We study the origin of attracting phenomena in the ray dynamics of coupled optical microcavities. To this end we investigate a combined map that is composed of standard and linear map, and a selection rule that defines when which map has to be used. We find that this system shows attracting dynamics, leading exactly to a quasiattractor, due to collapse of phase space. For coupled dielectric disks, we derive the corresponding mapping based on a ray model with deterministic selection rule and study the quasiattractor obtained from it. We also discuss a generalized Poincaré surface of section at dielectric interfaces.

Regimes of chemical reaction wave propagation initiated by initial temperature nonuniformity in gaseous mixtures, whose chemistry is governed by chain-branching kinetics, are studied using a multispecies transport model and a detailed chemical model. Possible regimes of reaction wave propagation are identified for stoichiometric hydrogen-oxygen and hydrogen-air mixtures in a wide range of initial pressures and temperature levels, depending on the initial non-uniformity steepness. The limits of the regimes of reaction wave propagation depend upon the values of the spontaneous wave speed and the characteristic velocities of the problem. It is shown that one-step kinetics cannot reproduce either quantitative neither qualitative features of the ignition process in real gaseous mixtures because the difference between the induction time and the time when the exothermic reaction begins significantly affects the ignition, evolution, and coupling of the spontaneous reaction wave and the pressure wave, especially at lower temperatures. We show that all the regimes initiated by the temperature gradient occur for much shallower temperature gradients than predicted by a one-step model. The difference is very large for lower initial pressures and for slowly reacting mixtures. In this way the paper provides an answer to questions, important in practice, about the ignition energy, its distribution, and the scale of the initial nonuniformity required for ignition in one or another regime of combustion wave propagation.

The dust-modified ion-acoustic waves of Shukla and Silin are revisited within the theoretical framework of the Tsallis statistical mechanics. Nonextensivity may originate from correlation or long-range plasma interactions. Interestingly, we find that owing to electron nonextensivity, dust ion-acoustic (DIA) solitary waves may exhibit either compression or rarefaction. Our analysis is then extended to include self-consistent dust charge fluctuation. In this connection, the correct nonextensive electron charging current is rederived. The Korteweg–de Vries equation, as well as the Korteweg–de Vries–Burgers equation, is obtained, making use of the reductive perturbation method. The DIA waves are then analyzed for parameters corresponding to space dusty plasma situations.

We study exact matter-wave solutions of the quasi-one-dimensional Gross-Pitaevskii (GP) equation with the space- and/or time-modulated potential and nonlinearity and the time-dependent gain or loss term in Bose-Einstein condensates. In particular, based on the similarity transformation and symbolic analysis, we report several families of exact solutions of the quasi-one-dimensional GP equation in the combination of the harmonic and Gaussian potentials, in which some physically relevant solutions are described. The stability of the obtained matter-wave solutions is addressed numerically such that some stable solutions are found. Moreover, we also analyze the parameter regimes for the stable solutions. These results may raise the possibility of relative experiments and potential applications.

We propose a method for efficient simulations in extended ensembles, useful, e.g., for the study of problems with complex energy landscapes and for free energy calculations. The main difficulty in such simulations is the estimation of the a priori unknown weight parameters needed to produce flat histograms. The method combines several complementary techniques, namely, a Gibbs sampler for the parameter moves, a reweighting procedure to optimize data use, and a Bayesian update allowing for systematic refinement of the free energy estimate. In a certain limit the scheme reduces to the $1/t$ algorithm of B. E. Belardinelli and V. D. Pereyra [Phys. Rev. E 75, 046701 (2007)]. The performance of the method is studied on the two-dimensional Ising model, where comparison with the exact free energy is possible, and on an Ising spin glass.

The melting of an assembly of ice blocks contained in a vertical cylinder and under an unidirectional load was investigated. The total volume occupied by the ice blocks and the volume of ice were simultaneously measured which allowed one to determine the volume fraction of the ice in the cylinder. While the ice volume continuously decreases, sudden breakdowns of the total volume were observed. Large reorganizations of the whole assembly occur. However, the maximal volume fraction found just after a large reorganization decreased with time. In addition, the modifications of the pile structure were investigated using an x-ray tomography imaging before and after one collapse. As the packing is better ordered along the walls, we suggest that the motion of the piston is governed by the layer of ice blocks located along the container wall. This layer was modeled by a two-dimensional assembly of disks. The model supports the idea that the geometrical frustrations explain the dynamics of the successive reorganization due to the shrinkage of the grains. Finally, numerical simulations allow one to conclude that the dynamics of the melting of the ice blocks is governed (i) by the confinement effect which induces defects in the packing and (ii) by the low friction between the ice blocks.

We study the structure and phonon spectrum of a two-dimensional bilayer system of classical charged dipoles oriented perpendicular to the plane of the layers for equal density in each layer. This system can be tuned through six different crystalline phases by changing the interlayer separation or the charge and/or dipole moment of the particle. The presence of the charge on the dipole particles is responsible for the nucleation of five staggered phases and a disordered phase which are not found in the magnetic dipole bilayer system. These extra phases are a consequence of the competition between the repulsive Coulomb and the attractive dipole interlayer interaction. We present the phase diagram and determine the order of the phase transitions. The phonon spectrum of the system was calculated within the harmonic approximation, and a nonmonotonic behavior of the phonon spectrum is found as a function of the effective strength of the interparticle interaction. The stability of the different phases is determined.

The shear-transformation-zone (STZ) theory has been remarkably successful in accounting for broadly peaked, frequency-dependent, viscoelastic responses of amorphous systems near their glass temperatures $T_g$. This success is based on the theory's first-principles prediction of a wide range of internal STZ transition rates. Here, I show that the STZ rate distribution causes the Newtonian viscosity to be strongly temperature dependent; and I propose that it is this temperature dependence, rather than any heterogeneity-induced enhancement of diffusion, that is at least in part responsible for Stokes-Einstein violations near $T_g$. I also show that stretched-exponential relaxation of density fluctuations emerges naturally from the same distribution of STZ transition rates that predicts the viscoelastic behavior. To be consistent with observations of Fickian diffusion near $T_g$, however, an STZ-based diffusion theory somehow must include the cascades of correlated displacement events that are seen in low-temperature numerical simulations.

Phase singularity analysis provides a quantitative description of spiral wave patterns observed in chemical or biological excitable media. The configuration of phase singularities (locations and directions of rotation) is easily derived from phase maps in two-dimensional manifolds. The question arises whether one can construct a phase map with a given configuration of phase singularities. The existence of such a phase map is guaranteed provided that the phase singularity configuration satisfies a certain constraint associated with the topology of the supporting medium. This paper presents a constructive mathematical approach to numerically solve this problem in the plane and on the sphere as well as in more general geometries relevant to atrial anatomy including holes and a septal wall. This tool can notably be used to create initial conditions with a controllable spiral wave configuration for cardiac propagation models and thus help in the design of computer experiments in atrial electrophysiology.

A fluctuating nonideal fluid at its critical point is simulated with the lattice Boltzmann method. It is demonstrated that the method, employing a Ginzburg-Landau free energy functional, correctly reproduces the static critical behavior associated with the Ising universality class. A finite-size scaling analysis is applied to determine the critical exponents related to the order parameter, compressibility and specific heat. A particular focus is put on finite-size effects and issues related to the global conservation of the order parameter.

We study the dynamics of nonlinear oscillators under mean-field diffusive coupling. We observe that this form of coupling leads to amplitude death via a synchronization transition in the parameter space of the coupling strength and mean-field control parameter. A general criterion for amplitude death for any given dynamical system with mean-field diffusion is obtained, and these dynamical transitions are characterized using various indices such as average phase difference, Lyapunov exponents, and average amplitude. This behavior is analyzed in the parameter plane by numerical studies of specific cases of the Landau-Stuart limit-cycle oscillator, and Rössler, Lorenz, FitzHugh-Nagumo excitable, and Chua systems.

The effects of water confined in regions between self-assembling entities is relevant to numerous contexts such as macromolecular association, protein folding, protein-ligand association, and nanomaterials self-assembly. Thus assessing the impact of confined water, and the ability of current modeling techniques to capture the salient features of confined water is important and timely. We present molecular dynamics simulation results investigating the effect of confined water on qualitative features of potentials of mean force describing the free energetics of self-assembly of large planar hydrophobic plates. We consider several common explicit water models including the TIP3P, TIP4P, SPC/E, TIP4P-FQ, and SWM4-NDP, the latter two being polarizable models. Examination of the free energies for filling and unfilling the volume confined between the two plates (both in the context of average number of confined water molecules and “depth” of occupancy) suggests TIP4P-FQ water molecules generally occupy the confined volume at separation distances larger than observed for other models under the same conditions. The connection between this tendency of TIP4P-FQ water and the lack of a pronounced barrier in the potential of mean force for plate-plate association in TIP4P-FQ water is explored by artificially, but systematically, populating the confined volume with TIP4P-FQ water at low plate-plate separation distances. When the critical separation distance [denoting the crossover from an unoccupied (dry) confined interior to a filled (wet) interior] for TIP4P-FQ is reduced by 0.5 Å using this approach, a barrier is observed; we rationalize this effect based on increased resistant forces introduced by confined water molecules at these low separations. We also consider the dynamics of water molecules in the confined region between the hydrophobes. We find that the TIP4P-FQ water model exhibits nonbulklike dynamics, with enhanced lateral diffusion relative to bulk. This is consistent with the reduced intermolecular water-water interaction indicated by a decreased molecular dipole moment in the interplate region. Analysis of velocity autocorrelation functions and associated power spectra indicate that the interplate region for TIP4P-FQ at a plate separation of 14.4 Å approaches characteristics of the pure water liquid-vapor interface. This is in stark contrast to the other water models (including the polarizable SWM4-NDP model).

We analyze theoretically complete wetting of a substrate supporting an array of parallel, vertical plates which can tilt elastically. The adsorbed liquid tilts the plates, inducing clustering, and thus modifies the substrate geometry. In turn, this change in geometry alters the wetting properties of the substrate and, consequently, the adsorption of liquid. This geometry-wetting feedback loop leads to stepped adsorption isotherms with each step corresponding to an abrupt change in the substrate geometry. We discuss how this can be used for constructing substrates with tunable wetting and adsorption properties.

We consider a variant of the Kuramoto model of coupled oscillators in which both attractive and repulsive pairwise interactions are allowed. The sign of the coupling is assumed to be a characteristic of a given oscillator. Specifically, some oscillators repel all the others, thus favoring an antiphase relationship with them. Other oscillators attract all the others, thus favoring an in-phase relationship. The Ott-Antonsen ansatz is used to derive the exact low-dimensional dynamics governing the system's long-term macroscopic behavior. The resulting analytical predictions agree with simulations of the full system. We explore the effects of changing various parameters, such as the width of the distribution of natural frequencies and the relative strengths and proportions of the positive and negative interactions. For the particular model studied here we find, unexpectedly, that the mixed interactions produce no new effects. The system exhibits conventional mean-field behavior and displays a second-order phase transition like that found in the original Kuramoto model. In contrast to our recent study of a different model with mixed interactions [Phys. Rev. Lett. 106, 054102 (2011)], the $\pi$ state and traveling-wave state do not appear for the coupling type considered here.

The influences of spatial frequency distributions on complete amplitude death are explored by studying an array of diffusively coupled oscillators. We found that with all possible sets of spatial frequency distributions, the two critical coupling strengths ${\epsilon }_{c1}$ (lower-bounded value) and ${\epsilon }_{c2}$ (upper-bounded value) needed to get complete amplitude death exhibit a universal power law and a log-normal distribution respectively, which has long tails in both cases. This is significant for dynamics control, since large variations of ${\epsilon }_{c1}$ and ${\epsilon }_{c2}$ are possible for some spatial arrangements. Moreover, we explore optimal spatial distributions with the smallest (largest) ${\epsilon }_{c1}$ or ${\epsilon }_{c2}$.

In this study the direct-simulation Monte Carlo (DSMC) method is utilized to investigate thermal characteristics of micro- or nanocavity flow. The rarefied cavity flow shows unconventional behaviors which cannot be predicted by the Fourier law, the constitutive relation for the continuum heat transfer. Our analysis in this study confirms some recent observations and shows that the gaseous flow near the top-left corner of the cavity is in a strong nonequilibrium state even within the early slip regime, $\mathrm{Kn}=0.005$. As we obtained slip velocity and temperature jump on the driven lid of the cavity, we reported meaningful discrepancies between the direct and macroscopic sampling of rarefied flow properties in the DSMC method due to existence of nonequilibrium effects in the corners of cavity. The existence of unconventional nonequilibrium heat transfer mechanisms in the middle of slip regime, $\mathrm{Kn}=0.05$, results in the appearance of cold-to-hot heat transfer in the microcavity. In the current study we demonstrate that existence of such unconventional heat transfer is strongly dependent on the Reynolds number and it vanishes in the large values of the lid velocity. As we compared DSMC solution with the results of regularized 13 moments (R13) equations, we showed that the thermal characteristic of the microcavity obtained by the R13 method coincides with the DSMC prediction. Our investigation also includes the analysis of molecular entropy in the microcavity to explain the heat transfer mechanism with the aid of the second law of thermodynamics. To this aim, we obtained the two-dimensional velocity distribution functions to report the molecular-based entropy distribution, and show that the cold-to-hot heat transfer in the cavity is well in accordance with the second law of thermodynamics and takes place in the direction of increasing entropy. At the end we introduce the entropy density for the rarefied flow and show that it can accurately illustrate departure from the equilibrium state.

We show how a magnetic field can influence the motion of a paramagnetic drop made of liquid oxygen in a Leidenfrost state on solids at room temperature. It is demonstrated that the trajectory can be modified in both direction and velocity and that the results can be interpreted in terms of classical mechanics as long as the drop does not get too close to the magnet. We study the deviation and report that it can easily overcome ${180}^{\circ }$ and even diverge under certain conditions, leading to situations where a drop gets captured. In the vicinity of the magnet, another type of trapping is observed, due to the deformation of the drop in this region, which leads to a strong energy dissipation. Conversely, drops can be accelerated by moving magnets (slingshot effect).

We use an elastic model to explore faceting of solid-wall vesicles with elastic heterogeneities. We show that faceting occurs in regions where the vesicle wall is softer, such as areas of reduced wall thicknesses or concentrated in crystalline defects. The elastic heterogeneities are modeled as a second component with reduced elastic parameters. Using simulated annealing Monte Carlo simulations we obtain the vesicle shape by optimizing the distributions of facets and boundaries. Our model allows us to reduce the effects of the residual stress generated by crystalline defects, and reveals a robust faceting mechanism into polyhedra other than the icosahedron.

The time-dependent probability density function of the order parameter of a system evolving toward a stationary state exhibits an oscillatory behavior if the eigenvalues of the corresponding evolution operator are complex. The frequencies ${\omega }_n$, with which the system reaches its stationary state, correspond to the imaginary part of such eigenvalues. If the system (at the stationary state) is further driven by a small and oscillating perturbation with a given frequency $\omega$, we formally prove that the linear response to the probability density function is enhanced when $\omega ={\omega }_n$ for $n\in \mathbb{N}$. We prove that the occurrence of this phenomenon is characteristic of systems that are in a nonequilibrium stationary state. In particular, we obtain an explicit formula for the frequency-dependent mobility in terms of the relaxation to the stationary state of the (unperturbed) probability current. We test all these predictions by means of numerical simulations considering an ensemble of noninteracting overdamped particles on a tilted periodic potential.

We study fluctuating tilt Brownian ratchets based on fractional subdiffusion in sticky viscoelastic media characterized by a power law memory kernel. Unlike the normal diffusion case, the rectification effect vanishes in the adiabatically slow modulation limit and optimizes in a driving frequency range. It is shown also that the anomalous rectification effect is maximal (stochastic resonance effect) at optimal temperature and can be of surprisingly good quality. Moreover, subdiffusive current can flow in the counterintuitive direction upon a change of temperature or driving frequency. The dependence of anomalous transport on load exhibits a remarkably simple universality.