Stochastic resonance (SR) and coherence resonance (CR) have been studied experimentally in discharge plasmas close to a homoclinic bifurcation. For the SR phenomenon, it is observed that a superimposed subthreshold periodic signal can be recovered via stochastic modulations of the discharge voltage. Furthermore, it is realized that even in the absence of a subthreshold deterministic signal, the system dynamics can be recovered and optimized using noise. This effect is defined as CR in the literature. In the present experiments, induction of SR and CR is quantified using the absolute mean difference and normalized variance techniques, respectively.

The dyadic Green functions for the Proca fields in free space are derived to include singular terms. Both the electric and magnetic types will be obtained with the results reduced back to those for the Maxwell fields in the limit of zero photon mass. Moreover, the singular terms are identical in both massless and massive electrodynamics. As an illustration, the results are applied to obtain the exact dynamical fields for an oscillating dipole which reduce back to the well-known expressions for static fields derived previously in the literature for massive electrodynamics.

We develop a systematic analytical approach to study the linear and nonlinear solitary excitations of quasi-one-dimensional Bose-Einstein condensates trapped in an optical lattice. For the linear case, the Bloch wave in the $n\text{th}$ energy band is a linear superposition of Mathieu’s functions ${\mathrm{ce}}_{n-1}$ and ${\mathrm{se}}_n$; and the Bloch wave in the $n\text{th}$ band gap is a linear superposition of ${\mathrm{ce}}_n$ and ${\mathrm{se}}_n$. For the nonlinear case, only solitons inside the band gaps are likely to be generated and there are two types of solitons—fundamental solitons (which is a localized and stable state) and subfundamental solitons (which is a localized but unstable state). In addition, we find that the pinning position and the amplitude of the fundamental soliton in the lattice can be controlled by adjusting both the lattice depth and spacing. Our numerical results on fundamental solitons are in quantitative agreement with those of the experimental observation [B. Eiermann et al., Phys. Rev. Lett. 92, 230401 (2004)]. Furthermore, we predict that a localized gap-soliton train consisting of several fundamental solitons can be realized by increasing the length of the condensate in currently experimental conditions.

We examine the dynamical evolution of the one-dimensional self-organized forest-fire model (FFM), when the system is far from its statistically steady state. In particular, we investigate situations in which conditions change on a time scale that is faster than, or of the order of the typical time needed for relaxation. An analytical approach is introduced based on a hierarchy of first-order nonlinear differential equations. This hierarchy can be closed at any level, yielding a sequence of successively more accurate descriptions of the dynamics. It is found that our approximate description can yield a faithful description of the FFM dynamics, even when a low order truncation is used. Employing both full simulations of the FFM and our approximate descriptions, we examine the time scales and cluster-size-dependent dynamics of relaxation to the statistical equilibrium. As an example of changing external conditions in a natural forest, the effects of a time-dependent lightning frequency are considered.

We demonstrate, using kinetic Monte Carlo simulations of submonolayer epitaxial growth, that long jumps and reversible aggregation have a major impact on the evolution of island morphologies. Long jumps are responsible for a supra-Arrhenius behavior of the effective diffusion coefficient as the attachment and detachment kinetics give rise to a bimodal island size distribution that depends on temperature and long jump extent limits. As the islands density increases with temperature, the average size of stable islands reaches a maximum before decreasing. We have also observed that the diffusion coefficient cannot be used alone to predict the evolution of island sizes and morphologies, the relative rate of each process having a major importance. Our theoretical developments are of direct relevance for materials systems such as Au, Pd, Ag, Cu, Ni, $\mathrm{H}∕\mathrm{Si}$, H/W(110), $\mathrm{Co}∕\mathrm{Ru}$, and $\mathrm{Co}∕\mathrm{Ru}\left(\mathrm{S}\right)$, that are known for exhibiting a compensation effect that cannot be contained within experimental uncertainties.

Single-molecule force spectroscopy provide details of the underlying energy surfaces of proteins which are essential to the understanding of their unfolding process. Recently, it has been observed experimentally that by pulling proteins in different directions relative to their secondary structure, one can gain a better understanding of the shape of the energy landscape. We consider simple lattice models which are anisotropic in nature to study the response of a force in unfolding of a polymer. Our analytical solution of the model, supported by extensive numerical calculations, reveal that the force temperature diagrams are very different depending on the direction of the applied force. We find that either unzipping or shearing kind transitions dominate the dynamics of the unfolding process depending solely on the direction of the applied force.

Chemical oscillations are shown to be responsible for very low frequency modulations of a bubble oscillating nonlinearly in a high intensity ultrasound field. In the parameter space of incomplete dissociation near the onset of sonoluminescence a small bubble is shown to grow on a long time scale by the intake of dissolved air. Bubble collapses get hotter and more dense, noninert gases are dissociated and removed, and a small growing argon bubble is left behind continuing the circle.

The formation and dynamics of a laser-produced aluminum plasma have been experimentally and theoretically investigated. The visible-emitting regions of the plasma form two structures with different lifetimes and expansion velocities. The first part of the transient ionic signal simultaneously recorded by a Langmuir probe presents an oscillatory structure. A hydrodynamic model in a nondifferentiable space-time has been established. The numerical simulation of the plasma expansion showed the plasma plume separation into two patterns. Moreover, the self-structuring of the interface appears through a negative differential conductance and the current oscillations are explained as being induced by thermal fluctuations that appear in the plasma cooling processes.

Fractional diffusion equations are widely used to describe anomalous diffusion processes where the characteristic displacement scales as a power of time. For processes lacking such scaling the corresponding description may be given by diffusion equations with fractional derivatives of distributed order. Such equations were introduced in A. V. Chechkin, R. Gorenflo, and I. Sokolov [Phys. Rev. E 66, 046129 (2002)] for the description of the processes getting more anomalous in the course of time (decelerating subdiffusion and accelerating superdiffusion). Here we discuss the properties of diffusion equations with fractional derivatives of the distributed order for the description of anomalous relaxation and diffusion phenomena getting less anomalous in the course of time, which we call, respectively, accelerating subdiffusion and decelerating superdiffusion. For the former process, by taking a relatively simple particular example with two fixed anomalous diffusion exponents we show that the proposed equation effectively describes the subdiffusion phenomenon with diffusion exponent varying in time. For the latter process we demonstrate by a particular example how the power-law truncated Lévy stable distribution evolves in time to the distribution with power-law asymptotics and Gaussian shape in the central part. The special case of two different orders is characteristic for the general situation in which the extreme orders dominate the asymptotics.

We study vacancy diffusion on the classical triangular-lattice dimer model, subject to the kinetic constraint that dimers can only translate, but not rotate. A single vacancy, i.e., a monomer, in an otherwise fully packed lattice, is always localized in a treelike structure. The distribution of tree sizes is asymptotically exponential and has an average of $8.16\pm 0.01$ sites. A connected pair of monomers has a finite probability of being delocalized. When delocalized, the diffusion of monomers is anomalous: $⟨{\vec{x}}^2⟩\propto t^{\beta }$, with $\beta =0.46\pm 0.06$. We also find that the same exponent $\beta$ governs diffusion of clusters of three or four monomers, as well as the diffusion of dimers at finite but low monomer densities. We argue that coordinated motion of monomer pairs is the basic mechanism allowing large-scale transport at low monomer densities. We further identify a “swap-tunneling” mechanism for diffusion of monomer pairs, where a subtle interplay between swap moves (translations of dimers transverse to their axes) and glide moves (translations of dimers parallel to their axes) plays an essential role.

We have performed Monte Carlo simulations to obtain the thermodynamic properties of fluids with two kinds of hard-core plus attractive-tail or oscillatory potentials. One of them is the square-well potential with small well width. The other is a model potential with oscillatory and decaying tail. Both model potentials are suitable for modeling the effective potential arising in complex fluids and fluid mixtures with extremely-large-size asymmetry, as is the case of the solvent-induced depletion interactions in colloidal dispersions. For the former potential, the compressibility factor, the excess energy, the constant-volume excess heat capacity, and the chemical potential have been obtained. For the second model potential only the first two of these quantities have been obtained. The simulations cover the whole density range for the fluid phase and several temperatures. These simulation data have been used to test the performance of a third-order thermodynamic perturbation theory (TPT) recently developed by one of us [S. Zhou, Phys. Rev. E 74, 031119 (2006)] as compared with the well-known second-order TPT based on the macroscopic compressibility approximation due to Barker and Henderson. It is found that the first of these theories provides much better accuracy than the second one for all thermodynamic properties analyzed for the two effective potential models.

We have investigated the effect of cold drawing on the motion of phenylene rings in bisphenol-A polycarbonate by neutron scattering. The intensity scattered by isotropic and stretched polycarbonate is different, the quasielastic broadening being larger for the isotropic sample. This difference can be well accounted for by considering that preferentially oriented rings in the stretched polymer have their motion sterically hindered. The extent of the effect of stretching on the phenylene-ring motion obtained from this neutron-scattering investigation is in good agreement with that obtained when studying the effect of cold drawing on the $\gamma$ relaxation by dielectric spectroscopy.

A simple model is proposed for the buckling and coiling instability of a viscous “fluid rope” falling on a plane. By regarding a fluid rope as a one-dimensional flow, this model accounts for only the axial and shared viscous forces. Our model successfully reproduces several experiments with no adjustable parameters, such as the existence of three distinct coiling regimes reported in the paper by Maleki et al. [Phys. Rev. Lett. 93, 214502 (2004)]. Our model allows for the discussion of unsteady motion. An expression for the critical fall height at which the coiling frequency changes from a decrease to increase was phenomenologically derived. It was found that the coil-uncoil transition shows remarkable hysteresis only for weak gravity condition.

We present a stochastic two-population model that describes the migration and growth of semisedentary foragers and sedentary farmers along a river valley during the Neolithic transition. The main idea is that random migration and transition from a sedentary to a foraging way of life, and backwards, is strongly coupled with the local crop production and associated degradation of land. We derive a nonlinear integral equation for the population density coupled with the equations for the density of soil nutrients and crop production. Our model provides a description of the formation of human settlements along the river valley. The numerical results show that the individual farmers have a tendency for aggregation and clustering. We show that the large-scale pattern is a transient phenomenon which eventually disappears due to land degradation.

An analytical approach is used to calculate an ion energy distribution function (IEDF) in a dual frequency (DF) collisionless rf discharge in argon. Three possible limit regimes for frequency relations in the DF discharge are discussed. The analytical IEDF is obtained for the intermediate-frequency case, which is most applicable in plasma-processing technologies. The analytical expressions for an ion spectrum width as well as for the minimum and maximum ion energies are derived. The analytical theory is compared with a particle-in-cell Monte Carlo numerical simulation and also with the results of a semianalytical model.

This paper questions the mode of collapse of some simple softening nonlocal structural systems comprising the classical cantilever beam. Nanobeams can be concerned by such an elementary model. The homogeneous cantilever beam loaded by a concentrated force at its extremity is first considered as a structural paradigm. A nonlocal plasticity model is developed in order to control the localization process induced by microcracking phenomena. An implicit gradient plasticity model equivalent to a nonlocal integral plasticity model is used in this paper. It is shown that the regularized problem is well posed. Closed-form solutions of the elastoplastic deflection are finally derived. The length of the plastic zone grows during the softening process until an asymptotic limited value, which depends on the characteristic length of the material. Scale effects are clearly obtained for these static bending tests. Other structural cases are also presented, including the simply supported beam under uniform transverse loading. It is concluded that the mode of collapse is firmly a nonlocal phenomenon.

A coupling lattice Boltzmann equation (LBE) model with multiple relaxation times is proposed for thermal flows with viscous heat dissipation and compression work. In this model the fixed Prandtl number and the viscous dissipation problems in the energy equation, which exist in most of the LBE models, are successfully overcome. The model is validated by simulating the two-dimensional Couette flow, thermal Poiseuille flow, and the natural convection flow in a square cavity. It is found that the numerical results agree well with the analytical solutions and/or other numerical results.

We consider the growth of a single fcc dendrite into an undercooled melt. Unlike most simulations of this well-studied phenomenon, we adopt an atomistic growth model that uses a kinetic Monte Carlo technique to track the free boundary. The model allows for both phase change and exchange between liquid and solid atoms on the surface of the crystal and is coupled to a continuum model for heat transport away from the interface. For small length and time scales, this approach provides simple, effective front tracking with fully resolved atomistic detail. An interesting finding is that the surface exchange mechanism appears to be important for capturing effects due to anisotropy that are needed to produce realistic growth shapes.

We investigate thresholds of percolation in two-phase macroscopically inhomogeneous media. It is shown that, unlike standard percolation behavior there are systems in which effective kinetic coefficients of two-phase macroscopically inhomogeneous media have two percolation thresholds. As examples, thermoelectric and galvanomagnetic phenomena in such media are considered.