The behavior of the percolation threshold and the jamming coverage for isotropic random sequential adsorption samples has been studied by means of numerical simulations. A parallel algorithm that is very efficient in terms of its speed and memory usage has been developed and applied to the model involving large linear k-mers on a square lattice with periodic boundary conditions. We have obtained the percolation thresholds and jamming concentrations for lengths of k-mers up to 2^{17}. A large k regime of the percolation threshold behavior has been identified. The structure of the percolating and jamming states has been investigated. The theorem of Kondrat, Koza, and Brzeski [Phys. Rev. E 96, 022154 (2017)] has been generalized to the case of periodic boundary conditions. We have proved that any cluster at jamming is a percolating cluster and that percolation occurs before jamming.

We study the planar matching problem, defined by a symmetric random matrix with independent identically distributed entries, taking values 0 and 1. We show that the existence of a perfect planar matching structure is possible only above a certain critical density of allowed contacts, $p_{c}$. This problem has an important application for the prediction of the optimal folding of RNA-type polymers. Using an alternative formulation of the problem in terms of Dyck paths and a matrix model of planar contact structures, we provide an analytical estimation for the value of the transition point, $p_{c}$, in the thermodynamic limit. This estimation is close to the critical value, $p_{c}\approx 0.38$, obtained in numerical simulations based on an exact dynamic-programming algorithm. We characterize the corresponding critical behavior of the model and discuss the relation of the perfect-imperfect matching transition to the known molten-glass transition in the context of random RNA secondary structure's formation. In particular, we provide strong evidence supporting the conjecture that the molten-glass transition at $T=0$ occurs at $p_{c}$

We propose two models of social segregation inspired by the Schelling model. Agents in our models are nodes of evolving social networks. The total number of social connections of each node remains constant in time, though may vary from one node to the other. The first model describes a “polychromatic” society, in which colors designate different social categories of agents. The parameter μ favors/disfavors connected “monochromatic triads,” i.e., connected groups of three individuals *within the same social category*, while the parameter ν controls the preference of interactions between two individuals *from different social categories*. The polychromatic model has several distinct regimes in (μ,ν)-parameter space. In ν-dominated region, the phase diagram is characterized by the plateau in the number of the intercolor connections, where the network is bipartite, while in μ-dominated region, the network looks as two weakly connected unicolor clusters. At μ>μcrit and ν>νcrit two phases are separated by a critical line, while at small values of μ and ν, a gradual crossover between the two phases occurs. The second “colorless” model describes a society in which the advantage or disadvantage of forming small fully connected communities (short cycles or cliques in a graph) is controlled by a parameter γ. We analyze the topological structure of a social network in this model and demonstrate that above a critical threshold, γ+>0, the entire network splits into a set of weakly connected clusters, while below another threshold, γ−<0, the network acquires a bipartite graph structure. Our results propose mechanisms of formation of self-organized communities in international communication between countries, as well as in crime clans and prehistoric societies.

We propose a toy model of a heteropolymer chain capable of forming planar secondary structures typical for RNA molecules. In this model, the sequential intervals between neighboring monomers along a chain are considered as quenched random variables, and energies of nonlocal bonds are assumed to be concave functions of those intervals. A few factors are neglected: the contribution of loop factors to the partition function, the variation in energies of different types of complementary nucleotides, the stacking interactions, and constraints on the minimal size of loops. However, the model captures well the formation of folded structures without pseudoknots in an arbitrary sequence of nucleotides. Using the optimization procedure for a special class of concave-type potentials, borrowed from optimal transport analysis, we derive the *local* difference equation for the ground state free energy of the chain with the planar (RNA-like) architecture of paired links. We consider various distribution functions of intervals between neighboring monomers (truncated Gaussian and scale free) and demonstrate the existence of a topological crossover from sequential to essentially nested configurations of paired links.

The effect of a local shear transformation on plastic deformation of a three-dimensional amorphous solid is studied using molecular dynamics simulations.We consider a spherical inclusion, which is gradually transformed into an ellipsoid of the same volume and then converted back into the sphere. It is shown that at sufficiently large strain amplitudes, the deformation of the material involves localized plastic events that are identified based on the relative displacement of atoms before and after the shear transformation.We find that the density profiles of cage jumps decay away from the inclusion, which correlates well with the radial dependence of the local deformation of the material. At the same strain amplitude, the plastic deformation becomes more pronounced in the cases of weakly damped dynamics or large time scales of the shear transformation. We show that the density profiles can be characterized by the universal function of the radial distance multiplied by a dimensionless factor that depends on the friction coefficient and the time scale of the shear event.

We consider a linear model of optical transmission through a fiber with birefringent disorder in the presence of amplifier noise. Both disorder and noise are assumed to be weak, i.e., the average bit-error rate (BER) is small. The probability distribution function (PDF) of rare violent events leading to the values of BER much larger than its typical value is estimated. We show that the PDF has a long algebraiclike tail.

The effect of oscillatory shear strain on nonaffine rearrangements of individual particles in a three-dimensional binary glass is investigated using molecular dynamics simulations. The amorphous material is represented by the Kob-Andersen mixture at the temperature well below the glass transition. We find that during periodic shear deformation of the material, some particles undergo reversible nonaffine displacements with amplitudes that are approximately power-law distributed. Our simulations show that particles with large amplitudes of nonaffine displacement exhibit a collective behavior; namely, they tend to aggregate into relatively compact clusters that become comparable with the system size near the yield strain. Along with reversible displacements there exist a number of irreversible ones. With increasing strain amplitude, the probability of irreversible displacements during one cycle increases, which leads to permanent structural relaxation of the material.

We study the behavior of a minimal model of synaptically sustained persistent activity that consists of two quadratic integrate-and-fire neurons mutually coupled via excitatory synapses. Importantly, each of the neurons is excitable, as opposed to an oscillator; hence when uncoupled it sits at a subthreshold rest state. When the constituent neurons are mutually coupled via sufficiently strong fast excitatory synapses, the system demonstrates bistability between a fixed point (quiescent background state) and a limit cycle (memory state with synaptically driven spiking activity). Previous work showed that this persistent activity can be stopped by an excitatory input that synchronizes the network. Here we analyzed how this persistent state reacts to partial synchronization. We considered three types of progressively more complex excitatory synaptic kernels: delta pulse, square, and exponential. The first two cases were treated analytically, and the latter case numerically. Using phase-plane methods, we characterized the shape of the region, such that all orbits starting within it correspond to infinite spike trains; this constitutes the persistent activity region. In the case of instant coupling, all such active orbits were neutrally stable; in the case of noninstant coupling, the activity region contained a unique stable limit cycle (so the activity region was the basin of attraction for the limit cycle). This limit cycle corresponded to purely antiphase spiking of two neurons. Increasing synchronization shifted the system toward the border of the activity region, eventually terminating spiking activity. We calculated three measures of robustness of the active state: width of the activity region in the phase plane, critical level of synchronization that can be tolerated by the persistent spiking activity, and speed of reconvergence to the limit cycle. Our analysis revealed that the self-sustained activity is more robust to synchronization when each individual neuron is closer to SNIC bifurcation (closer to being an intrinsic oscillator), the recurrent synaptic excitation is stronger, and the synaptic decay is slower, which is in agreement with the existing data on local circuits in the cortex that show sustained activity.

A plasma model of relaxation of a medium in heavy-ion tracks in condensed matter is proposed. The model is based on three assumptions: the Maxwell distribution of plasma electrons, localization of plasma inside the track nanochannel, and constant values of the plasma electron density and temperature during the x-ray irradiation. The model of multiple ionization of target atoms by a fast projectile ion is used to determine the initial conditions. An analysis of the results of the calculations performed makes it possible to define when the atomic relaxation model is a very rough approximation and the plasma relaxation model must be used. It is demonstrated that the plasma relaxation model adequately describes the x-ray spectra observed upon interaction of a fast ion with condensed target. The comparison with the experimental data justifies the reliability of the plasma relaxation model. Preassumptions of plasma relaxation model are validated by the moleculardynamics simulation. An x-ray spectral method based on the plasma relaxation model is proposed for diagnostics of the plasma in fast ion tracks. The results obtained can be useful in examining the initial stage of defect formation in solids under irradiation with single fast heavy ions.

Dynamics of solitons is considered in the framework of an extended nonlinear Schrödinger equation (NLSE), which is derived from a Zakharov-type model for wind-driven high-frequency (HF) surface waves in the ocean, coupled to damped low-frequency (LF) internal waves. The drive gives rise to a convective (but not absolute) instability in the system. The resulting NLSE includes a* pseudo-stimulated-Raman-scattering* (pseudo-SRS) term, which is a spatial-domain counterpart of the SRS term, a well-known ingredient of the temporal-domain NLSE in optics. Analysis of the field-momentum balance and direct simulations demonstrate that wavenumber downshift by the pseudo-SRS may be compensated by the upshift induced by the wind traction, thus maintaining robust bright solitons in both stationary and oscillatory forms; in particular, they are not destroyed by the underlying convective instability. Analytical soliton solutions are found in an approximate form and verified by numerical simulations. Solutions for soliton pairs are obtained in the numerical form.

An effect which suppresses recombination in ion plasmas is considered both theoretically and experimentally. Experimental results are presented for the ion recombination rate in fluorine plasma, which are obtained from data for the gas discharge afterglow. To interpret them, a suppression factor is considered: ion solvation in weakly ionized plasma. It is shown that the recombination process has a two-stage character with the formation of intermediate metastable ion pairs. The pairs consist of negative and positive ion-molecular clusters. A theoretical explanation is given for the slowing down of the ion recombination with the increase of the Coulomb coupling compared to the ion recombination rate calculated in the ideal plasma approximation. The approximate similarity of the recombination rate of the ion temperature and concentration and reasons for the slight deviation from the similarity are elucidated.

The dynamical response of metallic clusters up to 103 atoms is investigated using the restricted molecular dynamics simulations scheme. Exemplarily, a sodium like material is considered. Correlation functions are evaluated to investigate the spatial structure of collective electron excitations and the optical response of laserexcited clusters. In particular, the spectrum of bilocal correlation functions shows resonances representing different modes of collective excitations inside the nano plasma. The spatial structure, the resonance energy, and the width of the eigenmodes have been investigated for various values of electron density, temperature, cluster size, and ionization degree. Comparison with bulk properties is performed and the dispersion relation of collective excitations is discussed.

We consider an equilibrium ensemble of large Erdos-Renyi topological random networks with fixed vertex ˝ degree and two types of vertices, black and white, prepared randomly with the bond connection probability p. The network energy is a sum of all unicolor triples (either black or white), weighted with chemical potential of triples μ. Minimizing the system energy, we see for some positive μ the formation of two predominantly unicolor clusters, linked by a string of Nbw black-white bonds. We have demonstrated that the system exhibits critical behavior manifested in the emergence of a wide plateau on the Nbw(μ) curve, which is relevant to a spinodal decomposition in first-order phase transitions. In terms of a string theory, the plateau formation can be interpreted as an entanglement between baby universes in two-dimensional gravity. We conjecture that the observed classical phenomenon can be considered as a toy model for the chiral condensate formation in quantum chromodynamics.

Steady statistics of a passive scalar advected by a random two-dimensional flow of an incompressible fluid is described in the range of scales between the correlation length of the flow and the diffusion scale. This corresponds to the so-called Batchelor regime where the velocity is replaced by its large-scale gradient. The probability distribution of the scalar in the locally comoving reference frame is expressed via the probability distribution of the line stretching rate. The description of line stretching can be reduced to a classical problem of the product of many random matrices with a unit determinant. We have found the change of variables that allows one to map the matrix problem onto a scalar one and to thereby prove the central limit theorem for the stretching rate statistics. The proof is valid for any finite correlation time of the velocity field. Whatever the statistics of the velocity field, the statistics of the passive scalar (averaged over time locally in space) is shown to approach Gaussian statistics with increase in the Péclet number Pe (the pumping-to-diffusion scale ratio).

We discuss the structure and geometrical characteristics of coherent vortices appearing as a result of the inverse cascade in two-dimensional turbulence in a finite box.We demonstrate that the universal velocity profile, established by J. Laurie et al. [Phys. Rev. Lett. 113, 254503 (2014)], corresponds to the passive regime of flow fluctuations.We find the vortex core radius and the vortex size, and we argue that the amount of vortices generated in the box depends on the system parameters

The rogue wave solutions (rational multibreathers) of the nonlinear Schr¨odinger equation (NLS) are tested in numerical simulations of weakly nonlinear and fully nonlinear hydrodynamic equations. Only the lowest order solutions from 1 to 5 are considered. A higher accuracy of wave propagation in space is reached using the modified NLS equation, also known as the Dysthe equation. This numerical modeling allowed us to directly compare simulations with recent results of laboratory measurements in Chabchoub et al. [Phys. Rev. E 86, 056601 (2012)]. In order to achieve even higher physical accuracy, we employed fully nonlinear simulations of potential Euler equations. These simulations provided us with basic characteristics of long time evolution of rational solutions of the NLS equation in the case of near-breaking conditions. The analytic NLS solutions are found to describe the actual wave dynamics of steep waves reasonably well.

We examine the question of the influence of sparse long-range communications on the synchronization in parallel discrete event simulations (PDES). We build a model of the evolution of local virtual times (LVT) in a conservative algorithm including several choices of local links. All network realizations belong to the small-world network class. We find that synchronization depends on the average shortest path of the network. The time profile dynamics are similar to the surface profile growth, which helps to analyze synchronization effects using a statistical physics approach. Without long-range links of the nodes, the model belongs to the universality class of the Kardar--Parisi--Zhang equation for surface growth. We find that the critical exponents depend logarithmically on the fraction of long-range links. We present the results of simulations and discuss our observations.

We propose a theoretical explanation for the long-standing problem of the anomalous critical behavior of the heat capacity near the smectic-A–hexatic phase transition. Experiments find a large specific heat critical exponent α=0.5–0.7, which is inconsistent with a small negative value α=-0.01 expected for the three- dimensional XYuniversality class. We show that most of the observed features can be explained by treating simultaneously fluctuations of the hexatic orientational and translational (positional) order parameters. Assuming that the translational correlation length ξ is much larger than the hexatic correlation length ξh, we calculate thetemperature dependence of the heat capacity in the critical region near the smectic- A–hexatic phase transition. Our results are in quantitative agreement with the calorimetric experimental data.

We propose a theoretical explanation for the long-standing problem of the anomalous critical behavior of the heat capacity near the smectic-A–hexatic phase transition. Experiments find a large specific heat critical exponent α=0.5–0.7, which is inconsistent with a small negative value α≈−0.01 expected for the three-dimensional XY universality class. We show that most of the observed features can be explained by treating simultaneously fluctuations of the hexatic orientational and translational (positional) order parameters. Assuming that the translational correlation length ξtr is much larger than the hexatic correlation length ξh, we calculate the temperature dependence of the heat capacity in the critical region near the smectic-A–hexatic phase transition. Our results are in quantitative agreement with the calorimetric experimental data.