Discrete random tessellations appear not infrequently in describing nucleation and growth transformations. Generally, several non-Euclidean metrics are possible in this case. Previously [A. Korobov, Phys. Rev. B 76, 085430 (2007)] continual analogs of such tessellations have been studied. Here one of the simplest discrete varieties of the Kolmogorov-Johnson-Mehl-Avrami model, namely, the model with von Neumann neighborhoods, has been examined per se, i.e., without continualization. The tessellation is uniform in the sense that domain boundaries consist of tiles. Similarities and distinctions between discrete and continual models are discussed.

The spatial structure and dynamics of hen egg white lysozyme have been investigated by small-angle and inelastic neutron scattering. Analysis of the results was carried using the fractal approach, which allowed determination of the fractal and fracton dimensions of lysozyme, i.e., consideration of the protein structure and dynamics by using a unified approach. Small-angle neutron scattering studies of thermal denaturation of lysozyme have revealed changes in the fractal dimension in the vicinity of the thermal denaturation temperature that reflect changes in the spatial organization of protein.

Actin polymerization time courses can exhibit rich nonequilibrium dynamics that have not yet been accurately described by simplified rate equations. Sophisticated stochastic simulations and elaborate recursion schemes have been used to model the nonequilibrium dynamics resulting from the hydrolysis and subsequent exchange of the nucleotide bound within the actin molecules. In this work, we use a truncation approach to derive a set of readily accessible deterministic rate equations which are significantly simpler than previous attempts at such modeling. These equations may be incorporated into whole-cell motility models which otherwise quickly become computationally inaccessible if polymerization of individual actin filaments is stochastically simulated within a virtual cell. Our equations accurately predict the relative concentrations of both monomeric and polymerized actin in differing nucleotide hydrolysis states throughout entire polymerization time courses nucleated via seed filaments. We extend our model to include the effects of capping protein. We also detail how our rate-equation method may be used to extract key parameters from experimental data.

We study the effect of membrane viscosity in the dynamics of liquid membranes—possibly with free or internal boundaries—driven by conservative forces (curvature elasticity and line tension) and dragged by the bulk dissipation of the ambient fluid and the friction occurring when the amphiphilic molecules move relative to each other. To this end, we formulate a continuum model which includes a form of the governing equations for a two-dimensional viscous fluid moving on a curved, time-evolving surface. The effect of membrane viscosity has received very limited attention in previous continuum studies of the dynamics of fluid membranes, although recent coarse-grained discrete simulations suggest its importance. By applying our model to the study of vesiculation and membrane fusion in a simplified geometry, we conclude that membrane viscosity plays a dominant role in the relaxation dynamics of fluid membranes of sizes comparable to those found in eukaryotic cells, and is not negligible in many large synthetic systems of current interest.

Polar liquid crystalline phases are relevant for fluid liquid crystal phases observed in banana liquid crystals as well as for a class of polymeric liquid crystalline materials investigated recently. In this Brief Report we present the reversible dynamics for polar nematic liquid crystals with $C_{\infty v}$ symmetry, where the macroscopic polarization representing polar order acts as an independent macroscopic variable. We find reversible coupling terms, for example, between flow and temperature and concentration gradients specific for the existence of a polar preferred direction. We suggest concrete experiments to check the importance of the reversible dynamic cross-coupling terms presented here.

We study a simplified scheme of $k$ coupled autocatalytic reactions, previously introduced by Togashi and Kaneko. The role of stochastic fluctuations is elucidated through the use of the van Kampen system-size expansion and the results compared with direct stochastic simulations. Regular temporal oscillations are predicted to occur for the concentration of the various chemical constituents, with an enhanced amplitude resulting from a resonance which is induced by the intrinsic graininess of the system. The associated power spectra are determined and have a different form depending on the number of chemical constituents $k$. We make detailed comparisons in the two cases $k=4$ and $k=8$. Agreement between the theoretical and numerical results for the power spectrum is good in both cases. The resulting spectrum is especially interesting in the $k=8$ system, since it has two peaks, which the system-size expansion is still able to reproduce accurately.

This paper considers nonlinear dynamics in an ensemble of uncoupled lasers, each being a limit-cycle oscillator, which are driven by the same external white Gaussian noise. As the external-noise strength increases, there is an onset of synchronization and then subsequent loss of synchrony. Local analysis of the laser equations shows that synchronization becomes unstable via stochastic bifurcation to chaos, defined as a passing of the largest Lyapunov exponent through zero. The locus of this bifurcation is calculated in the three-dimensional parameter space defined by the Hopf parameter, amount of amplitude-phase coupling, and external-noise strength. Numerical comparison between the laser system and the normal form of Hopf bifurcation uncovers a square-root law for this stochastic bifurcation as well as strong enhancement in noise-induced chaos due to the laser’s relaxation oscillation.

We present a mathematical approach that simplifies the theoretical treatment of electromagnetic localization in random media and leads to closed-form analytical solutions. Starting with the assumption that the dielectric permittivity of the medium has delta-correlated spatial fluctuations, and using Ito’s lemma, we derive a linear stochastic differential equation for a one-dimensional random medium. The equation leads to localized wave solutions. The localized wave solutions have a localization length that scales as $L\sim {\omega }^{-2}$ for low frequencies whereas in the high-frequency regime this length behaves as $L\sim {\omega }^{-2/3}$.

We explain that the effects of electron degeneracy on the calculation of ionization equilibrium can be implemented and simply realized as virtual upshifting in the ionization energies in the classical Saha equation. Previous quantitative findings indicating depressed quantum statistical ionization compared to classical ionization are derived and abstracted in an analytical form. A simple ready-to-use approximate formula for the upshifting in ionization energies due to partial degeneracy is presented and used to work a sample problem.

We experimentally investigated the thermal escape from a metastable state in a Josephson tunnel junction subjected to an oscillating effective temperature. A minimum of the average escape time is observed at certain oscillation frequency. Our results confirm that the resonant activation can be caused not only by the oscillating barrier but also by the oscillating temperature. The linear dependence of the minimum average escape time on the resonant frequency suggests that the correlation between the oscillation and the escape process leads to the resonant escape.

In this paper we give explicit examples of long-range correlated stationary Markovian processes $y\left(t\right)$ where the stationary probability density function (pdf) shows tails which are Gaussian or exponential. These processes are obtained by simply performing appropriate coordinate transformations of a specific power–law correlated additive process $x\left(t\right)$, already known in the literature, whose pdf shows power-law tails. We give analytical and numerical evidences that although the new processes are Markovian and have Gaussian or exponential tails, their autocorrelation function shows a power-law decay with logarithmic corrections. For a generic continuous and monotonously increasing coordinate transformation, we also analytically investigate what is the relationship between the asymptotic decay of the autocorrelation function and the tails of the stationary pdf. Extreme events seem to be associated to long-range correlated processes with power-law decaying autocorrelation function. However, the occurrence of extreme events is not necessary in order to have more general long-range correlated processes in which the autocorrelation shows a slow decay characterized by a power-law times a correction function such as the logarithm. Our results help in clarifying that even in the context of stationary Markovian processes long-range dependencies are not necessarily associated to the occurrence of extreme events. Moreover, our results can be relevant in the modeling of complex systems with long memory. In fact, we provide simple stationary processes associated to Langevin equations with white noise thus confirming that long-memory effects can be modeled in the context of continuous time stationary Markovian processes.

We derive an effective boundary condition for dense granular flow taking into account the effect of the heterogeneity of the force network on sliding friction dynamics. This yields an intermediate boundary condition which lies in the limit between no slip and Coulomb friction; two simple functions relating wall stress, velocity, and velocity variance are found from numerical simulations. Moreover, we show that this effective boundary condition corresponds to Navier slip condition when the model of G. D. R. Midi [Eur. Phys. J. E 14, 341 (2004)] is assumed to be valid, and that the slip length depends on the length scale that characterizes the system, viz. the particle diameter.

The steady state of a vibrated granular gas confined by a movable piston on top is discussed. Particular attention is given to the hydrodynamic boundary conditions to be used when solving the inelastic Navier-Stokes equations. The relevance of an exact general condition relating the grain fluxes approaching and moving away from each of the walls is emphasized. It is shown how it can be used to get a consistent hydrodynamic description of the boundaries. The obtained expressions for the fields do not contain any undetermined parameter. Comparison of the theoretical predictions with molecular-dynamics simulation results is carried out, and a good agreement is observed for low density and not too large inelasticity. A practical way of introducing small finite density corrections to the dilute limit theory is proposed to improve the accuracy of the theory.

The nonequilibrium dynamics of an amorphous solid is studied with a soft-spin model. We show that the aging behavior in the glassy state follows a modified Kohlrausch-Williams-Watts form similar to that obtained in Lunkenheimer et al. [Phys. Rev. Lett. 95, 055702 (2005)] from analysis of the dielectric loss data. The nature of the fluctuation-dissipation theorem violation is also studied in time as well as correlation windows.

Transcriptional pulsing has been observed in both prokaryotes and eukaryotes and plays a crucial role in cell-to-cell variability of protein and mRNA numbers. An important issue is how the time constants associated with episodes of transcriptional bursting and mRNA and protein degradation rates lead to different cellular mRNA and protein distributions, starting from the transient regime leading to the steady state. We address this by deriving and then investigating the exact time-dependent solution of the master equation for a transcriptional pulsing model of mRNA distributions. We find a plethora of results. We show that, among others, bimodal and long-tailed (power-law) distributions occur in the steady state as the rate constants are varied over biologically significant time scales. Since steady state may not be reached experimentally we present results for the time evolution of the distributions. Because cellular behavior is determined by proteins, we also investigate the effect of the different mRNA distributions on the corresponding protein distributions using numerical simulations.

We investigate a two-dimensional problem of an isolated self-interacting end-grafted polymer, pulled by one end. In the thermodynamic limit, we find that the model has only two different phases, namely a collapsed phase and a stretched phase. We show that the phase diagram obtained by Kumar et al. [Phys. Rev. Lett. 98, 128101 (2007)] for small systems, where differences between various statistical ensembles play an important role, differs from the phase diagram obtained here in the thermodynamic limit.

We extend the phase-field-crystal model to accommodate exact atomic configurations and vacancies by requiring the order parameter to be non-negative. The resulting theory dictates the number of atoms and describes the motion of each of them. By solving the dynamical equation of the model, which is a partial differential equation, we are essentially performing molecular dynamics simulations on diffusive time scales. To illustrate this approach, we calculate the two-point correlation function of a fluid.

We propose and study a model of molecular motor-induced ordering in a cytoskeletal filament solution for the semidilute case. Motors attach to a pair of filaments and walk along the pair bringing them into closer alignment. In the semidilute regime multiple motors can bind a filament to several others and, for a critical motor density, induce a transition to an ordered phase with a nonzero mean orientation. The motors, on the one hand, cause closer filament alignment, and, on the other hand, induce fluctuations that are dependent on the relative orientation of the filaments to which the motors are attached. We develop a spatially homogenous, mean-field theory that explicitly accounts for a force-dependent detachment rate of motors, which in turn affects the mean and the fluctuations of the net force acting on a filament. This model considers each filament to be in motor contact with all other filaments in the solution. We show that the transition to the oriented state changes from second order to first order when the force-dependent detachment becomes important.

Long-lasting small traveling clusters are studied in the Hamiltonian mean-field model by comparing between attractive and repulsive interactions. Nonlinear Landau damping theory predicts that a Gaussian momentum distribution on a spatially homogeneous background permits the existence of traveling clusters in the repulsive case, as in plasma systems, but not in the attractive case. Nevertheless, extending the analysis to a two-parameter family of momentum distributions of Fermi-Dirac type, we theoretically predict the existence of traveling clusters in the attractive case; these findings are confirmed by direct $N$-body numerical simulations. The parameter region with the traveling clusters is much reduced in the attractive case with respect to the repulsive case.

We report the results of a series of molecular dynamics simulations of water inside a carbon-slit pore at supercritical conditions. A range of densities corresponding from liquid $\left(0.66\mathrm{g}{\mathrm{cm}}^{-3}\right)$ to gas environments $\left(0.08\mathrm{g}{\mathrm{cm}}^{-3}\right)$ at the supercritical temperature of $673\mathrm{K}$ were considered. Our findings are compared with previous studies of liquid water confined in graphene nanochannels at ambient and high temperatures, and indicate that the microscopic structure of water evolves from hydrogen bond networks characteristic of hot dense liquids to looser arrangements where the dominant units are water monomers and dimers. Water permittivity was found to be very small at low densities, with a tendency to grow with density and to reach typical values of unconfined supercritical water at $0.66\mathrm{g}{\mathrm{cm}}^{-3})$. In supercritical conditions, the residence time of water at interfaces is roughly similar to that of water in the central regions of the slabs, if the size of the considered region is taken into account. That time span is long enough to compute dynamical properties such as diffusion or spectral densities. Water diffusion in supercritical states is much faster at low densities, and it is produced in such a way that, at interfaces, translational diffusion is mainly produced along planes parallel to the carbon walls. Spectral frequency shifts depend on several factors, being temperature and density effects the most relevant. However, we can observe corrections due to confinement, important both at the graphene interface and in the central region of the water slab.