Overdamped motion of Brownian particles in an asymmetric double-well potential driven by an additive nonequilibrium three-level noise and a thermal noise is considered. In the stationary regime, an exact formula for the mean occupancy of the metastable state is derived, and the phenomenon of enhancement of stability versus temperature is investigated. It is established that in a certain region of the system parameters the mean occupancy can be either multiply enhanced or suppressed by variations of temperature. We show that this effect is due to the involvement of different time scales in the problem. The necessary conditions for several different behaviors of the mean occupancy as a function of temperature are also discussed. The effect is more pronounced when the kurtosis of the three-level noise tends to $-2$, i.e., in the case of dichotomous noise.

The statistical mechanics of a noninteracting polymer chain in the limit of a large number of monomers is considered when the total angular momentum $\mathbf{L}$ is fixed. The radius of gyration for a ring polymer in this situation is derived exactly in closed form by functional integration techniques. Even when $L=0$ the radius of gyration differs from that of a random walk by a prefactor of order unity. The dependence on $L$ is discussed qualitatively and the large-$L$ limit can be understood by physical arguments, which can also be extended to self-avoiding chains.

A theoretical calculation is presented to describe the confined motion of transmembrane molecules in cell membranes. The study is analytic, based on Master equations for the probability of the molecules moving as random walkers, and leads to explicit usable solutions including expressions for the molecular mean square displacement and effective diffusion constants. One outcome is a detailed understanding of the dependence of the time variation of the mean square displacement on the initial placement of the molecule within the confined region. How to use the calculations is illustrated by extracting (confinement) compartment sizes from experimentally reported published observations from single particle tracking experiments on the diffusion of gold-tagged $G$-protein coupled $\mu$-opioid receptors in the normal rat kidney cell membrane, and by further comparing the analytical results to observations on the diffusion of phospholipids, also in normal rat kidney cells.

In drylands the soil water availability is a key factor ruling the architecture of the ecosystem. The soil water reflects the exchanges of water among soil, vegetation, and atmosphere. Here, a dryland ecosystem is investigated through the analysis of the local interactions between soil water and vegetation forced by rainfall having seasonal and stochastic occurrence. The evolution of dryland ecosystems is represented by a system of two differential equations, having two steady states, one vegetated and the other unvegetated. The rainfall forcing is described by a diffusion process with monthly parameters. In each of the two possible steady states, the probability density functions of soil water and vegetation are derived analytically in terms of the rainfall distribution. The results show how the seasonality of rainfall influences the oscillation of the ecosystem between its vegetated steady state during the wet season and its unvegetated steady state during the dry season.

A phase response curve (PRC) characterizes the signal transduction between oscillators such as neurons on a fixed network in a minimal manner, while spike-timing-dependent plasiticity (STDP) characterizes the way of rewiring networks in an activity-dependent manner. This paper demonstrates that these two key properties both related to the interaction times of oscillators work synergetically to carve functionally useful circuits. STDP working on neurons that prefer asynchrony converts the initial asynchronous firing to clustered firing with synchrony within a cluster. They get synchronized within a cluster despite their preference to asynchrony because STDP selectively disrupts intracluster connections, which we call wireless clustering. Our PRC analysis reveals a triad mechanism: the network structure affects how the PRC is read out to determine the synchrony tendency, the synchrony tendency affects how the STDP works, and STDP affects the network structure, closing the loop.

Analyzing the $d$-dimensional spherical model, we show that underlying saddles, defined through a map in the configuration space, play a central role in driving the phase transition. At the phase transition point the underlying saddle energy reaches its lowest value, corresponding to the trivial boundary topological singularity.

We study the dynamics of unidirectionally delay-coupled nonlinear oscillators. Cascading them within a ring of fixed total propagation delay, we demonstrate simple scaling behavior of correlation properties. In fact, the correlation properties of a ring with $N$ elements can be deduced from the autocorrelation of the single delayed feedback system. Coupling a ring element to a chain of unidirectionally coupled identical oscillators, we achieve complete synchronization between elements of chain and ring, evidencing generalized synchronization among the other elements, even if uncorrelated.

The static and dynamic critical properties of the ferromagnetic $q$-state Potts models on a square lattice with $q=2$ and 3 are numerically studied via the nonequilibrium relaxation method. The relaxation behavior of both the order parameter and energy as well as that of the second moments are investigated, from which static and dynamic critical exponents can be obtained. We find that the static exponents thus obtained from the relaxation of the order parameter and energy together with the second moments of the order parameter exhibit a close agreement with the exact exponents, especially for the case of the $q=2$ (Ising) model, when care is taken in the choice of the initial states for the relaxation of the second moments. As for the case of $q=3$, the estimates for the static exponents become less accurate, but still exhibit reasonable agreement with the exactly known static exponents. The dynamic critical exponent for the $q=2$ (Ising) model is estimated from the relaxation of the second moments of the order parameter with mixed initial conditions to give $z\left(q=2\right)\simeq 2.1668\left(19\right)$.

Various ways of implementing boundary conditions for the numerical solution of the Navier-Stokes equations by a lattice Boltzmann method are discussed. Five commonly adopted approaches are reviewed, analyzed, and compared, including local and nonlocal methods. The discussion is restricted to velocity Dirichlet boundary conditions, and to straight on-lattice boundaries which are aligned with the horizontal and vertical lattice directions. The boundary conditions are first inspected analytically by applying systematically the results of a multiscale analysis to boundary nodes. This procedure makes it possible to compare boundary conditions on an equal footing, although they were originally derived from very different principles. It is concluded that all five boundary conditions exhibit second-order accuracy, consistent with the accuracy of the lattice Boltzmann method. The five methods are then compared numerically for accuracy and stability through benchmarks of two-dimensional and three-dimensional flows. None of the methods is found to be throughout superior to the others. Instead, the choice of a best boundary condition depends on the flow geometry, and on the desired trade-off between accuracy and stability. From the findings of the benchmarks, the boundary conditions can be classified into two major groups. The first group comprehends boundary conditions that preserve the information streaming from the bulk into boundary nodes and complete the missing information through closure relations. Boundary conditions in this group are found to be exceptionally accurate at low Reynolds number. Boundary conditions of the second group replace all variables on boundary nodes by new values. They exhibit generally much better numerical stability and are therefore dedicated for use in high Reynolds number flows.

The effect of dissipation when due to the load of a transmission line coupled to a Josephson junction is reconsidered and evaluated by means of a simple direct procedure that supplies analytical expressions. The results are in good agreement with the ones previously reported in the literature. A simple criterion for testing experimental results is introduced.

KIF1A kinesins are single-headed motor proteins which move on cylindrical nanotubes called microtubules (MTs). A normal MT consists of 13 protofilaments on which the equispaced motor binding sites form a periodic array. The collective movement of the kinesins on a MT is, therefore, analogous to vehicular traffic on multilane highways where each protofilament is the analog of a single lane. Does lane changing increase or decrease the motor flux per lane? We address this fundamental question here by appropriately extending a recent model [P. Greulich et al., Phys. Rev. E 75, 041905 (2007)]. By carrying out analytical calculations and computer simulations of this extended model, we predict that the flux per lane can increase or decrease with the increasing rate of lane changing, depending on the concentrations of motors and the rate of hydrolysis of ATP, the “fuel” molecules. Our predictions can be tested, in principle, by carrying out in vitro experiments with fluorescently labeled KIF1A molecules.

The origin of diffusive transport of light in dry foams is still under debate. In this paper, we consider the random walks of photons as they are reflected or transmitted by liquid films according to the rules of ray optics. The foams are approximately modeled by three-dimensional Voronoi tessellations with varying degree of disorder. We study two cases: A constant intensity reflectance and the reflectance of thin films. Especially in the second case, we find that in the experimentally important regime for the film thicknesses, the transport-mean-free path $l^{\ast }$ does not significantly depend on the topological and geometrical disorder of the Voronoi foams including the periodic Kelvin foam. This may indicate that the detailed structure of foams is not crucial for understanding the diffusive transport of light. Furthermore, our theoretical values for $l^{\ast }$ fall in the same range as the experimental values observed in dry foams. One can therefore argue that liquid films contribute substantially to the diffusive transport of light in dry foams.

We extend the formalism of the thermodynamic two-time Green’s functions to nonextensive quantum statistical mechanics. Working in the optimal Lagrangian multiplier representation, the $q$-spectral properties and the methods for a direct calculation of the two-time $q$ Green’s functions and the related $q$-spectral density ($q$ measures the nonextensivity degree) for two generic operators are presented in strict analogy with the extensive $\left(q=1\right)$ counterpart. Some emphasis is devoted to the nonextensive version of the less known spectral density method whose effectiveness in exploring equilibrium and transport properties of a wide variety of systems has been well established in conventional classical and quantum many-body physics. To check how both the equations of motion and the spectral density methods work to study the $q$-induced nonextensivity effects in nontrivial many-body problems, we focus on the equilibrium properties of a second-quantized model for a high-density Bose gas with strong attraction between particles for which exact results exist in extensive conditions. Remarkably, the contributions to several thermodynamic quantities of the $q$-induced nonextensivity close to the extensive regime are explicitly calculated in the low-temperature regime by overcoming the calculation of the $q$ grand-partition function.

We follow the dynamics of an ensemble of interacting self-propelled motorized particles in contact with an equilibrated thermal bath. We find that the fluctuation-dissipation relation allows for the definition of an effective temperature that is compatible with the results obtained using a tracer particle as a thermometer. The effective temperature takes a value which is higher than the temperature of the bath, and it is continuously controlled by the motor intensity.

We study electroconvection patterns that appear above the splay Fréedericksz transition in a bent-core nematic liquid crystal with positive dielectric and negative conductivity anisotropy. In contrast to most of the previously observed convection rolls in nematics, they are not shadowgraph patterns at onset. Unusual effects are observed like a transition between longitudinal and normal rolls, controlled by the excitation frequency, as well as a voltage dependent reorientation of the convection rolls in a metastable domain. We present experimentally determined pattern state diagrams for planar alignment and characterize the patterns optically.

We present an experimental study of a different pattern-forming instability occurring when a ferrofluid droplet is immersed in a thin layer of a nonmagnetic fluid, and subjected to a uniform perpendicular magnetic field. The formation of intriguing interfacial structures is observed, and the development of a hybrid-type ferrohydrodynamic instability is verified, where peak and labyrinthine ferrofluid patterns coexist and share a coupled dynamic evolution. Based on our experimental findings we have identified the occurrence of three well defined regimes for the evolution of the miscible Rosensweig peak in which it first grows rapidly, and then gradually decays, to ultimately reimmerse into the surrounding nonmagnetic solvent layer. This unique scenario for the rise and fall of the Rosensweig peak implies the simultaneous emergence of peculiar labyrinthine structures induced by an outward radial flow within the thin nonmagnetic layer. A variety of possible morphologies is revealed (labyrinth, broken tentaclelike fingers, etc.), which result from the interplay between magnetic, diffusive, and convective effects. These free surface flow labyrinthine structures are contrasted to alternative interfacial designs obtained when the experimental system is spatially confined.

The percolation properties and permeability of a group of anisotropic three-dimensional fracture networks are studied numerically. Finite-size scaling is used to extrapolate the percolation thresholds of infinite networks in three spatial directions, i.e., $X$, $Y$, and $Z$ directions. The influence of the angular dispersion parameter of fracture orientations on percolation thresholds is analyzed. In this analysis, we considered a family of fractures in a three-dimensional space that are oriented around the $Z$ axis based on the Fisher distribution. We revealed that increased anisotropy leads to decreased percolation thresholds in both $X$ and $Y$ directions, and in these two directions percolation thresholds in anisotropic networks demonstrate a declining trend as anisotropy goes up. However, in the $Z$ direction the trend is the opposite. The fracture networks are triangulated via an advancing front technique and the macroscopic permeability of the networks is determined by solving the two-dimensional Darcy equation in each fracture. We found that the macroscopic permeability in the $X$ and $Y$ directions is higher than the associated permeability of isotropic fracture networks, and this property for anisotropic networks in the $Z$ direction is lower compared with that of the isotropic case. Furthermore, as the anisotropy of networks increases the differences become more remarkable.

We investigate the short-range structure in strongly coupled fluidlike plasmas using the hypernetted chain approach generalized to multicomponent systems. Good agreement with numerical simulations validates this method for the parameters considered. We found a strong mutual impact on the spatial arrangement for systems with multiple ion species which is most clearly pronounced in the static structure factor. Quantum pseudopotentials were used to mimic diffraction and exchange effects in dense electron-ion systems. We demonstrate that the different kinds of pseudopotentials proposed lead to large differences in both the pair distributions and structure factors. Large discrepancies were also found in the predicted ion feature of the x-ray scattering signal, illustrating the need for comparison with full quantum calculations or experimental verification.

We investigate the crystallization rate of a one-component plasma (OCP) in the context of classical nucleation theory. From our derivation of the free energy of an arbitrary distribution of solid clusters embedded in a liquid phase, we derive the steady-state nucleation rate of an OCP as a function of the Coulomb coupling parameter $\Gamma$. Our result for the rate is in accordance with recent molecular dynamics simulations, but it is greater than that of previous analytical estimates by many orders of magnitude. Further molecular dynamics simulations of the nucleation rate of a supercooled liquid OCP for several values of $\Gamma$ would clarify the physics of this process.

A theoretical approach to calculate the correlation functions in binary hard-sphere (HS) solid mixtures is developed. The method is motivated by the theory of correlations in one-component HS solids [Rascon et al., Phys. Rev. E 54, 1261 (1996)] and the Kirkwood-Buff theory for solutions. Combined with the fundamental measure density functional theory the approach provides correlation functions in good agreement with the numerical simulations results for the moderately asymmetric mixtures.