We calculated the evolution of the electron system in solid-density matter irradiated by high-intensity x-ray pulses between 2 and 8 keV using molecular dynamics. For pulses shorter than 40 fs, the kinetic energy distribution of the electrons is highly nonthermal during and right after the pulse, and a large fraction of the absorbed x-ray energy resides with the fast photoelectrons which equilibrate on the timescale of the pulse length. The average ionization and electron temperature of the bulk of the electrons are significantly lower than their equilibrium values.

We present a theoretical treatment of overdamped Brownian motion on a multidimensional tilted periodic potential that is analogous to the tight-binding model of quantum mechanics. In our approach, we expand the continuous Smoluchowski equation in the localized Wannier states of the periodic potential to derive a discrete master equation. This master equation can be interpreted in terms of hopping within and between Bloch bands, and for weak tilting and long times we show that a single-band description is valid. In the limit of deep potential wells, we derive a simple functional dependence of the hopping rates and the lowest band eigenvalues on the tilt. We also derive formal expressions for the drift and diffusion in terms of the lowest band eigenvalues.

In this paper, we study experimentally the configurations of a plastic wire injected into a cubic cavity containing periodic obstacles placed along a fixed direction. The wire moves in a wormlike manner within the cavity until it becomes jammed in a crumpled state. The maximum packing fraction of the wire depends on the topology of the cavity, which in turn depends on the number of obstacles. The experimental results exhibit scaling laws and display similarities as well as differences with a recently reported two-dimensional version of this complex packing problem. We discuss in detail several aspects of this problem that seem as intricate as the problem of a self-avoiding random walk. Analogies between the experiment reported and some statistical aspects of the bond-percolation problem, as well as of the interacting electron gas at finite temperature, and other physical issues are also discussed.

As a possible generalization of Beck-Cohen superstatistical processes, we study non-Gaussian processes with temporal heterogeneity of local variance. To characterize the variance heterogeneity, we define log-amplitude cumulants and log-amplitude autocovariance and derive closed-form expressions of the log-amplitude cumulants for ${\chi }^2$, inverse ${\chi }^2$, and log-normal superstatistical distributions. Furthermore, we show that ${\chi }^2$ and inverse ${\chi }^2$ superstatistics with degree 2 are closely related to an extreme value distribution, called the Gumbel distribution. In these cases, the corresponding superstatistical distributions result in the $q$-Gaussian distribution with $q=5/3$ and the bilateral exponential distribution, respectively. Thus, our finding provides a hypothesis that the asymptotic appearance of these two special distributions may be explained by a link with the asymptotic limit distributions involving extreme values. In addition, as an application of our approach, we demonstrated that non-Gaussian fluctuations observed in a stock index futures market can be well approximated by the ${\chi }^2$ superstatistical distribution with degree 2.

We study the diffusion of a Brownian particle quadratically coupled to a thermally fluctuating field. In the weak-coupling limit, a path-integral formulation allows us to compute the effective diffusion coefficient in the cases of an active particle, which tends to suppress field fluctuations, and of a passive particle, which only undergoes field fluctuations. We show that the behavior is similar to what was previously found for a linear coupling: an active particle is always slowed down, whereas a passive particle is slowed down in a slow field and accelerated in a fast field. Numerical simulations show a good agreement with the analytical calculations. The examples of a membrane protein coupled to the curvature or composition of the membrane are discussed, with a focus on the room for anomalous diffusion.

We evaluate analytically and numerically the size of the frozen core and various scaling laws for critical Boolean networks that have a power-law in- and/or out-degree distribution. To this purpose, we generalize an efficient method that has previously been used for conventional random Boolean networks and for networks with power-law in-degree distributions. With this generalization, we can also deal with power-law out-degree distributions. When the power-law exponent is between 2 and 3, the second moment of the distribution diverges with network size, and the scaling exponent of the nonfrozen nodes depends on the degree distribution exponent. Furthermore, the exponent depends also on the dependence of the cutoff of the degree distribution on the system size. Altogether, we obtain an impressive number of different scaling laws depending on the type of cutoff as well as on the exponents of the in- and out-degree distributions. We confirm our scaling arguments and analytical considerations by numerical investigations.

We study distributions of the partition function zeros in the complex temperature plane for a square-lattice homopolymer with nearest-neighbor (NN) and next-nearest-neighbor (NNN) interactions. The dependence of distributions on the ratio of NN and NNN interaction strengths $R$ is examined. The finite-size scaling of the zeros is performed to obtain the crossover exponent, which is shown to be independent of $R$ within error bars, suggesting that all of these models belong to the same universality class. The transition temperatures are also computed by the zeros to obtain the phase diagram, and the results confirm that the model with stronger NNN interaction exhibits stronger effects of cooperativity.

Biological information processing is often carried out by complex networks of interconnected dynamical units. A basic question about such networks is that of reliability: If the same signal is presented many times with the network in different initial states, will the system entrain to the signal in a repeatable way? Reliability is of particular interest in neuroscience, where large, complex networks of excitatory and inhibitory cells are ubiquitous. These networks are known to autonomously produce strongly chaotic dynamics—an obvious threat to reliability. Here, we show that such chaos persists in the presence of weak and strong stimuli, but that even in the presence of chaos, intermittent periods of highly reliable spiking often coexist with unreliable activity. We elucidate the local dynamical mechanisms involved in this intermittent reliability, and investigate the relationship between this phenomenon and certain time-dependent attractors arising from the dynamics. A conclusion is that chaotic dynamics do not have to be an obstacle to precise spike responses, a fact with implications for signal coding in large networks.

We introduce a simple improvement on the method to calculate equilibrium entropy differences between classical energy levels proposed by Davis [S. Davis, Phys. Rev. E 84, 050101 (2011)]. We demonstrate that the modification is superior to the original whenever the energy levels are sufficiently closely spaced or whenever the microcanonical averaging needed in the method is carried out by importance sampling Monte Carlo. We also point out the necessary adjustments if Davis's method (improved or not) is to be used with molecular dynamics simulations.

We report the effects of system geometry on the clogging of granular material flowing out of flat-bottomed hoppers with variable aperture size $D$ and with variable angle $\theta$ of tilt of the hopper away from horizontal. In general, larger tilt angles make the system more susceptible to clogging. To quantify this effect for a given $\theta$, we measure the distribution of mass discharged between clogging events as a function of aperture size and extrapolate to the critical size at which the average mass diverges. By repeating for different angles, we map out a clogging phase diagram as a function of $D$ and $\theta$ that demarcates the regimes of free flow (large $D$, small $\theta$) and clogging (small $D$, large $\theta$). We do this for both circular holes and long rectangular slits. Additionally, we measure four types of grain: smooth spheres (glass beads), compact angular grains (beach sand), disklike grains (lentils), and rodlike grains (rice). For circular apertures, the clogging phase diagram is found to be the same for all grain types. For narrow slit apertures and compact grains, the shape is also the same as for circular holes when expressed in terms of projected area of the aperture against the average flow direction. For lentils and rice discharged from slits, the behavior differs and may be due to alignment between grain and slit axes.

The closure of long equilibrated denaturation bubbles in DNA is studied using Brownian dynamics simulations. A minimal mesoscopic model is used where the double helix is made of two interacting bead-spring freely rotating strands, with a nonzero torsional modulus in the duplex state, ${\kappa }_{\varphi }=200$ to $300k_{\mathrm{B}}T$. For DNAs of lengths $N=40$ to 100 base pairs (bps) with a large initial bubble in their middle, long closure times of 0.1 to $100\mu$s are found. The bubble starts winding from both ends until it reaches a $\approx 10$ bp metastable state due to the large elastic energy stored in the bubble. The final closure is limited by three competing mechanisms depending on ${\kappa }_{\varphi }$ and $N$: arms diffusion until their alignment, bubble diffusion along the DNA until one end is reached, or local Kramers process (crossing over a torsional energy barrier). For clamped ends or long DNAs, the closure occurs via this last temperature-activated mechanism, yielding a good quantitative agreement with the experiments.

In this work the instability of the Taylor-Couette flow for Newtonian and non-Newtonian fluids (dilatant and pseudoplastic fluids) is investigated for cases of finite aspect ratios. The study is conducted numerically using the lattice Boltzmann method (LBM). In many industrial applications, the apparatuses and installations drift away from the idealized case of an annulus of infinite length, and thus the end caps effect can no longer be ignored. The inner cylinder is rotating while the outer one and the end walls are maintained at rest. The lattice two-dimensional nine-velocity (D2Q9) Boltzmann model developed from the Bhatnagar-Gross-Krook approximation is used to obtain the flow field for fluids obeying the power-law model. The combined effects of the Reynolds number, the radius ratio, and the power-law index $n$ on the flow characteristics are analyzed for an annular space of finite aspect ratio. Two flow modes are obtained: a primary Couette flow (CF) mode and a secondary Taylor vortex flow (TVF) mode. The flow structures so obtained are different from one mode to another. The critical Reynolds number Re${}_c$ for the passage from the primary to the secondary mode exhibits the lowest value for the pseudoplastic fluids and the highest value for the dilatant fluids. The findings are useful for studies of the swirling flow of non-Newtonians fluids in axisymmetric geometries using LBM. The flow changes from the CF to TVF and its structure switches from the two-cells to four-cells regime for both Newtonian and dilatant fluids. Contrariwise for pseudoplastic fluids, the flow exhibits 2-4-2 structure passing from two-cells to four cells and switches again to the two-cells configuration. Furthermore, the critical Reynolds number presents a monotonic increase with the power-law index $n$ of the non-Newtonian fluid, and as the radius ratio grows, the transition flow regimes tend to appear for higher critical Reynolds numbers.

Air plasma density decay in a filament produced by an intense femtosecond laser pulse in an external electric field was investigated experimentally and theoretically. It was demonstrated by means of the terahertz scattering technique that the rate of plasma decay decreases with increasing electric field. At the electric field of 7 kV/cm the lifetime of plasma with the density above ${10}^{16}$ cm${}^{-3}$ was prolonged from 0.5 ns to 1 ns. Numerical simulation of electron density decay and electron temperature evolution was performed, taking into consideration dissociative and three-body electron-ion recombination as well as formation of complex positive ions. The simulation showed that under the electric field the electron temperature evolves nonmonotonically and passes through a minimum due to varying contribution of electron-ion collisions to electron heating in the field. The rate of three-body electron recombination with O${}_2$${}^{+}$ ions of $2\times {10}^{-19}($300$/$T${}_e{)}^{9/2}$ cm${}^6$/s was found from the experimental measurements at electron temperatures in the 0.25–0.4 eV range and electron densities in the ${10}^{15}$$-{10}^{17}$ cm${}^{-3}$ range.

Owing to its conceptual simplicity and computational efficiency, the pseudopotential multiphase lattice Boltzmann (LB) model has attracted significant attention since its emergence. In this work, we aim to extend the pseudopotential LB model to simulate multiphase flows at large density ratio and relatively high Reynolds number. First, based on our recent work [Q. Li, K. H. Luo, and X. J. Li, Phys. Rev. E 86, 016709 (2012)], an improved forcing scheme is proposed for the multiple-relaxation-time pseudopotential LB model in order to achieve thermodynamic consistency and large density ratio in the model. Next, through investigating the effects of the parameter $a$ in the Carnahan-Starling equation of state, we find that the interface thickness is approximately proportional to $1/\sqrt{a}$. Using a smaller $a$ will lead to a wider interface thickness, which can reduce the spurious currents and enhance the numerical stability of the pseudopotential model at large density ratio. Furthermore, it is found that a lower liquid viscosity can be gained in the pseudopotential model by increasing the kinematic viscosity ratio between the vapor and liquid phases. The improved pseudopotential LB model is numerically validated via the simulations of stationary droplet and droplet oscillation. Using the improved model as well as the above treatments, numerical simulations of droplet splashing on a thin liquid film are conducted at a density ratio in excess of 500 with Reynolds numbers ranging from 40 to 1000. The dynamics of droplet splashing is correctly reproduced and the predicted spread radius is found to obey the power law reported in the literature.

The conventional theory of homogeneous and heterogeneous nucleation in a supersaturated vapor is tested by Monte Carlo simulations of the lattice gas (Ising) model with nearest-neighbor attractive interactions on the simple cubic lattice. The theory considers the nucleation process as a slow (quasistatic) cluster (droplet) growth over a free energy barrier $\Delta F^{*}$, constructed in terms of a balance of surface and bulk term of a critical droplet of radius $R^{*}$, implying that the rates of droplet growth and shrinking essentially balance each other for droplet radius $R=R^{*}$. For heterogeneous nucleation at surfaces, the barrier is reduced by a factor depending on the contact angle. Using the definition of physical clusters based on the Fortuin-Kasteleyn mapping, the time dependence of the cluster size distribution is studied for quenching experiments in the kinetic Ising model and the cluster size ${\ell }^{*}$ where the cluster growth rate changes sign is estimated. These studies of nucleation kinetics are compared to studies where the relation between cluster size and supersaturation is estimated from equilibrium simulations of phase coexistence between droplet and vapor in the canonical ensemble. The chemical potential is estimated from a lattice version of the Widom particle insertion method. For large droplets it is shown that the physical clusters have a volume consistent with the estimates from the lever rule. Geometrical clusters (defined such that each site belonging to the cluster is occupied and has at least one occupied neighbor site) yield valid results only for temperatures less than 60$\%$ of the critical temperature, where the cluster shape is nonspherical. We show how the chemical potential can be used to numerically estimate $\Delta F^{*}$ also for nonspherical cluster shapes.

Quantum dynamics of a particle in the vicinity of a hyperbolic point is considered. Expectation values of dynamical variables are calculated, and the singular behavior is analyzed. Exponentially fast extension of quantum dynamics is obtained, and conditions for this realization are analyzed.

This paper analyzes the effect of particle-hole symmetry on the behavior of the tracer diffusion coefficient as well as the jump diffusion coefficient. The coefficients are obtained by performing a random walk of individual atoms in a two-dimensional square lattice at monolayer, using the $n$-fold way Monte Carlo simulation. Different hopping mechanisms have been introduced to study the effect of particle-hole symmetry. For hopping kinetics where the initial-state interactions are involved, the diffusion coefficient at high coverage falls several orders of magnitude due to the effect of particle-hole symmetry. For hopping kinetics where the final-state interactions are present, the effect is the opposite. For those involving both initial- and final-state interactions, like the so-called interaction kinetics, the effect of particle-hole symmetry is also discussed. This effect seems to be critical for repulsive lateral interactions, for which the behavior of the diffusion coefficients is modified by introducing the particle-hole symmetry condition.

Phenotypic fluctuations and plasticity can generally affect the course of evolution, a process known as the Baldwin effect. Several studies have recast this effect and claimed that phenotypic plasticity accelerates evolutionary rate (the Baldwin expediting effect); however, the validity of this claim is still controversial. In this study, we investigate the evolutionary population dynamics of a quantitative genetic model under a multipeaked fitness landscape, in order to evaluate the validity of the effect. We provide analytical expressions for the evolutionary rate and average population fitness. Our results indicate that under a multipeaked fitness landscape, phenotypic fluctuation always accelerates evolutionary rate, but it decreases the average fitness. As an extreme case of the trade-off between the rate of evolution and average fitness, phenotypic fluctuation is shown to accelerate the error catastrophe, in which a population fails to sustain a high-fitness peak. In the context of our findings, we discuss the role of phenotypic plasticity in adaptive evolution.