Examining a nonlinear instability of sliding rate on a frictional interface of elastic bodies, we investigate whether laboratory-constrained frictional relations suggest universal scaling under even the simplest of configurations. We find blowup solutions by solving an equivalent, classical problem in fracture mechanics. The solutions are fixed points of a dynamical system and we show that their stability is lost by a cascade of Hopf bifurcations as a single problem parameter is increased, leading to chaotic dynamics.

Models of noninteracting fermions coupled to auxiliary classical fields are relevant to the understanding of a wide variety of problems in many-body physics, e.g., the description of manganites, diluted magnetic semiconductors, or strongly interacting electrons on lattices. We present a flat-histogram Monte Carlo algorithm that simulates a statistical ensemble that allows one to directly acquire the partition function at all temperatures for such systems. The defining feature of the algorithm is that it utilizes the complete thermodynamic information from the full energy spectrum of noninteracting fermions available during sampling of the configuration space of the classical fields. We benchmark the method for the classical Ising and Potts models in two dimensions, as well as the Falicov-Kimball model describing itinerant electrons interacting with heavy ions.

We investigate the geometric structure of a nonequilibrium process and its geodesic solutions. By employing an exactly solvable model of a driven dissipative system (generalized nonautonomous Ornstein-Uhlenbeck process), we compute the time-dependent probability density functions (PDFs) and investigate the evolution of this system in a statistical metric space where the distance between two points (the so-called information length) quantifies the change in information along a trajectory of the PDFs. In this metric space, we find a geodesic for which the information propagates at constant speed, and demonstrate its utility as an optimal path to reduce the total time and total dissipated energy. In particular, through examples of physical realizations of such geodesic solutions satisfying boundary conditions, we present a resonance phenomenon in the geodesic solution and the discretization into cyclic geodesic solutions. Implications for controlling population growth are further discussed in a stochastic logistic model, where a periodic modulation of the diffusion coefficient and the deterministic force by a small amount is shown to have a significant controlling effect.

Ratchets rectify the motion of randomly moving particles, which are driven by isotropic sources of energy such as thermal and chemical energy, without applying a net, time-averaged force between source and drain. This paper describes the behavior of a damped electron, modeled by a quantum Lindblad master equation, within a flashing ratchet (a one-dimensional potential that oscillates between a flat surface and a periodic asymmetric surface). By examining the complete space of all biharmonic potential shapes and a large range of oscillation frequencies, two modes of ratchet operation, differentiated by their oscillation frequencies (relative to the rate of electron relaxation), are identified. Slow-oscillating, strong friction ratchets operate by a classical, overdamped mechanism. In fast-oscillating, weak friction ratchets, current is primarily produced when the frequency of the oscillating potential is resonant with the beating of the electron wave function in the potential well. The shape of the ratchet potential determines the direction of the current (and, in some cases, straightforwardly accounts for current reversals), but the maximum achievable current at any shape is controlled by the degree of friction applied to the electron.

Recently a nonlinear Fick-Jacobs equation has been proposed for the description of transport and diffusion of particles interacting through a hard-core potential in tubes or channels of varying cross section [Suárez et al., Phys. Rev. E 91, 012135 (2015)]. Here we focus on the analysis of the current and mobility when the channel is composed by a chain of asymmetric cavities and a force is applied in one or the opposite direction, for both interacting and noninteracting particles, and compare analytical and Monte Carlo simulation results. We consider a cavity with a shape given by exponential functions; the linear Fick-Jacobs equation for noninteracting particles can be exactly solved in this case. The results of the current difference (when a force is applied in opposite directions) are more accurate for the modified Fick-Jacobs equation for particles with hard-core interaction than for noninteracting ones.

A two-dimensional periodic optical force field, which combines conservative dipolar forces with vortices from radiation pressure, is proposed in order to influence the diffusion properties of optically susceptible nanoparticles. The different deterministic flow patterns are identified. In the low-noise limit, the diffusion coefficient is computed from a mean first passage time and the most probable escape paths are identified for those flow patterns which possess a stable stationary point. Numerical simulations of the associated Langevin equations show remarkable agreement with the analytically deduced expressions. Modifications of the force field are proposed so that a wider range of phenomena could be tested.

The nonlinear dielectric effect describes changes of dielectric permittivity induced by the strong electric field. This report shows the evidence for the critical-like pretransitional behavior for the liquid-solid transition in the supercooled nitrobenzene. Hallmarks of such behavior extend even above the melting temperature. A method for the analysis of pretransitional effects, avoiding the biasing impact of the noncritical background contribution, is proposed.

For quite a few systems in the continuum, such as carbon nanotube polymer composites and segregated composites, percolation electrical conductivity exponents that are much smaller than the universal value have been reported. This is unexpected in view of the classical lattice percolation theory. Here we provide a simple general phenomenological model that accounts for such observations within the framework of universality. We suggest that these small value exponents are due to the interplay between the connectivity and the structural variations that follow the increase of the fractional volume content of the conducting phase.

The ranges of transmission of the mobiles in a mobile ad hoc network are not uniform in reality. They are affected by the temperature fluctuation in air, obstruction due to the solid objects, even the humidity difference in the environment, etc. How the varying range of transmission of the individual active elements affects the global connectivity in the network may be an important practical question to ask. Here a model of percolation phenomena, with an additional source of disorder, is introduced for a theoretical understanding of this problem. As in ordinary percolation, sites of a square lattice are occupied randomly with probability $p$. Each occupied site is then assigned a circular disk of random value $R$ for its radius. A bond is defined to be occupied if and only if the radii $R_1$ and $R_2$ of the disks centered at the ends satisfy a certain predefined condition. In a very general formulation, one divides the $R_1-R_2$ plane into two regions by an arbitrary closed curve. One defines a point within one region as representing an occupied bond; otherwise it is a vacant bond. The study of three different rules under this general formulation indicates that the percolation threshold always varies continuously. This threshold has two limiting values, one is $p_c\left(\text{sq}\right)$, the percolation threshold for the ordinary site percolation on the square lattice, and the other is unity. The approach of the percolation threshold to its limiting values are characterized by two exponents. In a special case, all lattice sites are occupied by disks of random radii $R\in \{0,R_0\}$ and a percolation transition is observed with $R_0$ as the control variable, similar to the site occupation probability.

We propose and examine an integrable system of nonlinear equations that generalizes the nonlinear Schrödinger equation to $2+1$ dimensions. This integrable system of equations is a promising starting point to elaborate more accurate models in nonlinear optics and molecular systems within the continuum limit. The Lax pair for the system is derived after applying the singular manifold method. We also present an iterative procedure to construct the solutions from a seed solution. Solutions with one-, two-, and three-lump solitons are thoroughly discussed.

Rotation dynamics of eigenvectors of modular network adjacency matrices under random perturbations are presented. In the presence of $q$ communities, the number of eigenvectors corresponding to the $q$ largest eigenvalues form a “community” eigenspace and rotate together, but separately from that of the “bulk” eigenspace spanned by all the other eigenvectors. Using this property, the number of modules or clusters in a network can be estimated in an algorithm-independent way. A general argument and derivation for the theoretical detectability limit for sparse modular networks with $q$ communities is presented, beyond which modularity persists in the system but cannot be detected. It is shown that for detecting the clusters or modules using the adjacency matrix, there is a “band” in which it is hard to detect the clusters even before the theoretical detectability limit is reached, and for which the theoretically predicted detectability limit forms the sufficient upper bound. Analytic estimations of these bounds are presented and empirically demonstrated.

Randomly coupled neural fields demonstrate irregular variation of firing rates, if the coupling is strong enough, as has been shown by [Phys. Rev. Lett. 61, 259 (1988)]. We present a method for reconstruction of the coupling matrix from a time series of irregular firing rates. The approach is based on the particular property of the nonlinearity in the coupling, as the latter is determined by a sigmoidal gain function. We demonstrate that for a large enough data set and a small measurement noise, the method gives an accurate estimation of the coupling matrix and of other parameters of the system, including the gain function.

Transcription is a key process in gene expression, in which RNA polymerases produce a complementary RNA copy from a DNA template. RNA polymerization is frequently interrupted by backtracking, a process in which polymerases perform a random walk along the DNA template. Recovery of polymerases from the transcriptionally inactive backtracked state is determined by a kinetic competition between one-dimensional diffusion and RNA cleavage. Here we describe backtrack recovery as a continuous-time random walk, where the time for a polymerase to recover from a backtrack of a given depth is described as a first-passage time of a random walker to reach an absorbing state. We represent RNA cleavage as a stochastic resetting process and derive exact expressions for the recovery time distributions and mean recovery times from a given initial backtrack depth for both continuous and discrete-lattice descriptions of the random walk. We show that recovery time statistics do not depend on the discreteness of the DNA lattice when the rate of one-dimensional diffusion is large compared to the rate of cleavage.

Focusing on shear-stress fluctuations, we investigate numerically a simple generic model for self-assembled transient networks formed by repulsive beads reversibly bridged by ideal springs. With $\mathrm{\Delta }t$ being the sampling time and $t_{☆}\left(f\right)\sim 1/f$ the Maxwell relaxation time (set by the spring recombination frequency $f$), the dimensionless parameter $\mathrm{\Delta }x=\mathrm{\Delta }t/t_{☆}\left(f\right)$ is systematically scanned from the liquid limit ($\mathrm{\Delta }x\gg 1)$ to the solid limit ($\mathrm{\Delta }x\ll 1$) where the network topology is quenched and an ensemble average over $m$-independent configurations is required. Generalizing previous work on permanent networks, it is shown that the shear-stress relaxation modulus $G\left(t\right)$ may be efficiently determined for all $\mathrm{\Delta }x$ using the simple-average expression $G\left(t\right)={\mu }_{\mathrm{A}}-h\left(t\right)$ with ${\mu }_{\mathrm{A}}=G\left(0\right)$ characterizing the canonical-affine shear transformation of the system at $t=0$ and $h\left(t\right)$ the (rescaled) mean-square displacement of the instantaneous shear stress as a function of time $t$. This relation is compared to the standard expression $G\left(t\right)=\tilde{c}\left(t\right)$ using the (rescaled) shear-stress autocorrelation function $\tilde{c}\left(t\right)$. Lower bounds for the $m$ configurations required by both relations are given.

We study numerically the shapes of a liquid meniscus in contact with ultrahydrophobic pillar surfaces in Cassie's wetting regime, when the surface is covered with identical and periodically distributed micropillars. Using the full capillary model we obtain the advancing and the receding equilibrium meniscus shapes when the cross-sections of the pillars are both of square and circular shapes, for a broad interval of pillar concentrations. The bending of the liquid interface in the area between the pillars is studied in the framework of the full capillary model and compared to the results of the heterogeneous approximation model. The contact angle hysteresis is obtained when the three-phase contact line is located on one row (block case) or several rows (kink case) of pillars. It is found that the contact angle hysteresis is proportional to the line fraction of the contact line on pillars tops in the block case and to the surface fraction for pillar concentrations $0.1–0.5$ in the kink case. The contact angle hysteresis does not depend on the shape (circular or square) of the pillars cross-section. The expression for the proportionality of the receding contact angle to the line fraction [Raj et al., Langmuir 28, 15777 (2012)] in the case of block depinning is theoretically substantiated through the capillary force, acting on the solid plate at the meniscus contact line.

When we elastically impose a homogeneous, affine deformation on amorphous solids, they also undergo an inhomogeneous, nonaffine deformation, which can have a crucial impact on the overall elastic response. To correctly understand the elastic modulus $M$, it is therefore necessary to take into account not only the affine modulus $M_A$, but also the nonaffine modulus $M_N$ that arises from the nonaffine deformation. In the present work, we study the bulk ($M=K$) and shear ($M=G$) moduli in static jammed particulate packings over a range of packing fractions $\phi$. The affine $M_A$ is determined essentially by the static structural arrangement of particles, whereas the nonaffine $M_N$ is related to the vibrational eigenmodes. We elucidate the contribution of each vibrational mode to the nonaffine $M_N$ through a modal decomposition of the displacement and force fields. In the vicinity of the (un)jamming transition ${\phi }_c$, the vibrational density of states $g\left(\omega \right)$ shows a plateau in the intermediate-frequency regime above a characteristic frequency ${\omega }^{*}$. We illustrate that this unusual feature apparent in $g\left(\omega \right)$ is reflected in the behavior of $M_N$: As $\phi \to {\phi }_c$, where ${\omega }^{*}\to 0$, those modes for $\omega <{\omega }^{*}$ contribute less and less, while contributions from those for $\omega >{\omega }^{*}$ approach a constant value which results in $M_N$ to approach a critical value $M_{Nc}$, as $M_N-M_{Nc}\sim {\omega }^{*}$. At ${\phi }_c$ itself, the bulk modulus attains a finite value $K_c=K_{Ac}-K_{Nc}>0$, such that $K_{Nc}$ has a value that remains below $K_{Ac}$. In contrast, for the critical shear modulus $G_c, G_{Nc}$ and $G_{Ac}$ approach the same value so that the total value becomes exactly zero, $G_c=G_{Ac}-G_{Nc}=0$. We explore what features of the configurational and vibrational properties cause such a distinction between $K$ and $G$, allowing us to validate analytical expressions for their critical values.

We demonstrate that diffusiophoretic, thermophoretic, and chemotactic phenomena in turbulence lead to clustering of particles on multifractal sets that can be described using one single framework, valid when the particle size is much smaller than the smallest length scale of turbulence $l_0$. To quantify the clustering, we derive positive pair correlations and fractal dimensions that hold for scales smaller than $l_0$. For scales larger than $l_0$ the pair-correlation function is predicted to show a stretched exponential decay towards 1. In the case of inhomogeneous turbulence we find that the fractal dimension depends on the direction of inhomogeneity. By performing experiments with particles in a turbulent gravity current we demonstrate clustering induced by salinity gradients in conformity to the theory. The particle size in the experiment is comparable to $l_0$, outside the strict validity region of the theory, suggesting that the theoretical predictions transfer to this practically relevant regime. This clustering mechanism may provide the key to the understanding of a multitude of processes such as formation of marine snow in the ocean and population dynamics of chemotactic bacteria.

A new set of generalized transport equations is derived for higher-order moments which are generated in evolution equation for stress tensor and heat flux vector in 13-moment equations. The closure we employ satisfies Onsager's symmetry principle. In the derivation, we do not employ a phase density function based on Hermite polynomial series in terms of higher-order moments, unlike Grad's approach. The distribution function is rather chosen to satisfy collision invariance, and H-theorem and capture relatively strong deviations from equilibrium. The phase density function satisfies the linearized Boltzmann equation and provides the correct value of the Prandtl number for monatomic gas. The derived equations are compared with Grad's 13-moments equations for gas modeled as Maxwellian molecule. The merits of the proposed equations against Grad's and R13 equations are discussed. In particular, it is noted that the proposed equations contain higher-order terms compared to these equations but require a fewer number of boundary conditions as compared to the R13 equations. The Knudsen number envelope which can be covered to describe flows with these equations is therefore expected to be larger as compared to the earlier equations.

We analyze the effect of asymmetric finite ion size in nanoconfinement in the view of osmotic pressure and electrocapillarity. When the confinement width becomes comparable with the Debye length, the overlapped electric double layer is significantly deformed by the steric effects. We derive the osmotic pressure from the modified Poisson-Boltzmann equation in a nanoslit to examine the deviation from the ideal osmotic pressure and the repulsive force on the wall considering the asymmetry of ion sizes. Then the electrocapillarity due to the steric effect is investigated under constant potential condition with the flat interface assumption. Later, the deformation by the electrocapillarity is also considered in the first order approximation.

For a nonlinear dynamical system described by the first-order differential equation with Poisson white noise having exponentially distributed amplitudes of $\delta$ pulses, some exact results for the stationary probability density function are derived from the Kolmogorov-Feller equation using the inverse differential operator. Specifically, we examine the “effect of normalization” of non-Gaussian noise by a linear system and the steady-state probability density function of particle velocity in the medium with Coulomb friction. Next, the general formulas for the probability distribution of the system perturbed by a non-Poisson $\delta$-pulse train are derived using an analysis of system trajectories between stimuli. As an example, overdamped particle motion in the bistable quadratic-cubic potential under the action of the periodic $\delta$-pulse train is analyzed in detail. The probability density function and the mean value of the particle position together with average characteristics of the first switching time from one stable state to another are found in the framework of the fast relaxation approximation.