We study localized traveling waves and chaotic states in strongly nonlinear one-dimensional Hamiltonian lattices. We show that the solitary waves are superexponentially localized and present an accurate numerical method allowing one to find them for an arbitrary nonlinearity index. Compactons evolve from rather general initially localized perturbations and collide nearly elastically. Nevertheless, on a long time scale for finite lattices an extensive chaotic state is generally observed. Because of the system’s scaling, these dynamical properties are valid for any energy.

We experimentally and numerically observe synchronization of chaos in two mutually coupled vertical-cavity surface-emitting lasers (VCSELs) with time delay. We observe in-phase and antiphase synchronization of polarization-resolved chaotic temporal wave forms under the condition of wavelength matching. We investigate leader-laggard relationship between two chaotic wave forms of mutually coupled VCSELs and find that the laser with longer wavelength becomes the leader.

We perform molecular dynamics simulation of a small number of particles in a box with periodic boundary conditions from a viewpoint of chaotic dynamical systems. There is a transition at a critical energy $E_c$ that each particle is confined in each unit cell for $E<E_c$, and the chaotic diffusion occurs for $E>E_c$. We find an anomalous behavior of the jump frequency above the critical energy in a two-particle system, which is related with the infinitely alternating stability change of the straight motion passing through a saddle point. We find simultaneous jump motions just above the critical energy in a four-particle system and 16-particle system, which is also related with the motion passing through the saddle point.

Despite its appeal, real and simulated glass forming systems do not undergo an ergodic-nonergodic (ENE) transition. We reconsider whether the fluctuating nonlinear hydrodynamics (FNH) model for this system, introduced by us in 1986, supports an ENE transition. Using nonperturbative arguments, with no reference to the hydrodynamic regime, we show that the FNH model does not support an ENE transition. Our results support the findings in the original paper. Assertions in the literature questioning the validity of the original work are shown to be in error.

A computational study of morphological instabilities of a two-dimensional nematic front under directional growth was performed using a Landau–de Gennes-type quadrupolar tensor order parameter model for the first-order isotropic-nematic transition of 5CB (pentyl-cyanobiphenyl). A previously derived energy balance, taking anisotropy into account, was utilized to account for latent heat and an imposed morphological gradient in the time-dependent model. Simulations were performed using an initially homeotropic isotropic-nematic interface. Thermal instabilities in both the linear and nonlinear regimes were observed and compared to past experimental and theoretical observations. A sharp-interface model for the study of linear morphological instabilities, taking into account additional complexity resulting from liquid-crystalline order, was derived. Results from the sharp-interface model were compared to those from full two-dimensional simulation identifying the specific limitations of simplified sharp-interface models for this liquid-crystal system. In the nonlinear regime, secondary instabilities were observed to result in the formation of defects, interfacial heterogeneities, and bulk texture dynamics.

We present experimental results for the rolling of spheres on a granular bed. We use two sets of glass and steel spheres with varying diameters and a high-speed camera to follow the motion of the spheres. Despite the complex phenomena occurring during the rolling, the results show a friction coefficient nearly independent of the velocity (0.45–0.5 for glass and 0.6–0.65 for steel). It is found that for a given sphere density, the large spheres reach a longer distance, a result that may also help explain the rock sorting along natural stone accumulations at the foot of mountain slopes.

We present two different designs of electrohydrodynamic micropumps for microfluidic systems. The micropumps have no movable parts, and their simple design allows for fabrication by microsystems technology. The pumps are operated by ac voltages from $1\text{to}60\mathrm{V}$ and were tested with aqueous solutions in the conductivity range of $1–112\mathrm{mS}{\mathrm{m}}^{-1}$. The pump effect is induced by an ac electric field across a fluid medium with an inhomogeneous temperature distribution. It is constant over a wide range of the ac field frequency with a conductivity-dependent drop-off at high frequencies. The temperature-dependent conductivity and permittivity distributions in the fluid induce space charges that interact with the electric field and induce fluid motion. The temperature distribution can be generated either by Joule heating in the medium or by external heating. We present experimental results obtained with two prototypes featuring Joule heating and external heating by a heating filament. Experimental and numerical results are compared with an analytical model.

A spectral element method (SEM) is proposed for the accurate calculation of band structures of two-dimensional anisotropic photonic crystals. It uses Gauss-Lobatto-Legendre polynomials as the basis functions in the finite-element framework with curvilinear quadrilateral elements. Coordination mapping is introduced to make the curved quadrilateral elements conformal with the problem geometry. Mixed order basis functions are used in the vector SEM for full vector calculation. The numerical convergence speed of the method is investigated with both square and triangular lattices, and with isotropic and in-plane anisotropic media. It is shown that this method has spectral accuracy, i.e., the numerical error decreases exponentially with the order of basis functions. With only four points per wavelength, the SEM can achieve a numerical error smaller than 0.1%. The full vector calculation method can suppress all spurious modes with nonzero eigenvalues, thus making it easy to filter out real modes. It is thus demonstrated that the SEM is an efficient alternative method for accurate determination of band structures of two-dimensional photonic crystals.

The conventional Navier-Stokes-Fourier equations with no-slip boundary conditions are unable to capture the phenomenon of gas thermal transpiration. While kinetic approaches such as the direct simulation Monte Carlo method and direct solution of the Boltzmann equation can predict thermal transpiration, these methods are often beyond the reach of current computer technology, especially for complex three-dimensional flows. We present a computationally efficient nonequilibrium thermal lattice Boltzmann model for simulating temperature-gradient-induced flows. The good agreement between our model and kinetic approaches demonstrates the capabilities of the proposed lattice Boltzmann method.

Nonzero currents characterize the nonequilibrium state in stochastic dynamics (or master equation) models of natural systems. In such models there is a matrix $R$ of transition probabilities connecting the states of the system. We show that if the strength of a transition increases, so does the current along the corresponding bond. We also address the inverse problem: given a set of observed currents, we show the extent to which the original “$R$” can be recovered. These considerations lead to a general discussion of time scales and substance flows.

A freely cooling granular gas with a velocity-dependent restitution coefficient is studied in one dimension. The restitution coefficient becomes near elastic when the relative velocity of the colliding particles is less than a velocity scale $\delta$. Different statistical quantities, namely, density distribution, occupied and empty cluster length distributions, and spatial density and velocity correlation functions, are obtained using event driven molecular dynamic simulations. We compare these with the corresponding quantities of the sticky gas (inelastic gas with zero coefficient of restitution). We find that in the inhomogeneous cooling regime, for times smaller than a crossover time $t_1$, where $t_1\sim {\delta }^{-1}$, the behavior of the granular gas is equivalent to that of the sticky gas. When $\delta \to 0$, then $t_1\to \infty$ and, hence, the results support an earlier claim that the freely cooling inelastic gas is described by the inviscid Burgers equation. For a real granular gas with finite $\delta$, the existence of the time scale $t_1$ shows that, for large times, the granular gas is not described by the inviscid Burgers equation.

The clustering phenomenon within two-dimensional, rapid granular, simple shear flows is investigated. Two characterizations are developed and implemented for monodisperse systems, revealing physically meaningful insight. First, a new feature of the radial distribution function is identified for these dissipative granular systems, which is not present in molecular (nondissipative) systems. Namely, a long-scale minimum occurs at a distance representing the average distance between the center of a cluster and the center of a dilute region. Results indicate that center-to-center distances are least (i.e., clusters are most tightly packed) for systems of moderate particle concentrations and low restitution coefficients. In addition, concentration and temperature measurements of clustered and dilute regions are also obtained using a Gaussian filter that is based on this center-to-center distance and, thus, provides a means of appropriately defining local concentrations. These results confirm previous findings that cluster prevalence increases with decreasing dissipation and that clustered regions have lower temperatures than their dilute counterparts. Surprisingly, however, the results indicate that cluster prevalence, defined by normalized concentration differences between the two regions, decrease monotonically with an increase in overall particle concentration.

Recently, it was argued that a three-point susceptibility equal to the density derivative of the intermediate scattering function, ${\chi }_n(k;t)=dF(k;t)∕dn$, enters into an expression for the divergent part of an integrated four-point dynamic density correlation function of a colloidal suspension [Berthier et al., J. Chem. Phys. 126, 184503 (2007)]. We show that, within the mode-coupling theory, the equation of motion for ${\chi }_n(k;t)$ is essentially identical as the equation of motion for the $\mathbf{q}\to 0$ limit of the three-point susceptibility ${\chi }_{\mathbf{q}}(\mathbf{k};t)$ introduced by Biroli et al. [Phys. Rev. Lett. 97, 195701 (2006)]. We present a numerical solution of the equation of motion for ${\chi }_n(k;t)$. We also derive and numerically solve an equation of motion for the density derivative of the self-intermediate scattering function, ${\chi }_n^s(k;t)=d{F}^s(k;t)∕dn$. We contrast the wave vector dependence of ${\chi }_n(k;t)$ and ${\chi }_n^s(k;t)$.

Most of the theoretical models describing the translocation of a polymer chain through a nanopore use the hypothesis that the polymer is always relaxed during the complete process. In other words, models generally assume that the characteristic relaxation time of the chain is small enough compared to the translocation time that nonequilibrium molecular conformations can be ignored. In this paper, we use molecular dynamics simulations to directly test this hypothesis by looking at the escape time of unbiased polymer chains starting with different initial conditions. We find that the translocation process is not quite in equilibrium for the systems studied, even though the translocation time $\tau$ is about 10 times larger than the relaxation time ${\tau }_{\mathrm{r}}$. Our most striking result is the observation that the last half of the chain escapes in less than $\sim 12\%$ of the total escape time, which implies that there is a large acceleration of the chain at the end of its escape from the channel.

In this work we develop a theoretical framework of the interaction of microbubbles with bacteria in the ultrasound field using a shell model of the bacteria, following an approach developed previously [P. V. Zinin et al., Phys. Rev. E 72, 61907 (2005)]. Within the shell model, the motion of the cell in an ultrasonic field is determined by the motion of three components: the internal viscous fluid, a thin elastic shell, and the surrounding viscous fluid. Several conclusions can be drawn from the modeling of sound interaction with a biological cell: (a) the characteristics of a cell’s oscillations in an ultrasonic field are determined both by the elastic properties of the shell the viscosities of all components of the system, (b) for dipole quadrupole oscillations the cell’s shell deforms due to a change in the shell area this oscillation depends on the surface area modulus $K_A$, (c) the relative change in the area has a maximum at frequency $f_K\sim \frac{1}{2\pi }\sqrt{K_A∕\left(\rho a^3\right)}$, where $a$ is the cell’s radius and $\rho$ is its density. It was predicted that deformation of the cell wall at the frequency $f_K$ is high enough to rupture small bacteria such as $E$. coli in which the quality factor of natural vibrations is less than 1 $(Q<1)$. For bacteria with high value quality factors $(Q>1)$, the area deformation has a strong peak near a resonance frequency $f_K$; however, the value of the deformation near the resonance frequency is not high enough to produce sufficient mechanical effect. The theoretical framework developed in this work can be extended for describing the deformation of a biological cell under any arbitrary, external periodic force including radiation forces unduced by acoustical (acoustical levitation) or optical waves (optical tweezers).

In this paper we describe how an ordinary differential equation model of corticothalamic interactions may be obtained from a more general system of delay differential equations. We demonstrate that transitions to epileptic dynamics via changes in system parameters are qualitatively the same as in the original model with delay, as well as demonstrating that the onset of epileptic activity may arise due to regions of bistability. Hence, the model presents in one unique framework, two competing theories for the genesis of epileptiform activity. Similarities between model transitions and clinical data are presented and we argue that statistics obtained from, and a parameter estimation of this model may be a potential means of classifying and predicting the onset and offset of seizure activity.

The phase diagram, structural evolution, and kinetics of temperature-induced protein gelation of protein Bovine Serum Albumin (BSA) have been studied as a function of solution $p\mathrm{H}$ and protein concentration. The protein gelation temperature represents the onset of turbidity in the protein solution, which increases significantly with increasing $p\mathrm{H}$ beyond the isoelectric $p\mathrm{H}$ of the protein molecule. On the other hand, the gelation temperature decreases with an increase in protein concentration only in the low-protein-concentration regime and shows a small increasing trend at higher protein concentrations. The structural evolution and kinetics of protein gelation have been studied using small-angle neutron scattering. The structure of the protein molecule remains stable up to temperatures very close to the gelation temperature. On increasing the temperature above the gelation temperature, the protein solution exhibits a fractal structure, an indication of gel formation due to aggregation. The fractal dimension of the gel increases with increasing temperature, suggesting an increase in branching between the aggregates, which leads to stronger gels. The increase in both solution $p\mathrm{H}$ and protein concentration is found to delay the growth in the fractal structure and its saturation. The kinetics of gelation has been studied using the temperature-jump process of heating. It is found that the structure of the protein gels remains invariant after the heating time $(\sim 1\min )$, indicating a rapid formation of gel structure within this time. The protein gels prepared through gradual and temperature-jump heating routes do not always show the same structure. In particular, at higher temperatures (e.g., $85°\mathrm{C}$), while gradual heating shows a fractal structure, there is collapse of such fractal structure during temperature-jump heating.

It has been demonstrated that, in a one-dimensional wave system, monochromatic waves may be generated which are completely localized to the region of excitation or which propagate in only one direction. We further the discussion of such nonpropagating and directional excitations and demonstrate that they can be extended to excitations of an arbitrary finite number of frequencies. Two techniques for mathematically constructing these excitations are discussed. Furthermore, the relation between nonpropagating excitations and nonscattering scatterers is discussed. The results presented here may be useful in the development of devices for one-dimensional and quasi-one-dimensional wave systems.

Results of a previous paper with the same title are retrieved by a different method. A one-component plasma is bounded by a plane surface. The plasma is fully coupled to the electromagnetic field, therefore, the charge correlations are retarded. The quantum correlation function of the surface charge densities, at times different by $t$, at asymptotical large distances $R$, at inverse temperature $\beta$, decays as $-1∕\left(8{\pi }^2\beta R^3\right)$, a surprisingly simple result: The decay is independent of Planck’s constant $\hslash$, the time difference $t$, and the velocity of light $c$. The present paper is based on the analysis of the collective vibration modes of the system.

The Kelvin equation relates the equilibrium vapor pressure of a fluid to the curvature of the fluid-vapor interface and predicts that vapor condensation will occur in pores or irregularities that are sufficiently small. Past analyses of capillary condensation in porous systems with fractal structure have related the phenomenon to the fractal dimension of the pore volume distribution. Recent work, however, suggests that porous systems can exhibit distinct fractal dimensions that are characteristic of both their pore volume and the surfaces of the pores themselves. We show that both fractal dimensions have an effect on the thermodynamics that governs capillary condensation and that previous analyses can be obtained as limiting cases of a more general formulation.