We present a unified approach for qualitative and quantitative analysis of stability and instability dynamics of positive bright solitons in multidimensional focusing nonlinear media with a potential (lattice), which can be periodic, periodic with defects, quasiperiodic, single waveguide, etc. We show that when the soliton is unstable, the type of instability dynamic that develops depends on which of two stability conditions is violated. Specifically, violation of the slope condition leads to a focusing instability, whereas violation of the spectral condition leads to a drift instability. We also present a quantitative approach that allows one to predict the stability and instability strength.

The dynamics of three-wave parametric coupling is considered on an example of nonequilibrium magnetostrictive medium under electromagnetic pumping. Subthreshold and supercritical mode of three-wave excitation are described analytically and simulated numerically for a triad of magnetoelastic waves. Theoretical analysis of the supercritical mode shows that space-time development of three-wave excitation in such a nonequilibrium system has the character of explosive instability and localization of “positive energy” waves.

Homogeneous shear flows (with constant strainrate $d{v}_x∕dy$) are generated with the Doll’s and Sllod algorithms and compared to corresponding inhomogeneous boundary-driven flows. We use one-, two-, and three-dimensional smooth-particle weight functions for computing instantaneous spatial averages. The nonlinear normal-stress differences are small, but significant, in both two and three space dimensions. In homogeneous systems the sign and magnitude of the shearplane stress difference, $P_{xx}-P_{yy}$, depend on both the thermostat type and the chosen shearflow algorithm. The Doll’s and Sllod algorithms predict opposite signs for this normal-stress difference, with the Sllod approach definitely wrong, but somewhat closer to the (boundary-driven) truth. Neither of the homogeneous shear algorithms predicts the correct ordering of the kinetic temperatures: $T_{xx}>T_{zz}>T_{yy}$.

The problem of competitive nucleation in the framework of probabilistic cellular automata is studied from the dynamical point of view. The dependence of the metastability scenario on the self-interaction is discussed. An intermediate metastable phase, made of two flip-flopping chessboard configurations, shows up depending on the ratio between the magnetic field and the self-interaction. A behavior similar to the one of the stochastic Blume-Capel model with Glauber dynamics is found.

This paper extends traditional two-player prisoners’ dilemma (PD) to three-player PD. We have studied spatial patterns of cooperation behaviors, growth patterns of cooperator clusters and defector clusters, and cooperation frequency of the players. It is found while three-player PD exhibits many properties similar to two-player PD, some new features arise. Specifically, (i) a new region appears, in which neither a $3\times 3$ cooperator cluster nor a $3\times 3$ defector cluster could grow; (ii) more growth patterns of cooperator clusters and defector clusters are identified; (iii) multiple cooperation frequencies exist in the region that exhibits dynamic chaos. Some theoretical analysis of these features is presented.

Stochastic sandpiles self-organize to an absorbing-state critical point with scaling behavior different from directed percolation (DP) and characterized by the presence of an additional conservation law. This is usually called the C-DP or Manna universality class. There remains, however, an exception to this universality principle: a sandpile automaton introduced by Maslov and Zhang, which was claimed to be in the DP class despite the existence of a conservation law. We show, by means of careful numerical simulations as well as by constructing and analyzing a field theory, that (contrarily to what was previously thought) this sandpile is also in the C-DP or Manna class. This confirms the hypothesis of universality for stochastic sandpiles and gives rise to a fully coherent picture of self-organized criticality in systems with conservation. In passing, we obtain a number of results for the C-DP class and introduce a strategy to easily discriminate between DP and C-DP scaling.

Hydrodynamic equations are used to identify the final state reached by a freely evolving granular gas above but close to its shear instability. The theory predicts the formation of a two bands shear state with a steady density profile. There is a modulation between temperature and density profiles as a consequence of the energy balance, the density fluctuations remaining small, without producing clustering. Moreover, the time dependence of the velocity field can be scaled out with the squared root of the average temperature of the system. The latter follows the Haff law, but with an effective cooling rate that is smaller than that of the free homogeneous state. The theoretical predictions are compared with numerical results for inelastic hard disks obtained by using the direct Monte Carlo simulation method, and a good agreement is obtained for low inelasticity.

We report on a series of three bent-core liquid crystals containing tetrathiafulvalene units. Their characterization consisted of electro-optical observations, second-harmonic generation (SHG) analysis, and x-ray diffraction measurements. Compound I exhibits a lamellar optically isotropic phase on cooling from the isotropic liquid and undergoes a nonreversible field-induced transition to a birefringent state. The two others present two-dimensional structural periodicities, being only compound II switchable. Additionally, the electron density maps of compounds II and III have been obtained based on the analysis of the x-ray diffraction intensities. According to SHG measurements the ground state is antiferroelectric in the three compounds. A quite good SHG performance is found in compounds I and II.

We have constructed the phase diagrams for a binary-mixture system of antiferroelectric and ferroelectric liquid-crystalline materials in both thick and thin cells. In the phase diagrams the boundary between the smectic-$C^{*}$ and smectic-$C_A^{*}$ phases runs almost parallel to the temperature axis below from ca. $70°\mathrm{C}$ down to at least $-25°\mathrm{C}$. The $\mathrm{Sm}{C}^{*}\text{−}\mathrm{Sm}{C}_A^{*}$ phase transition for a thin cell shows a large supercooling, and a gradual transition occurs near the boundary. Moreover, the thin cell shows a continuous evolution from the antiferroelectric to the ferroelectric state by increasing the electric field applied across the cell. The continuous evolution seemingly reflects the phenomenon of thresholdless antiferroelectricity. In order to explain these phenomena and in clarifying the mechanism of the so-called frustration between ferroelectricity and antiferroelectricity, we have measured the interlayer interaction energy by varying the constituent concentrations in the binary-mixture system. The measured interlayer interaction close to the boundary indicates that the gradual phase transition and continuous evolution result from the suppression of the solitary-wave propagation by the effect of surfaces.

The details of conformational changes undergone by transmembrane ion channels in response to stimuli, such as electric fields and membrane tension, remain controversial. We approach this problem by considering how the conformational changes impose deformations in the lipid bilayer. We focus on the role of bilayer deformations in the context of voltage-gated channels because we hypothesize that such deformations are relevant in this case as well as for channels that are explicitly mechanosensitive. As a result of protein conformational changes, we predict that the lipid bilayer suffers deformations with a characteristic free-energy scale of $10k_{\mathrm{B}}T$. This free energy is comparable to the voltage-dependent part of the total gating energy, and we argue that these deformations could play an important role in the overall free-energy budget of gating. As a result, channel activity will depend upon mechanical membrane parameters such as tension and leaflet thickness. We further argue that the membrane deformation around any channel can be divided into three generic classes of deformation that exhibit different mechanosensitive properties. Finally, we provide the theoretical framework that relates conformational changes during gating to tension and leaflet thickness dependence in the critical gating voltage. This line of investigation suggests experiments that could discern the dominant deformation imposed upon the membrane as a result of channel gating, thus providing clues as to the channel deformation induced by the stimulus.

The population dynamics of a weakly scattering system can often be characterized by Hartree equations, and those of a living system by Lotka-Volterra (LV) equations. In principle, can the population statistics of the quantum scattering system follow those of the living system? The answer is yes, provided the interactive potentials of the Hartree equations are made equal, on a one-to-one basis, to corresponding fitness functions of the LV equations. Of course this correspondence can be achieved only if the requirements of the Hartree approximation are satisfied, including that the scatter occurs within the coherence time of the quantum system. Examples are given of Hartree systems that obey the population dynamics of required predator-prey systems.

A one-dimensional $A+A\to \varnothing$ reaction with alternating dichotomic velocities is investigated to study the effects of velocity relaxation on the anomalous kinetics of this reaction. While we keep the magnitudes constant, the particle velocities are allowed to change from one moving direction to the other with a relaxation time, $\beta$. The kinetics of the reaction is studied for various relaxation times. Although the anomalous slower reaction rate is anticipated for the reaction in one-dimension, compared to the classical rate law, the rate is found to speed up at intermediate times for intermediate values of $\beta$. The time evolution for the spatial distribution of particles is also discussed to elucidate the effects of the velocity relaxation times on the kinetics of the reaction.

Homoclinic snaking is a term used to describe the back and forth oscillation of a branch of time-independent spatially localized states in a bistable, spatially reversible system as the localized structure grows in length by repeatedly adding rolls on either side. This behavior is simplest to understand within the subcritical Swift-Hohenberg equation, but is also present in the subcritical regime of doubly diffusive convection driven by horizontal gradients. In systems that are unbounded in one spatial direction homoclinic snaking continues indefinitely as the localized structure grows to resemble a spatially periodic state of infinite extent. In finite domains or in periodic domains with finite spatial period the process must terminate. In this paper we show that the snaking branches in general turn over once the length of the localized state becomes comparable to the domain, and examine the factors that determine the location of the termination point or points, and their relation to the Eckhaus instability of the spatially periodic state.

The rectified oscillatory motion of the “bistable” fronts (BFs) joining two states of the different stability in a spatially extended system with two stable equilibria is studied by use of the macroscopic kinetic equation of the reaction-diffusion type. The adiabatic approximation is used: We assume that the period of the ac force acting on the front in the system significantly exceeds the characteristic relaxation time of the system. By using the arguments based on the symmetry properties of the rate function in the governing equation of the ac driven front, we show that a close corelation (one-to-one correspondence) between the rate functions of the different symmetry, the symmetrical and asymmetrical ones, and the response functions performing the “input-output” conversion between the oscillatory forcing (input) function and the speed (output) function, which describes the temporal oscillations of the moment velocity of the ac driven BF, exists. Making use of the symmetry analysis we are able to show that the average characteristics of the ratchetlike transport of the ac driven BFs derivable by the symmetrical and asymmetrical rate functions radically differ. In particular, we find that depending on the symmetry of the rate function used, either symmetrical or asymmetrical one, the complete ensemble of the forward and backward running fronts propagating at the different initial velocities in the ac driven system remains either permanently at rest on average or it travels at some fixed nonzero velocity. We confirm our predictions being derived with the rate function of the general form by the direct calculations carried out by use of the cubic polynomial rate function and its piecewise linear emulations satisfying the different symmetry properties.

The regularized 13 moment (R13) equations and their boundary conditions are considered for plane channel flows. Chapman-Enskog scaling based on the Knudsen number is used to reduce the equations. The reduced equations yield second-order slip conditions, and allow us to describe the characteristic dip in the temperature profile observed in force driven flow. Due to the scaling, the R13 equations’ ability to describe Knudsen layers is lost. Solutions with Knudsen layers are discussed as well, and it is shown that these give a better match to direct solutions of the Boltzmann equations than the reduced equations without Knudsen layers. For a radiatively heated gas the R13 equations predict a dependence of the average gas temperature on the Knudsen number with a distinct minimum around $\mathrm{Kn}=0.2$, similar to the well-known Knudsen minimum for Poiseuille flow.

Relativistic energy loss and photon emission in the interaction of ideal and nonideal metamaterial cloaks with an external electron beam are studied based on the classical electrodynamics. The effects of various imperfect parameters on the efficiency of the cloak are emphasized. The energy-loss spectra and the photon emission for such structures with the different combinations of electron velocity and impact parameter are calculated. It is shown that the efficiency of nonideal electromagnetic cloaks and the effect of various nonideal parameters on the cloak invisibility can be exhibited in the electron energy loss spectroscopy. This means that the properties of cloak can be explored by scanning transmission electron microscopy.

We study a simple reaction-diffusion population model [proposed by A. Windus and H. J. Jensen, J. Phys. A: Math. Theor. 40, 2287 (2007)] on scale-free networks. In the case of fully random diffusion, the network topology cannot affect the critical death rate, whereas the heterogeneous connectivity can cause smaller steady population density and critical population density. In the case of modified diffusion, we obtain a larger critical death rate and steady population density, at the meanwhile, lower critical population density, which is good for the survival of species. The results were obtained using a mean-field-like framework and were confirmed by computer simulations.

In this paper, we report experimental evidence of wave chaos using the double slit water surface wave experiment. We demonstrate that classical dynamics of a domain manifests itself in the interference patterns after the diffraction behind the double slit. For a domain whose classical dynamics is integrable clear interference fringes can be observed behind the double slits; for a domain whose classical dynamics is chaotic, however, interference fringes can totally disappear. Our experimental results clearly demonstrate that the centuries-old double slit experiment can render an excellent tool to observe the manifestations of wave chaos.

Self-consistent-field theory is used to reproduce the behavior of polymer surface tension with molecular-weight for both lower and higher molecular-weight polymers. The change in behavior of the surface tension between these two regimes is shown to be due to the almost total exclusion of polymer from the nonpolymer bulk phase. The predicted two regime surface tension behavior with molecular-weight and the exclusion explanation are shown to be valid for a range of different polymer compressibilities.