In previous papers I have argued that the fusion rules hypothesis, which was originally introduced by L’vov and Procaccia in the context of the problem of three-dimensional turbulence, can be used to gain a deeper insight in understanding the enstrophy cascade and inverse energy cascade of two-dimensional turbulence. In the present paper, we show that the fusion rules hypothesis, combined with nonperturbative locality, itself a consequence of the fusion rules hypothesis, dictates the location of the boundary separating the inertial range from the dissipation range. In so doing, the hypothesis that there may be an anomalous enstrophy sink at small scales and an anomalous energy sink at large scales emerges as a consequence of the fusion rules hypothesis. More broadly, we illustrate the significance of viewing inertial ranges as multi-dimensional regions where the fully unfused generalized structure functions of the velocity field are self-similar, by considering, in this paper, the simplified projection of such regions in a two-dimensional space, involving a small scale $r$ and a large scale $R$, which we call, in this paper, the $\left(r,R\right)$-plane. We see, for example, that the logarithmic correction in the enstrophy cascade, under standard molecular dissipation, plays an essential role in inflating the inertial range in the $\left(r,R\right)$ plane to ensure the possibility of local interactions. We have also seen that increasingly higher orders of hyperdiffusion at large scales or hypodiffusion at small scales make the predicted sink anomalies more resilient to possible violations of the fusion rules hypothesis.

We present experimental results on pressure and resistivity on expanded nickel at a density of $0.1\text{g}/{\text{cm}}^3$ and temperature of a few eV. These data, corresponding to the warm dense matter regime, are used to benchmark different theoretical approaches. A comparison is presented between fully three-dimensional quantum molecular dynamics (QMD) methods, based on density functional theory, with average atom methods, that are essentially one dimensional. In this regime the evaluation of the thermodynamic properties as well as electrical properties is difficult due to the concurrence of density and thermal effects which directly drive the metal-nonmetal transition. Experimental pressures and resistivities are given in a tabular form with temperatures deduced from QMD simulations.

Transport properties of a Brownian particle in thermal-inertial ratchets subject to an external time-oscillatory drive and a constant bias force are investigated. Since the phenomena of negative mobility, resonant activation and noise-enhance stability were reported before, in the present paper, we report some additional aspects of negative mobility, resonant activation and noise-enhance stability, such as the ingredients for the appearances of these phenomena, multiple resonant activation peaks, current reversals, noise-weakened stability, and so on.

Excitable systems are of great theoretical and practical interest in mathematics, physics, chemistry, and biology. Here, we numerically study models of excitable media, namely, networks whose nodes may occasionally be dormant and the connection weights are allowed to vary with the system activity on a short-time scale, which is a convenient and realistic representation. The resulting global activity is quite sensitive to stimuli and eventually becomes unstable also in the absence of any stimuli. Outstanding consequences of such unstable dynamics are the spontaneous occurrence of various nonequilibrium phases—including associative-memory phases and one in which the global activity wanders irregularly, e.g., chaotically among all or part of the dynamic attractors—and $1/f$ noise as the system is driven into the phase region corresponding to the most irregular behavior. A net result is resilience which results in an efficient search in the model attractor space that can explain the origin of some observed behavior in neural, genetic, and ill–condensed matter systems. By extensive computer simulation we also address a previously conjectured relation between observed power-law distributions and the possible occurrence of a “critical state” during functionality of, e.g., cortical networks, and describe the precise nature of such criticality in the model which may serve to guide future experiments.

The problem of relaxation of a nonequilibrium state to the state of molecular hydrodynamics is considered for a classical system of interacting particles using the Zubarev nonequilibrium statistical operator method. The wave-vector and frequency dependencies of the dynamical structure factor and momentum-momentum transverse correlation function are investigated on the basis of the appropriate generalized transport equations. Comparison with the results of molecular hydrodynamics and molecular-dynamics simulations is given and the characteristic time intervals of the studied relaxation processes are determined.

A three-dimensional lattice Boltzmann method (LBM) has been developed for multiphase (liquid and vapor) flows with solid particles suspended within the liquid phases. The method generalizes our recent two-dimensional model [A. Joshi and Y. Sun, Phys. Rev. E 79, 066703 (2009)] to three dimensions, extends the implicit scheme presented therein to include interparticle forces and introduces an evaporation model to simulate drying of the colloidal drop. The LBM is used to examine the dynamical wetting behavior of drops containing suspended solid particles on homogeneous and patterned substrates. The influence of the particle volume fraction and particle size on the drop spreading dynamics is studied as is the final deposition of suspended particles on the substrate after the carrier liquid evaporates. The final particle deposition can be controlled by substrate patterning, adjusting the substrate surface energies and by the rate of evaporation. Some of the envisioned applications of the model are to develop a fundamental understanding of colloidal drop dynamics, predict particle deposition during inkjet printing of functional materials and to simulate the drying of liquids in porous media.

Structural and orientational order properties of the liquid crystal $4,4^{\prime }$-bis-heptyl-azoxybenzene (HAB) have been obtained in its nematic and smectic-$A$ phases by simultaneously analyzing several observables extracted from ${}^2\text{H}$ and ${}^{13}\text{C}$ nuclear magnetic resonance (NMR) spectra, i.e., ${}^2\text{H}$ quadrupolar, ${}^2\text{H}\text{−}{}^1\text{H}$ and ${}^{13}\text{C}\text{−}{}^2\text{H}$ dipolar couplings, as well as ${}^{13}\text{C}$ chemical shift anisotropy. ${}^{13}\text{C}$ experiments required the application of high-resolution solid-state NMR techniques like ${}^1\text{H}$ high-power decoupling and cross polarization, as well as the independent determination of chemical shift tensors by means of density functional theory (DFT) calculations, here performed taking into account the effect of the anisotropic medium by the polarizable continuum model method. The approach, consisting in the simultaneous analysis of all the ${}^2\text{H}$ and ${}^{13}\text{C}$ experimental data to derive orientational order parameters, and in the use of geometrical parameters determined by DFT methods, allows more detailed and reliable results to be obtained with respect to the traditional approach based on the sole analysis of ${}^2\text{H}$ experiments.

The existence of juxtaposed regions of distinct cultures in spite of the fact that people’s beliefs have a tendency to become more similar to each other’s as the individuals interact repeatedly is a puzzling phenomenon in the social sciences. Here we study an extreme version of the frequency-dependent bias model of social influence in which an individual adopts the opinion shared by the majority of the members of its extended neighborhood, which includes the individual itself. This is a variant of the majority-vote model in which the individual retains its opinion in case there is a tie among the neighbors’ opinions. We assume that the individuals are fixed in the sites of a square lattice of linear size $L$ and that they interact with their nearest neighbors only. Within a mean-field framework, we derive the equations of motion for the density of individuals adopting a particular opinion in the single-site and pair approximations. Although the single-site approximation predicts a single opinion domain that takes over the entire lattice, the pair approximation yields a qualitatively correct picture with the coexistence of different opinion domains and a strong dependence on the initial conditions. Extensive Monte Carlo simulations indicate the existence of a rich distribution of opinion domains or clusters, the number of which grows with $L^2$ whereas the size of the largest cluster grows with $\text{ln}{L}^2$. The analysis of the sizes of the opinion domains shows that they obey a power-law distribution for not too large sizes but that they are exponentially distributed in the limit of very large clusters. In addition, similarly to other well-known social influence model—Axelrod’s model—we found that these opinion domains are unstable to the effect of a thermal-like noise.

We uncover and characterize different chaotic transport scenarios in perfect two-dimensional periodic potentials by controlling the chaotic dynamics of particles subjected to periodic external forces in the absence of a ratchet effect (i.e., with no directed transport by symmetry breaking of zero-mean forces). After identifying relevant symmetries of the equations of motion, analytical estimates in parameter space for the occurrence of different transport scenarios are provided and confirmed by numerical simulations. These scenarios are highly sensitive to variations of the system’s asymmetry parameters, including the eccentricity of the two-dimensional periodic potential and the direction of dc and ac forces, which could be useful for particle sorting purposes in those cases where chaos is unavoidable.

Current reversal is an intriguing phenomenon that has been central to recent experimental and theoretical investigations of transport based on ratchet mechanism. By considering a system of two interacting ratchets, we demonstrate how the coupling can be used to control the reversals. In particular, we find that current reversal that exists in a single driven ratchet system can ultimately be eliminated with the presence of a second ratchet. For specific coupling strengths a current-reversal free regime has been detected. Furthermore, in the fully synchronized state characterized by the coupling threshold $k_{th}$, a specific driving amplitude $a_{opt}$ is found for which the transport is optimum.

Phase separation of binary fluids quenched by contact with cold external walls is considered. Navier-Stokes, convection-diffusion, and energy equations are solved by lattice Boltzmann method coupled with finite-difference schemes. At high viscosity, different morphologies are observed by varying the thermal diffusivity. In the range of thermal diffusivities with domains growing parallel to the walls, temperature and phase separation fronts propagate toward the inner of the system with power-law behavior. At low viscosity hydrodynamics favors rounded shapes, and complex patterns with different length scales appear. Off-symmetrical systems behave similarly but with more ordered configurations.

Several parallel adaptive biasing methods are applied to the calculation of free-energy pathways along reaction coordinates, choosing as a difficult example the double-funnel landscape of the 38-atom Lennard-Jones cluster. In the case of classical statistics, the Wang-Landau and adaptively biased molecular-dynamics (ABMD) methods are both found efficient if multiple walkers and replication and deletion schemes are used. An extension of the ABMD technique to quantum systems, implemented through the path-integral MD framework, is presented and tested on ${\text{Ne}}_{38}$ against the quantum superposition method.

We present a mesoscopic description of the anomalous transport and reactions of particles in spiny dendrites. As a starting point we use two-state Markovian model with the transition probabilities depending on residence time variable. The main assumption is that the longer a particle survives inside spine, the smaller becomes the transition probability from spine to dendrite. We extend a linear model presented in Fedotov et al. [Phys. Rev. Lett. 101, 218102 (2008)] and derive the nonlinear Master equations for the average densities of particles inside spines and parent dendrite by eliminating residence time variable. We show that the flux of particles between spines and parent dendrite is not local in time and space. In particular the average flux of particles from a population of spines through spines necks into parent dendrite depends on chemical reactions in spines. This memory effect means that one cannot separate the exchange flux of particles and the chemical reactions inside spines. This phenomenon does not exist in the Markovian case. The flux of particles from dendrite to spines is found to depend on the transport process inside dendrite. We show that if the particles inside a dendrite have constant velocity, the mean particle’s position $⟨x\left(t\right)⟩$ increases as $t^{\mu }$ with $\mu <1$ (anomalous advection). We derive a fractional advection-diffusion equation for the total density of particles.

A numerical investigation of jamming effect during the spontaneous interparticle percolation process of small beads through an unconsolidated porous media has been performed. The size ratio between the moving beads and the ones building up the porous medium was chosen larger than the geometrical trapping threshold: ${\xi }_c={\left(\frac{2}{\sqrt{3}}-1\right)}^{-1}=6.464\dots$. In this paper, we used the discrete element method algorithm to study the rebounds of particles on the top of the porous medium and the transit times of an assembly of particles through it. Several parameters such as the number of injected particles, the size ratio between beads, and the energy restitution coefficient are investigated. This study leads to give some important results of the evolution of the transit time versus the contiguous volume occupied by the percolating particles.

We study the effect of molecule sizes and intermolecular interactions on Frank elastic constants in nematic liquid crystals with ellipsoid of revolution molecules. We use the Poniewierski-Stecki equations which depend on direct correlation functions of ellipsoid molecules and apply the new direct correlation function using the Marko method and contact distance of ellipsoids. The elastic constants for different molecular elongations, using repulsive interaction of hard ellipsoids of revolution and attractive dispersion interaction are calculated. These elastic constants are deduced from a new direct correlation function. It is shown that they are in good agreement with Singh and singh results and qualitatively corresponds to the experiments. The ratios of calculated elastic constants are in agreement with the available experimental results.

The interplay of seasonality, the system’s nonlinearities and intrinsic stochasticity, is studied for a seasonally forced susceptible-exposed-infective-recovered stochastic model. The model is explored in the parameter region that corresponds to childhood infectious diseases such as measles. The power spectrum of the stochastic fluctuations around the attractors of the deterministic system that describes the model in the thermodynamic limit is computed analytically and validated by stochastic simulations for large system sizes. Size effects are studied through additional simulations. Other effects such as switching between coexisting attractors induced by stochasticity often mentioned in the literature as playing an important role in the dynamics of childhood infectious diseases are also investigated. The main conclusion is that stochastic amplification, rather than these effects, is the key ingredient to understand the observed incidence patterns.

Dynamics on networks are often characterized by the second smallest eigenvalue of the Laplacian matrix of the network, which is called the spectral gap. Examples include the threshold coupling strength for synchronization and the relaxation time of a random walk. A large spectral gap is usually associated with high network performance, such as facilitated synchronization and rapid convergence. In this study, we seek to enhance the spectral gap of undirected and unweighted networks by removing nodes because, practically, the removal of nodes often costs less than the addition of nodes, addition of links, and rewiring of links. In particular, we develop a perturbative method to achieve this goal. The proposed method realizes better performance than other heuristic methods on various model and real networks. The spectral gap increases as we remove up to half the nodes in most of these networks.

Nonlinear waves on sheets of dielectric liquid in the presence of an external tangential electric field are studied theoretically. It is shown that waves of arbitrary shape in three-dimensional geometry can propagate along (or against) the electric field direction without distortion, i.e., the equations of motion admit a wide class of exact traveling wave solutions. This unusual situation occurs for nonconducting ideal liquids with high dielectric constants in the case of a sufficiently strong field strength. Governing equations for evolution of plane symmetric waves on fluid sheets are derived using conformal variables. A dispersion relation for the evolution of small perturbations of the traveling wave solutions is obtained. It follows from this relation that, regardless of the wave shape, the amplitudes of small-scale perturbations do not increase with time and, hence, the traveling waves are stable. We also study the interaction of counterpropagating symmetric waves with small but finite amplitudes. The corresponding solution of the equations of motion describes the nonlinear superposition of the oppositely directed waves. The results obtained are applicable for the description of long waves on fluid sheets in a horizontal magnetic field.

We introduce a model of media with the cubic attractive nonlinearity concentrated along a single or double stripe in the two-dimensional (2D) plane. The model can be realized in terms of nonlinear optics (in the spatial and temporal domains alike) and BEC. It is known from recent works that search for stable 2D solitons in models with a spatially localized self-attractive nonlinearity is a challenging problem. We make use of the variational approximation (VA) and numerical methods to investigate conditions for the existence and stability of solitons in the present setting. The result crucially depends on the transverse shape of the stripe: while the rectangular profile supports stable 2D solitons, its smooth Gaussian-shaped counterpart makes all the solitons unstable. This difference is explained, in particular, by the VA. The double stripe with the rectangular profile admits stable solitons of three distinct types: symmetric and asymmetric ones with a single-peak, and double-peak symmetric solitons. The shape and stability of the single-peak solitons of either type are accurately predicted by the VA. Collisions between identical stable solitons are briefly considered too, by means of direct simulations. Depending on the collision velocity, we observe excitation of intrinsic oscillations of the solitons, or their decay, or the collapse (catastrophic self-focusing).

Intracellular and extracellular spaces are separately considered in an electrical bidomain model of tissue. We propose a mechanical bidomain model separately considering the intracellular and extracellular spaces, coupled through a linear restoring force proportional to the displacement difference of the two spaces. We consider a mechanically passive model of heart fibers (no tension) with an action potential, and an electrically passive model (no action potential) in tissue with an ischemic boundary. We find the pressure and displacement fields arising from our consideration of a bidomain instead of a monodomain and note interesting characteristics evident only with a bidomain approach.