We describe numerical solutions of two nonpotential models of pattern formation in nonequilibrium systems to address the motion and decay of grain boundaries separating domains of stripe configurations of different orientations. We first address wave-number selection because of the boundary, and possible decay modes when the periodicity of the stripe phases is different from the selected wave number for a stationary boundary. We discuss several decay modes including long wavelength undulations of the moving boundary, as well as the formation of localized defects and their subsequent motion. We find three different regimes as a function of the distance to the stripe phase threshold and initial wave number, and then correlate these findings with domain morphology during domain coarsening in a large aspect ratio configuration.

We study the space-time evolution of electromagnetic wave packets through optical superlattices. We present rigorous analytical solutions describing the multiple-scattering processes of Gaussian wave packets defined in the band gap and in the resonant energy regions. Following their space-time evolution, we obtain the Maxwell equations prediction for the time spent inside the superlattice. From a close and careful observation of the reflected and transmitted parts of Gaussian packets in a photonic band gap, we conclude unambiguously that the superluminal transmission and the Hartman effect are inherent properties of the electromagnetic theory. It is also shown that the theoretical predictions for the time spent inside an optical superlattice are in good agreement with the experimental results and the phase time predictions.

In this paper we answer positively a question raised by Metzler and Klafter [Phys. Rep. 339, 1 (2000)]: can one see a competition between subdiffusion and Lévy flights in the framework of the fractional Fokker-Planck dynamics? Our method of Monte Carlo simulations demonstrates the competition on the level of realizations as well as on the level of probability density functions of the anomalous diffusion process. The simulation algorithm is based on a stochastic representation of the above dynamics.

We study the diffusion equation with a position-dependent, power-law diffusion coefficient. The equation possesses the Riesz-Weyl fractional operator and includes a memory kernel. It is solved in the diffusion limit of small wave numbers. Two kernels are considered in detail: the exponential kernel, for which the problem resolves itself to the telegrapher’s equation, and the power-law one. The resulting distributions have the form of the Lévy process for any kernel. The renormalized fractional moment is introduced to compare different cases with respect to the diffusion properties of the system.

We present results of computer simulations for neutrally buoyant intruders in a vertically vibrated three-dimensional granular bed of smaller host particles. Under sinusoidal excitation, pairs of intruders interact over a distance of several intruder diameters; a group of intruders forms a cluster. The strength of the interaction grows as the number of intruders is increased. We show that the tendency to cluster may be manipulated through the use of nonsinusoidal excitation, which allows partial mixing. Finally, we investigate the effects of walls on the clustering of intruders.

A binary mixture of oppositely charged colloids which is driven by an external electric field is studied by extensive Brownian dynamics computer simulations, ignoring hydrodynamic interactions. The particle interaction is modeled via a screened Coulomb potential together with a steric repulsion. A strong electric field leads to lane formation of oppositely driven lanes. Each lane comprises particles of the same charge. A nonequilibrium “phase diagram” classifying different steady states is obtained as a function of the colloidal volume fraction and the Coulomb coupling. Different steady states are characterized by structural correlations perpendicular and parallel to the applied field. We find a variety of different phases involving lane chains at small volume fraction and low screening, and lanes with two-dimensional crystalline order perpendicular to the field at high volume fraction. The lateral crystalline order can be a square, triangular, or rhombic lattice. In between there is a lateral network structure. These predictions can be verified in real-space experiments on oppositely charged colloids.

We investigate by molecular dynamics simulations the validity of the frequency-dependent Stokes-Einstein (SE) relation in supercooled liquids at different temperatures. The results indicate that the SE relation holds at intermediate frequencies that correspond to the $\beta$-relaxation and the onset of the $\alpha$-relaxation regimes. Large deviations, which increase as the temperature decreases, are observed at frequencies well below the frequency at which the non-Gaussian parameter ${\alpha }_2$ is maximum. We argue that the breakdown of the SE relation in supercooled liquids arises from underestimation of the diffusion coefficient due to neglect of correlated motions.

We have investigated the dynamics of phenylene rings in the engineering thermoplastic bisphenol-A poly(hydroxyether)—phenoxy—below its glass transition temperature by means of neutron scattering techniques. A relatively wide dynamic range has been covered thanks to the combination of two different types of neutron spectrometers, time of flight and backscattering. Partially deuterated samples have been used in order to isolate the phenylene ring dynamics. The resulting neutron scattering signal of phenoxy has been described by a model that considers $\pi$ flips and oscillation motions for phenylene rings. The associated time scales are broadly distributed with mean activation energies equal to 0.41 and $0.21\mathrm{eV}$, respectively. Finally, a comparative study with the literature shows that the dielectric and mechanical $\gamma$ relaxation in phenoxy exhibit good correlation with the characteristic times of the aliphatic chain published elsewhere and with the characteristic times observed for the motion of phenylene rings by neutron scattering. These findings are discussed in a more general framework that considers, in addition, previous results on other polymers, which also contain the bisphenol-A unit.

Neuronal activities have recently been reported to exhibit power-law scaling behavior. However, it has not been demonstrated that the power-law component can play an important role in human perceptual functions. Here, we demonstrate that the power spectrum of magnetoencephalograph recordings of brain activity varies in coordination with perception of subthreshold visual stimuli. We observed that perceptual performance could be better explained by modulation of the power-law component than by modulation of the peak power in particular narrow frequency ranges. The results suggest that the brain operates in a state of self-organized criticality, modulating the power spectral exponent of its activity to optimize its internal state for response to external stimuli.

A method is proposed to construct the weighted amino acid network. The weight of the link is based on the contact energy between residues. For the 197 proteins with low homology, the “small-world” property was studied based on this method. Additionally, analyses were carried out for the statistic characteristics of the network parameters, the influence of the weight on the network parameters, the network parameter difference of amino acids, and the links between the hydrophobic and hydrophilic residues. Using this method, we studied the network parameter change for the protein chymotrypsin inhibitor 2 (CI2) on its high-temperature unfolding pathway. It is found that the unfolding of the protein is mainly exhibited as the derogation of the hydrophobic core and the shortest path length rise in the unfolding process. This work is helpful for studies of protein folding and the relationship between structure and function using complex network theory.

We examine two mechanisms that have been put forward to explain the selection of quasipatterns in single- and multifrequency forced Faraday wave experiments. Both mechanisms can be used to generate stable quasipatterns in a parametrically forced partial differential equation that shares some characteristics of the Faraday wave experiment. One mechanism, which is robust and works with single-frequency forcing, does not select a specific quasipattern: we find, for two different forcing strengths, 12-fold and 14-fold quasipatterns. The second mechanism, which requires more delicate tuning, can be used to select particular angles between wavevectors in the quasipattern.

We introduce a model including two linearly coupled Bragg gratings, with a mismatch (phase shift $\theta$) between them. The model may be realized as parallel-coupled fiber Bragg gratings (FBGs), or, in the spatial domain, as two parallel planar waveguides carrying diffraction gratings. The phase shift induced by a shear stress may be used to design a different type of FBG sensor. In the absence of the mismatch, the symmetry-breaking bifurcation of gap solitons (GSs) in this model was investigated before. Our objective is to study how mismatch $\theta$ affects families of symmetric and asymmetric GSs, and the bifurcation between them. We find that the system’s band gap is always filled with solitons (for $\theta \ne 0$, the gap’s width does not depend on coupling constant $\lambda$ if it exceeds some minimum value). The largest velocity of the moving soliton, $c_{\max }$, is found as a function of $\theta$ and $\lambda$ ($c_{\max }$ grows with $\theta$). The mismatch transforms symmetric GSs into quasisymmetric (QS) ones, in which the two components are not identical, but their peak powers and energies are equal. The mismatch also breaks the spatial symmetry of the GSs. The QS solitons are stable against symmetry-breaking perturbations as long as asymmetric (AS) solutions do not exist. If $\theta$ is small, AS solitons emerge from their QS counterparts through a supercritical bifurcation. However, the bifurcation may become subcritical at larger $\theta$. The condition for the stability against oscillatory perturbations (unrelated to the symmetry breaking) is essentially the same as in the ordinary FBG model: both QS and AS solitons are stable if their intrinsic frequency is positive (i.e., in a half of the band gap).

We use hydrodynamics to investigate clustering in a gas of inelastically colliding spheres. The hydrodynamic equations exhibit a finite-time density blowup, where the gas pressure remains finite. The density blowup signals the formation of close-packed clusters. The blowup dynamics is universal and describable by exact analytic solutions continuable beyond the blowup time. These solutions show that dilute hydrodynamic equations yield a powerful effective description of a granular gas flow with close-packed clusters, described as finite-mass pointlike singularities of the density. This description is similar in spirit to the description of shocks in ordinary ideal gas dynamics.

In this Rapid Communication we demonstrate the applicability of an augmented Gibbs ensemble Monte Carlo approach for the phase behavior determination of model colloidal systems with short-ranged depletion attraction and long-ranged repulsion. This technique allows for a quantitative determination of the phase boundaries and ground states in such systems. We demonstrate that gelation may occur in systems of this type as the result of arrested microphase separation, even when the equilibrium state of the system is characterized by compact microphase structures.

We study the extremal dynamics emerging in an out-of-equilibrium one-dimensional Jepsen gas of $(N+1)$ hard-point particles. The particles undergo binary elastic collisions, but move ballistically in between collisions. The gas is initially uniformly distributed in a box $[-L,0]$ with the “leader” (or the rightmost particle) at $X=0$, and a random positive velocity, independently drawn from a distribution $\varphi \left(V\right)$, is assigned to each particle. The gas expands freely at subsequent times. We compute analytically the distribution of the leader’s velocity at time $t$, and also the mean and the variance of the number of collisions that are undergone by the leader up to time $t$. We show that in the thermodynamic limit and at fixed time $t⪢1$ (the so-called “growing regime”), when interactions are strongly manifest, the velocity distribution exhibits universal scaling behavior of only three possible varieties, depending on the tail of $\varphi \left(V\right)$. The associated scaling functions are entirely different from the usual extreme-value distributions of uncorrelated random variables. In this growing regime the mean and the variance of the number of collisions of the leader up to time $t$ increase logarithmically with $t$, with universal prefactors that are computed exactly. The implications of our results in the context of biological evolution modeling are pointed out.

We study the phase diagram of a generalized Winfree model. The modification is such that the coupling depends on the fraction of synchronized oscillators, a situation which has been noted in some experiments on coupled Josephson junctions and mechanical systems. We let the global coupling $k$ be a function of the Kuramoto order parameter $r$ through an exponent $z$ such that $z=1$ corresponds to the standard Winfree model, $z<1$ strengthens the coupling at low $r$ (low amount of synchronization), and at $z>1$, the coupling is weakened for low $r$. Using both analytical and numerical approaches, we find that $z$ controls the size of the incoherent phase region and that one may make the incoherent behavior less typical by choosing $z<1$. We also find that the original Winfree model is a rather special case; indeed, the partial locked behavior disappears for $z>1$. At fixed $k$ and varying $\gamma$, the stability boundary of the locked phase corresponds to a transition that is continuous for $z<1$ and first order for $z>1$. This change in the nature of the transition is in accordance with a previous study of a similarly modified Kuramoto model.

Monte Carlo simulations have been performed to study the interfacial properties of the liquid-vapor interface of alkanes. We highlight the chemical equilibrium of the liquid-vapor interface by calculating a local chemical potential including the appropriate long-range corrections profiles. We extend the “test-area” (TA) technique developed by Gloor et al. [J. Chem. Phys. 123, 134703 (2005)] on Lennard-Jones and square-well fluids to molecular systems. We establish both operational expressions of the TA approach for the calculation of the surface tension profile and the corresponding long-range corrections by underlining the approximations used. We compare the results between the different operational expressions of the surface tension and focus on the truncation procedures to explain the difference between the different techniques using either the potential or force equations. We make the results of surface tension identical between the different methods by using consistent potential and force equations. In the case of a relatively small cutoff, we propose to show that the Irving-Kirkwood definition and TA methods lead to the same value of the surface tension under condition that appropriate long-range corrections be included in the calculation. We end this paper by calculation of the entropy change profile and a comparison with experiments.

The size distributions of all known coding and noncoding DNA sequences are studied in all human chromosomes. In a unified approach, both introns and intergenic regions are treated as noncoding regions. The distributions of noncoding segments $P_{\mathit{nc}}\left(S\right)$ of size $S$ present long tails $P_{\mathit{nc}}\left(S\right)\sim S^{-1-{\mu }_{\mathit{nc}}}$, with exponents ${\mu }_{\mathit{nc}}$ ranging between 0.71 (for chromosome 13) and 1.2 (for chromosome 19). On the contrary, the exponential, short-range decay terms dominate in the distributions of coding (exon) segments $P_c\left(S\right)$ in all chromosomes. Aiming to address the emergence of these statistical features, minimal, stochastic, mean-field models are proposed, based on randomly aggregating DNA strings with duplication, influx and outflux of genomic segments. These minimal models produce both the short-range statistics in the coding and the observed power law and fractal statistics in the noncoding DNA. The minimal models also demonstrate that although the two systems (coding and noncoding) coexist, alternating on the same linear chain, they act independently: the coding as a closed, equilibrium system and the noncoding as an open, out-of-equilibrium one.