We propose a general model to study the interplay between spatial dispersal and environment spatiotemporal fluctuations in metapopulation dynamics. An ecological landscape of favorable patches is generated like a Lévy dust, which allows to build a range of patterns, from dispersed to clustered ones. Locally, the dynamics is driven by a canonical model for the time evolution of the population density, consisting of a logistic expression plus multiplicative noises. Spatial coupling is introduced by means of two spreading mechanisms: diffusion and selective dispersal driven by patch suitability. We focus on the long-time population size as a function of habitat configurations, environment fluctuations, and coupling schemes. We obtain the conditions, that the spatial distribution of favorable patches and the coupling mechanisms must fulfill, to grant population survival. The fundamental phenomenon that we observe is the positive feedback between environment fluctuations and spatial spread preventing extinction.

We present a theoretical study of nanorod translocation events through solid-state nanopores of different sizes which result in positive or negative ion conductance changes. Using theoretical models, we show that positive conductance changes or up events happen for nanopore diameters smaller than a transition diameter $d_t$, and negative conductance changes or down events occur for nanopore diameters larger than $d_t$. We investigate the underlying physics of such translocation phenomena and describe the significance of the electric double-layer effects for nanopores with small diameters. Furthermore, for nanopores with large diameters, it is shown that a geometric model, formulated based on the nanoparticle blockade inside the nanopore, provides a straightforward and reasonably accurate prediction of ion conductance change. Based on this concept, we also implement a method to distinguish and detect nanorods of different sizes by focusing solely on the sign and not the exact value of the conductance change.

We investigate the onset of broadband microwave chaos in the miniband semiconductor superlattice coupled to an external resonator. Our analysis shows that the transition to chaos, which is confirmed by calculation of Lyapunov exponents, is associated with the intermittency scenario. The evolution of the laminar phases and the corresponding Poincare maps with variation of a supercriticality parameter suggest that the observed dynamics can be classified as type I intermittency. We study the spatiotemporal patterns of the charge concentration and discuss how the frequency band of the chaotic current oscillations in semiconductor superlattice depends on the voltage applied.

We present an alternative methodology for the stabilization and control of infinite-dimensional dynamical systems exhibiting low-dimensional spatiotemporal chaos. We show that with an appropriate choice of time-dependent controls we are able to stabilize and/or control all stable or unstable solutions, including steady solutions, traveling waves (single and multipulse ones or bound states), and spatiotemporal chaos. We exemplify our methodology with the generalized Kuramoto-Sivashinsky equation, a paradigmatic model of spatiotemporal chaos, which is known to exhibit a rich spectrum of wave forms and wave transitions and a rich variety of spatiotemporal structures.

We present a unified theoretical study of the bright solitons governed by self-focusing and defocusing nonlinear Schrödinger (NLS) equations with generalized parity-time- ($\mathcal{PT}$) symmetric Scarff-II potentials. Particularly, a $\mathcal{PT}$-symmetric $k$-wave-number Scarff-II potential and a multiwell Scarff-II potential are considered, respectively. For the $k$-wave-number Scarff-II potential, the parameter space can be divided into different regions, corresponding to unbroken and broken $\mathcal{PT}$ symmetry and the bright solitons for self-focusing and defocusing Kerr nonlinearities. For the multiwell Scarff-II potential the bright solitons can be obtained by using a periodically space-modulated Kerr nonlinearity. The linear stability of bright solitons with $\mathcal{PT}$-symmetric $k$-wave-number and multiwell Scarff-II potentials is analyzed in detail using numerical simulations. Stable and unstable bright solitons are found in both regions of unbroken and broken $\mathcal{PT}$ symmetry due to the existence of the nonlinearity. Furthermore, the bright solitons in three-dimensional self-focusing and defocusing NLS equations with a generalized $\mathcal{PT}$-symmetric Scarff-II potential are explored. This may have potential applications in the field of optical information transmission and processing based on optical solitons in nonlinear dissipative but $\mathcal{PT}$-symmetric systems.

Dynamics and properties of nonlinear matter waves in a trapped BEC subject to a $\mathcal{PT}$-symmetric linear potential, with the trap in the form of a super-Gaussian potential, are investigated via a variational approach accounting for the complex nature of the soliton. In the process, we address how the shape of the imaginary part of the potential, that is, a gain-loss mechanism, affects the self-localization and the stability of the condensate. Variational results are found to be in good agreement with full numerical simulations for predicting the shape, width, and chemical potential of the condensate until the $\mathcal{PT}$ breaking point. Variational computation also predicts the existence of solitary solution only above a threshold in the particle number as the gain-loss is increased, in agreement with numerical simulations.

We performed numerical simulations of Rayleigh-Bénard convection of an electrically conductive low-Prandtl-number fluid under a uniform horizontal magnetic field. We reproduced the flow reversals observed in laboratory experiments previously reported by us. The flow pattern is moderately constrained, as the axes of convection rolls tend to align in the direction of the horizontal magnetic field. The flow reversals occur when the intensity of horizontal circulation in a vessel exceeds a certain value, which induces bending and reconnection of convection rolls and causes rearrangement of these rolls. The wave number selection mechanism is responsible for the instability leading to the flow reversals. The total heat flow drastically decreases at the occurrences of reversal, reflecting the reduction of roll flow velocity. The irregularity of the reversal sequence and the change in symmetry in the flow pattern during the reversals are consistent with that in cessation-led flow reversals.

The understanding of cavitation from nanoparticles has been hindered by the inability to control nanobubble size. We present a method to manufacture nanoparticles with a tunable single hemispherical depression (nanocups) of mean diameter 90, 260, or 650 nm entrapping a nanobubble. A modified Rayleigh-Plesset crevice model predicts the inertial cavitation threshold as a function of cavity size and frequency, and is verified experimentally. The ability to tune cavitation nanonuclei and predict their behavior will be useful for applications ranging from cancer therapy to ultrasonic cleaning.

In this article a dense nonideal, nonisothermal plasma is considered. New effective screened interaction potentials taking into account quantum-mechanical diffraction and symmetry effects have been obtained. The effective potential of the ion-ion interaction in plasmas with a strongly coupled ion subsystem and semiclassical electron subsystem is presented. Based on the obtained effective potentials the analytical expressions for internal energy and the pressure of the considered plasma were obtained.

We propose a site random-cluster model by introducing an additional cluster weight in the partition function of the traditional site percolation. To simulate the model on a square lattice, we combine the color-assignation and the Swendsen-Wang methods to design a highly efficient cluster algorithm with a small critical slowing-down phenomenon. To verify whether or not it is consistent with the bond random-cluster model, we measure several quantities, such as the wrapping probability $R_e$, the percolating cluster density $P_{\infty }$, and the magnetic susceptibility per site ${\chi }_p$, as well as two exponents, such as the thermal exponent $y_t$ and the fractal dimension $y_h$ of the percolating cluster. We find that for different exponents of cluster weight $q=1.5$, 2, $2.5$, 3, $3.5$, and 4, the numerical estimation of the exponents $y_t$ and $y_h$ are consistent with the theoretical values. The universalities of the site random-cluster model and the bond random-cluster model are completely identical. For larger values of $q$, we find obvious signatures of the first-order percolation transition by the histograms and the hysteresis loops of percolating cluster density and the energy per site. Our results are helpful for the understanding of the percolation of traditional statistical models.

Ionic clusters control the structure, dynamics, and transport in soft matter. Incorporating a small fraction of ionizable groups in polymers substantially reduces the mobility of the macromolecules in melts. These ionic groups often associate into random clusters in melts, where the distribution and morphology of the clusters impact the transport in these materials. Here, using molecular dynamic simulations we demonstrate a clear correlation between cluster size and morphology with the polymer mobility in melts of sulfonated polystyrene. We show that in low dielectric media ladderlike clusters that are lower in energy compared with spherical assemblies are formed. Reducing the electrostatic interactions by enhancing the dielectric constant leads to morphological transformation from ladderlike clusters to globular assemblies. Decrease in electrostatic interaction significantly enhances the mobility of the polymer.

A two-state epidemic model in networks with links mimicking two kinds of relationships between connected nodes is introduced. Links of weights $w_1$ and $w_0$ occur with probabilities $p$ and $1-p$, respectively. The fraction of infected nodes $\rho \left(p\right)$ shows a nonmonotonic behavior, with $\rho$ drops with $p$ for small $p$ and increases for large $p$. For small to moderate $w_1/w_0$ ratios, $\rho \left(p\right)$ exhibits a minimum that signifies an optimal suppression. For large $w_1/w_0$ ratios, the suppression leads to an absorbing phase consisting only of healthy nodes within a range $p_L\le p\le p_R$, and an active phase with mixed infected and healthy nodes for $p<p_L$ and $p>p_R$. A mean field theory that ignores spatial correlation is shown to give qualitative agreement and capture all the key features. A physical picture that emphasizes the intricate interplay between infections via $w_0$ links and within clusters formed by nodes carrying the $w_1$ links is presented. The absorbing state at large $w_1/w_0$ ratios results when the clusters are big enough to disrupt the spread via $w_0$ links and yet small enough to avoid an epidemic within the clusters. A theory that uses the possible local environments of a node as variables is formulated. The theory gives results in good agreement with simulation results, thereby showing the necessity of including longer spatial correlations.

In this paper we investigate capture into resonance of a pair of coupled Duffing oscillators, one of which is excited by periodic forcing with a slowly varying frequency. Previous studies have shown that, under certain conditions, a single oscillator can be captured into persistent resonance with a permanently growing amplitude of oscillations (autoresonance). This paper demonstrates that the emergence of autoresonance in the forced oscillator may be insufficient to generate oscillations with increasing amplitude in the attachment. A parametric domain, in which both oscillators can be captured into resonance, is determined. The quasisteady states determining the growth of amplitudes are found. An agreement between the theoretical and numerical results is demonstrated.

Mode selection and bifurcation of a synchronized motion involving two symmetric self-propelled objects in a periodic one-dimensional domain were investigated numerically and experimentally by using camphor disks placed on an annular water channel. Newton's equation of motion for each camphor disk, whose driving force was the difference in surface tension, and a reaction-diffusion equation for camphor molecules on water were used in the numerical calculations. Among various dynamical behaviors found numerically, four kinds of synchronized motions (reversal oscillation, stop-and-move rotation, equally spaced rotation, and clustered rotation) were also observed in experiments by changing the diameter of the water channel. The mode bifurcation of these motions, including their coexistence, were clarified numerically and analytically in terms of the number density of the disk. These results suggest that the present mathematical model and the analysis of the equations can be worthwhile in understanding the characteristic features of motion, e.g., synchronization, collective motion, and their mode bifurcation.

We review common extensions of particle-in-cell (PIC) schemes which account for strong field phenomena in laser-plasma interactions. After describing the physical processes of interest and their numerical implementation, we provide solutions for several associated methodological and algorithmic problems. We propose a modified event generator that precisely models the entire spectrum of incoherent particle emission without any low-energy cutoff, and which imposes close to the weakest possible demands on the numerical time step. Based on this, we also develop an adaptive event generator that subdivides the time step for locally resolving QED events, allowing for efficient simulation of cascades. Further, we present a unified technical interface for including the processes of interest in different PIC implementations. Two PIC codes which support this interface, picador and elmis, are also briefly reviewed.

When a bubble ruptures at a liquid surface the collapsing cavity produces a central jet that frequently breaks up into a series of droplets. Current experiment and theory predict that the production of jet drops will be limited by either viscous or gravitational effects. However, while there are a number of studies focusing on these two limiting cases, less is understood about the production of jet drops when both gravitational and viscous effects are significant. Here, we uncover the existence of an intermediate region where both gravitational and viscous effects play a critical role in jet-drop formation. We propose that the role of gravity is most important before rupture, and carry out simulations that demonstrate the importance of the equilibrium bubble shape in the production of jet drops.

We present an analytical treatment of the acoustics of liquid-filled wine glasses, or “glass harps.” The solution is generalized such that under certain assumptions it reduces to previous glass harp models, but also leads to a proposed musical instrument, the “inverted glass harp,” in which an empty glass is submerged in a liquid-filled basin. The versatility of the solution demonstrates that all glass harps are governed by a family of solutions to Laplace's equation around a vibrating disk. Tonal analyses of recordings for a sample glass are offered as confirmation of the scaling predictions.

In this work we investigate the nonequilibrium dynamics of closed quantum systems. In particular we focus on the stationary properties of integrable systems. Here we show how a generalized Gibbs ensemble (GGE) can be constructed as the best approximation to the time-dependent density matrix. Our procedure allows for a systematic construction of the GGE by a constrained minimization of the distance between the latter and the true state. Moreover, we show that the entropy of the GGE is a direct measure for the quality of the approximation. We apply our method to a quenched hard core Bose gas. Whereas a correlated GGE properly describes all stationary nonlocal correlations, a simple harmonic GGE is sufficient to completely describe reduced local states.

Behavior of two-time autocorrelation during the phase separation in solid binary mixtures is studied via numerical solutions of the Cahn-Hilliard equation as well as Monte Carlo simulations of the Ising model. Results are analyzed via state-of-the-art methods, including the finite-size scaling technique. Full forms of the autocorrelation in space dimensions 2 and 3 are obtained empirically. The long-time behavior is found to be power law, with exponents unexpectedly higher than the ones for the ferromagnetic ordering. Both Cahn-Hilliard and Ising models provide consistent results.

Monte Carlo simulations and probabilistic modeling are employed to understand the strength distribution of a planar bundle of local load-sharing fibers. The fibers are distributed randomly within a unit square according to a Poisson process, and the fiber strengths are Weibull distributed with exponent $\rho$. Monte Carlo failure simulations of bundles comprised of up to ${10}^5$ fibers suggests that the bundle strength distribution obeys weakest-link scaling for all $\rho$. Also, a probabilistic model of the weakest-link event is proposed. This model introduces a failure event at a size scale between that of the fiber and that of the bundle, whose failure statistics follows that of equal load-sharing bundles. The weakest-link event is modelled as the growth of a tight cluster of these equal load-sharing bundles. The size of the equal load-sharing bundles increases with decreasing $\rho$. The simulated bundle strength distributions and those predicted by the model are compared, and excellent agreement is obtained.