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arXiv2013

Grad's moment method for relativistic gas mixtures of Maxwellian particles

Mixtures of relativistic gases are analyzed within the framework of Boltzmann equation by using Grad's moment method. A relativistic mixture of $r$ constituent is characterized by the moments of the distribution function: particle four-flows, energy-momentum tensors and third-order moment tensors. By using Eckart's decomposition and introducing $13r+1$ scalar fields -- related with the four-velocity, temperature of the mixture, particle number densities, diffusion fluxes, non-equilibrium pressures, heat fluxes and pressure deviator tensors -- Grad's distribution functions are obtained. Grad's distribution functions are used to determine the third-order tensors and their production terms for mixtures whose constituent's rest masses are not too disparate, so that it follows a system of $13r+1$ scalar field equations. By restricting to a binary mixture characterized by the six fields of partial particle number densities, four-velocity and temperature, the remainder 21 scalar equations are used to determine the constitutive equations for the non-equilibrium pressures, diffusion fluxes, pressure deviator tensors and heat fluxes. Hence the Navier-Stokes and generalized Fourier and Fick laws are obtained and the transport coefficients of bulk and shear viscosities, thermal conductivity, diffusion, thermal-diffusion and diffusion-thermal are determined. Furthermore, solutions of the relativistic field equations for the binary mixture are obtained in form of forced and free waves. In the low frequency limiting case the phase velocity and the attenuation coefficient are determined for forced waves. In the small wavenumber limiting case it is shown that there exist four longitudinal eigenmodes, two of them corresponding to propagating sound modes and two associated with non-propagating diffusive modes.

cond-mat.stat-mech↗

arXiv2013

Density anomalies and high-order jamming crossovers

Jamming crossovers occur at zero temperature in assemblies of particles interacting via finite range repulsive potentials, when on increasing the density particles make contacts with those of subsequent coordination shells. Density anomalies, including an increased diffusivity upon isothermal compression and a negative thermal expansion coefficient, are the finite temperature signatures of the jamming crossovers. In this manuscript we show that the jamming crossovers are correlated to an increase of the non affine response of the system to density changes, and clarify that jammed systems evolve upon compression through subsequent Eshlby-like plastic instabilities.

cond-mat.soft↗

arXiv2013

Diffusion transport coefficients for granular binary mixtures at low density. Thermal diffusion segregation

The mass flux of a low-density granular binary mixture obtained previously by solving the Boltzmann equation by means of the Chapman-Enskog method is considered further. As in the elastic case, the associated transport coefficients $D$, $D_p$ and $D'$ are given in terms of the solutions of a set of coupled linear integral equations which are approximately solved by considering the first and second Sonine approximations. The diffusion coefficients are explicitly obtained as functions of the coefficients of restitution and the parameters of the mixture (masses, diameters and concentration) and their expressions hold for an arbitrary number of dimensions. In order to check the accuracy of the second Sonine correction for highly inelastic collisions, the Boltzmann equation is also numerically solved by means of the direct simulation Monte Carlo (DSMC) method to determine the mutual diffusion coefficient $D$ in some special situations (self-diffusion problem and tracer limit). The comparison with DSMC results reveals that the second Sonine approximation to $D$ improves the predictions made from the first Sonine approximation. We also study the granular segregation driven by a uni-directional thermal gradient. The segregation criterion is obtained from the so-called thermal diffusion factor $Λ$, which measures the amount of segregation parallel to the temperature gradient. The factor $Λ$ is determined here by considering the second-order Sonine forms of the diffusion coefficients and its dependence on the coefficients of restitution is widely analyzed across the parameter space of the system. The results obtained in this paper extend previous works carried out in the tracer limit (vanishing mole fraction of one of the species) by some of the authors of the present paper.

cond-mat.stat-mech↗

arXiv2013

Crystallization in a sheared colloidal suspension

We study numerically the crystallization process in a supersaturated suspension of repulsive colloidal particles driven by simple shear flow. The effect of the shear flow on crystallization is two-fold: while it suppresses the initial nucleation, once a large enough critical nucleus has formed its growth is enhanced by the shear flow. Combining both effects implies an optimal strain rate at which the overall crystallization rate has a maximum. To gain insight into the underlying mechanisms, we employ a discrete state model describing the transitions between the local structural configurations around single particles. We observe a time-scale separation between these transitions and the overall progress of the crystallization allowing for an effective Markovian description. By using this model, we demonstrate that the suppression of nucleation is due to the inhibition of a pre-structured liquid.

cond-mat.soft↗

arXiv2013

Predicting the thermodynamics by using state-dependent interactions

We reconsider the structure-based route to coarse graining in which the coarse-grained model is defined in such a way to reproduce some distributions functions of the original system as accurately as possible. We consider standard expressions for pressure and chemical potential applied to this family of coarse-grained models with density-dependent interactions and show that they only provide approximations to the pressure and chemical potential of the underlying original system. These approximations are then carefully compared in two cases: we consider a generic microscopic system in the low-density regime and polymer solutions under good-solvent conditions. Moreover, we show that the state-dependent potentials depend on the ensemble in which they have been derived. Therefore, care must be used in applying canonical state-dependent potentials to predict phase lines, which is typically performed in other ensembles.

cond-mat.stat-mech↗

arXiv2012

Classical nucleation theory from a dynamical approach to nucleation

It is shown that diffusion-limited classical nucleation theory (CNT) can be recovered as a simple limit of the recently proposed dynamical theory of nucleation based on fluctuating hydrodynamics (Lutsko, JCP 136, 034509 (2012)). The same framework is also used to construct a more realistic theory in which clusters have finite interfacial width. When applied to the dilute solution/dense solution transition in globular proteins, it is found that the extension gives corrections to the the nucleation rate even for the case of small supersaturations due to changes in the monomer distribution function and to the excess free energy. It is also found that the monomer attachement/detachment picture breaks down at high supersaturations corresponding to clusters smaller than about 100 molecules. The results also confirm the usual assumption that most important corrections to CNT can be acheived by means of improved estimates of the free energy barrier. The theory also illustrates two topics that have received considerable attention in the recent literature on nucleation: the importance sub-dominant corrections to the capillary model for the free energy and of the correct choice of the reaction coordinate.

physics.chem-ph↗

arXiv2013

Mode coupling theory for sheared granular liquids

Sheared granular liquids are studied by the mode coupling theory. It is shown that, in contrast to thermostatted systems, current correlations play an essential role in the dynamics. The theory predicts that the plateau of the density time-correlator disappears for most situations, while it appears in the elastic limit. The result is compatible with molecular dynamics simulations.

cond-mat.stat-mech↗

arXiv2013

Controlling the efficiency of trapping in treelike fractals

Efficiently controlling the trapping process, especially the trapping efficiency, is central in the study of trap problem in complex systems, since it is a fundamental mechanism for diverse other dynamic processes. Thus, it is of theoretical and practical significance to study the control technique for trapping problem. In this paper, we study the trapping problem in a family of proposed directed fractals with a deep trap at a central node. The directed fractals are a generalization of previous undirected fractals by introducing the directed edge weights dominated by a parameter. We characterize all the eigenvalues and their degeneracies for an associated matrix governing the trapping process. The eigenvalues are provided through an exact recursive relation deduced from the self-similar structure of the fractals. We also obtain the expressions for the smallest eigenvalue and the mean first-passage time (MFPT) as a measure of trapping efficiency, which is the expected time for the walker to first visit the trap. The MFPT is evaluated according to the proved fact that it is approximately equal to reciprocal of the smallest eigenvalue. We show that the MFPT is controlled by the weight parameter, by modifying which, the MFPT can scale superlinealy, linearly, or sublinearly with the system size. Thus, this work paves a way to delicately controlling the trapping process in the fractals.

cond-mat.stat-mech↗

arXiv2013

Numerical Integration of the Extended Variable Generalized Langevin Equation with a Positive Prony Representable Memory Kernel

Generalized Langevin dynamics (GLD) arise in the modeling of a number of systems, ranging from structured fluids that exhibit a viscoelastic mechanical response, to biological systems, and other media that exhibit anomalous diffusive phenomena. Molecular dynamics (MD) simulations that include GLD in conjunction with external and/or pairwise forces require the development of numerical integrators that are efficient, stable, and have known convergence properties. In this article, we derive a family of extended variable integrators for the Generalized Langevin equation (GLE) with a positive Prony series memory kernel. Using stability and error analysis, we identify a superlative choice of parameters and implement the corresponding numerical algorithm in the LAMMPS MD software package. Salient features of the algorithm include exact conservation of the first and second moments of the equilibrium velocity distribution in some important cases, stable behavior in the limit of conventional Langevin dynamics, and the use of a convolution-free formalism that obviates the need for explicit storage of the time history of particle velocities. Capability is demonstrated with respect to accuracy in numerous canonical examples, stability in certain limits, and an exemplary application in which the effect of a harmonic confining potential is mapped onto a memory kernel.

physics.comp-ph↗

arXiv2013

Random loop representations for quantum spin systems

We describe random loop models and their relations to a family of quantum spin systems on finite graphs. The family includes spin 1/2 Heisenberg models with possibly anisotropic spin interactions and certain spin 1 models with SU(2)-invariance. Quantum spin correlations are given by loop correlations. Decay of correlations is proved in 2D-like graphs, and occurrence of macroscopic loops is proved in the cubic lattice in dimensions 3 and higher. As a consequence, a magnetic long-range order is rigorously established for the spin 1 model, thus confirming the presence of a nematic phase.

math-ph↗

arXiv2013

Large Scale Molecular Dynamics Simulations of Homogeneous Nucleation

We present results from large-scale molecular dynamics (MD) simulations of homogeneous vapor-to-liquid nucleation. The simulations contain between one and eight billion Lennard-Jones (LJ) atoms, covering up to 1.2 μs (56 million time-steps). They cover a wide range of supersaturation ratios, S=1.55 to 10^4, and temperatures from kT = 0.3 to 1.0 ε (where ε is the depth of the LJ potential, and k the Boltzmann constant). We have resolved nucleation rates as low as 10^{17} cm^{-3} s^{-1} (in the argon system), and critical cluster sizes as large as 100 atoms. Recent argon nucleation experiments probe nucleation rates in an overlapping range, making the first direct comparison between laboratory experiments and molecular dynamics simulations possible: We find very good agreement within the uncertainties, which are mainly due to the extrapolations of argon and LJ saturation curves to very low temperatures. The self-consistent, modified classical nucleation model of Girshick and Chiu [J. Chem. Phys. 93, 1273 (1990)] underestimates the nucleation rates by up to 9 orders of magnitudes at low temperatures, and at kT = 1.0 ε it overestimates them by up to 10^5. The predictions from a semi-phenomenological model by Laaksonen et al. [Phys. Rev. E 49, 5517 (1994)] are much closer to our MD results, but still differ by factors of up to 104 in some cases. At low temperatures, the classical theory predicts critical clusters sizes, which match the simulation results (using the first nucleation theorem) quite well, while the semi-phenomenological model slightly underestimates them. At kT = 1.0 ε the critical sizes from both models are clearly too small. (abridged)

physics.chem-ph↗

arXiv2013

Derivation of a true (t->0+) quantum transition-state theory. II. Recovery of the exact quantum rate in the absence of recrossing

In Part I [J. Chem. Phys. 138, 084108 (2013)] we derived a quantum transition-state theory by taking the t->0+ (short-time) limit of a new form of quantum flux-side time-correlation function containing a ring-polymer dividing surface. This t->0+ limit appears to be unique in giving positive-definite Boltzmann statistics, and is identical to ring-polymer molecular dynamics (RPMD) TST. Here, we show that quantum TST (i.e. RPMD-TST) is exact if there is no recrossing (by the real-time quantum dynamics) of the ring-polymer dividing surface, nor of any surface orthogonal to it in the space describing fluctuations in the polymer-bead positions along the reaction coordinate. In practice, this means that RPMD-TST gives a good approximation to the exact quantum rate for direct reactions, provided the temperature is not too far below the cross-over to deep tunnelling. We derive these results by comparing the long-time limit of the ring-polymer flux-side time-correlation function with that of a hybrid flux-side time-correlation function (containing a ring-polymer flux operator and a Miller-Schwarz-Tromp side function), and by representing the resulting ring-polymer momentum integrals as hypercubes. Together with Part I, the results of this article validate a large number of RPMD calculations of reaction rates.

physics.chem-ph↗

arXiv2013

Homogeneous TIP4P/2005 ice nucleation at low supercooling

We present a partial free energy profile for the homogeneous nucleation of ice using an all-atom model of water at low supercooling, at which ice growth dynamics are reasonably accessible to simulation. We demonstrate that the free energy profile is well described by classical nucleation theory, and that the nucleation barrier is entropic in origin. We also estimate to first order the temperature dependence of the interfacial free energy.

physics.chem-ph↗

arXiv2013

Dipolar Poisson-Boltzmann Approach to Ionic Solutions: A Mean Field and Loop Expansion Analysis

We study the variation of the dielectric response of ionic aqueous solutions as function of their ionic strength. The effect of salt on the dielectric constant appears through the coupling between ions and dipolar water molecules. On a mean-field level, we account for any internal charge distribution of particles. The dipolar degrees of freedom are added to the ionic ones and result in a generalization of the Poisson-Boltzmann (PB) equation called the Dipolar PB (DPB). By looking at the DPB equation around a fixed point-like ion, a closed-form formula for the dielectric constant is obtained. We express the dielectric constant using the "hydration length" that characterizes the hydration shell of dipoles around ions, and thus the strength of the dielectric decrement. The DPB equation is then examined for three additional cases: mixture of solvents, polarizable medium and ions of finite size. Employing field-theoretical methods we expand the Gibbs free-energy to first order in a loop expansion and calculate self-consistently the dielectric constant. For pure water, the dipolar fluctuations represent an important correction to the mean-field value and good agreement with the water dielectric constant is obtained. For ionic solutions we predict analytically the dielectric decrement that depends on the ionic strength in a non-linear way. Our prediction fits rather well a large range of concentrations for different salts using only one fit parameter related to the size of ions and dipoles. A linear dependence of the dielectric constant on the salt concentration is observed at low salinity, and a noticeable deviation from linearity can be seen for ionic strength above 1\,M, in agreement with experiments.

cond-mat.soft↗

arXiv2013

Potential fluctuations in graphene due to correlated charged impurities in substrate

We evaluate the autocorrelation function of the electrostatic potential in doped graphene due to nearby charged impurities. The screening of those impurities is described by a combination of the polarization function for graphene in random phase approximation with the electrostatic Green's function of the surrounding dielectrics. Using the hard-disk model for a two-dimensional distribution of impurities, we show that large correlation lengths between impurities can give rise to anti-correlation in the electrostatic potential, in agreement with recent experiments.

cond-mat.mtrl-sci↗

arXiv2013

Investigating isomorphs with the topological cluster classification

Isomorphs are lines in the density-temperature plane of certain "strongly-correlating" or "Roskilde simple" liquids where two-point structure and dynamics have been shown to be close to identical up to a scale transformation. Here we consider such a liquid, a Lennard-Jones glassformer, and investigate the behavior along isomorphs of higher-order structural and dynamical correlations. We then consider an inverse power law reference system mapped to the Lennard-Jones system [Pedersen et al., Phys. Rev. Lett. 105, 157801 (2010)]. Using the topological cluster classification to identify higher-order structures, in both systems we find bicapped square anti-prisms, which are known to be a locally favored structure in the Lennard-Jones glassformer. The population of these locally favored structures is up to 80% higher in the Lennard-Jones system than the equivalent inverse power law system. The structural relaxation time of the two systems, on the other hand, is almost identical, and the four-point dynamical susceptibility is marginally higher in the inverse power law system. Upon cooling the lifetime of the locally favored structures in the Lennard-Jones system are up to 40% higher relative to the reference system.

cond-mat.soft↗

arXiv2013

Resummed thermodynamic perturbation theory for bond cooperativity in associating fluids

We develop a resummed thermodynamic perturbation theory for bond cooperativity in associating fluids by extension of Wertheim's multi - density formalism. We specifically consider the case of an associating hard sphere with two association sites and both pairwise and triplet contributions to the energy. To test the theory we perform new monte carlo simulations. Theory and simulation are found to be in excellent agreement.

cond-mat.soft↗

arXiv2013

Evidence for structural crossover in the supercritical state

The state of matter above the critical point is terra incognita, and is loosely discussed as a physically homogeneous flowing state where no differences can be made between a liquid and a gas and where properties undergo no marked or distinct changes with pressure and temperature. In particular, the structure of supercritical state is currently viewed to be the same everywhere on the phase diagram, and to change only gradually and in a featureless way while moving along any temperature and pressure path above the critical point. Here, we demonstrate that this is not the case, but that there is a well-defined structural crossover instead. Evidenced by the qualitative changes of distribution functions of interatomic distances and angles, the crossover demarcates liquid-like and gas-like configurations and the presence of medium-range structural correlations. Importantly, the discovered structural crossover is closely related to both dynamic and thermodynamic crossovers operating in the supercritical state, providing new unexpected fundamental interlinks between the supercritical structure, dynamics and thermodynamics.

cond-mat.stat-mech↗