We study the effect of team and hierarchy on the waiting-time dynamics of priority-queue networks. To this end, we introduce generalized priority-queue network models incorporating interaction rules based on team-execution and hierarchy in decision making, respectively. It is numerically found that the waiting-time distribution exhibits a power law for long waiting times in both cases, yet with different exponents depending on the team size and the position of queue nodes in the hierarchy, respectively. The observed power-law behaviors have in many cases a corresponding single or pairwise-interacting queue dynamics, suggesting that the pairwise interaction may constitute a major dynamic consequence in the priority-queue networks. It is also found that the reciprocity of influence is a relevant factor for the priority-queue network dynamics.

A generalized set of nonlinear electromagnetic quantum hydrodynamic (QHD) equations is derived for a magnetized quantum plasma, including collisional, electron spin-$\frac{1}{2}$, and relativistically degenerate electron pressure effects that are relevant for dense astrophysical systems, such as white dwarfs. For illustrative purposes, linear dispersion relations are derived for one-dimensional magnetoacoustic waves for a collisionless nonrelativistic degenerate gas in the presence of the electron spin-$\frac{1}{2}$ contribution and for magnetoacoustic waves in a plasma containing relativistically degenerate electrons. It is found that both the spin and relativistic degeneracy at high densities tend to slow down the magnetoacoustic wave due to the Pauli paramagnetic effect and relativistic electron mass increase. The present study outlines the theoretical framework for the investigation of linear and nonlinear behaviors of electromagnetic waves in dense astrophysical systems. The results are applied to calculate the magnetoacoustic speeds for both the nonrelativistic and relativistic electron degeneracy cases typical for white dwarf stars.

We investigate the effects of anisotropy on the finite-size scaling of connectivity and conductivity of continuum percolation in three dimensions. We consider a system of size $X\times Y\times Z$ in which cubic bodies of size $a\times b\times c$ are placed randomly. We define two aspect ratios to request anisotropy then we expect that the displacement of average connected fraction $P$ (averaged over the realizations), about the isotropic universal curves will be a function of the two aspect ratios. This is accounted by considering an apparent percolation threshold in each direction which leads to 50% of realizations connecting in that direction. We find the aspect ratios’ dependency of the apparent threshold and investigate the finite-size scaling transformations for the mean connected fraction and its associated fluctuations. Moreover, we apply a single phase pressure solver to determine the conductivity of various realizations of the system. Finally we apply the same idea to account for the effect of anisotropy on the conductivity scaling.

We consider overdamped Brownian dynamics in a periodic potential with temporally oscillating amplitude. We analyze the transport which shows effective diffusion enhanced by the oscillations and derive approximate expressions for the diffusion coefficient. Furthermore we analyze the effect of the oscillating potential on the transport if additionally a constant force is applied. We show the existence of synchronization regimes at which the deterministic dynamics is in resonance with the potential oscillations, giving rise to transport with extremely low dispersion. We distinguish slow and fast oscillatory driving and give analytical expressions for the mean velocity and effective diffusion.

This paper develops a formulation of the quasispecies equations appropriate for polysomic, semiconservatively replicating genomes. This paper is an extension of previous work on the subject, which considered the case of haploid genomes. Here, we develop a more general formulation of the quasispecies equations that is applicable to diploid and even polyploid genomes. Interestingly, with an appropriate classification of population fractions, we obtain a system of equations that is formally identical to the haploid case. As with the work for haploid genomes, we consider both random and immortal DNA strand chromosome segregation mechanisms. However, in contrast to the haploid case, we have found that an analytical solution for the mean fitness is considerably more difficult to obtain for the polyploid case. Accordingly, whereas for the haploid case we obtained expressions for the mean fitness for the case of an analog of the single-fitness-peak landscape for arbitrary lesion repair probabilities (thereby allowing for noncomplementary genomes), here we solve for the mean fitness for the restricted case of perfect lesion repair.

We demonstrate the preservation of the Lyapunov modes in a system of hard disks by the underlying tangent space dynamics. This result is exact for the Zero modes and correct to order $ϵ$ for the Transverse and Longitudinal-Momentum modes, where $ϵ$ is linear in the mode number. For sufficiently large mode numbers, the $ϵ$ terms become significant and the dynamics no longer preserves the mode structure. We propose a modified Gram-Schmidt procedure based on orthogonality with respect to the center zero space that produces the exact numerical mode. This Gram-Schmidt procedure can also exploit the orthogonality between conjugate modes and their symplectic structure in order to find a simple relation that determines the Lyapunov exponent from the Lyapunov mode. This involves a reclassification of the modes into either direction preserving or form preserving. These analytic methods assume a knowledge of the ordering of the modes within the Lyapunov spectrum, but gives both predictive power for the values of the exponents from the modes and describes the modes in greater detail than was previously achievable. Thus the modes and the exponents contain the same information.

In an equilibrium chemical reaction mixture, the number of molecules present obeys a Poisson distribution. We report that, surprisingly, the same is true of a large class of nonequilibrium reaction networks. In particular, we show that certain topological features imply a Poisson distribution, whatever the reaction rates. Such driven systems also obey an analog of the fluctuation-dissipation theorem. Our results shed light on the fundamental question of when equilibrium concepts might apply to nonequilibrium systems and may have applications to models of noise in biochemical networks.

In confined systems near a continuous phase transition the long-ranged fluctuations of the corresponding order parameter are subject to boundary conditions. These constraints result in so-called critical Casimir forces acting as effective forces on the confining surfaces. For systems belonging to the Ising bulk universality class corresponding to a scalar order parameter the critical Casimir force is studied for the film geometry in the crossover regime characterized by different surface fields at the two surfaces. The scaling function of the critical Casimir force is calculated within mean-field theory. Within our approach, the scaling functions of the critical Casimir force and of the order parameter profile for finite surface fields can be mapped by rescaling, except for a narrow crossover regime, onto the corresponding scaling function of the so-called normal fixed point of strong surface fields. In the crossover regime, the critical Casimir force as function of temperature exhibits more than one extremum and for certain ranges of surface field strengths it changes sign twice upon varying temperature. Monte Carlo simulation data obtained for a three-dimensional Ising film show similar trends. The sign of the critical Casimir force can be inferred from the comparison of the order parameter profiles in the film and in the semi-infinite geometry.

The effects of network clustering on diversity-induced resonance of an ensemble of bistable systems subjected to weak signals are investigated. A class of network models based on hidden metric spaces is used to generate networks with different levels of clustering. The propensity of triples of nodes is to form triangles. By numerical simulations and analytical calculations, it is shown that the maximum response is suppressed by network clustering. The optimal diversity strength for maximum response is also reduced. A pronounced resonance phenomenon is observed at an intermediate clustering strength. Either low or high clustering strength will undermine the response of the systems to external signals. The results imply that it is possible to control the response of spatially extended systems to external signals by the manipulation of network clustering.

Relative stability of uniaxial and biaxial nematic phases is analyzed in a model nematic liquid crystal composed of flat molecules of $C_{2h}$ symmetry with four mesogenic groups rigidly linked to the same center. The generalized effective quadrupole mean-field potential is proposed and its constants are evaluated numerically for the pair intermolecular potential based on Gay-Berne interaction between mesogenic groups. The dependencies of the constants on molecular shape parameters are systematically analyzed. Order parameters of the uniaxial and biaxial nematic phases are evaluated by direct minimization of the free energy at different temperatures. The corresponding phase diagrams are obtained enabling one to study the effects of molecular model parameters on the stability regions of uniaxial and biaxial phases. The results are used to clarify the nature of experimentally observed biaxial ordering in nematic liquid crystals composed of tetrapode molecules with the same symmetry.

The addition of a macromolecular crowding agent to a dilute solution of polymer exerts a compressive force that tends to reduce the size of the chain. We study here the effect of changing the size ratio between the random coil and the crowding agent. The compression occurs at lower crowding agent concentration, $\Phi$ when polymer molecular weight increases. The Flory exponent $\nu \left(\Phi \right)$ decreases from $\nu \left(0\right)\simeq 0.48$ in water down to 0.3 with macromolecular crowding. The effective polymer-polymer interactions change from repulsive to strongly attractive inducing aggregation of the chains. This effect changes drastically for larger polymer sizes, being much more pronounced at high molecular weights.

Oscillatory regulatory networks have been discovered in many regulatory pathways. Due to their enormous complexity, it is necessary to study their dynamics by means of highly simplified models. These models have received particular value because artificial regulatory networks can be engineered experimentally. In this paper, we study dynamical properties of an artificial regulatory oscillator called repressilator. We have shown that oscillations arise from the existence of an absorbing toruslike region in the phase space of the model. This geometric structure requires monotonic repression at all promoters and the absence of any regulatory connections apart from a cyclic repression loop. We show that oscillations collapse as only weak extra connections are introduced if there is imbalance between the attended concentrations and those sufficient for saturation of the promoters. We found that a pair of diffusively coupled repressilators displays synchronization properties similar to those of relaxation oscillators if the regulatory connections in the cyclic repression loop are strong. Thus, the role of strengthening these connections can be viewed as introducing time scale separation among variables. This may explain controversial synchronization properties reported for repressilators in earlier studies.

External forcing can greatly affect the evolution of Turing patterns in reaction-diffusion (RD) media. Here, we employ spatially periodic illumination in a photosensitive RD system to create Turing structures that are repetitive in one direction. We then study their relaxation in the absence of light. These unforced, fishbonelike configurations undergo self-reorganization and establish stationary arrangements, some of which fully exhibit, while others partially or completely lose, the symmetry of the initially imposed pattern.

We present an analytical study of the linearized impulsive Richtmyer-Meshkov flow for incompressible elastic solids. Seminumerical prior investigations of a related shock-driven compressible elastic problem suggest that the interface amplitude remains bounded in time, in contrast to the unstable behavior found for gases. Our approach considers a base unperturbed flow and a linearization of the conservation equations around the base solution. The resulting initial and boundary value problem is solved using Laplace transform techniques. Analysis of the singularities of the resultant function in the Laplace domain allows us to perform a parametric study of the behavior of the interface in time. We identify two differentiated long-term patterns for the interface, which depends on the material properties: standing wave and oscillating decay. Finally, we present results for the vorticity distribution, which show that the shear stiffness of the solids is responsible both for the stabilization of the interface, and also for the period of the interface oscillations. Comparisons with previous results are discussed.

It is shown that nonlinear three-wave interaction, described by vector-product-type nonlinearities, in pair plasmas implies much more restrictive conditions for a double energy transfer, as compared to electron-ion plasmas.

We study Lévy walks in quenched disordered one-dimensional media, with scatterers spaced according to a long-tailed distribution. By analyzing the scaling relations for the random-walk probability and for the resistivity in the equivalent electric problem, we obtain the asymptotic behavior of the mean-square displacement as a function of the exponent characterizing the scatterers distribution. We demonstrate that in quenched media different average procedures can display different asymptotic behavior. In particular, we estimate the moments of the displacement averaged over processes starting from scattering sites. Our results are compared with numerical simulations, with excellent agreement.

A gravity-driven flow of grains through a narrow pipe in vacuum is studied by means of a one-dimensional model with two coefficients of restitution. Numerical simulations show clearly how density waves form when a strikingly simple criterion is fulfilled: that dissipation due to collisions between the grains and the walls of the pipe is greater per collision than that which stems from collisions between particles. Counterintuitively, the highest flow rate is observed when the number of grains per density wave grows large. We find strong indication that the number of grains per density wave always approaches a constant as the particle number tends to infinity, and that collapse to a single wave, which was often observed also in previous simulations, occurs because the number of grains is insufficient for multiple wave formation.

The spheropolyhedra method has been used earlier for efficient and accurate molecular dynamics simulations of granular matter with particles with complex shapes. Also the Voronoi construction is a tool of proved utility for the virtual representation of powders and grains. In this paper a technique that combines the two methods and provides a framework for the study of the three-dimensional mechanical behavior of granular matter is proposed. In order to understand the capabilities of the new method, a number of computer simulations of the cubic (true) triaxial test, measuring the mechanical behavior of packing of particles, is carried out. Results from tests with packing of complex-shaped particles represented by “Voronoi particles” are compared with corresponding results of packing of spherical particles. Features such as the saturation value for the macroscopically observed coefficient of friction, as reported in the literature, are compared for the packing of spheres and for the packing of “Voronoi particles,” showing that the difference in shape strongly affects the results. The proposed technique and simulation results can be used to help understand how the individual shape of grains affects the macroscopic mechanical behavior of granular matter such as cohesionless soils.