Description

Physical Review E (PRE), interdisciplinary in scope, focuses on many-body phenomena, in­cluding recent developments in quantum and classical chaos and soft matter physics. It has sections on statistical physics, equilibrium and transport properties of fluids, liquid crystals, complex fluids, polymers, chaos, fluid dynam­ics, plasma physics, classical physics including nonlinear media and computational physics. In addition, the journal features sections on two rapidly growing areas: biological physics and granular materials.

Publisher details

American Physiological Society

Publications in this journal

• Crossover in growth laws for phase-separating binary fluids: Molecular dynamics simulations

  Authors: Shaista Ahmad, Subir K. Das, Sanjay Puri

  Physical Review E.

• Crossover in growth laws for phase-separating binary fluids: Molecular dynamics simulations

  Authors: Shaista Ahmad, Subir K. Das, Sanjay Puri

  Physical Review E.

  Pattern and dynamics during phase separation in a symmetrical binary (A+B) Lennard-Jones fluid are studied via molecular dynamics simulations after quenching homogeneously mixed critical (50:50)Pattern and dynamics during phase separation in a symmetrical binary (A+B) Lennard-Jones fluid are studied via molecular dynamics simulations after quenching homogeneously mixed critical (50:50) systems to temperatures below the critical one. The morphology of the domains, rich in A or B particles, is observed to be bicontinuous. The early-time growth of the average domain size is found to be consistent with the Lifshitz-Slyozov law for diffusive domain coarsening. After a characteristic time, dependent on the temperature, we find a clear crossover to an extended viscous hydrodynamic regime where the domains grow linearly with time. Pattern formation in the present system is compared with that in solid binary mixtures, as a function of temperature. Important results for the finite-size and temperature effects on the small-wave-vector behavior of the scattering function are also presented.

• Inhomogeneities on all scales at a phase transition altered by disorder.

  Authors: I Balog, K Uzelac

  Physical review. E, Statistical, nonlinear, and soft matter physics. 85(3-1):030101.

  We have done a finite-size scaling study of a continuous phase transition altered by the quenched bond disorder, investigating systems at quasicritical temperatures of each disorder realization byWe have done a finite-size scaling study of a continuous phase transition altered by the quenched bond disorder, investigating systems at quasicritical temperatures of each disorder realization by using the equilibriumlike invaded cluster algorithm. Our results indicate that in order to access the thermal critical exponent y_{τ}, it is necessary to average the free energy at quasicritical temperatures of each disorder configuration. Despite the thermal fluctuations on the scale of the system at the transition point, we find that spatial inhomogeneities form in the system and become more pronounced as the size of the system increases. This leads to different exponents describing rescaling of the fluctuations of observables in disorder and thermodynamic ensembles.

• Jammed spheres: Minkowski tensors reveal onset of local crystallinity.

  Authors: Sebastian C Kapfer, Walter Mickel, Klaus Mecke, Gerd E Schröder-Turk

  Physical review. E, Statistical, nonlinear, and soft matter physics. 85(3-1):030301.

  The local structure of disordered jammed packings of monodisperse spheres without friction, generated by the Lubachevsky-Stillinger algorithm, is studied for packing fractions above and below 64%.The local structure of disordered jammed packings of monodisperse spheres without friction, generated by the Lubachevsky-Stillinger algorithm, is studied for packing fractions above and below 64%. The structural similarity of the particle environments to fcc or hcp crystalline packings (local crystallinity) is quantified by order metrics based on rank-four Minkowski tensors. We find a critical packing fraction φ_{c}≈0.649, distinctly higher than previously reported values for the contested random close packing limit. At φ_{c}, the probability of finding local crystalline configurations first becomes finite and, for larger packing fractions, increases by several orders of magnitude. This provides quantitative evidence of an abrupt onset of local crystallinity at φ_{c}. We demonstrate that the identification of local crystallinity by the frequently used local bond-orientational order metric q_{6} produces false positives and thus conceals the abrupt onset of local crystallinity. Since the critical packing fraction is significantly above results from mean-field analysis of the mechanical contacts for frictionless spheres, it is suggested that dynamic arrest due to isostaticity and the alleged geometric phase transition in the Edwards framework may be disconnected phenomena.

• Glassy dynamics in relaxation of soft-mode turbulence.

  Authors: Fahrudin Nugroho, Takayuki Narumi, Yoshiki Hidaka, Junichi Yoshitani, Masaru Suzuki, Shoichi Kai

  Physical review. E, Statistical, nonlinear, and soft matter physics. 85(3-1):030701.

  The autocorrelation function of pattern fluctuation is used to study soft-mode turbulence (SMT), a spatiotemporal chaos observed in homeotropic nematics. We show that relaxation near theThe autocorrelation function of pattern fluctuation is used to study soft-mode turbulence (SMT), a spatiotemporal chaos observed in homeotropic nematics. We show that relaxation near the electroconvection threshold deviates from the exponential. To describe this relaxation, we propose a compressed exponential appearing in dynamics of glass-forming liquids. Our findings suggest that coherent motion contributes to SMT dynamics. We also confirmed that characteristic time is inversely proportional to electroconvection's control parameter.

• Validity of nonequilibrium work relations for the rapidly expanding quantum piston.

  Authors: H T Quan, Christopher Jarzynski

  Physical review. E, Statistical, nonlinear, and soft matter physics. 85(3-1):031102.

  Recent work by Teifel and Mahler [Eur. Phys. J. B 75, 275 (2010)] raises legitimate concerns regarding the validity of quantum nonequilibrium work relations in processes involving moving hard walls.Recent work by Teifel and Mahler [Eur. Phys. J. B 75, 275 (2010)] raises legitimate concerns regarding the validity of quantum nonequilibrium work relations in processes involving moving hard walls. We study this issue in the context of the rapidly expanding one-dimensional quantum piston. Utilizing exact solutions of the time-dependent Schrödinger equation, we find that the evolution of the wave function can be decomposed into static and dynamic components, which have simple semiclassical interpretations in terms of particle-piston collisions. We show that nonequilibrium work relations remain valid at any finite piston speed, provided both components are included, and we study explicitly the work distribution for this model system.

• Continuous transition of social efficiencies in the stochastic-strategy minority game.

  Authors: Soumyajyoti Biswas, Asim Ghosh, Arnab Chatterjee, Tapan Naskar, Bikas K Chakrabarti

  Physical review. E, Statistical, nonlinear, and soft matter physics. 85(3-1):031104.

  We show that in a variant of the minority game problem, the agents can reach a state of maximum social efficiency, where the fluctuation between the two choices is minimum, by following a simpleWe show that in a variant of the minority game problem, the agents can reach a state of maximum social efficiency, where the fluctuation between the two choices is minimum, by following a simple stochastic strategy. By imagining a social scenario where the agents can only guess about the number of excess people in the majority, we show that as long as the guessed value is sufficiently close to the reality, the system can reach a state of full efficiency or minimum fluctuation. A continuous transition to less efficient condition is observed when the guessed value becomes worse. Hence, people can optimize their guess for excess population to optimize the period of being in the majority state. We also consider the situation where a finite fraction of agents always decide completely randomly (random trader) as opposed to the rest of the population who follow a certain strategy (chartist). For a single random trader the system becomes fully efficient with majority-minority crossover occurring every 2 days on average. For just two random traders, all the agents have equal gain with arbitrarily small fluctuations.

• Singular response of bistable systems driven by telegraph noise.

  Authors: Akihisa Ichiki, Yukihiro Tadokoro, M I Dykman

  Physical review. E, Statistical, nonlinear, and soft matter physics. 85(3-1):031106.

  We show that weak periodic driving can exponentially strongly change the rate of escape from a potential well of a system driven by telegraph noise. The analysis refers to an overdamped system, whereWe show that weak periodic driving can exponentially strongly change the rate of escape from a potential well of a system driven by telegraph noise. The analysis refers to an overdamped system, where escape requires that the noise amplitude θ exceed a critical value θ_{c}. For θ close to θ_{c}, the exponent of the escape rate displays a nonanalytic dependence on the amplitude of an additional low-frequency modulation. This leads to giant nonlinearity of the response of a bistable system to periodic modulation. Also studied is the linear response to periodic modulation far from θ_{c}. We analyze the scaling of the logarithm of the escape rate with the distance to the saddle-node and pitchfork bifurcation points. The analytical results are in excellent agreement with numerical simulations.

• Out-of-equilibrium relaxation of the thermal Casimir effect in a model polarizable material.

  Authors: David S Dean, Vincent Démery, V Adrian Parsegian, Rudolf Podgornik

  Physical review. E, Statistical, nonlinear, and soft matter physics. 85(3-1):031108.

  Relaxation of the thermal Casimir or van der Waals force (the high temperature limit of the Casimir force) for a model dielectric medium is investigated. We start with a model of interactingRelaxation of the thermal Casimir or van der Waals force (the high temperature limit of the Casimir force) for a model dielectric medium is investigated. We start with a model of interacting polarization fields with a dynamics that leads to a frequency dependent dielectric constant of the Debye form. In the static limit, the usual zero frequency Matsubara mode component of the Casimir force is recovered. We then consider the out-of-equilibrium relaxation of the van der Waals force to its equilibrium value when two initially uncorrelated dielectric bodies are brought into sudden proximity. For the interaction between dielectric slabs, it is found that the spatial dependence of the out-of-equilibrium force is the same as the equilibrium one, but it has a time dependent amplitude, or Hamaker coefficient, which increases in time to its equilibrium value. The final relaxation of the force to its equilibrium value is exponential in systems with a single or finite number of polarization field relaxation times. However, in systems, such as those described by the Havriliak-Negami dielectric constant with a broad distribution of relaxation times, we observe a much slower power law decay to the equilibrium value.

• Quantum-trajectory approach to the stochastic thermodynamics of a forced harmonic oscillator.

  Authors: Jordan M Horowitz

  Physical review. E, Statistical, nonlinear, and soft matter physics. 85(3-1):031110.

  I formulate a quantum stochastic thermodynamics for the quantum trajectories of a continuously monitored forced harmonic oscillator coupled to a thermal reservoir. Consistent trajectory-dependentI formulate a quantum stochastic thermodynamics for the quantum trajectories of a continuously monitored forced harmonic oscillator coupled to a thermal reservoir. Consistent trajectory-dependent definitions are introduced for work, heat, and entropy, through engineering the thermal reservoir from a sequence of two-level systems. Within this formalism the connection between irreversibility and entropy production is analyzed and confirmed by proving a detailed fluctuation theorem for quantum trajectories. Finally, possible experimental verifications are discussed.

• Nonequilibrium fluctuations in a driven stochastic Lorentz gas.

  Authors: G Gradenigo, A Puglisi, A Sarracino, U Marini Bettolo Marconi

  Physical review. E, Statistical, nonlinear, and soft matter physics. 85(3-1):031112.

  We study the stationary state of a one-dimensional kinetic model where a probe particle is driven by an external field E and collides, elastically or inelastically, with a bath of particles atWe study the stationary state of a one-dimensional kinetic model where a probe particle is driven by an external field E and collides, elastically or inelastically, with a bath of particles at temperature T. We focus on the stationary distribution of the velocity of the particle, and of two estimates of the total entropy production Δs_{tot}. One is the entropy production of the medium Δs_{m}, which is equal to the energy exchanged with the scatterers, divided by a parameter θ, coinciding with the particle temperature at E=0. The other is the work W done by the external field, again rescaled by θ. At small E, a good collapse of the two distributions is found: in this case, the two quantities also verify the fluctuation relation (FR), indicating that both are good approximations of Δs_{tot}. Differently, for large values of E, the fluctuations of W violate the FR, while Δs_{m} still verifies it.

• Multiparticle quantum Szilard engine with optimal cycles assisted by a Maxwell's demon.

  Authors: C Y Cai, H Dong, C P Sun

  Physical review. E, Statistical, nonlinear, and soft matter physics. 85(3-1):031114.

  We present a complete-quantum description of a multiparticle Szilard engine that consists of a working substance and a Maxwell's demon. The demon is modeled as a multilevel quantum system withWe present a complete-quantum description of a multiparticle Szilard engine that consists of a working substance and a Maxwell's demon. The demon is modeled as a multilevel quantum system with specific quantum control, and the working substance consists of identical particles obeying Bose-Einstein or Fermi-Dirac statistics. In this description, a reversible scheme to erase the demon's memory by a lower-temperature heat bath is used. We demonstrate that (1) the quantum control of the demon can be optimized for a single-particle Szilard engine so that the efficiency of the demon-assisted thermodynamic cycle could reach the Carnot cycle's efficiency and (2) the low-temperature behavior of the working substance is very sensitive to the quantum statistics of the particles and the insertion position of the partition.

• Irreversibilities and efficiency at maximum power of heat engines: The illustrative case of a thermoelectric generator.

  Authors: Y Apertet, H Ouerdane, C Goupil, Ph Lecoeur

  Physical review. E, Statistical, nonlinear, and soft matter physics. 85(3-1):031116.

  Energy conversion efficiency at maximum output power, which embodies the essential characteristics of heat engines, is the main focus of the present work. The so-called Curzon and Ahlborn efficiencyEnergy conversion efficiency at maximum output power, which embodies the essential characteristics of heat engines, is the main focus of the present work. The so-called Curzon and Ahlborn efficiency η_{CA} is commonly believed to be an absolute reference for real heat engines; however, a different but general expression for the case of stochastic heat engines, η_{SS}, was recently found and then extended to low-dissipation engines. The discrepancy between η_{CA} and η_{SS} is here analyzed considering different irreversibility sources of heat engines, of both internal and external types. To this end, we choose a thermoelectric generator operating in the strong-coupling regime as a physical system to qualitatively and quantitatively study the impact of the nature of irreversibility on the efficiency at maximum output power. In the limit of pure external dissipation, we obtain η_{CA}, while η_{SS} corresponds to the case of pure internal dissipation. A continuous transition between from one extreme to the other, which may be operated by tuning the different sources of irreversibility, also is evidenced.

• Propagation on networks: An exact alternative perspective.

  Authors: Pierre-André Noël, Antoine Allard, Laurent Hébert-Dufresne, Vincent Marceau, Louis J Dubé

  Physical review. E, Statistical, nonlinear, and soft matter physics. 85(3-1):031118.

  By generating the specifics of a network structure only when needed (on-the-fly), we derive a simple stochastic process that exactly models the time evolution of susceptible-infectious dynamics onBy generating the specifics of a network structure only when needed (on-the-fly), we derive a simple stochastic process that exactly models the time evolution of susceptible-infectious dynamics on finite-size networks. The small number of dynamical variables of this birth-death Markov process greatly simplifies analytical calculations. We show how a dual analytical description, treating large scale epidemics with a Gaussian approximation and small outbreaks with a branching process, provides an accurate approximation of the distribution even for rather small networks. The approach also offers important computational advantages and generalizes to a vast class of systems.

• Fractional Brownian motion and the critical dynamics of zipping polymers.

  Authors: J-C Walter, A Ferrantini, E Carlon, C Vanderzande

  Physical review. E, Statistical, nonlinear, and soft matter physics. 85(3-1):031120.

  We consider two complementary polymer strands of length L attached by a common-end monomer. The two strands bind through complementary monomers and at low temperatures form a double-strandedWe consider two complementary polymer strands of length L attached by a common-end monomer. The two strands bind through complementary monomers and at low temperatures form a double-stranded conformation (zipping), while at high temperature they dissociate (unzipping). This is a simple model of DNA (or RNA) hairpin formation. Here we investigate the dynamics of the strands at the equilibrium critical temperature T=T_{c} using Monte Carlo Rouse dynamics. We find that the dynamics is anomalous, with a characteristic time scaling as τ∼L^{2.26(2)}, exceeding the Rouse time ∼L^{2.18}. We investigate the probability distribution function, velocity autocorrelation function, survival probability, and boundary behavior of the underlying stochastic process. These quantities scale as expected from a fractional Brownian motion with a Hurst exponent H=0.44(1). We discuss similarities to and differences from unbiased polymer translocation.

• Relaxation in finite and isolated classical systems: An extension of Onsager's regression hypothesis.

  Authors: Marcus V S Bonança

  Physical review. E, Statistical, nonlinear, and soft matter physics. 85(3-1):031122.

  In order to derive the reciprocity relations, Onsager formulated a relation between thermal equilibrium fluctuations and relaxation widely known as regression hypothesis. It is shown in the presentIn order to derive the reciprocity relations, Onsager formulated a relation between thermal equilibrium fluctuations and relaxation widely known as regression hypothesis. It is shown in the present work how such a relation can be extended to finite and isolated classical systems. This extension is derived from the fluctuation-dissipation theorem for the microcanonical ensemble. The results are exemplified with a nonintegrable system in order to motivate possible applications to dynamical systems and statistical mechanics of finite systems.

• Reaction-diffusion process driven by a localized source: First-passage properties.

  Authors: P L Krapivsky

  Physical review. E, Statistical, nonlinear, and soft matter physics. 85(3-1):031124.

  We study a reaction-diffusion process that involves two species of atoms, immobile and diffusing. We start with only immobile atoms uniformly distributed throughout the entire space. Diffusing atomsWe study a reaction-diffusion process that involves two species of atoms, immobile and diffusing. We start with only immobile atoms uniformly distributed throughout the entire space. Diffusing atoms are injected at the origin by a source that is turned on at time t=0. When a diffusing atom collides with an immobile atom, the two atoms form an immobile stable molecule. The region occupied by molecules is asymptotically spherical with radius growing as t^{1/d} in d⩾2 dimensions. We investigate the survival probability that a diffusing atom has not become a part of a molecule during the time interval t after its injection. We show that, asymptotically, the survival probability (i) saturates in one dimension, (ii) vanishes algebraically with time in two dimensions (with exponent being a function of the dimensionless flux and determined as a zero of a confluent hypergeometric function), and (iii) exhibits a stretched exponential decay in three dimensions.

• Mean-field-like behavior of the generalized voter-model-class kinetic Ising model.

  Authors: Sebastian M Krause, Philipp Böttcher, Stefan Bornholdt

  Physical review. E, Statistical, nonlinear, and soft matter physics. 85(3-1):031126.

  We analyze a kinetic Ising model with suppressed bulk noise, which is a prominent representative of the generalized voter model phase transition. On the one hand, we discuss the model in the contextWe analyze a kinetic Ising model with suppressed bulk noise, which is a prominent representative of the generalized voter model phase transition. On the one hand, we discuss the model in the context of social systems and opinion formation in the presence of a tunable social temperature. On the other hand, we characterize the abrupt phase transition. The system shows nonequilibrium dynamics in the presence of absorbing states. We slightly change the system to get a stationary-state model variant exhibiting the same kind of phase transition. Using a Fokker-Planck description and comparing to mean-field calculations, we investigate the phase transition, finite-size effects, and the effect of the absorbing states resulting in a dynamic slowing down.

• Entropic dynamical hysteresis in a driven system.

  Authors: Debasish Mondal, Moupriya Das, Deb Shankar Ray

  Physical review. E, Statistical, nonlinear, and soft matter physics. 85(3-1):031128.

  We show that the application of a time periodic field driving a Brownian particle between the two lobes of a two-dimensional bilobal enclosure results in a hysteresis loop in the variation ofWe show that the application of a time periodic field driving a Brownian particle between the two lobes of a two-dimensional bilobal enclosure results in a hysteresis loop in the variation of integrated probability of residence of the particle as a function of the field. The confinement of the particle is characterized by symmetry breaking of the hysteresis loop, and the area of the loop exhibits a turnover with variation of frequency of the field. This dynamical hysteresis is geometry controlled, entropic in nature, and amenable to theoretical analysis with a two-state model.

• Poisson-Helmholtz-Boltzmann model of the electric double layer: Analysis of monovalent ionic mixtures.

  Authors: Klemen Bohinc, Ahis Shrestha, Milan Brumen, Sylvio May

  Physical review. E, Statistical, nonlinear, and soft matter physics. 85(3-1):031130.

  In the classical mean-field description of the electric double layer, known as the Poisson-Boltzmann model, ions interact exclusively through their Coulomb potential. Ion specificity can ariseIn the classical mean-field description of the electric double layer, known as the Poisson-Boltzmann model, ions interact exclusively through their Coulomb potential. Ion specificity can arise through solvent-mediated, nonelectrostatic interactions between ions. We employ the Yukawa pair potential to model the presence of nonelectrostatic interactions. The combination of Yukawa and Coulomb potential on the mean-field level leads to the Poisson-Helmholtz-Boltzmann model, which employs two auxiliary potentials: one electrostatic and the other nonelectrostatic. In the present work we apply the Poisson-Helmholtz-Boltzmann model to ionic mixtures, consisting of monovalent cations and anions that exhibit different Yukawa interaction strengths. As a specific example we consider a single charged surface in contact with a symmetric monovalent electrolyte. From the minimization of the mean-field free energy we derive the Poisson-Boltzmann and Helmholtz-Boltzmann equations. These nonlinear equations can be solved analytically in the weak perturbation limit. This together with numerical solutions in the nonlinear regime suggests an intricate interplay between electrostatic and nonelectrostatic interactions. The structure and free energy of the electric double layer depends sensitively on the Yukawa interaction strengths between the different ion types and on the nonelectrostatic interactions of the mobile ions with the surface.

• Subdiffusive master equation with space-dependent anomalous exponent and structural instability.

  Authors: Sergei Fedotov, Steven Falconer

  Physical review. E, Statistical, nonlinear, and soft matter physics. 85(3-1):031132.

  We derive the fractional master equation with space-dependent anomalous exponent. We analyze the asymptotic behavior of the corresponding lattice model both analytically and by Monte CarloWe derive the fractional master equation with space-dependent anomalous exponent. We analyze the asymptotic behavior of the corresponding lattice model both analytically and by Monte Carlo simulation. We show that the subdiffusive fractional equations with constant anomalous exponent μ in a bounded domain [0,L] are not structurally stable with respect to the nonhomogeneous variations of parameter μ. In particular, the Gibbs-Boltzmann distribution is no longer the stationary solution of the fractional Fokker-Planck equation whatever the space variation of the exponent might be. We analyze the random distribution of μ in space and find that in the long-time limit, the probability distribution is highly intermediate in space and the behavior is completely dominated by very unlikely events. We show that subdiffusive fractional equations with the nonuniform random distribution of anomalous exponent is an illustration of a "Black Swan," the low probability event of the small value of the anomalous exponent that completely dominates the long-time behavior of subdiffusive systems.

• Predictability of extreme events in a nonlinear stochastic-dynamical model.

  Authors: Christian Franzke

  Physical review. E, Statistical, nonlinear, and soft matter physics. 85(3-1):031134.

  The objective of this work is to evaluate the potential of reduced order models to reproduce the extreme event and predictability characteristics of higher dimensional dynamical systems. A nonlinearThe objective of this work is to evaluate the potential of reduced order models to reproduce the extreme event and predictability characteristics of higher dimensional dynamical systems. A nonlinear toy model is used which contains key features of comprehensive climate models. First, we demonstrate that the systematic stochastic mode reduction strategy leads to a reduced order model with the same extreme value characteristics as the full dynamical models for a wide range of time-scale separations. Second, we find that extreme events in this model follow a generalized Pareto distribution with a negative shape parameter; thus extreme events are bounded in this model. Third, we show that a precursor approach has good forecast skill for extreme events. We then find that the reduced stochastic models capture the predictive skill of extreme events of the full dynamical models well. Consistent with previous studies we also find that the larger the extreme events, the better predictable they are. Our results suggest that systematically derived reduced order models have the potential to be used for the modeling and statistical prediction of weather- and climate-related extreme events and, possibly, in other areas of science and engineering too.

• Optimal estimates of the diffusion coefficient of a single Brownian trajectory.

  Authors: Denis Boyer, David S Dean, Carlos Mejía-Monasterio, Gleb Oshanin

  Physical review. E, Statistical, nonlinear, and soft matter physics. 85(3-1):031136.

  Modern developments in microscopy and image processing are revolutionizing areas of physics, chemistry, and biology as nanoscale objects can be tracked with unprecedented accuracy. The goal ofModern developments in microscopy and image processing are revolutionizing areas of physics, chemistry, and biology as nanoscale objects can be tracked with unprecedented accuracy. The goal of single-particle tracking is to determine the interaction between the particle and its environment. The price paid for having a direct visualization of a single particle is a consequent lack of statistics. Here we address the optimal way to extract diffusion constants from single trajectories for pure Brownian motion. It is shown that the maximum likelihood estimator is much more efficient than the commonly used least-squares estimate. Furthermore, we investigate the effect of disorder on the distribution of estimated diffusion constants and show that it increases the probability of observing estimates much smaller than the true (average) value.

• Operator solutions for fractional Fokker-Planck equations.

  Authors: K Górska, K A Penson, D Babusci, G Dattoli, G H E Duchamp

  Physical review. E, Statistical, nonlinear, and soft matter physics. 85(3-1):031138.

  We obtain exact results for fractional equations of Fokker-Planck type using the evolution operator method. We employ exact forms of one-sided Lévy stable distributions to generate a set ofWe obtain exact results for fractional equations of Fokker-Planck type using the evolution operator method. We employ exact forms of one-sided Lévy stable distributions to generate a set of self-reproducing solutions. Explicit cases are reported and studied for various fractional order of derivatives, different initial conditions, and for different versions of Fokker-Planck operators.

• Crossover in growth laws for phase-separating binary fluids: Molecular dynamics simulations.

  Authors: Shaista Ahmad, Subir K Das, Sanjay Puri

  Physical review. E, Statistical, nonlinear, and soft matter physics. 85(3-1):031140.

  Pattern and dynamics during phase separation in a symmetrical binary (A+B) Lennard-Jones fluid are studied via molecular dynamics simulations after quenching homogeneously mixed critical (50:50)Pattern and dynamics during phase separation in a symmetrical binary (A+B) Lennard-Jones fluid are studied via molecular dynamics simulations after quenching homogeneously mixed critical (50:50) systems to temperatures below the critical one. The morphology of the domains, rich in A or B particles, is observed to be bicontinuous. The early-time growth of the average domain size is found to be consistent with the Lifshitz-Slyozov law for diffusive domain coarsening. After a characteristic time, dependent on the temperature, we find a clear crossover to an extended viscous hydrodynamic regime where the domains grow linearly with time. Pattern formation in the present system is compared with that in solid binary mixtures, as a function of temperature. Important results for the finite-size and temperature effects on the small-wave-vector behavior of the scattering function are also presented.

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