Reflectivity of shocked compressed xenon plasma is calculated within the framework of the density functional theory approach. Dependencies on the frequency of incident radiation and on the plasma density are analyzed. The Fresnel formula for the reflectivity is used. The longitudinal expression in the long-wavelength limit is applied for the calculation of the imaginary part of the dielectric function. The real part of the dielectric function is calculated by means of the Kramers-Kronig transformation. The results are compared with experimental data. The approach for the calculation of plasma frequency is developed.
We study properties of Markov chain Monte Carlo simulations of classical spin models with local updates. We derive analytic expressions for the mean value of the acceptance rate of single-spin-flip algorithms for the one-dimensional Ising model. We find that for the Metropolis algorithm the average acceptance rate is a linear function of energy. We further provide numerical results for the energy dependence of the average acceptance rate for the three- and four-state Potts model, and the XY model in one and two spatial dimensions. In all cases, the acceptance rate is an almost linear function of the energy in the critical region. The variance of the acceptance rate is studied as a function of the specific heat. While the specific heat develops a singularity in the vicinity of a phase transition, the variance of the acceptance rate stays finite.
We study horizontal streaming excited by means of a low-frequency and low-intensity acoustic wave in 2D freely suspended films of thermotropic smectic liquid crystals. Acoustic pressure induces fast periodic transverse oscillations of the film, which produce in-plane stationary couples of vortices slowly rotating in opposite directions owing to hydrodynamic nonlinearity. The parameters of the vortices are measured using a new method, based on tracking solidlike disk-shaped islands. The horizontal motion occurs only when the amplitude of the acoustic pressure exceeds the threshold value, which can be explained by Bingham-like behavior of the smectic film. The measurements above threshold are in good agreement with existing theoretical predictions. We demonstrate experimentally that in-plane flow is well controlled by changing the acoustic pressure, excitation frequency, and geometry of the film. The observations open the way to using the phenomenon in nondisplay applications.
We investigate both analytically and by computer simulations the ensemble- and time-averaged, nonergodic,and aging properties of massive particles diffusing in a medium with a time dependent diffusivity. We call thisstochastic diffusion process the (aging) underdamped scaled Brownian motion (UDSBM). We demonstrate howthe mean squared displacement (MSD) and the time-averaged MSD of UDSBM are affected by the inertial term inthe Langevin equation, both at short, intermediate, and even long diffusion times. In particular, we quantify the bal-listic regime for the MSD and the time-averaged MSD as well as the spread of individual time-averaged MSD tra-jectories. One of the main effects we observe is that, both for the MSD and the time-averaged MSD, for superdiffu-sive UDSBM the ballistic regime is much shorter than for ordinary Brownian motion. In contrast, for subdiffusiveUDSBM, the ballistic region extends to much longer diffusion times. Therefore, particular care needs to be takenunder what conditions the overdamped limit indeed provides a correct description, even in the long time limit. Wealso analyze to what extent ergodicity in the Boltzmann-Khinchin sense in this nonstationary system is broken,both for subdiffusive and superdiffusive UDSBM. Finally, the limiting case of ultraslow UDSBM is considered,with a mixed logarithmic and power-law dependence of the ensemble- and time-averaged MSDs of the particles.In the limit of strong aging, remarkably, the ordinary UDSBM and the ultraslow UDSBM behave similarly in theshort time ballistic limit. The approaches developed here open ways for considering other stochastic processesunder physically important conditions when a finite particle mass and aging in the system cannot be neglected
Evolution on changing fitness landscapes (seascapes) is an important problem in evolutionary biology. We consider the Moran model of finite population evolution with selection in a randomly changing, dynamic environment. In the model, each individual has one of the two alleles, wild type or mutant. We calculate the fixation probability by making a proper ansatz for the logarithm of fixation probabilities. This method has been used previously to solve the analogous problem for the Wright-Fisher model. The fixation probability is related to the solution of a third-order algebraic equation (for the logarithm of fixation probability).We consider the strong interference of landscape fluctuations, sampling, and selection when the fixation process cannot be described by the mean fitness. Such an effect appears if the mutant allele has a higher fitness in one landscape and a lower fitness in another, compared with the wild type, and the product of effective population size and fitness is large. We provide a generalization of the Kimura formula for the fixation probability that applies to these cases. When the mutant allele has a fitness (dis-)advantage in both landscapes, the fixation probability is described by the mean fitness.
We provide theoretical analysis of the reflectance of shock-compressed plasmas and warm dense matter for normal incidence of laser radiation as well as for the dependence of s- and p-polarized reflectivity on the incidence angle. The self-consistent approach for the calculation of the optical and electronic properties of warm dense matter and nonideal plasmas developed in our previous works is extended for the description of normal and polarized reflectivity from the broadened optically nonuniform medium. Two methods are applied for the calculation of the reflectivity from spatially broadened optically nonuniform medium. The first one is based on the solution of the Helmholtz equation for the amplitudes of the electromagnetic field. Another one is based on Drude theory of reflection. It allows us to calculate the ratio of the s- and p-polarized reflectivity if dependence of the dielectric function on distance is known. For the case of the polarized reflectivity, the particular attention is concentrated on the Brewster angle. The calculation results for the dielectric function, obtained within the framework of the density-functional theory with the longitudinal expression for the dielectric tensor, are applied for the calculation of the reflectivity. Comparison with the experimental data for shock-compressed xenon is performed.
We theoretically study the phase dynamics in Josephson junctions, which maps onto the oscillatory motion of a pointlike particle in the washboard potential. Under appropriate driving and damping conditions, the Josephson phase undergoes intriguing bistable dynamics near a saddle point in the quasienergy landscape. The bifurcation mechanism plays a critical role in superconducting quantum circuits with relevance to nondemolition measurements such as high-fidelity readout of qubit states. We address the question “what is the probability of capture into either basin of attraction?” and answer it concerning both classical and quantum dynamics. Consequently, we derive the Arnold probability and numerically analyze its implementation of the controlled dynamical switching between two steady states under the various nonequilibrium conditions.
Using molecular dynamics simulations, we study the transient response of a binary Lennard-Jones glass subjected to periodic shear deformation. The amorphous solid is modeled as a three-dimensional Kob-Andersen binary mixture at a low temperature. The cyclic loading is applied to slowly annealed, quiescent samples, which induces irreversible particle rearrangements at large strain amplitudes, leading to stress-strain hysteresis and a drift of the potential energy towards higher values. We find that the initial response to cyclic shear near the critical strain amplitude involves disconnected clusters of atoms with large nonaffine displacements. In contrast, the amplitude of shear stress oscillations decreases after a certain number of cycles, which is accompanied by the initiation and subsequent growth of a shear band.
The Wang-Landau (WL) algorithm has been widely used for simulations in many areas of physics. Our analysis of the WL algorithm explains its properties and shows that the difference of the largest eigenvalue of the transition matrix in the energy space from unity can be used to control the accuracy of estimating the density of states. Analytic expressions for the matrix elements are given in the case of the one-dimensional Ising model. The proposed method is further confirmed by numerical results for the one-dimensional and two-dimensional Ising models and also the two-dimensional Potts model.
The Binder cumulant at the phase transition of Ising models on square lattices with ferromagnetic couplings between nearest neighbors and with competing antiferromagnetic couplings between next-nearest neighbors, along only one diagonal, is determined using Monte Carlo techniques. In the phase diagram a disorder line occurs separating regions with monotonically decaying and with oscillatory spin-spin correlations. Findings on the variation of the critical cumulant with the ratio of the two interaction strengths are compared to related recent results based on renormalization-group calculations.
We demonstrate that the Einstein relation for the diffusion of a particle in the random-energy landscape with the Gaussian density of states is an exclusive one-dimensional property and does not hold in higher dimensions. We also consider the analytical properties of the particle velocity and diffusivity for the limit of weak driving force and establish a connection between these properties and dimensionality and spatial correlation of the random-energy landscape.
We report on the results of a molecular dynamics simulation study of porous glassy media, formed in the process of isochoric rapid quenching from a high-temperature liquid state. The transition to a porous solid occurs due to the concurrent processes of phase separation and material solidification. The study is focused on topographies of the model porous structures and their dependence on temperature and average density. To quantify the pore-size distributions,we put forth a scaling relation that provides a satisfactory data collapse in systems with high porosity. We also find that the local density of the solid domains in the porous structures is broadly distributed, and, with increasing average density, a distinct peak in the local density distribution is displaced toward higher values.
Recently a theoretical scheme explaining the vorticity generation by surface waves in liquids was developed [Phys. Rev. Lett.116,054501(2016)]. Here we study how a thin (monomolecular) film presented on the surface of liquid affects the generated vorticity. We demonstrate that the vorticity becomes parametrically larger than for the case of liquid with a free surface, and the parameter is the quality factor of surface waves up to numerical factor. We also discuss the PIV experimental scheme intended to observe the generated vorticity and find that Stokes drift influences the measured velocity field. Explicit expression for the vertical vorticity was obtained.
Molecular dynamics simulations are used to investigate the rate and temperature dependence of the slip length in thin liquid films confined by smooth, thermal substrates. In our setup, the heat generated in a force-driven flow is removed by the thermostat applied on several wall layers away from liquid-solid interfaces. We found that for both high and low wall-fluid interaction (WFI) energies, the temperature of the fluid phase rises significantly as the shear rate increases. Surprisingly, with increasing shear rate, the slip length approaches a constant value from above for highWFI energies and from below for low WFI energies. The two distinct trends of the rate-dependent slip length are rationalized by examining S(G1), the height of the main peak of the in-plane structure factor of the first fluid layer (FFL) together with DWF, which is the average distance between the wall and FFL. The results of numerical simulations demonstrate that reduced values of the structure factor, S(G1), correlate with the enhanced slip, while smaller distances DWF indicate that fluid atoms penetrate deeper into the surface potential leading to larger friction and smaller slip. Interestingly, at the lowest WFI energy, the combined effect of the increase of S(G1) and decrease of DWF with increasing shear rate results in a dramatic reduction of the slip length.
We consider the canonical ensemble of N-vertex Erdos-Rényi (ER) random topological graphs with quenched vertex degree, and with fugacity μ for each closed triple of bonds. We claim complete defragmentation of large-N graphs into the collection of [p-1] almost full subgraphs (cliques) above critical fugacity, μc, where p is the ER bond formation probability. Evolution of the spectral density, ρ(λ), of the adjacency matrix with increasing μ leads to the formation of a multizonal support for μ>μc. Eigenvalue tunneling from the central zone to the side one means formation of a new clique in the defragmentation process. The adjacency matrix of the network ground state has a block-diagonal form, where the number of vertices in blocks fluctuates around the mean value Np. The spectral density of the whole network in this regime has triangular shape. We interpret the phenomena from the viewpoint of the conventional random matrix model and speculate about possible physical applications.
The generalized totally asymmetric exclusion process (TASEP) [J. Stat. Mech. (2012) P05014] is an integrable generalization of the TASEP equipped with an interaction, which enhances the clustering of particles. The process interpolates between two extremal cases: the TASEP with parallel update and the process with all particles irreversibly merging into a single cluster moving as an isolated particle. We are interested in the large time behavior of this process on a ring in the whole range of the parameter λ controlling the interaction. We study the stationary state correlations, the cluster size distribution, and the large-time fluctuations of integrated particle current. When λ is finite, we find the usual TASEP-like behavior: The correlation length is finite; there are only clusters of finite size in the stationary state and current fluctuations belong to the Kardar-Parisi-Zhang universality class. When λ grows with the system size, so does the correlation length. We find a nontrivial transition regime with clusters of all sizes on the lattice. We identify a crossover parameter and derive the large deviation function for particle current, which interpolates between the case considered by Derrida-Lebowitz and a single-particle diffusion.
Theoretical description and numerical simulation of an evaporating sessile drop are developed. We jointly take into account the hydrodynamics of an evaporating sessile drop, effects of the thermal conduction in the drop, and the diffusion of vapor in air. A shape of the rotationally symmetric drop is determined within the quasistationary approximation. Nonstationary effects in the diffusion of the vapor are also taken into account. Simulation results agree well with the data of evaporation rate measurements for the toluene drop. Marangoni forces associated with the temperature dependence of the surface tension generate fluid convection in the sessile drop. Our results demonstrate several dynamical stages of the convection characterized by different number of vortices in the drop. During the early stage the array of vortices arises near a surface of the drop and induces a nonmonotonic spatial distribution of the temperature over the drop surface. The initial number of near-surface vortices in the drop is controlled by the Marangoni cell size which is similar to that given by Pearson for flat fluid layers. This number quickly decreases with time resulting in three bulk vortices in the intermediate stage. The vortices finally transform into the single convection vortex in the drop existing during about 1/2 of the evaporation time.
Experimental and theoretical studies of a smectic-A–hexatic-B transition in freely suspended films of thickness 2–10μm of the n-pentyl-4′−n-pentanoyloxy-biphenyl-4-carboxylate (54COOBC) compound are presented. X-ray investigations revealed a discontinuous first-order transition into the hexatic phase. The temperature region of two-phase coexistence near the phase transition point diminishes with decreasing film thickness. The width of this temperature region as a function of the film thickness was derived on the basis of a Landau mean-field theory in the vicinity of a tricritical point (TCP). Close to TCP the surface hexatic-B order penetrates anomalously deep into the film interior.
Molecular dynamics simulations are carried out to investigate mechanical properties and porous structure of binary glasses subjected to steady shear. The model vitreous systems were prepared via thermal quench at constant volume to a temperature well below the glass transition. The quiescent samples are characterized by a relatively narrow pore size distribution whose mean size is larger at lower glass densities. We find that in the linear regime of deformation, the shear modulus is a strong function of porosity, and the individual pores become slightly stretched while their structural topology remains unaffected. By contrast, with further increasing strain, the shear stress saturates to a density-dependent plateau value, which is accompanied by pore coalescence and a gradual development of a broader pore size distribution with a discrete set of peaks at large length scales.