A magnetic system with a phase transition at temperature $T_c$ may exhibit double-resonance peaks under a periodic external magnetic field because the time scale matches the external frequency at two different temperatures, one above $T_c$ and the other below $T_c$. We study the double-resonance phenomena for the mean-field $q$-state clock model based on the heat-bath-type master equation. We find double peaks as observed in the kinetic Ising case ($q=2$) for all $q\ge 4$, but for the three-state clock model ($q=3$), the existence of double peaks is possible only above a certain external frequency since it undergoes a discontinuous phase transition.

The theory of stochastic resonance in multistable systems is extended to account for both direct transitions between all stable states present and indirect ones involving intermediate states. It is shown that to satisfy these requirements the dynamics needs to be embedded in phase spaces of dimension equal to at least two. Under well defined conditions, the conjunction of the presence of intermediate states and the multidimensional character of the process leads to an enhancement of the response of the system to an external periodic forcing.

In the framework of the paradigmatic prisoner's dilemma game, we investigate the evolutionary dynamics of social dilemmas in the presence of “cooperation facilitators.” In our model, cooperators and defectors interact as in the classical prisoner's dilemma, where selection favors defection. However, here the presence of a small number of cooperation facilitators enhances the fitness (reproductive potential) of cooperators, while it does not alter that of defectors. In a finite population of size $N$, the dynamics of the prisoner's dilemma with facilitators is characterized by the probability that cooperation takes over (fixation probability) by the mean times to reach the absorbing states. These quantities are computed exactly using Fokker-Planck equations. Our findings, corroborated by stochastic simulations, demonstrate that the influence of facilitators crucially depends on the difference between their density $z$ and the game's cost-to-benefit ratio $r$. When $z>r$, the fixation of cooperators is likely in a large population and, under weak selection pressure, invasion and replacement of defection by cooperation is favored by selection if $b(z-r)(1-z)>N^{-1}$, where $0<b⩽1$ is the cooperation payoff benefit. When $z<r$, the fixation probability of cooperators is exponentially enhanced by the presence of facilitators but defection is the dominating strategy.

We propose a methodology of estimating the scaling exponent for a long-range correlation in a nonstationary time series from the perspective of the regression analysis. By an adaptive degree determination of a regression polynomial, the proposed methodology is designed to properly remove various types of trends embedded in the nonstationary signal so that the scaling exponent can be estimated without artificial crossovers. To show the validity of the proposed methodology, we applied it to the detrended fluctuation analysis and tested it out against correlated data superimposed by various types of trends. It turned out that, unlike the conventional technique, our approach was capable of eliminating artificial crossovers. We also discuss the statistical characteristics of the proposed method with regard to the estimation of the scaling exponent.

Swarms of self-propelled particles exhibit complex behavior that can arise from simple models, with large changes in swarm behavior resulting from small changes in model parameters. We investigate the steady-state swarms formed by self-propelled Morse particles in three dimensions using molecular dynamics simulations optimized for graphics processing units. We find a variety of swarms of different overall shape assemble spontaneously and that for certain Morse potential parameters at most two competing structures are observed. We report a rich “phase diagram” of athermal swarm structures observed across a broad range of interaction parameters. Unlike the structures formed in equilibrium self-assembly, we find that the probability of forming a self-propelled swarm can be biased by the choice of initial conditions. We investigate how thermal noise influences swarm formation and demonstrate ways it can be exploited to reconfigure one swarm into another. Our findings validate and extend previous observations of self-propelled Morse swarms and highlight open questions for predictive theories of nonequilibrium self-assembly.

We explore a class of hybrid (piecewise deterministic) systems characterized by a large number of individuals inhabiting an environment whose state is described by a set of continuous variables. We use analytical and numerical methods from nonequilibrium statistical mechanics to study the influence that intrinsic noise has on the qualitative behavior of the system. We discuss the application of these concepts to the case of semiarid ecosystems. Using a system-size expansion we calculate the power spectrum of the fluctuations in the system. This predicts the existence of noise-induced oscillations.

The quantum dissipation of a fermionic oscillator in an environment of fermionic oscillators is considered. Since fermions anticommute, their eigenvalues are anticommuting numbers. Based on an expansion of the reduced density operator in terms of fermionic coherent states which make use of these anticommuting numbers or Grassmann variables, a Fokker-Planck equation for the associated quasiprobability distribution function is derived. The density operator approach to fermionic fields as introduced by Cahill and Glauber [Phys. Rev. A 59, 1538 (1999)] thus can be extended to the nonequilibrium domain.

Force chains, the primary load-bearing structures in dense granular materials, rearrange in response to applied stresses and strains. These self-organized grain columns rely on contacts from weakly stressed grains for lateral support to maintain and find new stable states. However, the dynamics associated with the regulation of the topology of contacts and strong versus weak forces through such contacts remains unclear. This study of local self-organization of frictional particles in a deforming dense granular material exploits a transition matrix to quantify preferred conformations and the most likely conformational transitions. It reveals that favored cluster conformations reside in distinct stability states, reminiscent of “magic numbers” for molecular clusters. To support axial loads, force chains typically reside in more stable states of the stability landscape, preferring stabilizing trusslike, three-cycle contact triangular topologies with neighboring grains. The most likely conformational transitions during force chain failure by buckling correspond to rearrangements among, or loss of, contacts which break the three-cycle topology.

The contact angle of a fluid droplet on an heterogeneous surface is analyzed using the statistical dynamics of the spreading contact line. The statistical properties of the final droplet radius and contact angle are obtained through applications of depinning transitions of contact lines with nonlocal elasticity and features of pinning-depinning dynamics. Such properties not only depend on disorder strength and surface details, but also on the droplet volume and disorder correlation length. Deviations from Wenzel or Cassie-Baxter behavior are particularly apparent in the case of small droplet volumes and small contact angles.

The biological requirements for an ecosystem to develop and maintain species diversity are in general unknown. Here we consider a model ecosystem of sessile and mutually excluding organisms competing for space [Mathiesen et al. Phys. Rev. Lett. 107, 188101 (2011)]. Competition is controlled by an interaction network with fixed links chosen by a Bernoulli process. New species are introduced in the system at a predefined rate. In the limit of small introduction rates, the system becomes bistable and can undergo a phase transition from a state of low diversity to high diversity. We suggest that isolated patches of metapopulations formed by the collapse of cyclic relations are essential for the transition to the state of high diversity.

Here we consider the spatially extended model incorporating the temperature-dependent autocatalytic coefficient into the Merkin-Needham-Scott version of the Selkov system and show that this model with temperature gradient quite reasonably explains the experimentally detected traveling glycolytic nonstationary waves, which can be attributed as kinematic ones. Additionally, we analyze the influence of possibly incorporating diffusion terms into the equations. It is shown that the value of diffusivity influences the timetable for the birth of new wave and their further evolution. This result could be used as a method for the determination of diffusivity.

We report a study of crack patterns formed in laponite gel drying in an electric field. The sample dries in a circular petri dish and the field is radial, acting inward or outward. A system of radial cracks forms in the setup with the center terminal positive, while predominantly cross-radial cracks form when the center is at a negative potential. The laponite accumulates near the negative terminal making the layer thicker at this end. A spring model on a square lattice is used to simulate the desiccation crack formation, with an additional radial force acting due to the electric field. With the radial force acting outward, radial cracks form and for the reversed field cross-radial cracks form. This conforms to the observation that laponite platelets become effectively positive due to overcharging and are attracted towards the negative terminal.

The concept of a bounded confidence level is incorporated in a nonconservative kinetic exchange model of opinion dynamics model where opinions have continuous values $\in [-1,1]$. The characteristics of the unrestricted model, which has one parameter $\lambda$ representing conviction, undergo drastic changes with the introduction of bounded confidence parametrized by $\delta$. Three distinct regions are identified in the phase diagram in the $\delta -\lambda$ plane and the evidences of a first order phase transition for $\delta ⩾0.3$ are presented. A neutral state with all opinions equal to zero occurs for $\lambda ⩽{\lambda }_{c_1}\simeq 2/3$, independent of $\delta$, while for ${\lambda }_{c_1}⩽\lambda ⩽{\lambda }_{c_2}\left(\delta \right)$, an ordered region is seen to exist where opinions of only one sign prevail. At ${\lambda }_{c_2}\left(\delta \right)$, a transition to a disordered state is observed, where individual opinions of both signs coexist and move closer to the extreme values ($\pm 1$) as $\lambda$ is increased. For confidence level $\delta <0.3$, the ordered phase exists for a narrow range of $\lambda$ only. The line $\delta =0$ is apparently a line of discontinuity, and this limit is discussed in some detail.

Since the Susceptible-Infected-Susceptible (SIS) epidemic threshold is not precisely defined in spite of its practical importance, the classical SIS epidemic process has been generalized to the $\varepsilon -$SIS model, where a node possesses a self-infection rate $\varepsilon$, in addition to a link infection rate $\beta$ and a curing rate $\delta$. The exact Markov equations are derived, from which the steady state can be computed. The major advantage of the $\varepsilon -$SIS model is that its steady state is different from the absorbing (or overall-healthy state) and approximates, for a certain range of small $\varepsilon >0$, the in reality observed phase transition, also called the “metastable” state, that is characterized by the epidemic threshold. The exact steady-state analysis for the complete graph illustrates the effect of small $\varepsilon$ and the quality of the first-order mean-field approximation, the $N$-intertwined model, proposed earlier. Apart from duality principles, often used in the mathematical literature, we present an exact recursion relation for the Markov infinitesimal generator.

Using advanced continuation techniques for dynamical systems, we elucidate the bifurcations leading to asymptotically stable square-wave pulsing and polarization mode switching in semiconductor lasers with mutual time-delayed and polarization rotating coupling. We find that the increase of coupling strength leads to a cascade of Hopf bifurcations on a mixed-mode steady state up to a transcritical bifurcation on a so-called pure-mode steady state where both lasers emit with the injected polarization state. From these successive Hopf bifurcations emerge time-periodic solutions that have a period close to the laser relaxation oscillation for weak coupling but a period close to twice the time delay for large coupling strength. The wave form of the time-periodic solutions also evolves from harmonic pulsing up to square-wave pulsing as has been observed recently in experiments.

We derive statistical equilibrium solutions of the truncated inviscid surface quasigeostrophic (SQG) equations, and verify the validity of these solutions at late times in numerical simulations. The results indicate the pseudoenstrophy thermalizes while the pseudoenergy can condense at the gravest modes, in agreement with previous indications of a direct cascade of pseudoenstrophy and an inverse cascade of pseudoenergy in forced-dissipative SQG systems. At early times, the truncated inviscid SQG simulations show a behavior reminiscent of forced-dissipative SQG turbulence, and we identify spectral scaling laws for the pseudoenergy and pseudoenstrophy spectra. More importantly, a comparison between viscous and inviscid simulations allows us to identify free-decay laws for the pseudoenstrophy in SQG turbulence at very large Reynolds number.

A significant effect of aggregation dynamics for aqueous ferrofluid (AF) and kerosene based ferrofluid (KF) using magnetic field dependent capillary viscosity and magneto-optical relaxation measurements is studied. For better comparison parameters of AF and KF are kept similar. Ferrohydrodynamic equations of chain forming ferrofluids, dilute ferrofluids, and Brownian dynamic simulations are compared. It is observed that the rotational viscosity of AF is larger than that of KF due to field induced aggregates in it and strong dipolar interactions. It is also observed that at Ωτ ∼ 0.04 both AF and KF viscosity becomes almost similar, suggesting similar behavior at that shear rate. The magneto-optical relaxation in AF exhibits nonexponential behavior when relaxed from higher magnetic field and follows irreversible thermodynamics, whereas for KF the relaxation is exponential and follows the effective field method. This discrepancy is explained based on aggregation dynamics of magnetic particles. Results are well described by the corresponding theoretical models.

We present an experimental study of turbulent Rayleigh-Bénard convection with polymer additives made in two convection cells, one with a smooth top and bottom plates and the other with a rough top and bottom plates. For the cell with smooth plates, a reduction of the measured Nusselt number (Nu) was observed. Furthermore, the amount of Nu reduction increases with increasing polymer concentration ($c$), reaching $\sim$12$\%$ for $c=120$ ppm and an apparent leveling off thereafter. For the cell with rough plates, however, an enhancement ($\sim$4$\%$) of Nu was observed when the polymer concentration is greater than 120 ppm. This increase in Nu is corroborated by an increased large-scale circulation (LSC) velocity in the same cell when polymers are added. In contrast, the LSC velocity in the smooth cell is found to be essentially the same with and without polymers. It is further found that in the smooth cell the rms values of the global Nu, ${\sigma }_{\mathrm{Nu}}$, and that of the local temperature, ${\sigma }_T$, both exhibit similar dependence on $c$ as Nu itself. In contrast, ${\sigma }_{\mathrm{Nu}}$ and ${\sigma }_T$ in the rough cell are found to be essentially independent of $c$.

A one-dimensional particle in cell simulation of large amplitude plasma oscillations is carried out to explore the physics beyond wave breaking in a cold homogeneous unmagnetized plasma. It is shown that after wave breaking, all energy of the plasma oscillation does not end up as random kinetic energy of particles, but some fraction, which is decided by Coffey's wave breaking limit in warm plasma, always remains with two oppositely propagating coherent Bernstein-Greene-Kruskal like modes with supporting trapped particle distributions. The randomized energy distribution of untrapped particles is found to be characteristically non-Maxwellian with a preponderance of energetic particles.

A radially decreasing toroidal rotation frequency can have a stabilizing effect on nonaxisymmetric magnetohydrodynamic (MHD) instabilities. We show that this is a consequence of the Coriolis effect that induces a restoring pressure gradient force when plasma is perturbed radially. In a rotating cylindrical plasma, this Coriolis-pressure effect is canceled by the centrifugal effect responsible for the magnetorotational instability. In a magnetically confined toroidal plasma, a large aspect ratio expansion shows that only half of the effect is canceled. This analytical result is confirmed by numerical computations. When the plasma rotates faster toroidally in the core than near the edge, the effect can contribute to the formation of transport barriers by stabilizing MHD instabilities.