Granular packings, especially near the jamming transition, form fragile networks where small perturbations can lead to destabilization and large scale rearrangements. A key stabilizing element in two dimensions is the contact loop, yet surprisingly little is known about contact loop statistics in realistic granular networks. In this paper, we use particle dynamics to study the evolution of contact loop structure in a gradually tilted two-dimensional granular bed. We find that the resulting contact loop distributions (1) are sensitive to material properties, (2) deviate from the expected structure of a randomly wired lattice, and (3) are uniquely dependent on tilting angle. Also, we introduce a quantitative measure of loop stability $\xi$ and show that increased tilting results in a gradual destabilization of individual loops. We briefly discuss the considerations for extending our approach to three dimensions.

Molecular dynamics simulations are carried out to investigate the dynamic behavior of the slip length in thin polymer films confined between atomically smooth thermal surfaces. For weak wall-fluid interactions, the shear rate dependence of the slip length acquires a distinct local minimum followed by a rapid growth at higher shear rates. With increasing fluid density, the position of the local minimum is shifted to lower shear rates. We found that the ratio of the shear viscosity to the slip length, which defines the friction coefficient at the liquid/solid interface, undergoes a transition from a nearly constant value to power law decay as a function of the slip velocity. In a wide range of shear rates and fluid densities, the friction coefficient is determined by the product of the value of the surface-induced peak in the structure factor and the contact density of the first fluid layer near the solid wall.

We have numerically studied chemotactic aggregation of microorganisms by introducing a model consisting of elements with intracellular dynamics, random walks with a state-dependent turnover rate, and secretion of attractant. Three phases with and without aggregation, as well as partial aggregation, were obtained as to the diffusion and degradation rates of the attractant, and conditions for cellular aggregation were analyzed. The size of aggregated clusters was shown to be independent of cell density, as is consistent with experiment.

We present a numerical investigation of the Brownian motion and diffusion of a dumbbell in a two-dimensional periodic potential. Its dynamics is described by a Langevin model including the hydrodynamic interaction. With increasing values of the amplitude of the potential we find along the modulated spatial directions a reduction of the diffusion constant and of the impact of the hydrodynamic interaction. For modulation amplitudes of the potential in the range of the thermal energy the dumbbell diffusion exhibits a pronounced local maximum at a wavelength of about 3/2 of the dumbbell extension. This is especially emphasized for stiff springs connecting the two beads.

We study the statistics of the dissipated energy in the two-dimensional random fuse model for fracture under different imposed strain conditions. By means of extensive numerical simulations we compare different ways to compute the dissipated energy. In the case of an infinitely slow driving rate (quasistatic model), we find that the probability distribution of the released energy shows two different scaling regions separated by a sharp energy crossover. At low energies, the probability of having an event of energy $E$ decays as $\sim E^{-1/2}$, which is robust and independent of the energy quantifier used (or lattice type). At high energies, fluctuations dominate the energy distribution, leading to a crossover to a different scaling regime, $\sim E^{-2.75}$, whenever the released energy is computed over the whole system. On the contrary, strong finite-size effects are observed if we consider only the energy dissipated at microfractures. In a different numerical experiment, the quasistatic dynamics condition is relaxed, so that the system is driven at finite strain load rates, and we find that the energy distribution decays as $\mathcal{P}\left(E\right)\sim E^{-1}$ for all the energy range.

The simple proportional feedback (SPF) control algorithm may, in principle, be used to attain periodic oscillations in dynamic systems exhibiting low-dimensional chaos. However, if implemented within a discrete control framework with sampling frequency limitations, controller performance may deteriorate. This phenomenon is illustrated using simulations of a chaotic autocatalytic reaction system. A two-dimensional (2D) SPF controller that explicitly takes into account some of the problems caused by limited sampling rates is then derived by introducing suitable modifications to the original SPF method. Using simulations, the performance of the 2D-SPF controller is compared to that of a conventional SPF control law when implemented as a sampled data controller. Two versions of the 2D-SPF controller are described: linear (L2D-SPF) and quadratic (Q2D-SPF). The performance of both the L2D-SPF and Q2D-SPF controllers is shown to be superior to the SPF when controller sampling frequencies are decreased. Furthermore, it is demonstrated that the Q2D-SPF controller provides better fixed point stabilization compared to both the L2D-SPF and the conventional SPF when concentration measurements are corrupted by noise.

This paper describes transport properties of linear water waves propagating within a square array of fixed square cylinders. The main focus is on achieving the conditions for all-angle-negative-refraction (AANR) thanks to anomalous dispersion in fluid-filled periodic structures. Of particular interest are two limit cases when either the edges or the vertices of the cylinders come close to touching. In the former case, the array can be approximated by a lattice of thin water channels (for which dispersion curves are given in closed form and thus frequencies at which AANR occurs) whereas in the latter case, the array behaves as a checkerboard with cells consisting either of water tanks or rigid cylinders (for which standing modes are given in closed form). The tools of choice for the present analysis are, on the one hand, the finite element method which solves numerically spectral problems in periodic media, and on the other hand, a two-scale asymptotic method which provides estimates of dispersion curves and associated eigenfields through a lattice approximation (namely thin water channels between rigid cylinders). Simple duality correspondences are found based on fourfold symmetry of square water checkerboards that allow us to get some insight into their spectra. Last, some numerical evidence is provided for water waves focusing with no astigmatism through such arrays, when they are of finite extent.

The left-handed properties of metamaterials with saturable nonlinearity are analyzed with respect to their electromagnetic response as a function of externally varying parameters. We demonstrate that the response of the medium is strongly affected by the saturation of the nonlinear effects. The last can be exploited to modulate the amplitude or tune the frequency of the response. Moreover, the existence of bistability regions in large parts of the external parameter space allows for switching between different magnetization states, with either positive or negative response. The stability issue of multiple possible states is addressed through modulational instability analysis of plane wave envelopes in each of those states.

Due to its computational efficiency, the kinetic-based lattice Boltzmann method has recently been used to model nonequilibrium gas dynamics. With appropriate boundary conditions, lattice Boltzmann models have been able to capture both velocity slip and temperature jump at a solid surface. To enable these models to simulate flows in the transition regime, both high-order and modified lattice Boltzmann models have been proposed. In this paper, we demonstrate the advantages of the standard lattice Bhatnagar-Gross-Krook model in predicting high-order rarefaction phenomenon. In addition, we show that current high-order lattice Boltzmann models are not yet able to capture the nonlinear constitutive relation for the stress in the Knudsen layer, despite the improved predictions of the wall slip-velocity, especially for Poiseuille flow. By considering how the wall affects the gas mean free path, we present a simplified high-order lattice Boltzmann model that can predict flow in the transition regime and is also able to capture the essential characteristics of the Knudsen layer.

We investigate the probability distribution functions of the free flight time and of the number of collisions in a hard-sphere gas at equilibrium. At variance with naive expectation, the latter quantity does not follow Poissonian statistics, even in the dilute limit, which is the focus of the present analysis. The corresponding deviations are addressed both numerically and analytically. In writing an equation for the generating function of the cumulants of the number of collisions, we came across a perfect mapping between our problem and a previously introduced model: the probabilistic ballistic annihilation process [Coppex et al., Phys. Rev. E 69, 11303 (2004)]. We exploit this analogy to construct a Monte Carlo–like algorithm able to investigate the asymptotically large time behavior of the collisional statistics within a reasonable computational time. In addition, our predictions are compared with the results of molecular dynamics simulations and the direct simulation Monte Carlo technique. An excellent agreement is reported.

We consider a class of quantum heat engines consisting of two subsystems interacting with a work-source and coupled to two separate baths at different temperatures $T_h>T_c$. The purpose of the engine is to extract work due to the temperature difference. Its dynamics is not restricted to the near equilibrium regime. The engine structure is determined by maximizing the extracted work under various constraints. When this maximization is carried out at finite power, the engine dynamics is described by well-defined temperatures and satisfies the local version of the second law. In addition, its efficiency is bounded from below by the Curzon-Ahlborn value $1-\sqrt{T_c/T_h}$ and from above by the Carnot value $1-\left(T_c/T_h\right)$. The latter is reached—at finite power—for a macroscopic engine, while the former is achieved in the equilibrium limit $T_h\to T_c$. The efficiency that maximizes the power is strictly larger than the Curzon-Ahloborn value. When the work is maximized at a zero power, even a small (few-level) engine extracts work right at the Carnot efficiency.

A notion of stochastic deformation is introduced and the corresponding algebraic deformation procedure is developed. This procedure is analogous to the deformation of an algebra of observables like deformation quantization, but for an imaginary deformation parameter (the Planck constant). This method is demonstrated on diverse relativistic and nonrelativistic models with finite and infinite degrees of freedom. It is shown that under stochastic deformation the model of a nonrelativistic particle interacting with the electromagnetic field on a curved background passes into the stochastic model described by the Fokker-Planck equation with the diffusion tensor being the inverse metric tensor. The first stochastic correction to the Newton equations for this system is found. The Klein-Kramers equation is also derived as the stochastic deformation of a certain classical model. Relativistic generalizations of the Fokker-Planck and Klein-Kramers equations are obtained by applying the procedure of stochastic deformation to appropriate relativistic classical models. The analog of the Fokker-Planck equation associated with the stochastic Lorentz-Dirac equation is derived too. The stochastic deformation of the models of a free scalar field and an electromagnetic field is investigated. It turns out that in the latter case the obtained stochastic model describes a fluctuating electromagnetic field in a transparent medium.

We found a stripe formation in an emulsion of a liquid crystalline polymer (LCP) and a machine oil (OIL) in electric and shear fields. Through the simultaneous measurement with a confocal scanning laser microscope and a rheometer, it was clearly shown that the formation of stripes, which are periodically arrayed, leads to the increase of the shear stress. The droplets, which are one component of the emulsion, start to be connected at low electric fields and then change into the stripes with the increase of electric field. Finally, a three-dimensional network is formed at high electric fields. The period and fluctuation of the stripe structure were also investigated in detail.

Melting of two-dimensional colloidal crystals is studied by video microscopy. The samples were composed of microgel spheres whose diameters could be temperature tuned, and whose pair potentials were measured to be short ranged and repulsive. We observed two-step melting from the crystal to a hexatic phase and from the hexatic to the liquid phase as a function of the temperature-tunable volume fraction. The translational and orientational susceptibilities enabled us to definitively determine the phase transition points, avoiding ambiguities inherent in other analyses and resolving a “dislocation precursor stage” in the solid phase that some of the traditional analyses may incorrectly associate with the hexatic phase. A prefreezing stage of the liquid with ordered patches was also found.

We propose a data-driven approach to measure interdependences between dissipative dynamical systems under the influence of noise. We estimate drift and diffusion coefficients of a Fokker-Planck equation and derive measures that allow one to quantify the asymmetry in coupling in a fully automated and computationally inexpensive and simple way. Our approach makes it possible to discriminate between interdependences in the deterministic and stochastic parts of the dynamics. We report results of numerical studies of exemplary time series from coupled stochastic and deterministic model systems and of an application to electroencephalographic recordings from epilepsy patients.

We present a kinetic theory for all-to-all coupled networks of identical, linear, integrate-and-fire, excitatory point neurons in which a fast and a slow excitatory conductance are driven by the same spike train in the presence of synaptic failure. The maximal-entropy principle guides us in deriving a set of three $\left(1+1\right)$-dimensional kinetic moment equations from a Boltzmann-like equation describing the evolution of the one-neuron probability density function. We explain the emergence of correlation terms in the kinetic moment and Boltzmann-like equations as a consequence of simultaneous activation of both the fast and slow excitatory conductances and furnish numerical evidence for their importance in correctly describing the coarse-grained dynamics of the underlying neuronal network.

The scaling properties of spectra of real world complex networks are studied by using the wavelet transform. It is found that the spectra of networks are multifractal. According to the values of the long-range correlation exponent, the Hust exponent $H$, the networks can be classified into three types, namely, $H>0.5$, $H=0.5$, and $H<0.5$. All real world networks considered belong to the class of $H\ge 0.5$, which may be explained by the hierarchical properties.

We present a comprehensive study of Vicsek-style self-propelled particle models in two and three space dimensions. The onset of collective motion in such stochastic models with only local alignment interactions is studied in detail and shown to be discontinuous (first-order-like). The properties of the ordered, collectively moving phase are investigated. In a large domain of parameter space including the transition region, well-defined high-density and high-order propagating solitary structures are shown to dominate the dynamics. Far enough from the transition region, on the other hand, these objects are not present. A statistically homogeneous ordered phase is then observed, which is characterized by anomalously strong density fluctuations, superdiffusion, and strong intermittency.

We present a numerical analysis of free-surface liquid metal flow and its three-dimensional linear stability. The flow is driven by an alternating magnetic field in a spinning cylindrical container. The electromagnetic and hydrodynamic fields are fully coupled via the shape of the liquid free surface. The hydrodynamic equations are solved by a spectral collocation method, and the alternating magnetic field distribution is found by a boundary-integral method. The flow stability is analyzed for various magnetohydrodynamic interaction parameters and Ekman numbers assuming a flat free surface. We find that only a sufficiently fast spinning suppresses and stabilizes the flow, but a moderate spinning can significantly destabilize it.