The structural properties of strongly coupled ions in dense plasmas with moderately to strongly degenerate electrons are investigated in the framework of the one-component plasma model of ions interacting through a screened pair interaction potential. Special focus is put on the description of the electronic screening in the Singwi-Tosi-Land-Sjölander (STLS) approximation. Different cross-checks and analyses using ion potentials obtained from ground-state quantum Monte Carlo data, the random phase approximation (RPA), and existing analytical models are presented for the computation of the structural properties, such as the pair distribution and the static structure factor, of strongly coupled ions. The results are highly sensitive to the features of the screened pair interaction potential. This effect is particularly visible in the static structure factor. The applicability range of the screened potential computed from STLS is identified in terms of density and temperature of the electrons. It is demonstrated that at $r_s>1$, where $r_s$ is the ratio of the mean interelectronic distance to the Bohr radius, electronic correlations beyond RPA have a nonnegligible effect on the structural properties. Additionally, the applicability of the hypernetted chain approximation for the calculation of the structural properties using the screened pair interaction potential is analyzed employing the effective coupling parameter approach.

In developing coarse-grained (CG) polymer models it is important to reproduce both local and molecule-scale structure. We develop a procedure for fast calculation of the bond-orientation correlation and the internal squared distance $\langle R^2\left(M\right)\rangle$ through evaluation of the probability distribution functions that represent a CG model. Different CG models inherently contain or omit correlations between CG variables. Here, we construct CG models that contain specific correlations between CG variables. The importance of different correlations is tested on CG models of polyethylene, polytetrafluoroethylene, and poly-L-lactic acid. The chain stiffness and $\langle R^2\left(M\right)\rangle$ are calculated using both analytic evaluation and Monte Carlo sampling, and approximate model results are compared with exact results from all-atom simulations. For polymers with an exponential correlation decay, the bond-orientation correlation and $\langle R^2\left(M\right)\rangle$ indicate which CG variable correlations are most important to reproduce molecule-scale structure. Analysis of the bond-orientation correlation and internal-squared distance indicates that for poly-L-lactic acid the bond-orientation correlation requires qualitatively different additional terms in CG models and quantifies the error in neglecting this important behavior.

We propose a simple formulation of the phase-field model for a stoichiometric compound growing in a binary liquid. In previous models, chemical free energies of stoichiometric compounds have been approximated by parabolic functions of composition; however, the curvature has been determined arbitrarily in spite of the fact that the stoichiometric composition was undesirably modified depending on the curvature. To avoid this uncertainty, we supposed that the chemical free energy of the stoichiometric compound is represented by a single value at a given temperature and derived the phase-field equations without the parabolic free-energy approximation. The phase mobility was derived both for diffusion- and interface-controlled solidification based on a thin interface limit analysis. We carried out numerical simulations of one-dimensional calculations both in diffusion-controlled and interface-controlled cases and found that the growth velocities agreed with the analytic predictions. We also examined two-dimensional solidification of a circular crystal and confirmed that the equilibrium state was shifted, as suggested by the Gibbs-Thomson effect. This study is an important step for phase-field modeling that includes stoichiometric compounds with their accurate thermodynamic properties.

We identify active phase separation as a generic demixing phenomenon in nonequilibrium systems with conservation constraints. Examples range from cell polarization to cell populations communicating via chemotaxis, and from self-propelled particle communities to mussels in ecology. We show that system-spanning properties of active phase separation in nonequilibrium systems near onset are described by the classical Cahn-Hilliard (CH) model. This result is rather surprising since the CH equation is famous as a model for phase separation at thermal equilibrium. We introduce a general reduction scheme to establish a unique mathematical link between the generic CH equation and system-specific models for active phase separation. This approach is exemplarily applied to a model for polarization of cells and a model for chemotactic cell communities. For cell polarization, we also estimate the validity range of the CH model.

With the stochastic Landau-Lifshitz-Gilbert (sLLG) equation, critical dynamic behaviors far from equilibrium or stationary around the order-disorder and pinning-depinning phase transitions in anisotropic magnetic films are investigated. From the dynamic relaxation with and without an external field, the Curie temperature and critical exponents of the order-disorder phase transition are accurately determined. For the pinning-depinning phase transition induced by quenched disorder, the nonstationary creep motion of domain wall activated by finite temperatures is simulated, and the thermal rounding exponent is extracted. The results show that the dynamic universality class of the sLLG equation is different from those of the Monte Carlo dynamics and quenched Edwards-Wilkinson equation, and it may lead to alternative understanding of experiments. The dynamic approach shows its great efficiency for the sLLG equation.

We explore the nonlinear dynamics of a driven power-law oscillator whose shape varies periodically in time covering a broad spectrum of anharmonicities. Combining weak and strong confinement of different geometry within a single driving period, the phase space allows not only for regular and chaotic bounded motion but in particular also for an unbounded motion which exhibits an exponential net growth of the corresponding energies. Our computational study shows that phases of motion with energy gain and loss as well as approximate energy conservation alternate within a single period of the oscillator and can be assigned to the change of the underlying confinement geometry. We demonstrate how the crossover from a single- to a two-component phase space takes place with varying frequency and amplitude and analyze the corresponding volumes in phase space. In the high-frequency regime an effective potential is derived that combines the different features of the driven power-law oscillator. Possible experimental realizations are discussed.

This paper investigates the effect of inertia on the dynamics of elongated chains to go beyond the overdamped case that is often used to study such systems. For that purpose, numerical simulations are performed considering the motion of freely jointed bead-rod chains in an extensional flow in the presence of thermal noise. The coil-stretch transition and the tumbling instability are characterized as a function of three parameters: the Péclet number, the Stokes number, and the chain length. Numerical results show that the coil-stretch transition remains when inertia is present and that it depends nonlinearly on the Stokes and Péclet numbers. Theoretical and numerical analyses also highlight the role of intermediate stable configurations in the dynamics of elongated chains: chains can indeed remain trapped for a certain time in these configurations, especially while undergoing a tumbling event.

Here we present a time-dependent correlation method that provides insight into how long a system takes to grow into its equal-time (Pearson) correlation. We also show a usage of an extant time-lagged correlation method that indicates the time for parts of a system to become decorrelated, relative to equal-time correlation. Given a completed simulation (or set of simulations), these tools estimate (i) how long of a simulation of the same system would be sufficient to observe the same correlated motions, (ii) if patterns of observed correlated motions indicate events beyond the timescale of the simulation, and (iii) how long of a simulation is needed to observe these longer timescale events. We view this method as a decision-support tool that will aid researchers in determining necessary sampling times. In principle, this tool is extendable to any multidimensional time series data with a notion of correlated fluctuations; however, here we limit our discussion to data from molecular-dynamics simulations.

An alternative method to simulate heat transport in the multiphase lattice Boltzmann (LB) method is proposed. To solve the energy transport equation when phase boundaries are present, the method of a passive scalar is considerably modified. The internal energy is represented by an additional set of distribution functions, which evolve according to an LB-like equation simulating the transport of a passive scalar. Parasitic heat diffusion near boundaries with a large density gradient is suppressed by using special “pseudoforces” which prevent the spreading of energy. The compression work and heat diffusion are calculated by finite differences. A new method to take into account the latent heat of a phase transition $Q\left(T\right)$ is realized. The latent heat is released or absorbed continuously inside a thin transition layer in a certain range of density, ${\rho }_1<\rho <{\rho }_2$. This allows one to avoid interface tracking. Several tests were carried out concerning all aspects of the processes. It is shown that the Galilean invariance and the scaling of the thermal conduction process hold, as well as the correct dependence of the sound speed on the heat capacity ratio. The method proposed has low scheme diffusion of the internal energy, and it can be applied to modeling a wide range of multiphase flows with heat and mass transfer even for high density ratios of liquid and vapor phases.

Grand-potential-based phase-field model for multiple phases, grains, and chemical components is derived from a grand-potential functional. Due to the grand-potential formulation, the chemical energy does not contribute to the interfacial energy between phases, simplifying parametrization and decoupling interface thickness from interfacial energy, which can potentially allow increased interface thicknesses and therefore improved computational efficiency. Two-phase interfaces are stable with respect to the formation of additional phases, simplifying implementation and allowing the variational form of the evolution equations to be used. Additionally, we show that grand-potential-based phase-field models are capable of simulating phase separation, and we derive conditions under which this is possible.

In the paper the phase diagram of $J_1\text{−}{J}_2$ frustrated antiferromagnet with spin $S=1$ and single-ion anisotropy is studied on the planar quadratic lattice in the cluster approximation. The Bogolyubov inequality is adopted for the Gibbs energy calculation for the case of $2\times 2$ and $4\times 4$ clusters. On this basis, the ranges of existence of the antiferromagnetic, superantiferromagnetic, and paramagnetic phases are investigated for the antiferromagnetic nearest-neighbor ($J_1<0$) and next-nearest-neighbor ($J_2<0$) interactions. In particular, the occurrence of tricritical and triple points is discussed and a comparison between the results for $2\times 2$ and $4\times 4$ clusters is made. The results are also compared with the classical MFA method, adopted here for the model in question, as well as with selected literature results for particular choices of interaction parameters.

Fully mechanized Maxwell's demons, also called information ratchets, are an important conceptual link between computation, information theory, and statistical physics. They exploit low-entropy information reservoirs to extract work from a heat reservoir. Previous models of such demons have either ignored the cost of delivering bits to the demon from the information reservoir or assumed random access or infinite-dimensional information reservoirs to avoid such an issue. In this work we account for this cost when exploiting information reservoirs with physical structure and show that the dimensionality of the reservoir has a significant impact on the performance and phase diagram of the demon. We find that for conventional one-dimensional tapes the scope for work extraction is greatly reduced. An expression for the net-extracted work by demons exploring information reservoirs by means of biased random walks on $d$-dimensional, ${\mathbb{Z}}^d$, information reservoirs is presented. Furthermore, we derive exact probabilities of recurrence in these systems, generalizing previously known results. We find that the demon is characterized by two critical dimensions. First, to extract work at zero bias the dimensionality of the information reservoir must be larger than $d=2$, corresponding to the dimensions where a simple random walker is transient. Second, for integer dimensions $d>4$ the unbiased random walk optimizes work extraction corresponding to the dimensions where a simple random walker is strongly transient.

It has been known for a long time that the kinetics of diffusion-limited reactions can be quantified by the time needed for a diffusing molecule to reach a target: the first-passage time (FPT). So far the general determination of the mean first-passage time to a target in confinement has left aside aging media, such as glassy materials, cellular media, or cold atoms in optical lattices. Here we consider general non-Markovian scale-invariant diffusion processes, which model a broad class of transport processes of molecules in aging media, and demonstrate that all the moments of the FPT obey universal scalings with the confining volume with nontrivial exponents. Our analysis shows that a nonlinear scaling with the volume of the mean FPT, which quantities the mean reaction time, is the hallmark of aging and provides a general tool to quantify its impact on reaction kinetics in confinement.

Low-dimensional dynamical systems are fruitful models for mixing in fluid and granular flows. We study a one-dimensional discontinuous dynamical system (termed “cutting and shuffling” of a line segment), and we present a comprehensive computational study of its finite-time mixing properties including the effect of diffusion. To explore a large parameter space, we introduce fit functions for two mixing metrics of choice: the number of cutting interfaces (a standard quantity in dynamical systems theory of interval exchange transformations) and a mixing norm (a more physical measure of mixing). We compute averages of the mixing metrics across different permutations (shuffling protocols), showing that the latter averages are a robust descriptor of mixing for any permutation choice. If the decay of the normalized mixing norm is plotted against the number of map iterations rescaled by the characteristic e-folding time, then universality emerges: mixing norm decay curves across all cutting and shuffling protocols collapse onto a single stretched-exponential profile. Next, we predict this critical number of iterations using the average length of unmixed subsegments of continuous color during cutting and shuffling and a Batchelor-scale-type diffusion argument. This prediction, called a “stopping time” for finite Markov chains, compares well with the e-folding time of the stretched-exponential fit. Finally, we quantify the effect of diffusion on cutting and shuffling through a Péclet number (a dimensionless inverse diffusivity), showing that the system transitions more sharply from an unmixed initial state to a mixed final state as the Péclet number becomes large. Our numerical investigation of cutting and shuffling of a line segment in the presence of diffusion thus presents evidence for the latter phenomenon, known as a “cut-off” for finite Markov chains, in interval exchange maps.

Electrokinetic phenomena in a nematic suspension are considered when one or more dielectric particles are suspended in a liquid crystal matrix in its nematic phase. The long-range orientational order of the nematic constitutes a fluid with anisotropic properties. This anisotropy enables charge separation in the bulk under an applied electric field, and leads to streaming flows even when the applied field is oscillatory. In the cases considered, charge separation is seen to result from director field distortions in the matrix that are created by the suspended particles. We use a recently introduced electrokinetic model to study the motion of a single-particle hyperbolic hedgehog pair. We find this motion to be parallel to the defect-particle center axis, independent of field orientation. For a two-particle configuration, we find that the relative force of electrokinetic origin is attractive in the case of particles with perpendicular director anchoring, and repulsive for particles with tangential director anchoring. The study reveals large scale flow properties that are respectively derived from the topology of the configuration alone and from short scale hydrodynamics phenomena in the vicinity of the particle and defect.

We present a thorough study of the plastic response of a granular material progressively loaded. We study experimentally the evolution of the plastic field from a homogeneous one to a heterogeneous one and its fluctuations in terms of incremental strain. We show that the plastic field can be decomposed in two components evolving on two decoupled strain increment scales. We argue that the slowly varying part of the field can be identified with the so-called fluidity field introduced recently to interpret the rheological behavior of amorphous materials. This fluidity field progressively concentrates along a macroscopic direction corresponding to the Mohr-Coulomb angle.

The Frenkel-Kontorova chain with a free end is used to study initiation and propagation of crowdions (antikinks) caused by impact of a molecule consisting of $K$ atoms. It is found that molecules with $1<K<10$ are more efficient in the initiation of crowdions as compared to a single atom ($K=1$) because the total energy needed to initiate the crowdions by molecules is smaller. This happens because a single atom can initiate in the chain only sharp, fast-moving crowdions that require relatively large energy. A molecule has finite length, and that is why it is able to excite a wider crowdion with a smaller velocity and smaller energy. Our results can shed light on the atomistic mechanisms of mass transfer in crystals subject to atom and molecule bombardment.

We report a theoretical equation of state (EOS) table for boron across a wide range of temperatures ($5.1\times {10}^4$–$5.2\times {10}^8$ K) and densities (0.25–49 g/${\mathrm{cm}}^3$) and experimental shock Hugoniot data at unprecedented high pressures ($5608\pm 118$ GPa). The calculations are performed with first-principles methods combining path-integral Monte Carlo (PIMC) at high temperatures and density-functional-theory molecular-dynamics (DFT-MD) methods at lower temperatures. PIMC and DFT-MD cross-validate each other by providing coherent EOS (difference $<1.5$ Hartree/boron in energy and $<5\%$ in pressure) at $5.1\times {10}^5$ K. The Hugoniot measurement is conducted at the National Ignition Facility using a planar shock platform. The pressure-density relation found in our shock experiment is on top of the shock Hugoniot profile predicted with our first-principles EOS and a semiempirical EOS table (LEOS 50). We investigate the self-diffusivity and the effect of thermal and pressure-driven ionization on the EOS and shock compression behavior in high-pressure and -temperature conditions. We also study the sensitivity of a polar direct-drive exploding pusher platform to pressure variations based on applying pressure multipliers to LEOS 50 and by utilizing a new EOS model based on our ab initio simulations via one-dimensional radiation-hydrodynamic calculations. The results are valuable for future theoretical and experimental studies and engineering design in high-energy density research.

We present kinetic two-dimensional Vlasov-Fokker-Planck simulations, including both self-consistent magnetic fields and ablating ion outflow, of a planar ablating foil subject to nonuniform laser irradiation. Even for small Hall parameters ($\omega {\tau }_{ei}\lesssim 0.05$) self-generated magnetic fields are sufficient to invert and enhance pressure perturbations. The mode inversion is caused by a combination of the Nernst advection of the magnetic field and the Righi-Leduc heat flux. Nonlocal effects modify these processes. The mechanism is robust under plasma conditions tested; it is amplitude independent and occurs for a broad spectrum of perturbation wavelengths, ${\lambda }_p=10–100\mu \mathrm{m}$. The ablating plasma response to a dynamically evolving speckle pattern perturbation, analogous to an optically smoothed beam, is also simulated. Similar to the single-mode case, self-generated magnetic fields increase the degree of nonuniformity at the ablation surface by up to an order of magnitude and are found to preferentially enhance lower modes due to the resistive damping of high mode number magnetic fields.

We use invasion percolation to compute highly accurate numerical values for bond and site percolation thresholds $p_c$ on the hypercubic lattice ${\mathbb{Z}}^d$ for $d=4,...,13$. We also compute the Fisher exponent $\tau$ governing the cluster size distribution at criticality. Our results support the claim that the mean-field value $\tau =5/2$ holds for $d\ge 6$, with logarithmic corrections to power-law scaling at $d=6$.