Living organisms use waves that propagate through excitable media to transport information. ${\text{Ca}}^{2+}$ waves are a paradigmatic example of this type of processes. A large hierarchy of ${\text{Ca}}^{2+}$ signals that range from localized release events to global waves has been observed in Xenopus laevis oocytes. In these cells, ${\text{Ca}}^{2+}$ release occurs trough inositol 1,4,5-trisphosphate receptors $\left({\text{IP}}_3\text{Rs}\right)$ which are organized in clusters of channels located on the membrane of the endoplasmic reticulum. In this article we construct a stochastic model for a cluster of ${\text{IP}}_3\text{R}$’s that replicates the experimental observations reported in [D. Fraiman et al., Biophys. J. 90, 3897 (2006)]. We then couple this phenomenological cluster model with a reaction-diffusion equation, so as to have a discrete stochastic model for calcium dynamics. The model we propose describes the transition regimes between isolated release and steadily propagating waves as the ${\text{IP}}_3$ concentration is increased.

We systematize and extend the description of vesicle growth and shape change using linear nonequilibrium thermodynamics. By restricting the study to shape changes from spheres to axisymmetric ellipsoids, we are able to give a consistent formulation which includes the lateral tension of the vesicle membrane. This allows us to generalize and correct a previous calculation. Our present calculations suggest that, for small growing vesicles, a prolate ellipsoidal shape should be favored over oblate ellipsoids, whereas for large growing vesicles oblates should be favored over prolates. The validity of this prediction is examined in the light of the various assumptions made in its derivation.

Normal dynamics in a quasi-one-dimensional channel of length $L$ $\left(\to \infty \right)$ of $N$ hard spheres are analyzed. The spheres are heterogeneous: each has a diffusion coefficient $D$ that is drawn from a probability density function (PDF), $W\sim D^{-\gamma }$ for small $D$, where $0\le \gamma <1$. The initial spheres’ density $\rho$ is nonuniform and scales with the distance (from the origin) $l$ as $\rho \sim l^{-\alpha }$, $0\le \alpha \le 1$. An approximation for the $N$-particle PDF for this problem is derived. From this solution, scaling law analysis and numerical simulations, we show here that the mean square displacement for a particle in such a system obeys $⟨r^2⟩\sim t^{\left(1-\gamma \right)/\left(2c-\gamma \right)}$, where $c=1/\left(1+\alpha \right)$. The PDF of the tagged particle is Gaussian in position. Generalizations of these results are considered.

We present experimental results on the shape of arches that block the outlet of a two-dimensional silo. For a range of outlet sizes, we measure some properties of the arches such as the number of particles involved, the span, the aspect ratio, and the angles between mutually stabilizing particles. These measurements shed light on the role of frictional tangential forces in arching. In addition, we find that arches tend to adopt an aspect ratio (the quotient between height and half the span) close to 1, suggesting an isotropic load. The comparison of the experimental results with data from numerical models of the arches formed in the bulk of a granular column reveals the similarities of both, as well as some limitations in the few existing models.

There are two categories of helical line defects in Sm-$A$ phases: screw dislocations of small Burgers vectors and double helices (DHs), whose macroscopic configuration constitutes a mode of splitting of screw dislocations of giant Burgers vectors. Their counterparts in Sm-$A^{\ast }$’s (Sm-$A$’s with chiral molecules) show a number of differences with the former and are investigated theoretically on the basis of recent observations [C. Meyer et al., Liq. Cryst. 37, 1047 (2010)]. The first part of the paper is a short review of the main features of helical defects in Sm-$A$’s proper. In Sm-$A^{\ast }$’s, small Burgers vector screw dislocations with the same chirality as the high-temperature $N^{\ast }$ phase are favored over the opposite ones, a result that is related to the defect core singularity. This is also true for the macroscopic ${\text{DH}}^{\ast }$s for a more subtle reason; we advance that the ${\text{DH}}^{\ast }$ nucleation at the $N^{\ast }\to \text{Sm-}{A}^{\ast }$ transition stems from a peculiar texture of the cybotactic groups, akin in the ideal case to a set of two twisted $\chi$ disclinations in the $N^{\ast }$ phase, linked by a stacking fault of continuous disclinations. This stacking fault vanishes in the Sm-$A^{\ast }$ phase, and one recovers a ${\text{DH}}^{\ast }$ much similar to a DH but with the appropriate chirality. Cases that differ from ideality are described: they involve small Burgers vector screw dislocations and can be evoked to explain the numerous observed distorted double helices (the Darboux condition is not obeyed) and twisted ribbons. The case when the $N^{\ast }\to \text{Sm-}{A}^{\ast }$ transition is type II (presence of a twist grain boundary phase in between) is briefly discussed.

We present a detailed analysis of the molecular packing of a strained liquid crystal elastomer composed of chiral mesogens in the smectic-$A$ phase. X-ray diffraction patterns of the elastomer collected over a range of orientations with respect to the x-ray beam were used to reconstruct the three-dimensional scattering intensity as a function of tensile strain. We show that the smectic domain order is preserved in these strained elastomers. Changes in the intensity within a given scattering plane are due to reorientation, and not loss, of the molecular order in directions orthogonal to the applied strain. Incorporating the physical parameters of the elastomer, a nonlinear elastic model is presented to describe the rotation of the smectic-layered domains under strain, thus providing a fundamental analysis to the mechanical response of these unique materials.

We investigated the effect of the torsional rigidity of a semiflexible chain on the wrapping transition around a spherical core, as a model of a nucleosome, the fundamental unit of chromatin. Through molecular dynamics simulation, we show that the torsional effect has a crucial effect on the chain wrapping around the core under the topological constraints. In particular, the torsional stress (i) induces the wrapping/unwrapping transition, and (ii) leads to a unique complex structure with an antagonistic wrapping direction which never appears without the topological constraints. We further examine the effect of the stretching stress for the nucleosome model in relation to the unique characteristic effect of the torsional stress on the manner of wrapping.

The influence of the multiscale fracture roughness on the heat exchange when a cold fluid enters a fractured hot solid is studied numerically on the basis of the Stokes equation and in the limit of both hydrolubrication and thermolubrication. The geometrical complexity of the fracture aperture is modeled by small self-affine perturbations added to a uniform aperture field. Thermal and hydraulic properties are characterized via the definition of hydraulic and thermal apertures both at microscopic and macroscopic scales and obtained by comparing the fluxes to the ones of flat fractures. Statistics over a large number of fracture configurations provide an estimate of the average behavior and its variability. We show that the long-range correlations of the fracture roughness induces strong channeling effects that significantly influence the hydraulic and thermal properties. An important parameter is the aspect ratio (length over width) of the fracture: we show, for example, that a downstream elongated rough fracture is more likely to inhibit the hydraulic flow and subsequently to enhance the thermal exchange. Fracture roughness might, in the opposite configuration, favor strong channeling which inhibits heating of the fluid. The thermal behavior is in general shown to be mainly dependent on the hydraulic one, which is expressed through a simple law.

Electron acceleration by ultrahigh intensity lasers is studied by means of two-dimensional planar particle-in-cell simulations. It is shown that the full divergence of the fast electron beam is defined by two complementary physical effects: the regular radial beam deviation depending on the electron radial position and the angular dispersion. If the scale length of the preplasma surrounding the solid target is sufficiently low, the radial deviation is determined by the transverse component of the laser ponderomotive force. The random angular dispersion is due to the small scale magnetic fields excited near the critical density due to the collisionless Weibel instability. When a preplasma is present, the radial beam deviation increases due to the electron acceleration in larger volumes and can become comparable to the local angular dispersion. This effect has been neglected so far in most of the fast electron transport calculations, overestimating significantly the beam collimation by resistive magnetic fields. Simulations with a two-dimensional cylindrically-symmetric hybrid code accounting for the electron radial velocity demonstrate a substantially reduced strength and a shorter penetration of the azimuthal magnetic field in solid targets.

Incomplete homoclinic scenarios were recently measured in a semiconductor laser with optoelectronic feedback. We show here that such a laser contains cascades of spirals of periodic oscillations and hubs which look identical to the familiar ones observed in complete homoclinic scenarios. This means that hubs are far more general than presumed so far, being not limited by Shilnikov’s theorem. Laser hubs open the possibility of measuring complex distributions of non-Shilnikov laser oscillations, and we briefly discuss how to do it.

Large fluctuations have received considerable attention as they encode information on the fine-scale dynamics. Large deviation relations known as fluctuation theorems also capture crucial nonequilibrium thermodynamical properties. Here we report that, using the technique of uniformization, the thermodynamic large deviation functions of continuous-time Markov processes can be obtained from Markov chains evolving in discrete time. This formulation offers theoretical and numerical approaches to explore large deviation properties. In particular, the time evolution of autonomous and nonautonomous processes can be expressed in terms of a single Poisson rate. In this way the uniformization procedure leads to a simple and efficient way to simulate stochastic trajectories that reproduce the exact fluxes statistics. We illustrate the formalism for the current fluctuations in a stochastic pump model.

We study the dynamics of charged macroscopic particles (millimetric steel balls) confined in a linear channel of finite length, sufficiently narrow to avoid particles crossing. We show that their individual response to thermal fluctuations strongly depends either on their position in the channel or the local potential they experience. Three different dynamical regimes are identified. At small times, a “free regime” takes place, with the outermost particles exhibiting the highest diffusion coefficient. This effect results from an “echo” of the thermal fluctuations reflected by the channel wall. Then, forbidden crossing induces a correlated regime similar to single file diffusion. Surprisingly, the corresponding mobility increases with the local potential. Lastly, the finite length of the channel induces the saturation of fluctuations. We show that those behaviors may be described heuristically with the help of models for $N$ hard-core interacting particles diffusing in a finite channel of length $L$, provided that we replace the uniform interparticle distance $L/N$ by a characteristic distance ${\left(k_{B}T/K\right)}^{1/2}$ built upon the temperature $T$ and the stiffness $K$ of the local potential. It provides a very satisfactory estimate for the fluctuations sizes, whereas they are greatly overestimated assuming hard-core interactions.

We construct a family of stochastic processes with nonstationary, correlated increments which allow a priori independent selections of both fractal dimension and mean-square displacement. The family is essentially fractional Brownian motion (fBm) run with a nonlinear clock (fBm-nlc). The fractal dimension of fBm-nlc is shown to be the same as that of the underlying fBm process. We also compute the $p$-variation and discuss the problems in using this to differentiate between diffusive processes. The fBm-nlc process illustrates that the range of anomalous diffusive processes has not been adequately explored.

We have studied the impact of time-dependent learning capacities of players in the framework of spatial prisoner’s dilemma game. In our model, this capacity of players may decrease or increase in time after strategy adoption according to a steplike function. We investigated both possibilities separately and observed significantly different mechanisms that form the stationary pattern of the system. The time decreasing learning activity helps cooperator domains to recover the possible intrude of defectors hence supports cooperation. In the other case the temporary restrained learning activity generates a cyclic dominance between defector and cooperator strategies, which helps to maintain the diversity of strategies via propagating waves. The results are robust and remain valid by changing payoff values, interaction graphs or functions characterizing time dependence of learning activity. Our observations suggest that dynamically generated mechanisms may offer alternative ways to keep cooperators alive even at very larger temptation to defect.

We describe the appearance and stability of spatiotemporal periodic patterns (rotating waves) in unidirectional rings of coupled oscillators with delayed couplings. We show how delays in the coupling lead to the splitting of each rotating wave into several new ones. The appearance of rotating waves is mediated by the Hopf bifurcations of the symmetric equilibrium. We also conclude that the coupling delays can be effectively replaced by increasing the number of oscillators in the chain. The phenomena are shown for the Stuart-Landau oscillators as well as for the coupled FitzHugh-Nagumo systems modeling an ensemble of spiking neurons interacting via excitatory chemical synapses.

The swelling of layered smectite clay particles consists of a change in the interlayer repetition distance ($d$-spacing) as a function of temperature and humidity. For the synthetic clay sodium fluorohectorite, hydrodynamically stable hydration states with zero, one and two intercalated monolayers of water have previously been reported, with discrete jumps in $d$-spacing at the transitions between the hydration states. Keeping the temperature fixed and varying the ambient relative humidity, we find small reproducible $d$-spacing changes also within the hydration states. These changes are monotonous as a function of relative humidity, and one order of magnitude smaller than the shift in $d$-spacing that is typical of the transition between two hydration states. The reproducibility and reliability of this relative humidity controlled $d$-shift enables us to use the interlayer repetition distance $d$ as a measure of the local humidity surrounding the clay particles. We provide an example of application of this observation: imposing a humidity gradient over a quasi-one-dimensional temperature-controlled sample, and using x-ray diffraction to record the $d$-spacing, we are able to extract profiles of the relative humidity along the sample length. Their time evolution describes the transport of water through the mesoporous space inside the clay. An analysis of the measured humidity profiles based on the Boltzmann transformation, under certain simplifying assumptions, yields a diffusive behavior that is either normal or possibly weakly anomalous.

A numerical analysis is made on the four-point correlation function in a similarity range of a model of two-dimensional passive scalar field $\psi$ advected by a turbulent velocity field with infinitely small correlation time. The model yields an exact closure equation for the four-point correlation ${\Psi }_4$ of $\psi$, which may be casted into the form of an eigenvalue problem in the similarity range. The analysis of the eigenvalue problem gives not only the scale dependence of ${\Psi }_4$, but also the dependence on the configuration of the four points. The numerical analysis gives $S_4\left(\mathit{R}\right)\propto R^{{\zeta }_4}$ in the similarity range in which $S_2\left(\mathit{R}\right)\propto R^{{\zeta }_2}$, where $S_N$ is the structure function defined by $S_N\left(\mathit{R}\right)\equiv ⟨{\left[\psi \left(\mathit{x}+\mathit{R}\right)-\psi \left(\mathit{x}\right)\right]}^N⟩$ and ${\zeta }_4\ne 2{\zeta }_2$. The estimate of ${\zeta }_4$ by the numerical analysis of the eigenvalue problem is in good agreement with numerical simulations so far reported. The agreement supports the idea of universality of the exponent ${\zeta }_4$ in the sense that ${\zeta }_4$ is insensitive to conditions of $\psi$ outside the similarity range. The numerical analysis also shows that the correlation $C\left(\mathit{R},\mathit{r}\right)\equiv ⟨{\left[\psi \left(\mathit{x}+\mathit{R}\right)-\psi \left(\mathit{x}\right)\right]}^2{\left[\psi \left(\mathit{x}+\mathit{r}\right)-\psi \left(\mathit{x}\right)\right]}^2⟩$ is stronger than that given by the joint-normal approximation, and scales like $C\left(\mathit{R},\mathit{r}\right)\propto {\left(r/R\right)}^{\chi }$ for $r/R⪡1$ with $R$ and $r$ in the similarity range, where $\chi$ is a constant depending on the angle between $\mathit{R}$ and $\mathit{r}$.

In a recent publication [Phys. Rev. E 80, 026105 (2009)], Devlin and Treloar characterized the effects of heterogeneity and degree-degree correlation on cooperation in correlated networks by using standardized variance and a correlated extension of standardized variance. We show that some statements made by them are problematic by considering the relation between these two types of standardized variance with Pearson correlation coefficient.