The multidimensional formulation of the quantum lattice Boltzmann (qLB) scheme is extended to the case of nonlinear quantum wave equations. More specifically, imaginary-time formulations of the qLB scheme are developed and applied to the numerical computation of the ground state of the Gross-Pitaevskii equation in one and two spatial dimensions. The calculation is validated through detailed comparison with other numerical methods, as well as with analytical results based on the Thomas-Fermi approximation. The linear scaling of the time-step size with the spatial mesh spacing, a distinctive feature of the present quantum kinetic approach, is also numerically demonstrated.

A lattice Boltzmann model is considered for immiscible binary fluids with species-dependent acoustic impedance. Acoustic waves and pulses are simulated within the model, and the reflection and transmission components at the fluid interface are found to compare well with theory. The model is then applied to simulate the acoustic field due to plane-wave propagation through a bubble.

The sol-gel transition of gelatin aqueous solutions has been investigated in terms of time-resolved dynamic light scattering (DLS) and rheological measurements during the cooling process. A drastic increase in the scattering intensity, ergodic-nonergodic transition, and a power-law behavior in the scattering intensity-time correlation function were observed at the gelation temperature $T_{\mathrm{gel}}$. Thus obtained “microscopic” $T_{\mathrm{gel}}$ was confirmed to be in good agreement with a “macroscopic” $T_{\mathrm{gel}}$ obtained by rheological measurements irrespective of gelatin concentration $C$. The fractal exponent $D_{\mathrm{p}}$ evaluated by DLS was found to be $q$ and $C$ independent and was also in good agreement with that obtained by rheology $\left(n\right)$, i.e., $D_{\mathrm{p}}\cong n\cong 0.73$, where $q$ is the magnitude of the scattering vector.

By using the transfer matrix approach, we investigate the asymptotic behavior of the entropy of flexible chains with $M$ monomers each placed on strips with periodic boundary conditions (cylinders). In the limit of high density of monomers, we study the behavior of the entropy as a function of the density of monomers and the width of the strip, inspired by recent analytical studies of this problem for the particular case of dimers $(M=2)$. We obtain the entropy in the asymptotic regime of high densities for chains with $M=2,\dots ,9$ monomers, as well as for the special case of polymers, where $M\to \infty$, and find that the results show a regular behavior similar to the one found analytically for dimers. We also verify that in the low-density limit the mean-field expression for the entropy is followed by the results from our transfer matrix calculations.

A relationship is established between the autocorrelation function of continuous Gaussian and non-Gaussian stochastic processes and the discrete process that describes their zero or level crossings. Random fractals occur when the distribution for the number of crossings is described by a class of Markov processes whose singlefold statistics are the discrete analog of the Lévy-stable continuous probability densities.

We investigate the dynamics of a one-dimensional asymmetric exclusion process with Langmuir kinetics and a fluctuating wall. At the left-hand boundary, particles are injected onto the lattice; from there, the particles hop to the right. Along the lattice, particles can adsorb or desorb, and the right-hand boundary is defined by a wall particle. The confining wall particle has intrinsic forward and backward hopping, a net leftward drift, and cannot desorb. Performing Monte Carlo simulations and using a moving-frame finite segment approach coupled to mean field theory, we find the parameter regimes in which the wall acquires a steady-state position. In other regimes, the wall will either drift to the left and fall off the lattice at the injection site, or drift indefinitely to the right. Our results are discussed in the context of nonequilibrium phases of the system, fluctuating boundary layers, and particle densities in the laboratory frame versus the frame of the fluctuating wall.

We test methods for measuring and characterizing rough profiles with emphasis on measurements of the self-affine roughness exponent, and describe a simple test to separate between roughness exponents originating from long range correlations in the signs of the profile, and roughness exponents originating from Lévy distributions of jumps. Based on tests on profiles with known roughness exponents we find that the power spectrum density analysis and the averaged wavelet coefficients method give the best estimates for roughness exponents in the range $0.1$–$0.9$. The error bars are found to be less than $0.03$ for profile lengths larger than $256$, and there is no systematic bias in the estimates. We present quantitative estimates of the error bars and the systematic error and their dependence on the value of the roughness exponent and the profile length. We also quantify how power-law noise can modify the measured roughness exponent for measurement methods different from the power spectrum density analysis and the second order correlation function method.

We study the continuous phase transition of the conserved lattice gas (CLG) model from an active phase into an absorbing phase on two fractal lattices, i.e., on a checkerboard fractal and on a Sierpinski gasket. In the CLG model, a particle is assumed to be active if any of the neighboring sites are occupied by a particle and inactive if all neighboring sites are empty. We estimate critical exponents $\theta$, $\beta$, ${\nu }_{\Vert }$, and ${\nu }_{\perp }$, characterizing, respectively, the density of active particles in time, the order parameter, the temporal and spatial correlation lengths near the critical point, and the results are confirmed by off-critical scaling and finite size scaling. The order parameter exponent $\beta$ on a checkerboard fractal appears to lie between the one-dimensional (1D) value and two-dimensional (2D) value of the CLG model, while that on a Sierpinski gasket lies between the 1D and 2D values of the conserved threshold transfer process. Such a difference is manifested based on the intrinsic properties of the underlying fractal lattices.

Recently it has been argued that the fluctuations of the order parameter of a system undergoing a second order transition, when considered as a time series, possess characteristic nonstochastic patterns at the critical point. These patterns can be described by a unimodal intermittent map (critical map) and are clearly distinguished from colored noise. In the present work we extend the method introduced in [Y. F. Contoyiannis, F. K. Diakonos, and A. Malakis, Phys. Rev. Lett. 89, 035701 (2002)], in order to reveal universal properties in the deformation of the dynamics of the order parameter fluctuations when departing from the critical point. We show that the obtained systematic change in the order parameter fluctuation pattern can be observed in the critical region of thermal critical systems such as the mean field and the 3D Ising model. In addition, we consider the case of order parameter fluctuations near a tricritical point and we derive an associated characteristic deterministic behavior. A corresponding analysis in the $Z\left(3\right)$ model confirms our results. Thus, the method of critical fluctuations introduced previously and generalized here, provides us with a classification scheme allowing for the characterization of temporal fluctuations in an observed time series in terms of critical phenomena.

A colloidal system of spheres interacting with both a deep and narrow attractive potential and a shallow long-ranged barrier exhibits a prepeak in the static structure factor. This peak can be related to an additional mesoscopic length scale of clusters and/or voids in the system. Simulation studies of this system have revealed that it vitrifies upon increasing the attraction into a gel-like solid at intermediate densities. The dynamics at the mesoscopic length scale corresponding to the prepeak represents the slowest mode in the system. Using mode coupling theory with all input directly taken from simulations, we reveal the mechanism for glassy arrest in the system at 40% packing fraction. The effects of the low-$q$ peak and of polydispersity are considered in detail. We demonstrate that the local formation of physical bonds is the process whose slowing down causes arrest. It remains largely unaffected by the large-scale heterogeneities, and sets the clock for the slow cluster mode. Results from mode-coupling theory without adjustable parameters agree semiquantitatively with the local density correlators but overestimate the lifetime of the mesoscopic structure (voids).

Ferromagnetic nanowires were employed to investigate the microrheology of wormlike micelle solutions composed of equimolar cetylpyridinium chloride–sodium salicylate. For a wire rotated about a short axis, the drag at low rotation rate ${\omega }_R$ is independent of ${\omega }_R$ and strongly temperature dependent, consistent with the macroscopic shear viscosity. Above a critical rotation rate ${\omega }_c$, the drag is independent of temperature and decreases as a power law with increasing rate. The onset of nonlinear drag is characterized by a peak associated with contributions from extensional flow. Above ${\omega }_c$, the fluid generates an additional torque that tilts the wire out of regions of high shear flow and that is interpreted as a consequence of a shear-induced transition to nematic order among the micelles. Rotation of the wire in response to this torque reveals directly the anisotropy of the drag in the nonlinear state.

Numerous experimental data on the rapid solidification of binary systems exhibit the formation of metastable solid phases with initial (nominal) chemical composition. This fact is explained by complete solute trapping leading to diffusionless (chemically partitionless) solidification at a finite growth velocity of crystals. Special attention is paid to developing a model of rapid solidification which describes a transition from chemically partitioned to diffusionless growth of crystals. Analytical treatments lead to the condition for complete solute trapping which directly follows from the analysis of the solute diffusion around the solid-liquid interface and atomic attachment and detachment at the interface. The resulting equations for the flux balance at the interface take into account two kinetic parameters: diffusion speed $V_{DI}$ on the interface and diffusion speed $V_D$ in bulk phases. The model describes experimental data on nonequilibrium solute partitioning in solidification of Si-As alloys for the whole range of solidification velocity investigated.

Our aim is to show the possibility of a “vibrational Fréedericksz’s transition” in nematic liquid crystals (LCs) consisting of asymmetric molecules (in the absence of the reflectional symmetry for the director field). For this purpose we study the effects of the external high-frequency vibrations imposed on LCs by employing the rigorous two-timing asymptotic averaging method to the governing LC equations in their most general form. We restrict our attention only to translational mechanical vibrations of an incompressible LC medium as a whole, so our vibrations are not related to acoustical waves. We show that the averaged “vibrogenic” torque acted on the director field is mathematically equivalent to the torque caused by an external magnetic field. This equivalence leads us to the key conclusion that the high-frequency mechanical vibrations can cause the vibrational Fréedericksz’s transition. Our evaluation of the relevant physical parameters shows that this phenomenon can be observed in laboratory experiments.

The Fisher equation is commonly used to model population dynamics. This equation allows describing reaction-diffusion processes, considering both population growth and diffusion mechanism. Some results have been reported about modeling human dispersion, always assuming isotropic diffusion. Nevertheless, it is well-known that dispersion depends not only on the characteristics of the habitats where individuals are but also on the properties of the places where they intend to move, then isotropic approaches cannot adequately reproduce the evolution of the wave of advance of populations. Solutions to a Fisher equation are difficult to obtain for complex geometries, moreover, when anisotropy has to be considered and so few studies have been conducted in this direction. With this scope in mind, we present in this paper a solution for a Fisher equation, introducing anisotropy. We apply a finite difference method using the Crank-Nicholson approximation and analyze the results as a function of the characteristic parameters. Finally, this methodology is applied to model South American human dispersal.

Interlinked positive feedback loops are frequently found in biological signaling pathways. It is intriguing to study the dynamics, functions, and robustness of these motifs. Using numerical simulations and theoretical analysis, here we explore the sensitiveness and robustness of positive feedback loops with various time scales. Both single and dual loops can behave as a bistable switch. We study the responses of five types of bistable switches to noisy stimuli. The noise-induced transitions between two states are discussed in detail by using energy landscape. The dual-time switch, consisting of interconnected fast and slow loops, is both sensitive to stimuli and resistant to fluctuations in stimulus. This provides a novel mechanism for creating optimal bistable switches and memory modules. Our results also suggest that the dual-time switch can act as a ubiquitous motif with sensitive robustness in biological systems.

Boolean network models of strongly connected modules are capable of capturing the high regulatory complexity of many biological gene regulatory circuits. We study numerically the previously introduced basin entropy, a parameter for the dynamical uncertainty or information storage capacity of a network as well as the average transient time in random relevant components as a function of their connectivity. We also demonstrate that basin entropy can be estimated from time-series data and is therefore also applicable to nondeterministic networks models.

We study a multilane totally asymmetric simple exclusion process (TASEP) with narrow entrances under parallel update. The narrow entrances are modeled in this way: the entry of a particle is not allowed if the exit site of the previous lane is occupied. It is shown the results depend on the number of lanes, $n$. If $n$ is an even number, the results are essentially the same as $n=2$: two symmetry-breaking phases—i.e., a high-density-low-density (HD-LD) phase and an asymmetric low-density-low-density phase—are identified. In contrast, if $n$ is an odd number, a periodic structure is observed and the period is found to be proportional to the lane number $n$ and system size $L$. It is also found when the injection rate $\alpha =1$ that the seesaw phase observed in the case of $n=2$ disappears and the HD-LD phase or symmetric LD phase appears. Some mean-field calculations are also presented. We show that it is not possible to have high densities in two successive lanes and also not possible to have high density in one lane and low densities in all other lanes. For odd $n$, we have obtained the period $T$ and it is in good agreement with simulations for a small removal rate $\beta$, but deviates from simulation results for large $\beta$ because correlation is neglected in the mean-field approximation.

We study a simple model of information propagation in social networks, where two quantities are introduced: the spread factor, which measures the average maximal reachability of the neighbors of a given node that interchange information among each other, and the spreading time needed for the information to reach such a fraction of nodes. When the information refers to a particular node at which both quantities are measured, the model can be taken as a model for gossip propagation. In this context, we apply the model to real empirical networks of social acquaintances and compare the underlying spreading dynamics with different types of scale-free and small-world networks. We find that the number of friendship connections strongly influences the probability of being gossiped. Finally, we discuss how the spread factor is able to be applied to other situations.

In this paper, we reinvestigate the period doubling of kink-antikink patterns in coupled periodic logistic map lattices. In contrast to earlier observations, we find an additional mode structure, a pulse. An unusual brushlike bifurcation diagram and an oscillation of the largest Lyapunov exponent versus the coupling are observed. We propose a mode analysis method to analyze the cases of different mode numbers for these two basic modes (kink and pulse). We believe that our investigations can shed improved light on the dynamics of coupled periodic map lattices.