We study several variants of the stochastic four-state rock-paper-scissors game or, equivalently, cyclic three-species predator-prey models with conserved total particle density, by means of Monte Carlo simulations on one- and two-dimensional lattices. Specifically, we investigate the influence of spatial variability of the reaction rates and site occupancy restrictions on the transient oscillations of the species densities and on spatial correlation functions in the quasistationary coexistence state. For small systems, we also numerically determine the dependence of typical extinction times on the number of lattice sites. In stark contrast with two-species stochastic Lotka-Volterra systems, we find that for our three-species models with cyclic competition quenched disorder in the reaction rates has very little effect on the dynamics and the long-time properties of the coexistence state. Similarly, we observe that site restriction only has a minor influence on the system’s dynamical properties. Our results therefore demonstrate that the features of the spatial rock-paper-scissors system are remarkably robust with respect to model variations, and stochastic fluctuations as well as spatial correlations play a comparatively minor role.

We investigate the statistical properties of an overdamped Brownian particle that is trapped by a harmonic potential and simultaneously exposed to a linear shear flow or to a plane Poiseuille flow. Its probability distribution is determined via the corresponding Smoluchowski equation, which is solved analytically for a linear shear flow. In the case of a plane Poiseuille flow, analytical approximations for the distribution are obtained by a perturbation analysis and are substantiated by numerical results. There is good agreement between the two approaches for a wide range of parameters.

Cyclic competition is a mechanism underlying biodiversity in nature and the competition between large numbers of interacting individuals under multifaceted environmental conditions. It is commonly modeled with the popular children’s rock-paper-scissors game. Here we probe cyclic competition systematically in a community of three strains of bacteria Escherichia coli. Recent experiments and simulations indicated the resistant strain of E. coli to win the competition. Other data, however, predicted the sensitive strain to be the final winner. We find a generic feature of cyclic competition that solves this puzzle: community size plays a decisive role in selecting the surviving competitor. Size-dependent effects arise from an easily detectable “period of quasiextinction” and may be tested in experiments. We briefly indicate how.

The shape and the dynamics of reversals of the magnetic field in a turbulent dynamo experiment are investigated. We report the evolution of the dipolar and the quadrupolar parts of the magnetic field in the VKS experiment, and show that the experimental results are in good agreement with the predictions of a recent model of reversals: when the dipole reverses, part of the magnetic energy is transferred to the quadrupole, reversals begin with a slow decay of the dipole and are followed by a fast recovery, together with an overshoot of the dipole. Random reversals are observed at the borderline between stationary and oscillatory dynamos.

We investigate numerically stationary convection and traveling wave structures of binary fluid mixtures with negative separation ratio in the Rayleigh-Bénard system filled with a porous medium. The bifurcation behavior of these roll structures is elucidated as well as the properties of the velocity, temperature, and concentration fields. Moreover, we discuss lateral averaged currents of temperature and concentration. Finally, we investigate the influence of the Lewis number, of the separation ratio, and of the normalized porosity on the bifurcation branches.

The introduction of brilliant free-electron lasers enables new pump-probe experiments to characterize warm dense matter states. For instance, a short-pulse optical laser irradiates a liquid hydrogen jet that is subsequently probed with brilliant soft x-ray radiation. The strongly inhomogeneous plasma prepared by the optical laser is characterized with particle-in-cell simulations. The interaction of the soft x-ray probe radiation for different time delays between pump and probe with the inhomogeneous plasma is also taken into account via radiative hydrodynamic simulations. We calculate the respective scattering spectrum based on the Born-Mermin approximation for the dynamic structure factor considering the full density and temperature-dependent Thomson scattering cross section throughout the target. We can identify plasmon modes that are generated in different target regions and monitor their temporal evolution. Therefore, such pump-probe experiments are promising tools not only to measure the important plasma parameters density and temperature but also to gain valuable information about their time-dependent profile through the target. The method described here can be applied to various pump-probe scenarios by combining optical lasers and soft x ray, as well as x-ray sources.

We propose a method to reduce the relaxation time toward equilibrium in stochastic sampling of complex energy landscapes in statistical systems with discrete degrees of freedom by generalizing the platform previously developed for continuous systems. The method starts from a master equation, in contrast to the Fokker-Planck equation for the continuous case. The master equation is transformed into an imaginary-time Schrödinger equation. The Hamiltonian of the Schrödinger equation is modified by adding a projector to its known ground state. We show how this transformation decreases the relaxation time and propose a way to use it to accelerate simulated annealing for optimization problems. We implement our method in a simplified kinetic Monte Carlo scheme and show acceleration by one order of magnitude in simulated annealing of the symmetric traveling salesman problem. Comparisons of simulated annealing are made with the exchange Monte Carlo algorithm for the three-dimensional Ising spin glass. Our implementation can be seen as a step toward accelerating the stochastic sampling of generic systems with complex landscapes and long equilibration times.

The general theory of the single-file multiparticle diffusion in the narrow pores could be greatly simplified in the case of inverted bell-like shape of the single-particle energy profile, which is often observed in biological ion channels. There is a narrow and deep groove in the energy landscape of multiple interacting ions in such profiles, which corresponds to the pre-defined optimal conduction pathway in the configurational space. If such groove exists, the motion of multiple ions can be reduced to the motion of single quasiparticle, called the superion, which moves in one-dimensional effective potential. The concept of the superions dramatically reduces the computational complexity of the problem and provides very clear physical interpretation of conduction phenomena in the narrow pores.

Using path integrals, we derive an exact expression—valid at all times $t$—for the distribution $P\left(Q,t\right)$ of the heat fluctuations $Q$ of a Brownian particle trapped in a stationary harmonic well. We find that $P\left(Q,t\right)$ can be expressed in terms of a modified Bessel function of zeroth order that in the limit $t\to \infty$ exactly recovers the heat distribution function obtained recently by Imparato et al. [Phys. Rev. E 76, 050101(R) (2007)] from the approximate solution to a Fokker-Planck equation. This long-time result is in very good agreement with experimental measurements carried out by the same group on the heat effects produced by single micron-sized polystyrene beads in a stationary optical trap. An earlier exact calculation of the heat distribution function of a trapped particle moving at a constant speed $v$ was carried out by van Zon and Cohen [Phys. Rev. E 69, 056121 (2004)]; however, this calculation does not provide an expression for $P\left(Q,t\right)$ itself, but only its Fourier transform (which cannot be analytically inverted), nor can it be used to obtain $P\left(Q,t\right)$ for the case $v=0$.

Clusters generated by the product-rule growth model of Achlioptas, D’Souza, and Spencer on a two-dimensional square lattice are shown to obey qualitatively different scaling behavior than standard (random growth) percolation. The threshold with unrestricted bond placement (allowing loops) is found precisely using several different criteria based on both moments and wrapping probabilities, yielding $p_c=0.526565\pm 0.000005$, consistent with the recent result of Radicchi and Fortunato. The correlation-length exponent $\nu$ is found to be close to 1. The qualitative difference from regular percolation is shown dramatically in the behavior of the percolation probability $P_{\infty }$ (size of largest cluster), of the susceptibility, and of the second moment of finite clusters, where discontinuities appear at the threshold. The critical cluster-size distribution does not follow a consistent power law for the range of system sizes we study $\left(L\le 8192\right)$ but may approach a power law with $\tau >2$ for larger $L$.

Numerical simulations are conducted to determine microstructure and rheology of sheared suspensions of charged colloidal particles at a volume fraction of $\varphi =0.33$. Over broad ranges of repulsive force strength $F_0$ and Péclet number Pe, dynamic simulations show coexistence of ordered and disordered stable states with the state dependent on the initial condition. In contrast to the common view, at low shear rates, the disordered phase exhibits a lower viscosity $\left({\mu }_r\right)$ than the ordered phase, while this behavior is reversed at higher shear rates. Analysis shows the stress reversal is associated with different shear induced microstructural distortions in the ordered and disordered systems. Viscosity vs shear rate data over a wide range of $F_0$ and Pe collapses well upon rescaling with the long-time self-diffusivity. Shear thinning viscosity in the ordered phase scaled as ${\mu }_r\sim {\text{Pe}}^{-0.81}$ at low shear rates. The microstructural dynamics revealed in these studies explains the anomalous behavior and hysteresis loops in stress data reported in the literature.

We analyze a stochastic model of neuronal population dynamics with intrinsic noise. In the thermodynamic limit $N\to \infty$, where $N$ determines the size of each population, the dynamics is described by deterministic Wilson-Cowan equations. On the other hand, for finite $N$ the dynamics is described by a master equation that determines the probability of spiking activity within each population. We first consider a single excitatory population that exhibits bistability in the deterministic limit. The steady-state probability distribution of the stochastic network has maxima at points corresponding to the stable fixed points of the deterministic network; the relative weighting of the two maxima depends on the system size. For large but finite $N$, we calculate the exponentially small rate of noise-induced transitions between the resulting metastable states using a Wentzel-Kramers-Brillouin (WKB) approximation and matched asymptotic expansions. We then consider a two-population excitatory or inhibitory network that supports limit cycle oscillations. Using a diffusion approximation, we reduce the dynamics to a neural Langevin equation, and show how the intrinsic noise amplifies subthreshold oscillations (quasicycles).

Dynamic light scattering performed on aqueous solutions of three sugars (glucose, maltose and sucrose) reveal a common pattern of sugar cluster formation with a narrow cluster size distribution. In each case, equilibrium clusters form whose size increases with increasing sugar content in an identical power law manner in advance of a common, critical-like, percolation threshold near $83\text{wt}\mathrm{\%}$ sugar. The critical exponent of the power law divergence of the cluster size varies with temperature, increasing with decreasing temperature, due to changes in the strength of the intermolecular hydrogen bond and appears to vanish for temperatures in excess of $90°\text{C}$. Detailed analysis of the cluster growth process suggests a two-stage process: an initial cluster phase formed at low volume fractions, $\varphi$, consisting of noninteracting, monodisperse sugar clusters whose size increases ${\varphi }^{1/3}$ followed by an aggregation stage, active at concentrations above about $\varphi =40\mathrm{\%}$, where cluster-cluster contact first occurs.

We study the geometry of biopolymer networks and effects of the geometry on bulk mechanical properties. It is shown numerically that the physical network geometry can be quantified statistically and regenerated from its statistical description, so that the regenerated network exhibits the same network mechanics as the physical network in the elastic regime. A collagen-I biopolymer network is used for validation. The method enables parametric studies of the network geometry, whose parameters are often difficult to vary independently in experiments.

We study a statistical-mechanical model of the binding of DNA-bending proteins to the double helix including applied tension and binding cooperativity effects. Intrinsic cooperativity of binding sharpens force-extension curves and causes enhancement of fluctuation of extension and protein occupation. This model also allows us to estimate the intrinsic cooperativity in experiments by measuring the peak value of the slope of extension versus chemical-potential curves. This analysis suggests the presence of force-dependent cooperativity even in the absence of explicit intrinsic (energetic) cooperativity. To further understand this effect, we analyze a model with a pair of bends at variable spacing to obtain a spacing-dependent free energy of interaction between the two proteins. We find that the interaction is always attractive and has an exponential decay as a function of bend spacing. For forces greater than $k_{B}T/A$, where $A$ is the persistence length, the interaction decay length is approximately ${\left[k_{B}TA/\left(4f\right)\right]}^{1/2}$ in accord with theoretical expectations. However, the force dependence of the strength of the interaction is more complex. For short interprotein separations, the interaction strength saturates at a level which varies roughly as $f^{1/2}$, while at longer separations the amplitude of the exponential decay increases faster than linearly with force. Our results can be applied to single molecule experiments to measure the cooperativity between DNA-bending proteins or between other molecules which deform the semiflexible polymer with which they bind. Force-mediated interaction of DNA-bending proteins suggests a mechanism whereby tension in DNA in vivo could alter the distribution of proteins bound along DNA, causing chromosome refolding, or changes in gene expression.

We show that the ground state of a system of magnetic dipoles, with no electric charge, is a ferromagnetic quantum Fermi liquid at high densities, driven by the dipolar exchange energy. As in the system of classical point dipoles, the direct dipole energy is zero in this case. With decreasing density, there is a transition to an antiferromagnetic lattice state. An addition of short range hard core repulsive potential will arrest the infinite density collapse of the ferromagnetic state, and possible melting of the low density antiferromagnetic lattice state.

In this Rapid Communication, we demonstrate that a non-Hermitian random matrix description can account for both spectral and spatial statistics of resonance states in a weakly open chaotic wave system with continuously distributed losses. More specifically, the statistics of resonance states in an open two-dimensional chaotic microwave cavity are investigated by solving the Maxwell equations with lossy boundaries subject to Ohmic dissipation. We successfully compare the statistics of its complex-valued resonance states and associated widths with analytical predictions based on a non-Hermitian effective Hamiltonian model defined by a finite number of fictitious open channels.

Biological materials such as spider silk display hierarchical structures, from nano to macro, effectively linking nanoscale constituents to larger-scale functional material properties. Here, we develop a model that is capable of determining the strength and toughness of elastic-plastic composites from the properties, percentages, and arrangement of its constituents, and of estimating the corresponding dissipated energy during damage progression, in crack-opening control. Specifically, we adopt a fiber bundle model approach with a hierarchical multiscale self-similar procedure which enables to span various orders of magnitude in size and to explicitly take into account the hierarchical topology of natural materials. Hierarchical architectures and self-consistent energy dissipation mechanisms (including plasticity), both omitted in common fiber bundle models, are fully considered in our model. By considering one of the toughest known materials today as an example application, a synthetic fiber composed of single-walled carbon nanotubes and polyvinyl alcohol gel, we compute strength and specific energy absorption values that are consistent with those experimentally observed. Our calculations are capable of predicting these values solely based on the properties of the constituent materials and knowledge of the structural multiscale topology. Due to the crack-opening control nature of the simulations, it is also possible to derive a critical minimal percentage of plastic component needed to avoid catastrophic behavior of the material. These results suggest that the model is capable of helping in the design of new supertough materials.

Phase resetting curves characterize the way a system with a collective periodic behavior responds to perturbations. We consider globally coupled ensembles of Sakaguchi-Kuramoto oscillators, and use the Ott-Antonsen theory of ensemble evolution to derive the analytical phase resetting equations. We show the final phase reset value to be composed of two parts: an immediate phase reset directly caused by the perturbation and the dynamical phase reset resulting from the relaxation of the perturbed system back to its dynamical equilibrium. Analytical, semianalytical and numerical approximations of the final phase resetting curve are constructed. We support our findings with extensive numerical evidence involving identical and nonidentical oscillators. The validity of our theory is discussed in the context of large ensembles approximating the thermodynamic limit.

We introduce a continuous analytical model of propagation of resistance in pressure-driven flow of two-phase fluid in a single channel. This model can be used to predict and interpret experimental results in droplet microfluidics where the hydrodynamic resistance of a capillary comprises a constant part, specific to the channel and the viscosity of the continuous fluid, and a variable part, related to the presence and distribution of droplets. The continuous model is a convenient generalization of the discrete models as demonstrated via comparisons with discrete simulations and with experiments.