We have studied the dynamics of chloride and potassium ions in the interior of the Outer membrane porin F (OmpF) under the influence of an external electric field. From the results of extensive all-atom molecular dynamics (MD) simulations of the system, we computed several first-passage-time (FPT) quantities to characterize the dynamics of the ions in the interior of the channel. Such FPT quantities obtained from MD simulations demonstrate that it is not possible to describe the dynamics of chloride and potassium ions inside the whole channel with a single constant diffusion coefficient. However, we showed that a valid, statistically rigorous description in terms of a constant diffusion coefficient $D$ and an effective deterministic force $F_{\text{eff}}$ can be obtained after appropriate subdivison of the channel in different regions suggested by the x-ray structure. These results have important implications for popular simplified descriptions of channels based on the one-dimensional Poisson-Nernst-Planck equations. Also, the effect of entropic barriers on the diffusion of the ions is identified and briefly discussed.

We discover that a synergistically amplifying role of stabilizing membrane proteins and continuous lipid recycling can explain the physics governing the stability, polydispersity, and dynamics of lipid raft domains in plasma membranes of biological cells. We establish the conjecture using a generalized order parameter based on theoretical formalism, endorsed by detailed scaling arguments and domain mapping. Quantitative agreements with morphological distributions of raft complexes, as obtained from Förster resonance energy transfer based visualization, support the present theoretical conjecture.

We have calculated the viscosity and self-diffusion coefficients of plutonium in the liquid phase using quantum molecular dynamics (QMD) and in the dense-plasma phase using orbital-free molecular dynamics (OFMD), as well as in the intermediate warm dense matter regime with both methods. Our liquid metal results for viscosity are about 40% lower than measured experimentally, whereas a previous calculation using an empirical interatomic potential (modified embedded-atom method) obtained results 3–4 times larger than the experiment. The QMD and OFMD results agree well at the intermediate temperatures. The calculations in the dense-plasma regime for temperatures from 50 to 5000 eV and densities about 1–5 times ambient are compared with the one-component plasma (OCP) model, using effective charges given by the average-atom code inferno. The inferno-OCP model results agree with the OFMD to within about a factor of 2, except for the viscosity at temperatures less than about 100 eV, where the disagreement is greater. A Stokes-Einstein relationship of the viscosities and diffusion coefficients is found to hold fairly well separately in both the liquid and dense-plasma regimes.

We investigate colloidal suspensions under shear flow through numerical experiments. By measuring the time-correlation function of a bond-orientational order parameter, we find a divergent time scale near a transition point from a disordered fluid phase to an ordered fluid phase, where the order is characterized by a nonzero value of the bond-orientational order parameter. We also present a phase diagram in the $(\rho ,{\mathrm{\gamma ̇}}^{\mathrm{ex}})$ plane, where $\rho$ is the density of the colloidal particles and ${\mathrm{\gamma ̇}}^{\mathrm{ex}}$ is the shear rate of the solvent. The transition line in the phase diagram terminates at the equilibrium transition point, while a critical region near the transition line vanishes continuously as ${\mathrm{\gamma ̇}}^{\mathrm{ex}}\to 0$.

Human migration has profound effects on social change. The introduction of success-driven migration to selfish individuals has revealed significant effects on the promotion of cooperation in spatial evolutionary games. In this study, we generalize the interaction structure from a spatial lattice to complex networks, such as Erdős-Renyi random networks and Barabási-Albert scale-free networks. Keeping the topology of networks, we investigate the robustness of cooperation when individuals can make decision errors. Numerical simulations demonstrate the effectiveness of success-driven migration on the enhancement of cooperation confronted with individual decision-making mistakes. In contrast, even a very low probability of decision errors can decrease the level of cooperation without mobility. Statistical analysis further exhibits the relation between network topology and migratory behavior.

The distribution of the first passage times (FPT) of a one-dimensional random walker to a target site follows a power law $F(t)~t^{-3/2}$. We generalize this result to another situation pertinent to compact exploration and consider the FPT of a random walker with specific source and target points on an infinite fractal structure with spectral dimension $d_s<2$. We show that the probability density of the first return to the origin has the form $F(t)~t^{d_s/2-2}$, and the FPT to a specific target at distance $r$ follows the law $F(\mathbf{r},t)~r^{d_w-d_f}{t}^{d_s/2-2}$, where $d_w$ and $d_f$ are the walk dimension and the fractal dimension of the structure, respectively. The distance dependence of $F(\mathbf{r},t)$ reproduces the one of the mean FPT of a random walk in a confined domain.

We study heat conduction in a harmonic crystal whose bulk dynamics is supplemented by random reversals (flips) of the velocity of each particle at a rate $\lambda$. The system is maintained in a nonequilibrium stationary state (NESS) by contacts with white-noise Langevin reservoirs at different temperatures. We show that the one-body and pair correlations in this system are the same (after an appropriate mapping of parameters) as those obtained for a model with self-consistent reservoirs. This is true both for the case of equal and random (quenched) masses. While the heat conductivity in the NESS of the ordered system is known explicitly, much less is known about the random mass case. Here we investigate the random system with velocity flips. We improve the bounds on the Green-Kubo conductivity obtained by Bernardin [J. Stat. Phys. 133, 417 (2008)]. The conductivity of the one-dimensional system is then studied both numerically and analytically. This sheds some light on the effect of noise on the transport properties of systems with localized states caused by quenched disorder.

In a recent paper [F. Vega Reyes et al., Phys. Rev. Lett. 104, 028001 (2010)] we presented a preliminary description of a special class of steady Couette flows in dilute granular gases. In all flows of this class the viscous heating is exactly balanced by inelastic cooling. This yields a uniform heat flux and a linear relationship between the local temperature and flow velocity. The class (referred to as the LTu class) includes the Fourier flow of ordinary gases and the simple shear flow of granular gases as special cases. In the present paper we provide further support for this class of Couette flows by following four different routes, two of them being theoretical (Grad’s moment method of the Boltzmann equation and exact solution of a kinetic model) and the other two being computational (molecular dynamics and Monte Carlo simulations of the Boltzmann equation). Comparison between theory and simulations shows a very good agreement for the non-Newtonian rheological properties, even for quite strong inelasticity, and a good agreement for the heat flux coefficients in the case of Grad’s method, the agreement being only qualitative in the case of the kinetic model.

Energy absorption due to viscous friction in a dilute suspension of single-domain ferromagnetic particles subjected to a rotating field is considered. The problem is treated in the framework of kinetic approach. The behavior of specific loss power (SLP) as a function of the field amplitude and frequency is studied. It is shown that for either of these parameters (while the other is kept constant) SLP first grows quadratically and then saturates. The cases of a rotating field and oscillating fields are compared, and the essential differences are revealed. The results obtained enable one to assess the allowable or optimal field parameters for a given magnetic suspension intended for rotational magneto-inductive heating.

The recently proposed universality near the glass transition [M. Tokuyama, Phys. Rev. E 80, 031503 (2009)] is tested for the dynamics of a single atom in ternary metallic glass-forming ${\mathrm{Cu}}_{60}{\mathrm{Ti}}_x{\mathrm{Zr}}_{40-x}$ melts by using molecular-dynamics simulations for different compositions, $x=$ 10, 20, and 30. First, a master curve for the dynamics of the atom, such as the mean-square and mean-fourth displacements, is shown to exist independently of $x$ if the long-time self-diffusion coefficient $D_S^L$ has the same value. Second, a master curve for the temperature dependence of $D_S^L$ is shown to exist independently of $x$. Finally, master curves for characteristic length and time scales of the atom are also shown to exist independently of $x$.

Motivated by the structure of networks of cross-linked cytoskeletal biopolymers, we study orientationally ordered phases in two-dimensional networks of randomly cross-linked semiflexible polymers. We consider permanent cross-links which prescribe a finite angle and treat them as quenched disorder in a semimicroscopic replica field theory. Starting from a fluid of un-cross-linked polymers and small polymer clusters (sol) and increasing the cross-link density, a continuous gelation transition occurs. In the resulting gel, the semiflexible chains either display long-range orientational order or are frozen in random directions depending on the value of the crossing angle, the cross-link concentration, and the stiffness of the polymers. A crossing angle $\theta ~2\pi /M$ leads to long-range $M$-fold orientational order, for example, “hexatic” or “tetratic” for $\hspace{0.5em}\theta ={60}^{°}$ or $\hspace{0.5em}{90}^{°}$, respectively. The transition to the orientationally ordered state is discontinuous and the critical cross-link density, which is higher than that of the gelation transition, depends on the bending stiffness of the polymers and the cross-link angle: The higher the stiffness and the lower the $M$, the lower is the critical number of cross-links. In between the sol and the long-range ordered state, we always expect a gel which is a statistically isotropic amorphous solid with random positional and random orientational localization of the participating polymers.

Some dynamical properties of time-dependent driven elliptical-shaped billiards are studied. It was shown that for conservative time-dependent dynamics the model exhibits Fermi acceleration [Phys. Rev. Lett. 100, 014103 (2008).] On the other hand, it was observed that damping coefficients upon collisions suppress such a phenomenon [Phys. Rev. Lett. 104, 224101 (2010)]. Here, we consider a dissipative model under the presence of in-flight dissipation due to a drag force which is assumed to be proportional to the square of the velocity of the particle. Our results reinforce that dissipation leads to a phase transition from unlimited to limited energy growth. The behavior of the average velocity is described using scaling arguments.

A subcritical Hopf bifurcation is prepared in a multisection semiconductor laser. In the free-running state, hysteresis is absent due to noise-induced escape processes. The missing branches are recovered by stabilizing them against noise through application of phase-sensitive noninvasive delayed optical feedback control. The same type of control is successfully used to stabilize the unstable pulsations born in the Hopf bifurcation. This experimental finding represents an optical counterexample to the so-called odd-number limitation of delayed feedback control. However, as a leftover of the limitation, the domains of control are extremely small.

The effect of electric fields on metal surfaces is fairly well studied, resulting in numerous analytical models developed to understand the mechanisms of ionization of surface atoms observed at very high electric fields, as well as the general behavior of a metal surface in this condition. However, the derivation of analytical models does not include explicitly the structural properties of metals, missing the link between the instantaneous effects owing to the applied field and the consequent response observed in the metal surface as a result of an extended application of an electric field. In the present work, we have developed a concurrent electrodynamic–molecular dynamic model for the dynamical simulation of an electric-field effect and subsequent modification of a metal surface in the framework of an atomistic molecular dynamics (MD) approach. The partial charge induced on the surface atoms by the electric field is assessed by applying the classical Gauss law. The electric forces acting on the partially charged surface atoms (Lorentz and Coulomb) are then introduced in the MD algorithm to correct the atomic motion in response to the applied field. The enhancement factor at sharp features on the surface for the electric field and the assessment of atomic charges are discussed. The results obtained by the present model compare well with the experimental and density-functional theory results.

Equations of fast phase transitions, in which the phase boundaries move with velocities comparable with the atomic diffusion speed or with the speed of local structural relaxation, are analyzed. These equations have a singular perturbation due to the second derivative of the order parameter with respect to time, which appears due to phenomenologically introduced local nonequilibrium. To develop unconditionally stable computational schemes, the Eyre theorem [D. J. Eyre, unpublished] proved for the classical equations, based on hypotheses of local equilibrium, is used. An extension of the Eyre theorem for the case of equations for fast phase transitions is given. It is shown that the expansion of the free energy on contractive and expansive parts, suggested by Eyre for the classical equations of Cahn-Hilliard and Allen-Cahn, is also true for the equations of fast phase transitions. Grid approximations of these equations lead to gradient-stable algorithms with an arbitrary time step for numerical modeling, ensuring monotonic nonincrease of the free energy. Special examples demonstrating the extended Eyre theorem for fast phase transitions are considered.

We have studied the properties of a classical $N_S$-body system coupled to a bath containing $N_B$-body harmonic oscillators, employing an $(N_S+N_B)$ model that is different from most of the existing models with $N_S=1$. We have performed simulations for $N_S$-oscillator systems, solving $2(N_S+N_B)$ first-order differential equations with $N_S\simeq 1$–10 and $N_B\simeq 10$–1000, in order to calculate the time-dependent energy exchange between the system and the bath. The calculated energy in the system rapidly changes while its envelope has a much slower time dependence. Detailed calculations of the stationary energy distribution of the system $f_S(u)$ ($u$: an energy per particle in the system) have shown that its properties are mainly determined by $N_S$ but weakly depend on $N_B$. The calculated $f_S(u)$ is analyzed with the use of the $\Gamma$ and $q$-$\Gamma$ distributions: the latter is derived with the superstatistical approach (SSA) and microcanonical approach (MCA) to the nonextensive statistics, where $q$ stands for the entropic index. Based on analyses of our simulation results, a critical comparison is made between the SSA and MCA. Simulations have been performed also for the $N_S$-body ideal-gas system. The effect of the coupling between oscillators in the bath has been examined by additional ($N_S+N_B$) models that include baths consisting of coupled linear chains with periodic and fixed-end boundary conditions.

A partially annealed mean-field spin-glass model with a locally embedded pattern is studied. The model consists of two dynamical variables, spins and interactions, that are in contact with thermal baths at temperatures $T_S$ and $T_J$, respectively. Unlike the quenched system, characteristic correlations among the interactions are induced by the partial annealing. The model exhibits three phases: paramagnetic, ferromagnetic and spin-glass. In the ferromagnetic phase, the embedded pattern is stably realized. The phase diagram depends significantly on the ratio of the two temperatures, $n=T_S/T_J$. In particular, a reentrant transition from the embedded ferromagnetic to the spin-glass phase with $T_S$ decreasing is found only below a certain value of $n$. This indicates that above the critical value $n_c$ the embedded pattern is supported by a local field from a nonembedded region. Some equilibrium properties of the interactions in the partial annealing are also discussed in terms of frustration.

The problem of tracer advection in random self-similar (fractal) media with strong anisotropy is solved. Transport regimes and concentration tails are described depending on the rate of velocity correlation function decay and on the degree of anisotropy. The influence of the finite correlation length of the fractal medium on transport regimes is analyzed. The derivation is conducted by means of scaling analysis.

We demonstrate supersymmetry in the counting statistics of stochastic particle currents and use it to derive exact nonperturbative relations for the statistics of currents induced by arbitrarily fast time-dependent protocols.