We conduct extensive independent numerical experiments considering frictionless disks without internal degrees of freedom (rotation, etc.) in two dimensions. We report here that for a large range of the packing fractions below random-close packing, all components of the stress tensor of wet granular materials remain finite in the limit of zero shear rate. This is direct evidence for a fluid-to-solid arrest transition. The offset value of the shear stress characterizes plastic deformation of the arrested state which corresponds to dynamic yield stress of the system. Based on an analytical line of argument, we propose that the mean number of capillary bridges per particle, $\nu$, follows a nontrivial dependence on the packing fraction, $\varphi$, and the capillary energy, $\varepsilon$. Most noticeably, we show that $\nu$ is a generic and universal quantity which does not depend on the driving protocol. Using this universal quantity, we calculate the arrest stress, ${\sigma }_a$, analytically based on a balance of the energy injection rate due to the external force driving the flow and the dissipation rate accounting for the rupture of capillary bridges. The resulting prediction of ${\sigma }_a$ is a nonlinear function of the packing fraction, $\varphi$, and the capillary energy, $\varepsilon$. This formula provides an excellent, parameter-free prediction of the numerical data. Corrections to the theory for small and large packing fractions are connected to the emergence of shear bands and of contributions to the stress from repulsive particle interactions, respectively.

We explore the phase behavior and structure of orthogonal smectic liquid crystals consisting of bent-core molecules (BCMs) by means of Monte Carlo molecular simulations. A simple athermal molecular model is introduced that describes the basic features of the BCMs. Phase transitions between uniaxial and biaxial (antiferroelectric) orthogonal smectics are obtained. The results indicate the presence of local in-plane polar correlations in the uniaxial smectic phase. The macroscopic uniaxial-biaxial transformation is rationalized in terms of local polar correlations giving rise to polar domains. The size of these polar domains grows larger under the action of an external vector field and their internal ordering is enhanced, leading to field-induced biaxial order-disorder transitions.

The dynamic alignment of the nematic director by near-orthogonal electric and magnetic fields has been investigated. The intermediate states during the relaxation process were found, with the aid of time-resolved deuterium NMR spectroscopy, to be markedly nonuniform. The macroscopic order was perturbed, although the initial and final states of the director appear to be essentially uniform. However, the initial state does have a profound influence on the uniformity of the director in the intermediate states. We have developed a fundamental model based on the effect of spontaneous director fluctuations to explain these unusual NMR observations.

A generalized (2+1)-dimensional coupled cubic-quintic Ginzburg-Landau equation with higher-order nonlinearities is fully investigated for modulational instability regions. We obtained the constraints that allow the modulational instability (MI) procedure to transform the system under consideration into an analysis of the roots of a polynomial equation of the fourth degree. Because of the complexity of the dispersion relation and its dependence on many parameters, we study numerous examples that are presented graphically. A numerical simulation based on a split-step Fourier method is implemented on the above equation. In addition to the general case, we have considered some special cases that allow us to investigate the behavior of MI in different regions.

The shear-induced dynamics of two-dimensional composite droplets in a narrow channel is investigated numerically. The droplets consist of a viscous inner droplet (core) and shell immersed in a continuous Newtonian fluid. Attention is focused on studying the effects of confinement at different core-to-shell radii ratios, relative viscosities of the medium components, and interfacial tensions on the steady-state deformation and orientation of a composite droplet. The role of the “sustaining” effect due to the internal core and competition between the near-wall shear flow and downward and upward secondary streams is discussed.

Using the particle-based method of movable cellular automata, we analyze the initiation and propagation of intersonic mode II cracks along a weak interface. We show that the stress concentration in front of the crack tip, which is believed to be the mechanism of acceleration of the crack beyond the speed of shear waves, is due to the formation of an elastic vortex. The vortex develops in front of the crack during the short initial period of crack propagation. It expands and moves away from the crack tip and finally detaches from it. Maximum stress concentration in the vortex is achieved at the moment of detachment of the vortex. The crack can accelerate towards the longitudinal wave speed if the magnitude of shear stresses in the elastic vortex reaches the material shear strength before vortex detachment. We have found that for given material parameters, the condition for the unstable accelerated crack propagation depends only on the ratio of the initial crack length to its width (e.g., due to surface roughness).

In this article we consider the one-dimensional totally asymmetric open-boundary exclusion process fed by a process with power-law-distributed waiting times. More specifically, we use a modified Pareto distribution to define the jump rate for jumps into the system. We then characterize the propagation of fluctuations through the system by kinetic Monte Carlo simulations and by numerical evaluation of the steady-state partition function.

Filtered shot noise processes have proven to be very effective in modeling the evolution of systems exposed to shot noise sources and have been applied to a wide variety of fields ranging from electronics through biology. In particular, they can model the membrane potential $V_m$ of neurons driven by stochastic input, where these filtered processes are able to capture the nonstationary characteristics of $V_m$ fluctuations in response to presynaptic input with variable rate. In this paper we apply the general framework of Poisson point processes transformations to analyze these systems in the general case of nonstationary input rates. We obtain exact analytic expressions, as well as different approximations, for the joint cumulants of filtered shot noise processes with multiplicative noise. These general results are then applied to a model of neuronal membranes subject to conductance shot noise with a continuously variable rate of presynaptic spikes. We propose very effective approximations for the time evolution of the $V_m$ distribution and a simple method to estimate the presynaptic rate from a small number of $V_m$ traces. This work opens the perspective of obtaining analytic access to important statistical properties of conductance-based neuronal models such as the first passage time.

In this paper we study how hyperbolic and nonhyperbolic regions in the neighborhood of a resonant island perform an important role allowing or forbidding stickiness phenomenon around islands in conservative systems. The vicinity of the island is composed of nonhyperbolic areas that almost prevent the trajectory to visit the island edge. For some specific parameters tiny channels are embedded in the nonhyperbolic area that are associated to hyperbolic fixed points localized in the neighborhood of the islands. Such channels allow the trajectory to be injected in the inner portion of the vicinity. When the trajectory crosses the barrier imposed by the nonhyperbolic regions, it spends a long time abandoning the vicinity of the island, since the barrier also prevents the trajectory from escaping from the neighborhood of the island. In this scenario the nonhyperbolic structures are responsible for the stickiness phenomena and, more than that, the strength of the sticky effect. We show that those properties of the phase space allow us to manipulate the existence of extreme events (and the transport associated to it) responsible for the nonequilibrium fluctuation of the system. In fact we demonstrate that by monitoring very small portions of the phase space (namely, $\approx 1\times {10}^{-5}\%$ of it) it is possible to generate a completely diffusive system eliminating long-time recurrences that result from the stickiness phenomenon.

We consider the inhomogeneous nonparaxial nonlinear Schrödinger (NLS) equation with varying dispersion, nonlinearity, and nonparaxiality coefficients, which governs the nonlinear wave propagation in an inhomogeneous optical fiber system. We present the similarity and Darboux transformations and for the chosen specific set of parameters and free functions, the first- and second-order rational solutions of the nonparaxial NLS equation are generated. In particular, the features of rogue waves throughout polynomial and Jacobian elliptic functions are analyzed, showing the nonparaxial effects. It is shown that the nonparaxiality increases the intensity of rogue waves by increasing the length and reducing the width simultaneously, by the way it increases their speed and penalizes interactions between them. These properties and the characteristic controllability of the nonparaxial rogue waves may give another opportunity to perform experimental realizations and potential applications in optical fibers.

We construct a mesoscale model of colloidal suspensions that contain solutes reversibly adsorbing onto the colloidal particle surfaces. The present model describes the coupled dynamics of the colloidal particles, the host fluid, and the solutes through the Newton-Euler equations of motion, the hydrodynamic equations, and the advection-diffusion equation, respectively. The solute adsorption is modeled through a square-well potential, which represents a short-range attractive interaction between a particle and a solute molecule. The present model is formulated to be solved through direct numerical simulations. Some numerical results are presented to validate the simulations. The present model enables investigations of solute adsorption effects in the presence of a fluid flow and an inhomogeneous solute concentration distribution.

We show that preferential rewiring, which is supposed to mimic the behavior of financial agents, changes a directed-network Ising ferromagnet with a single critical point into a model with robust critical behavior. For the nonrewired random graph version, due to a constant number of out-links for each site, we write a simple mean-field-like equation describing the behavior of magnetization; we argue that it is exact and support the claim with extensive Monte Carlo simulations. For the rewired version, this equation is obeyed only at low temperatures. At higher temperatures, rewiring leads to strong heterogeneities, which apparently invalidates mean-field arguments and induces large fluctuations and divergent susceptibility. Such behavior is traced back to the formation of a relatively small core of agents that influence the entire system.

The Bose-stimulated self-organization of a quasi-two-dimensional nonequilibrium Bose-Einstein condensate in an in-plane potential is proposed. We obtained the solution of the nonlinear, driven-dissipative Gross-Pitaevskii equation for a Bose-Einstein condensate trapped in an external asymmetric parabolic potential within the method of the spectral expansion. We found that, in sharp contrast to previous observations, the condensate can spontaneously acquire a solitonlike shape for spatially homogeneous pumping. This condensate soliton performs oscillatory motion in a parabolic trap and, also, can spontaneously rotate. Stability of the condensate soliton in the spatially asymmetric trap is analyzed. In addition to the nonlinear dynamics of nonequilibrium Bose-Einstein condensates of ultracold atoms, our findings can be applied to the condensates of quantum well excitons and cavity polaritons in semiconductor heterostructure, and to the condensates of photons.

A Kadomtsev-Petviashvili- (KP-) type equation appears in fluid mechanics, plasma physics, and gas dynamics. In this paper, we propose an integrable semidiscrete analog of a coupled $(2+1)$-dimensional system which is related to the KP equation and the Zakharov equation. $N$-soliton solutions of the discrete equation are presented. Some interesting examples of soliton resonance related to the two-soliton and three-soliton solutions are investigated. Numerical computations using the integrable semidiscrete equation are performed. It is shown that the integrable semidiscrete equation gives very accurate numerical results in the cases of one-soliton evolution and soliton interactions.

The current study extends previous analytical and numerical solutions of chronopotentiometric response of one-dimensional systems consisting of three layers to the more realistic two-dimensional (2D) heterogeneous ion-permselective medium. An analytical solution for the transient concentration-polarization problem, under the local electroneutrality approximation and assumption of ideal permselectivity, was obtained using the Laplace transform and separation of variables technique. Then the 2D electric potential was obtained numerically and was compared to the full Poisson-Nernst-Planck solution. It was then shown that the resultant voltage drop across the system varies between the initial Ohmic response and that of the steady state accounting for concentration polarization. Also, the field-focusing effect in a 2D system is shown to result in a faster depletion of ions at the permselective interface.

We find, in a two-dimensional air table granular system, that the reduced diffusion constant $D^{*}$ and excess entropy $S_2^{*}$ follow two distinct scaling laws: $D^{*}\sim e^{S_2^{*}}$ for dense liquids and $D^{*}\sim e^{3S_2^{*}}$ for dilute ones. The scaling for dense liquids is very similar to that for three-dimensional liquids proposed previously [M. Dzugutov, Nature (London) 381, 137 (1996); A. Samanta et al., Phys. Rev. Lett. 92, 145901 (2004)]. In the dilute regime, a power law [Y. Rosenfeld, J. Phys.: Condens. Matter 11, 5415 (1999)] also fits our data reasonably well. In our system, particles experience low air drag dissipation and interact with each others through embedded magnets. These near-conservative many-body interactions are responsible for the measured Gaussian velocity distribution functions and the scaling laws. The dominance of cage relaxations in dense liquids leads to the different scaling laws for dense and dilute regimes.

Protein evolution is frequently explored using minimalist polymer models, however, little attention has been given to the problem of structural drift, or diffusion. Here, we study neutral evolution of small protein motifs using an off-lattice heteropolymer model in which individual monomers interact as low-resolution amino acids. In contrast to most earlier models, both the length and folded structure of the polymers are permitted to change. To describe structural change, we compute the mean-square distance (MSD) between monomers in homologous folds separated by $n$ neutral mutations. We find that structural change is episodic, and, averaged over lineages (for example, those extending from a single sequence), exhibits a power-law dependence on $n$. We show that this exponent depends on the alignment method used, and we analyze the distribution of waiting times between neutral mutations. The latter are more disperse than for models required to maintain a specific fold, but exhibit a similar power-law tail.

Quantum molecular dynamics (QMD) simulations are used to calculate the equation of state, structure, and transport properties of liquid gallium along the principal shock Hugoniot. The calculated Hugoniot is in very good agreement with experimental data up to a pressure of 150 GPa as well as with our earlier classical molecular dynamics calculations using a modified embedded atom method (MEAM) potential. The self-diffusion and viscosity calculated using QMD agree with experimental measurements better than the MEAM results, which we attribute to capturing the complexity of the electronic structure at elevated temperatures. Calculations of the DC conductivity were performed around the Hugoniot. Above a density of 7.5 ${\mathrm{g/cm}}^3$, the temperature increases rapidly along the Hugoniot, and the optical conductivity decreases, indicating simple liquid metal behavior.

A model of particle transport through a large number of channels is introduced. Interactions among the particles can lead to a strong suppression of fluctuations in the particle number statistics. Within a mean-field-type limit, this becomes equivalent to a time-dependent (nonautonomous) collective feedback control mechanism. The dynamics can be interpreted as a diffusive spreading of a feedback signal across the channels that displays scaling, can be quantified via the flow of information, and becomes visible, e.g., in the spectral function of the particle noise.

We study the free diffusion in two dimensions of active Brownian swimmers subject to passive fluctuations on the translational motion and to active fluctuations on the rotational one. The Smoluchowski equation is derived from a Langevin-like model of active swimmers and analytically solved in the long-time regime for arbitrary values of the Péclet number; this allows us to analyze the out-of-equilibrium evolution of the positions distribution of active particles at all time regimes. Explicit expressions for the mean-square displacement and for the kurtosis of the probability distribution function are presented and the effects of persistence discussed. We show through Brownian dynamics simulations that our prescription for the mean-square displacement gives the exact time dependence at all times. The departure of the probability distribution from a Gaussian, measured by the kurtosis, is also analyzed both analytically and computationally. We find that for the inverse of Péclet numbers $\lesssim 0.1$, the distance from Gaussian increases as $\sim t^{-2}$ at short times, while it diminishes as $\sim t^{-1}$ in the asymptotic limit.