Motor proteins actively contract the actin cytoskeleton of cells and thereby give rise to nonequilibrium fluctuations as well as changes in the architecture of the cytoskeleton. Here, we show, by video microrheology of a reconstituted cytoskeleton, that motors generate time-dependent nonequilibrium fluctuations, which evolve as the network is remodeled. At earlier times, the fluctuation spectrum is dominated by strong non-Gaussian fluctuations, which arise from large displacements. At later times, directed displacements are infrequent and finally disappear. We show that these effects are due to contractile coarsening of the network into large actin-myosin foci.

The thermodynamic properties of the dipolar hard-sphere fluid are studied using theory and simulation. A new theory is derived using a convenient mathematical approximation for the Helmholtz free energy relative to that for the hard-sphere fluid. The approximation is designed to give the correct low-density virial expansion. New theoretical and numerical results for the fourth virial coefficient are given. Predictions of thermodynamic functions for dipolar coupling constants $\lambda =1$ and 2 show excellent agreement with simulation results, even at the highest value of the particle volume fraction $\varphi$. For higher values of $\lambda$, there are deviations at high volume fractions, but the correct low-density behavior is retained. The theory is compared critically against the established thermodynamic perturbation theory; it gives significant improvements at low densities and is more convenient in terms of the required numerics. Dipolar hard spheres provide a basic model for ferrofluids, and the theory is accurate for typical experimental parameters $\lambda \lesssim 2$ and $\varphi \lesssim 0.1$. This is demonstrated explicitly by fitting osmotic equations of state for real ferrofluids measured recently by analytical centrifugation.

The stochastic entropy generated during the evolution of a system interacting with an environment may be separated into three components, but only two of these have a non-negative mean. The third component of entropy production is associated with the relaxation of the system probability distribution towards a stationary state and with nonequilibrium constraints within the dynamics that break detailed balance. It exists when at least some of the coordinates of the system phase space change sign under time reversal, and when the stationary state is asymmetric in these coordinates. We illustrate the various components of entropy production, both in detail for particular trajectories and in the mean, using simple systems defined on a discrete phase space of spatial and velocity coordinates. These models capture features of the drift and diffusion of a particle in a physical system, including the processes of injection and removal and the effect of a temperature gradient. The examples demonstrate how entropy production in stochastic thermodynamics depends on the detail that is included in a model of the dynamics of a process. Entropy production from such a perspective is a measure of the failure of such models to meet Loschmidt's expectation of dynamic reversibility.

In many physical systems there is a time delay before an applied input (stimulation) has an impact on the output (response), and the quantification of this delay is of paramount interest. If the response can only be observed on top of an indistinguishable background signal, the estimation can be highly unreliable, unless the background signal is accounted for in the analysis. In fact, if the background signal is ignored, however small it is compared to the response and however large the delay is, the estimate of the time delay will go to zero for any reasonable estimator when increasing the number of observations. Here we propose a unified concept of response latency identification in event data corrupted by a background signal. It is done in the context of information transfer within a neural system, more specifically on spike trains from single neurons. The estimators are compared on simulated data and the most suitable for specific situations are recommended.

This paper studies the single-file diffusion process on a linear chain of identical pointlike particles with multiple-site occupation confined in a one-dimensional box. The particles are noninteracting, except that double occupancy is forbidden. When particles are confined in a finite box, the final stage is saturation. By means of combinatorial analysis, an exact numerical evaluation of the saturation values for both the mean-square displacement (MSD) of a tracer particle and the center of mass of the system are obtained. Different initial distributions of particles are introduced. The time dependence of the MSD is obtained by means of Monte Carlo simulations. The values of the MSD for the tracer particles as well as the center of mass of the system depend on the size of the particle, the size of the box, and the initial distribution. Moreover, the transient regime depends on the initial distribution. In fact, the crossover from normal to subdiffusive regime is observed for random and alternate initial distributions, while superdiffusive diffusion appears for any stacked initial distributions. In all cases, it is shown that the collisions between particles do not determine the time exponent of the MSD. A simple expression for the transient regime is also obtained for the especial case of random initial distribution.

We implement molecular dynamics simulations in canonical ensemble to study the effect of confinement on a two-dimensional crystal of point particles interacting with an inverse power law potential proportional to $r^{-12}$ in a narrow channel. This system can describe colloidal particles at the air-water interface. It is shown that the system characteristics depend sensitively on the boundary conditions at the two walls providing the confinement. The walls exert perpendicular forces on their adjacent particles. The potential between walls and particles varies as the inverse power of ten. Structural quantities such as density profile, structure factor, and orientational order parameter are computed. It is shown that orientational order persists near the walls even at temperatures where the system in the bulk is in fluid state. The dependence of elastic constants, stress tensor elements, shear, and bulk moduli on density as well as the channel width is discussed. Moreover, the effect of channel incommensurability with the triangular lattice structure is discussed. It is shown that incommensurability notably affects the system properties. We compare our findings to those obtained by Monte Carlo simulations in Rici et al. [Phys. Rev. E 75, 011405 (2007)] and to the case with the periodic boundary condition along the channel width.

Maximally random jammed states of hard spheres are prototypical glasses. We study the small wavenumber $k$ behavior of the structure factor $S\left(k\right)$ of overcompressed million-sphere packings as a function of density up to the jammed state. We find both a precursor to the glassy jammed state evident long before the jamming density is reached and two associated growing length scales, one extracted from the volume integral of the direct correlation function $c\left(r\right)$ and the other from the small-$k$ behavior of the structure factor $S\left(k\right)$, that can diverge at the “critical” jammed state. We also define a nonequilibrium index $X$ and use it to demonstrate that the packings studied are intrinsically nonequilibrium in nature well before the critical state is reached. The extension of the results reported in the present work to supercooled atomic-liquid models in which the atoms interact with both repulsive and attractive forces is also discussed.

Throughout development, chemical cues are employed to guide the functional specification of underlying tissues while the spatiotemporal distributions of such chemicals can be influenced by the growth of the tissue itself. These chemicals, termed morphogens, are often modeled using partial differential equations (PDEs). The connection between discrete stochastic and deterministic continuum models of particle migration on growing domains was elucidated by Baker, Yates, and Erban [Bull. Math. Biol. 72, 719 (2010)] in which the migration of individual particles was modeled as an on-lattice position-jump process. We build on this work by incorporating a more physically reasonable description of domain growth. Instead of allowing underlying lattice elements to instantaneously double in size and divide, we allow incremental element growth and splitting upon reaching a predefined threshold size. Such a description of domain growth necessitates a nonuniform partition of the domain. We first demonstrate that an individual-based stochastic model for particle diffusion on such a nonuniform domain partition is equivalent to a PDE model of the same phenomenon on a nongrowing domain, providing the transition rates (which we derive) are chosen correctly and we partition the domain in the correct manner. We extend this analysis to the case where the domain is allowed to change in size, altering the transition rates as necessary. Through application of the master equation formalism we derive a PDE for particle density on this growing domain and corroborate our findings with numerical simulations.

We demonstrate the existence of a percolationlike stiffness transition in fiber networks with a bidisperse orientation distribution and with fiber densities clearly above the geometrical and the ordinary stiffness transition. The fibers are oriented parallel and perpendicular to a strain direction and they have a large fiber aspect ratio. The stiffness $K$ of the fiber nets can be described by a scaling relation, $K\propto {\tau }^{\alpha }g[(\epsilon -{\epsilon }_c)/{\tau }^{-\beta }]$, where $\tau$ is the fraction of fibers parallel to strain. $g$ is a scaling function that is roughly described by a power law $g\left(x\right)\propto x^{\gamma }$ for stiffness above the transition and by a constant below the transition. The transition point is characterized by qualitative changes in the distribution of the elastic deformation energy of the fibers, the deformation mode of the fibers, the effective Poisson ratio of the nets, the distribution of elastic energy on fibers and cross links, and the ratio of elastic and viscous dissipation energy. This transition opens the possibility of extreme stiffness variations with minimal mesh manipulations in the vicinity of the transition (i.e., a stiffness gate). It is possible that this transition affects the mechanical behavior of the cytoskeleton in cells.

We report on a mean field theory of textured surface lubrication. We study the fluid flow dynamics occurring at the interface as a function of the texture characteristics, e.g. texture area density, shape and distribution of microstructures, and local slip lengths. The present results may be very important for the investigation of tailored microtextured surfaces for low-friction hydrodynamic applications.

In this work we apply point canonical transformations to solve some classes of nonautonomous, nonlinear Schrödinger equations, namely, those which possess specific cubic and quintic (time- and space-dependent) nonlinearities. In this way we generalize some procedures recently published which resort to an ansatz to the wave function and recover a time- and space-independent nonlinear equation which can be solved explicitly. The method applied here allows us to find wide localized (in space) soliton solutions to the nonautonomous, nonlinear Schrödinger equation. We also generalize the external potential which traps the system and the terms of the nonlinearities.

In this work we study localized solutions of a system of two coupled nonlinear Schrödinger equations, with the linear (potential) and nonlinear coefficients engendering spatial and temporal dependencies. Similarity transformations are used to convert the nonautonomous coupled equations into autonomous ones and we use the trial orbit method to help us solving them, presenting solutions in a general way. Numerical experiments are then used to verify the stability of the localized solutions.

We show that for quantum phase transitions with a single bosonic zero mode at the critical point, like the Dicke model and the Lipkin-Meshkov-Glick model, metric quantities such as fidelity, that is, the overlap between two ground states corresponding to two values ${\lambda }_1$ and ${\lambda }_2$ of the controlling parameter $\lambda$, depend only on the ratio $\eta =({\lambda }_1-{\lambda }_c)/({\lambda }_2-{\lambda }_c)$, where $\lambda ={\lambda }_c$ at the critical point. This scaling property is valid also for time-dependent quantities such as the Loschmidt echo, provided time is measured in units of the inverse frequency of the critical mode.

We give the exact critical frontier of the Potts model on bowtie lattices. For the case of $q=1$, the critical frontier yields the thresholds of bond percolation on these lattices, which are exactly consistent with the results given by Ziff et al. [J. Phys. A 39, 15083 (2006)]. For the $q=2$ Potts model on a bowtie A lattice, the critical point is in agreement with that of the Ising model on this lattice, which has been exactly solved. Furthermore, we do extensive Monte Carlo simulations of the Potts model on a bowtie A lattice with noninteger $q$. Our numerical results, which are accurate up to seven significant digits, are consistent with the theoretical predictions. We also simulate the site percolation on a bowtie A lattice, and the threshold is $s_c=0.5479148\left(7\right)$. In the simulations of bond percolation and site percolation, we find that the shape-dependent properties of the percolation model on a bowtie A lattice are somewhat different from those of an isotropic lattice, which may be caused by the anisotropy of the lattice.

In materials science the phase-field crystal approach has become popular to model crystallization processes. Phase-field crystal models are in essence Landau-Ginzburg-type models, which should be derivable from the underlying microscopic description of the system in question. We present a study on classical density functional theory in three stages of approximation leading to a specific phase-field crystal model, and we discuss the limits of applicability of the models that result from these approximations. As a test system we have chosen the three-dimensional suspension of monodisperse hard spheres. The levels of density functional theory that we discuss are fundamental measure theory, a second-order Taylor expansion thereof, and a minimal phase-field crystal model. We have computed coexistence densities, vacancy concentrations in the crystalline phase, interfacial tensions, and interfacial order parameter profiles, and we compare these quantities to simulation results. We also suggest a procedure to fit the free parameters of the phase-field crystal model. Thereby it turns out that the order parameter of the phase-field crystal model is more consistent with a smeared density field (shifted and rescaled) than with the shifted and rescaled density itself. In brief, we conclude that fundamental measure theory is very accurate and can serve as a benchmark for the other theories. Taylor expansion strongly affects free energies, surface tensions, and vacancy concentrations. Furthermore it is phenomenologically misleading to interpret the phase-field crystal model as stemming directly from Taylor-expanded density functional theory.

We describe how bend imposed on a nematic elastomer cantilever can be accommodated with little or no internal stress by the director rotating. Thus, for a range of imposed curvatures that we calculate, there is no countertorque. Equally nonclassically, in such beams there is associated transverse curvature (clasticity). When instead bend is induced by illumination which causes spatially dependent contractions, director rotation can also act to vitiate stresses, but then (anti-)clasticity and its suppression has to be resolved, sometimes at the cost of stress creation.

We have measured the flow of gas through single ion track pores in a polymer film using a mass spectroscopy technique. The pores are 12 $\mu$m long with diameters in the range of 50–1000 nm, and the flow was driven by pressure drops in the range 0–30 atm. When the mean free path is large compared to the pore diameter (large Knudsen number Kn), the flow rate is proportional to the pressure drop and the pore radius $R$ cubed, and is consistent with a model of diffusive scattering at the pore walls. For $\text{Kn}\le 0.1$, the hydrodynamic conductance increases, as predicted by standard kinetic theory models, and finally approaches the conventional Poiseuille value with zero slip length.

We consider an evolutionary prisoner's dilemma on a random network. We introduce a simple quantitative network-based parameter and show that it effectively predicts the success of cooperation in simulations on the network. The criterion is shown to be accurate on a variety of networks with degree distributions ranging from regular to Poisson to scale free. The parameter allows for comparisons of random networks regardless of their underlying topology. Finally, we draw analogies between the criterion for the success of cooperation introduced here and existing criteria in other contexts.

Generally, the excavation process of a gallery generates fractures in its immediate vicinity. The corresponding zone which is called the excavated damaged zone (EDZ), has a larger permeability than the intact surrounding medium. Therefore, some of its properties are of crucial importance for applications such as the storage of nuclear wastes. Field observations suggest that the fracture density is an exponentially decreasing function of the distance to the wall and that the fracture orientation is anisotropic and well approximated by a Fisher law whose pole is orthogonal to the wall. Numerical samples are generated according to these prescriptions and their percolation status and hydraulic transmissivity are systematically determined for a wide range of decay lengths and anisotropy parameters. All the numerical data are presented and discussed. A heuristic analytical expression for the percolation threshold is proposed which unifies and accurately represents all the numerical data. A simple parallel flow model yields an explicit analytical expression for the transmissivity as a function of the density, heterogeneity, and anisotropy parameters; the model also successfully accounts for all the numerical data.

This article pursues the idea that the degree of striations, called lamination, could be engineered to complement stretching and to design new sequential mixers. It explores lamination and mixing in three new mixing sequences experimentally driven by electromagnetic body forces. To generate these three mixing sequences, Lorentz body forces are dynamically controlled to vary the flow geometry produced by a pair of local jets. The first two sequences are inspired from the “tendril and whorl” and “blinking vortex” flows. The third novel sequence is called the “cat's eyes flip.” These three mixing sequences exponentially stretch and laminate material lines representing the interface between two domains to be mixed. Moreover, the mixing coefficient (defined as $1-{\sigma }^2/{\sigma }_0^2$ where ${\sigma }^2/{\sigma }_0^2$ is the rescaled variance) and its rate grow exponentially before saturation. This saturation of the mixing process is related to the departure of the mixing rate from an exponential growth when the striations’ thicknesses reach the diffusive length scale of the measurements or species and dyes. Incidentally, in our experiments, for the same energy or forcing input, the cat's eyes flip sequence has higher lamination, stretching, and mixing rates than the tendril and whorl and the blinking vortex sequences. These features show that bakerlike in situ mixers can be conceived by dynamically controlling a pair of local jets and by integrating lamination during stirring stages with persistent geometries. Combined with novel insights provided by the quantification of the lamination, this paper should offer perspectives for the development of new sequential mixers, possibly on all scales.