written in the form of banded matrices.

In paper I of this two-stage exposition, we introduced finite-range Coulomb gas (FRCG) models, and developed an integral-equation framework for their study. We obtained exact analytical results for $d = 0,1,2 $, where d denotes the range of eigenvalue interaction. We found that the integral-equation framework was not analytically tractable for higher values of $d$. In this paper II, we develop a Monte Carlo (MC) technique to study FRCG models. Our MC simulations provide a solution of FRCG models for arbitrary $d$. We show that, as d increases, there is a transition from Poisson to Wigner-Dyson classical random matrix statistics. Thus FRCG models provide a novel route for transition from Poisson to Wigner-Dyson statistics. The analytical formulation obtained in paper I, and MC techniques developed in this paper II, are used to study banded random matrices (BRM) and quantum kicked rotors (QKR). We demonstrate that, for a BRM of bandwidth $b$ and a QKR of chaos parameter $\alpha$, the appropriate FRCG model has range $d=b^2/N=\alpha^2/N$, for $N \rightarrow \infty $. Here, N is the dimensionality of the matrix in BRM, and the evolution operator matrix in QKR.

We study numerically the aging properties of the two-dimensional Ising model with quenched disorder considered in our recent paper [Phys. Rev. E 95, 062136 (2017)], where frustration can be tuned by varying the fraction a of antiferromagnetic interactions. Specifically we focus on the scaling properties of the autocorrelation and linear response functions after a quench of the model to a low temperature. We find that the interplay between equilibrium and aging occurs differently in the various regions of the phase diagram of the model. When the quench is made into the ferromagnetic phase the two-time quantities are made by the sum of an equilibrium and an aging part, whereas in the paramagnetic phase these parts combine in a multiplicative way. Scaling forms are shown to be obeyed with good accuracy, and the corresponding exponents and scaling functions are determined and discussed in the framework of what is known in clean and disordered systems., Comment: 31 pages, 11 figures

We present a comprehensive Monte Carlo study of the ordering kinetics in the $d=2$ ferromagnetic $q$-state clock model with nonconserved Glauber dynamics. In agreement with previous studies we find that $q \geqslant 5$ is characterized by two phase transitions occurring at temperatures $T_{c}^1$ and $T_{c}^2$ ($T_{c}^2

We present the first systematic observation of scaling of thermal hysteresis with the temperature scanning rate around an abrupt thermodynamic transition in correlated electron systems. We show that the depth of supercooling and superheating in vanadium sesquioxide (V2O3) shifts with the temperature quench rates. The dynamic scaling exponent is close to the mean field prediction of 2/3. These observations, combined with the purely dissipative continuous ordering seen in "quench-and-hold" experiments, indicate departures from classical nucleation theory toward a barrier-free phase ordering associated with critical dynamics. Observation of critical-like features and scaling in a thermally induced abrupt phase transition suggests that the presence of a spinodal-like instability is not just an artifact of the mean field theories but can also exist in the transformation kinetics of real systems, surviving fluctuations., Comment: 15 pages, includes supplemental material

While the ground-state problem for the random-field Ising model is polynomial, and can be solved using a number of well-known algorithms for maximum flow or graph cut, the analogue random-field Potts model corresponds to a multi-terminal flow problem that is known to be NP hard. Hence an efficient exact algorithm is very unlikely to exist. As we show here, it is nevertheless possible to use an embedding of binary degrees of freedom into the Potts spins in combination with graph-cut methods to solve the corresponding ground-state problem approximately in polynomial time. We benchmark this heuristic algorithm using a set of quasi-exact ground states found for small systems from long parallel tempering runs. For not too large number $q$ of Potts states, the method based on graph cuts finds the same solutions in a fraction of the time. We employ the new technique to analyze the breakup length of the random-field Potts model in two dimensions., Comment: 10 pages, 11 figures, 1 table

We study phase ordering kinetics in symmetric and asymmetric binary mixtures, undergoing an order-disorder transition below the critical temperature. Microscopically, we model the kinetics via antiferromagnetic Ising model with Kawasaki spin-exchange kinetics. This conserves the composition while the order-parameter (staggered magnetization) is not conserved. The order-parameter correlation function and structure factor show dynamical scaling, and the scaling functions are independent of the mixture composition. The average domain size shows a power-law growth: $L_\sigma(t)\sim t^\alpha$. The asymptotic growth regime has $\alpha=1/2$, though there can be prolonged transients with $\alpha<1/2$ for asymmetric mixtures. Our unambiguous observation of the asymptotic universal regime is facilitated by using an accelerated Monte Carlo technique. We also obtain the coarse-grained free energy from the Hamiltonian, as a function of two order-parameters. The evolution of these order-parameters is modeled by using \textit{Model C} kinetics. Similar to the microscopic dynamics, the average domain size of the nonconserved order-parameter (staggered magnetization) field exhibits a power-law growth: $L_m(t)\sim t^{1/2}$ at later times, irrespective of the mean value of the conserved order-parameter (composition) field., Comment: 21 Pages, 7 Figures, Accepted in EPJE

We perform large-scale molecular dynamics simulations to study heated granular fluids in three dimensions. Granular particles dissipate their kinetic energy due to solid frictional interaction with other particles. The velocity of each particle is perturbed by a uniformly-distributed random noise, which mimics the heating. At the early stage of evolution, the kinetic energy of the system decays with time and reaches a steady state at a later stage. The velocity distribution in the steady state shows a non-Gaussian distribution. This has been characterized by using the Sonine polynomial expansion for a wide range of densities. Particles show diffusive motion for densities below the jamming density $\phi_{\rm J}$, Comment: 28 Pages, 8 Figures

We present a comprehensive Monte Carlo study of domain growth in the random-bond XY model with non-conserved kinetics. The presence of quenched disorder slows down domain growth in d = 2; 3. In d = 2, we observe power-law growth with a disorder-dependent exponent on the time-scales of our simulation. In d = 3, we see the signature of an asymptotically logarithmic growth regime. The scaling functions for the real-space correlation function are seen to be independent of the disorder. However, the same does not apply for the two-time autocorrelation function, demonstrating the breakdown of superuniversality., Comment: To appear in PRE

Dyson demonstrated an equivalence between infinite-range Coulomb gas models and classical random matrix ensembles for study of eigenvalue statistics. We introduce finite-range Coulomb gas (FRCG) models via a Brownian matrix process, and study them analytically and by Monte-Carlo simulations. These models yield new universality classes, and provide a theoretical framework for study of banded random matrices (BRM) and quantum kicked rotors (QKR). We demonstrate that, for a BRM of bandwidth b and a QKR of chaos parameter {\alpha}, the appropriate FRCG model has the effective range d = (b^2)/N = ({\alpha}^2)/N, for large N matrix dimensionality. As d increases, there is a transition from Poisson to classical random matrix statistics.

Ordering dynamics of self-propelled particles in an inhomogeneous medium in two-dimensions is studied. We write coarse-grained hydrodynamic equations of motion for coarse-grained density and velocity fields in the presence of an external random disorder field, which is quenched in time. The strength of inhomogeneity is tuned from zero disorder (clean system) to large disorder. In the clean system, the velocity field grows algebraically as $L_{\rm V} \sim t^{0.5}$. The density field does not show clean power-law growth; however, it follows $L_{\rm \rho} \sim t^{0.8}$ approximately. In the inhomogeneous system, we find a disorder dependent growth. For both the density and the velocity, growth slow down with increasing strength of disorder. The velocity shows a disorder dependent power-law growth $L_{\rm V}(t,\Delta) \sim t^{1/\bar z_{\rm V}(\Delta)}$ for intermediate times. At late times, there is a crossover to logarithmic growth $L_{\rm V}(t,\Delta) \sim (\ln t)^{1/\varphi}$, where $\varphi$ is a disorder independent exponent. Two-point correlation functions for the velocity shows dynamical scaling, but the density does not.

We study the Brownian dynamics of a solid particle on a vibrating solid surface. Phenomenologically, the interaction between the two solid surfaces is modeled by solid friction, and the Gaussian white noise models the vibration of the solid surface. The solid friction is proportional to the sign of relative velocity. We derive the Fokker-Planck (FP) equation for the time-dependent probability distribution to find the particle at a given location. We calculate analytically the steady state velocity distribution function, mean-squared velocity and diffusion coefficient in $d$ dimensions. We present a generic method of calculating the autocorrelations in $d$ dimensions. This results in one dimension in an exact evaluation of the steady state velocity autocorrelation. In higher dimensions, our exact general expression enables the analytic evaluation of the autocorrelation to any required approximation. We present approximate analytic expressions in two and three dimensions. Next, we numerically calculate the mean-square velocity and steady state velocity autocorrelation function up to $d=3$. Our numerical results are in good agreement with the analytically obtained results., Comment: 2 figs, 2 tables, accepted in EPJE

We study numerically a two-dimensional random-bond Ising model where frustration can be tuned by varying the fraction $a$ of antiferromagnetic coupling constants. At low temperatures the model exhibits a phase with ferromagnetic order for sufficiently small values of $a$, $aa_a$ an antiferromagnetic phase exists. After a deep quench from high temperatures, slow evolution is observed for any value of $a$. We show that different amounts of frustration, tuned by $a$, affect the dynamical properties in a highly non trivial way. In particular, the kinetics is logarithmically slow in phases with ferromagnetic or antiferromagnetic order, whereas evolution is faster, i.e. algebraic, when spin glass order is prevailing. An interpretation is given in terms of the different nature of phase space., Comment: 19 pages, 10 figures. To appear on Phys. Rev. E

We study the free evolution of frictional granular gases using large scale molecular dynamics simulation in three dimensions. The system cools due to solid friction among the interacting particles. At early stages of evolution, the density field remains homogeneous and the velocity field follows the Maxwell-Boltzmann (MB) distribution. However, at later times, the density field shows clustering and the velocity field shows local ordering. The ordering in the velocity field is studied by invoking analogy from phase ordering systems. The equal-time correlation function of velocity field follows dynamical scaling. The correlation length of velocity field, $L_v(t)$, exhibits power law growth: $L_v(t)\sim t^{1/3}$., Comment: 8 pages, 4 figures, CCP-2016