We discuss the biochemical three-dimensional reaction-diffusion model, which does not provide temporal self-sustained oscillations via reaction terms. However, the self-sustained oscillations and waves could be obtained using the proper boundary conditions for systems with a finite thickness. We have carried out in our numerical simulation the results quite corresponding to the experimental ones. We discuss the range of models for which our approach is applicable.

Connections in complex networks are inherently fluctuating over time and exhibit more dimensionality than analysis based on standard static graph measures can capture. Here, we introduce the concepts of temporal paths and distance in time-varying graphs. We define as temporal small world a time-varying graph in which the links are highly clustered in time, yet the nodes are at small average temporal distances. We explore the small-world behavior in synthetic time-varying networks of mobile agents and in real social and biological time-varying systems.

An unbounded energy growth of particles bouncing off two-dimensional (2D) smoothly oscillating polygons is observed. Notably, such billiards have zero Lyapunov exponents in the static case. For a special 2D polygon geometry—a rectangle with a vertically oscillating horizontal bar—we show that this energy growth is not only unbounded but also exponential in time. For the energy averaged over an ensemble of initial conditions, we derive an a priori expression for the rate of the exponential growth as a function of the geometry and the ensemble type. We demonstrate numerically that the ensemble averaged energy indeed grows exponentially, at a close to the analytically predicted rate—namely, the process is controllable.

Our goal is to estimate the validity of the product rule by computing the effective permittivity and magnetic permeability of magnetoplasmonic core-shell (CS) nanostructures. We discuss the departure of the simulation from the quasistatic mean-field product rule when calculated close from resonance. The corrections to mean-field analysis are shown to be so large at a high fraction of CS inclusion that they can exceed the mean-field value by more than 750% (at the plasmon resonance). It is further shown how the spatially nonuniform electric and magnetic field enhancements extend over nanometer length scales.

In this study we derive a single-particle equation of motion, from first principles, starting out with a microscopic description of a tracer particle in a one-dimensional many-particle system with a general two-body interaction potential. Using a harmonization technique, we show that the resulting dynamical equation belongs to the class of fractional Langevin equations, a stochastic framework which has been proposed in a large body of works as a means of describing anomalous dynamics. Our work sheds light on the fundamental assumptions of these phenomenological models and a relation derived by Kollmann.

We present some results of Monte Carlo simulations for the deposition of particles of different sizes on a two-dimensional substrate. The particles are linear, height one, and can be deposited randomly only in the two $x$ and $y$ directions of the substrate and occupy an integer number of cells of the lattice. We show there are three different regimes for the temporal evolution of the interface width. At the initial times we observe an uncorrelated growth, with an exponent ${\beta }_1$ characteristic of the random deposition model. At intermediate times, the interface width presents an unusual behavior, described by a growing exponent ${\beta }_2$, which depends on the size of the particles added to the substrate. If the linear size of the particle is two we have ${\beta }_2<{\beta }_1$, otherwise we have ${\beta }_2>{\beta }_1$, for all other particle sizes. After the growth reaches the saturation regime where the interface width becomes constant and is described by the roughness exponent $\alpha$, which is nearly independent of the size of the particle. Similar results are found in the surface growth due to the electrophoretic deposition of polymer chains. Contrary to one-dimensional results the growth exponents are nonuniversal.

The unbiased translocation of a coarse-grained polymer through a nanopore is investigated via Langevin dynamics simulations for polymers ranging from $N=19$ to 299 monomers in length and pore widths $r_p$ ranging from 1 to 10 times the monomer diameter. The exponent $\alpha$ derived from the scaling of the translocation time $\tau$ with respect to the molecular weight $N$ is found to be heavily dependent on $r_p$ and increases from a value of 2.2 for $r_p=1.0$ up to a saturation value of 3. The details of the translocation process also reveal that the average number of monomers in the pore $⟨n_p⟩$ not only varies as translocation proceeds but that for any polymer where the radius of gyration is greater than the radius of the available pore width, $⟨n_p⟩$ decreases with increasing $N$. Using these data to rescale the results according to a blob picture, the results retain sensitivity on the pore geometry as $\alpha$ varies from 2.2 to 2.65—a range which covers all results reported in previous studies.

Starting with an initial random network of oscillators with a heterogeneous frequency distribution, its autonomous synchronization ability can be largely improved by appropriately rewiring the links between the elements. Ensembles of synchronization-optimized networks with different connectivities are generated and their statistical properties are studied.

A modification of Mott-Smith method for predicting the one-dimensional shock wave solution is presented. Mott-Smith distribution function is used to construct the system of moment equations to study the steady-state structure of shock wave in a gas of Maxwell molecules and in argon. The predicted shock solutions using the newly proposed formalism are compared to the experimental data, direct-simulation Monte Carlo (DSMC) solution, and the solutions predicted by other existing theories for Mach numbers $M<11$. The density, temperature, heat flux profiles, and shock thickness calculated at different Mach numbers have been shown to have good agreement with the experimental and DSMC solutions. In addition, the predicted shock thickness is in good agreement with the DSMC simulation result at low Mach numbers.

The viscoelastic properties of strongly coupled Yukawa liquids are characterized by computing the complex shear viscosity $\eta \left(\omega \right)$. This is done using three methods of molecular-dynamics simulation: equilibrium, nonequilibrium, and Langevin dynamics, all with a mutually repulsive Yukawa interparticle potential. A change from viscous to elastic response is observed with increasing frequency, as well as a decrease of the magnitude of the viscosity with increasing frequency. The Langevin simulation reveals that the dependence of the complex viscosity on the friction has a different character for hot and cool liquids. At $\omega =0$, we find that as friction increases, the viscosity diminishes at high temperature but increases at low temperature. In addition to finding its frequency dependence, we also derive the wave-number (length-scale) dependence of the shear viscosity.

We analyze the effects of disorder on the thermal Casimir interaction for the case of two semi-infinite planar slabs across an intervening homogeneous unstructured dielectric. The semi-infinite bounding layers are assumed to be composed of plane-parallel layers of random dielectric materials. We show that the effective thermal Casimir interaction at long distances is self-averaging and can be written in the same form as the one between nonrandom media but with the effective dielectric tensor of the corresponding random media. On the contrary, the behavior at short distances becomes random, and thus sample dependent, dominated by the local values of the dielectric constants proximal to each other across the central homogeneous unstructured dielectric layer. We extend these results to the regime of intermediate slab separations by using perturbation theory for weak disorder as well as by extensive numerical simulations for a number of systems where the dielectric function has a log-normal distribution. Numerical simulation completely corroborates all the main features of the disorder dependent thermal Casimir interaction deduced analytically.

The results of a recent investigation of the nematic biaxiality in a bent-core mesogen (A131) are in apparent disagreement with earlier claims. Samples of mesogen A131 used in the two studies were investigated with polarized optical microscopy, conoscopy, carbon-13 NMR, and crossover frequency measurements. The results demonstrate that textural changes associated with the growth of biaxial nematic order appear at $\sim 149°\text{C}$. The Maltese cross observed in the conoscopic figure gradually splits into two isogyres at lower temperatures indicating phase biaxiality. Presence of the uniaxial to biaxial nematic phase transition is further confirmed by temperature trends of local order parameters based on ${}^{13}\text{C}$ chemical shifts in NMR experiments. Frequency switching measurements also clearly reveal a transition at $149°\text{C}$. Differences between the two reports appear to be related to the presence of solvent, impurities, and/or adsorbed gases in samples of A131 used in the study of Van Le et al. [Phys. Rev. E 79, 030701 (2009)].

Power stroke in skeletal muscles is a result of a conformational change in the globular portion of the molecular motor myosin II. In this paper we show that the fast tension recovery data reflecting the inner working of the power stroke mechanism can be quantitatively reproduced by a Langevin dynamics of a simple mechanical system with only two structural states. The proposed model is a generalization of the two state model of Huxley and Simmons. The main idea is to replace the rigid bistable device of Huxley and Simmons with an elastic bistable snap spring. In this setting the attached configuration of a cross bridge is represented not only by the discrete energy minima but also by a continuum of intermediate states where the fluctuation induced dynamics of the system takes place. We show that such soft-spin approach explains the load dependence of the power stroke amplitude and removes the well-known contradiction inside the conventional two state model regarding the time scale of the power stroke.

Front propagation in one- and two-dimensional spatially modulated media is studied both experimentally and theoretically. The pinning-depinning phenomenon, long ago predicted by Pomeau [Physica D 23, 3 (1986)], is obtained and verified experimentally in a nematic liquid-crystal cell under various configurations of optical forcing. The front dynamics is characterized with respect to the different forcing parameters and the observations are compared with numerical simulations of a full model for the tilt angle of the liquid crystals under optical feedback. A spatially forced dissipative ${\varphi }^4$ model is derived near the points of nascent bistability. From this model we derive analytical results that account qualitatively for the observed front dynamics and pinning range. Localized structures of different sizes and shapes are found to exist inside the pinning range and experimentally proved to be stable states of the spatially forced system.

We measure the frequencies of small-amplitude shape oscillations of a magnetically levitated water droplet. The droplet levitates in a magnetogravitational potential trap. The restoring forces of the trap, acting on the droplet’s surface in addition to the surface tension, increase the frequency of the oscillations. We derive the eigenfrequencies of the normal mode vibrations of a spherical droplet in the trap and compare them with our experimental measurements. We also consider the effect of the shape of the potential trap on the eigenfrequencies.

We have predicted theoretically and detected in laboratory experiments a tangling clustering of inertial particles in a stably stratified turbulence with imposed mean vertical temperature gradient. In the stratified turbulence a spatial distribution of the mean particle number density is nonuniform due to the phenomenon of turbulent thermal diffusion, i.e., the inertial particles are accumulated in the vicinity of the minimum of the mean temperature of the surrounding fluid, and a nonzero gradient of the mean particle number density, $\mathbf{\nabla }N$, is formed. It causes generation of fluctuations of the particle number density by tangling of the large-scale gradient $\mathbf{\nabla }N$ by velocity fluctuations. In addition, the mean temperature gradient $\mathbf{\nabla }T$ produces the temperature fluctuations by tangling of the large-scale gradient $\mathbf{\nabla }T$ by velocity fluctuations. The anisotropic temperature fluctuations contribute to the two-point correlation function of the divergence of the particle velocity field, i.e., they increase the rate of formation of the particle clusters in small scales. We have demonstrated that in the laboratory stratified turbulence this tangling clustering is much more effective than a pure inertial clustering (preferential concentration) that has been observed in isothermal turbulence. In particular, in our experiments in oscillating grid isothermal turbulence in air without imposed mean temperature gradient, the inertial clustering is very weak for solid particles with the diameter of $\approx 10\mu \text{m}$ and Reynolds numbers based on turbulent length scale and rms velocity, $\text{Re}=250$. In the experiments the correlation function for the inertial clustering in isothermal turbulence is much smaller than that for the tangling clustering in nonisothermal turbulence. The size of the tangling clusters is on the order of several Kolmogorov length scales. The clustering described in our study is found for inertial particles with small Stokes numbers and with the material density that is much larger than the fluid density. Our theoretical predictions are in a good agreement with the obtained experimental results.

A relativistic, warm fluid model of a nonequilibrium, collisionless plasma is developed and applied to examine nonlinear Langmuir waves excited by relativistically intense, short-pulse lasers. Closure of the covariant fluid theory is obtained via an asymptotic expansion assuming a nonrelativistic plasma temperature. The momentum spread is calculated in the presence of an intense laser field and shown to be intrinsically anisotropic. Coupling between the transverse and longitudinal momentum variances is enabled by the laser field. A generalized dispersion relation is derived for Langmuir waves in a thermal plasma in the presence of an intense laser field. Including thermal fluctuations in three-velocity-space dimensions, the properties of the nonlinear electron plasma wave, such as the plasma temperature evolution and nonlinear wavelength, are examined and the maximum amplitude of the nonlinear oscillation is derived. The presence of a relativistically intense laser pulse is shown to strongly influence the maximum plasma wave amplitude for nonrelativistic phase velocities owing to the coupling between the longitudinal and transverse momentum variances.

We present results from a study of finite-size effect in the kinetics of domain growth with conserved order parameter for a critical quench. Our observation of a weak size effect is a significant and surprising result. For diffusive dynamics, appropriate scaling analysis of Monte Carlo results obtained for small systems using a two-dimensional Ising model also shows that the correction to the expected Lifshitz-Slyozov law for the domain growth is very small. The methods used in this work to understand the growth dynamics should find application in other nonequilibrium systems with increasing length scales.

This paper analyzes a binary channel by means of information measures based on the Rényi entropy. The analysis extends, and contains as a special case, the classic reference model of binary information transmission based on the Shannon entropy measure. The extended model is used to investigate further possibilities and properties of stochastic resonance or noise-aided information transmission. The results demonstrate that stochastic resonance occurs in the information channel and is registered by the Rényi entropy measures at any finite order, including the Shannon order. Furthermore, in definite conditions, when seeking the Rényi information measures that best exploit stochastic resonance, then nontrivial orders differing from the Shannon case usually emerge. In this way, through binary information transmission, stochastic resonance identifies optimal Rényi measures of information differing from the classic Shannon measure. A confrontation of the quantitative information measures with visual perception is also proposed in an experiment of noise-aided binary image transmission.

We present a functional formalism to derive a generating functional for correlation functions of a multiplicative stochastic process represented by a Langevin equation. We deduce a path integral over a set of fermionic and bosonic variables without performing any time discretization. The usual prescriptions to define the Wiener integral appear in our formalism in the definition of Green’s functions in the Grassman sector of the theory. We also study nonperturbative constraints imposed by Becchi, Rouet and Stora symmetry (BRS) and supersymmetry on correlation functions. We show that the specific prescription to define the stochastic process is wholly contained in tadpole diagrams. Therefore, in a supersymmetric theory, the stochastic process is uniquely defined since tadpole contributions cancels at all order of perturbation theory.