The focusing nonlinear Schrödinger equation (NLSE) describes propagation of quasimonochromatic waves in weakly nonlinear media. The aim of this study is to determine conditions of soliton synchronization in the NLSE in terms of the solitons' position and phase parameters. For this purpose, the concept of asymptotic middle states of solitons in the NLSE is first introduced. With soliton solutions of the NLSE, it is shown that soliton synchronization can be achieved by synchronizing the asymptotic middle states of the solitons, and conditions of soliton synchronization in terms of the solitons' position and phase parameters are given. Although the interaction of the solitons is nonlinear, the conditions are linear equations. Then, aided with the synchronization conditions, simple initial conditions are presented for producing synchronized interaction of solitons without the need to obtain analytic expressions for the synchronized interaction of the solitons. The initial conditions are summations of fundamental solitons with no mutual overlap, so they might be convenient to implement in applicative contexts.

We study the existence of chimera states in a network of locally coupled chaotic and limit-cycle oscillators. The necessary condition for chimera state in purely local coupled oscillators is discussed. At first, we numerically observe the existence of chimera or multichimera states in the locally coupled Hindmarsh–Rose neuron model. We find that delay time in the nonlinear local coupling reduces the domain of the coherent island in the parameter space of the synaptic coupling strength and time delay, and thus the coherent region can be completely eliminated once the time delay exceeds a certain threshold. We then consider another form of nonlinearity in the local coupling, and the existence of chimera states is observed in the time-delayed Mackey–Glass system and in a Van der Pol oscillator. We also discuss the effect of time delay in local coupling for the existence of chimera states in Mackey–Glass systems. The nonlinearity present in the coupling function plays a key role in the emergence of chimera or multichimera states. A phase diagram for the chimera state is identified over a wide parameter space.

Distributions of abundances or frequencies play an important role in many fields of science, from biology to sociology, as does the Rényi entropy, which measures the diversity of a statistical ensemble. We derive a mathematical relation between the abundance distribution and the Rényi entropy, by analogy with the equivalence of ensembles in thermodynamics. The abundance distribution is mapped onto the density of states, and the Rényi entropy to the free energy. The two quantities are related in the thermodynamic limit by a Legendre transform, by virtue of the equivalence between the micro-canonical and canonical ensembles. In this limit, we show how the Rényi entropy can be constructed geometrically from rank-frequency plots. This mapping predicts that non-concave regions of the rank-frequency curve should result in kinks in the Rényi entropy as a function of its order. We illustrate our results on simple examples, and emphasize the limitations of the equivalence of ensembles when a thermodynamic limit is not well defined. Our results help choose reliable diversity measures based on the experimental accuracy of the abundance distributions in particular frequency ranges.

We present a quantitative thermodynamic model to elucidate the effects of a nanopatterned surface on bacterial adhesion. Based on the established model, we studied the equilibrium state of rodlike bacterial cells adhered to a nanopillar-patterned surface. Theoretical analyses showed the physical origin of bacterial adhesion on a nanopatterned surface is actually determined by the balance between adhesion energy and deformation energy of the cell membrane. We found that there are enhancement effects on bacterial adhesion to the patterned surface with large radius and small spacing of nanopillars, but suppression effects for nanopillars with a radius smaller than a critical value. In addition, according to our model, a phase diagram has been constructed which can clarify the interrelated effects of the radius and the spacing of nanopillars. The broad agreement with experimental observations implies that these studies would provide useful guidance to the design of nanopatterned surfaces for biomedical applications.

A recently developed hybrid method is employed to study the mechanical behavior of silica-polystyrene nanocomposites (NCs) under uniaxial elongation. The hybrid method couples a particle domain to a continuum domain. The region of physical interest, i.e., the interphase around a nanoparticle (NP), is treated at molecular resolution, while the surrounding elastic continuum is handled with a finite-element approach. In the present paper we analyze the polymer behavior in the neighborhood of one or two nanoparticle(s) at molecular resolution. The coarse-grained hybrid method allows us to simulate a large polymer matrix region surrounding the nanoparticles. We consider NCs with dilute concentration of NPs embedded in an atactic polystyrene matrix formed by 300 chains with 200 monomer beads. The overall orientation of polymer segments relative to the deformation direction is determined in the neighborhood of the nanoparticle to investigate the polymer response to this perturbation. Calculations of strainlike quantities give insight into the deformation behavior of a system with two NPs and show that the applied strain and the nanoparticle distance have significant influence on the deformation behavior. Finally, we investigate to what extent a continuum-based description may account for the specific effects occurring in the interphase between the polymer matrix and the NPs.

We study dynamics of charged particle in current sheets with magnetic fluctuations. We use the adiabatic theory to describe the nonperturbed charged particle motion and show that magnetic field fluctuations destroy the adiabatic invariant. We demonstrate that the evolution of particle adiabatic invariant's distribution is described by a diffusion equation and derive analytical estimates of the rate of adiabatic invariant's diffusion. This rate is proportional to power density of magnetic field fluctuations. We compare analytical estimates with numerical simulations. We show that adiabatic invariant diffusion results in transient particles trapping in the current sheet. For magnetic field fluctuation amplitude a few times larger than a normal magnetic field component, more than 50% of transient particles become trapped. We discuss the possible consequences of destruction of adiabaticity of the charged particle motion on the state of the current sheets.

In this work, a self-consistent transport theory for a relativistic plasma is developed. Using the notation of Braginskii [S. I. Braginskii, in Reviews of Plasma Physics, edited by M. A. Leontovich (Consultants Bureau, New York, 1965), Vol. 1, p. 174], we provide semianalytical forms of the electrical resistivity, thermoelectric, and thermal conductivity tensors for a Lorentzian plasma in a magnetic field. This treatment is then generalized to plasmas with arbitrary atomic number by numerically solving the linearized Boltzmann equation. The corresponding transport coefficients are fitted by rational functions in order to make them suitable for use in radiation-hydrodynamic simulations and transport calculations. Within the confines of linear transport theory and on the assumption that the plasma is optically thin, our results are valid for temperatures up to a few MeV. By contrast, classical transport theory begins to incur significant errors above $k_{B}T\sim 10$ keV, e.g., the parallel thermal conductivity is suppressed by 15% at $k_{B}T=20$ keV due to relativistic effects.

The single component pseudopotential lattice Boltzmann model has been widely applied in multiphase simulation due to its simplicity and stability. In many studies, it has been claimed that this model can be stable for density ratios larger than 1000. However, the application of the model is still limited to small density ratios when the contact angle is considered. The reason is that the original contact angle adjustment method influences the stability of the model. Moreover, simulation results in the present work show that, by applying the original contact angle adjustment method, the density distribution near the wall is artificially changed, and the contact angle is dependent on the surface tension. Hence, it is very inconvenient to apply this method with a fixed contact angle, and the accuracy of the model cannot be guaranteed. To solve these problems, a contact angle adjustment method based on the geometry analysis is proposed and numerically compared with the original method. Simulation results show that, with our contact angle adjustment method, the stability of the model is highly improved when the density ratio is relatively large, and it is independent of the surface tension.

Demonstrating how microscopic dynamics cause large systems to approach thermal equilibrium remains an elusive, longstanding, and actively pursued goal of statistical mechanics. We identify here a dynamical mechanism for thermalization in a general class of two-component dynamical Lorentz gases and prove that each component, even when maintained in a nonequilibrium state itself, can drive the other to a thermal state with a well-defined effective temperature.

We report the experimental realization of a rod diffusing in a two-dimensional obstacle field following the single rod dynamics. We use a silver nanowire as our rod and two types of obstacles: repelling light beams and polymer pillars. We study the effect of hydrodynamic interactions on the transport of the rod, comparing both experimental realizations and recent simulations. We propose a framework for analyzing the transport through such systems, and we predict a new superdiffusive regime of rod transport at high obstacle concentration and short times.

We derive the dependence of the Reynolds number $\text{Re}$ and the Nusselt number $\text{Nu}$ on the Rayleigh number $\text{Ra}$ and the Prandtl number $\text{Pr}$ in laminar vertical convection (VC), where a fluid is confined between two differently heated isothermal vertical walls. The boundary layer equations in laminar VC yield two limiting scaling regimes: $\text{Nu}\sim {\text{Pr}}^{1/4}{\text{Ra}}^{1/4}, \text{Re}\sim {\text{Pr}}^{-1/2}{\text{Ra}}^{1/2}$ for $\text{Pr}\ll 1$ and $\text{Nu}\sim {\text{Pr}}^0{\text{Ra}}^{1/4}, \text{Re}\sim {\text{Pr}}^{-1}{\text{Ra}}^{1/2}$ for $\text{Pr}\gg 1$. These theoretical results are in excellent agreement with direct numerical simulations for $\text{Ra}$ from ${10}^5$ to ${10}^{10}$ and $\text{Pr}$ from ${10}^{-2}$ to 30. The transition between the regimes takes place for $\text{Pr}$ around ${10}^{-1}$.

We propose a method for the detection and localization of different types of coexisting oscillatory regimes that alternate with each other leading to multistate intermittency. Our approach is based on consideration of wavelet spectrum energies. The proposed technique is tested in an erbium-doped fiber laser with four coexisting periodic orbits, where external noise induces intermittent switches between the coexisting states. Statistical characteristics of multistate intermittency, such as the mean duration of the phases for every oscillation type, are examined with the help of the developed method. We demonstrate strong advantages of the proposed technique over previously used amplitude methods.

We provide a generic scheme offering real-time control of directed particle transport using superimposed driven lattices. This scheme allows one to accelerate, slow, and freeze the transport on demand by switching one of the lattices subsequently on and off. The underlying physical mechanism hinges on a systematic opening and closing of channels between transporting and nontransporting phase space structures upon switching and exploits cantori structures which generate memory effects in the population of these structures. Our results should allow for real-time control of cold thermal atomic ensembles in optical lattices but might also be useful as a design principle for targeted delivery of molecules or colloids in optical devices.

In this article, we present an approach for the thermodynamics of phase oscillators induced by an internal multiplicative noise. We analytically derive the free energy, entropy, internal energy, and specific heat. In this framework, the formulation of the first law of thermodynamics requires the definition of a synchronization field acting on the phase oscillators. By introducing the synchronization field, we have consistently obtained the susceptibility and analyzed its behavior. This allows us to characterize distinct phases in the system, which we have denoted as synchronized and parasynchronized phases, in analogy with magnetism. The system also shows a rich complex behavior, exhibiting ideal gas characteristics for low temperatures and susceptibility anomalies that are similar to those present in complex fluids such as water.

In oscillatory reaction-diffusion systems, time-delay feedback can lead to the instability of uniform oscillations with respect to formation of standing waves. Here, we investigate how the presence of additive, Gaussian white noise can induce the appearance of standing waves. Combining analytical solutions of the model with spatiotemporal simulations, we find that noise can promote standing waves in regimes where the deterministic uniform oscillatory modes are stabilized. As the deterministic phase boundary is approached, the spatiotemporal correlations become stronger, such that even small noise can induce standing waves in this parameter regime. With larger noise strengths, standing waves could be induced at finite distances from the (deterministic) phase boundary. The overall dynamics is defined through the interplay of noisy forcing with the inherent reaction-diffusion dynamics.

We study a model of a population making a binary decision based on information spreading within the population, which is fully connected or covering a square grid. We assume that a fraction of the population wants to make the choice of the minority, whereas the rest want to make the majority choice. This resembles opinion spreading with “contrarian” agents but has the game theoretic aspect that agents try to optimize their own situation in ways that are incompatible with the common good. When this fraction is less than 1/2, the population can efficiently self-organize to a state where agents get what they want—the majority (i.e., the majority seekers) have one opinion, the minority seekers have the other. If the fraction is larger than 1/2, there is a frustration in the population that dramatically changes the dynamics. In this region, the population converges, through some distinct phases, to a state of approximately equal-sized opinions. Just over the threshold the state of the population is furthest from the collectively optimal solution.

Human beings develop the land and transform land use patterns, constructing artificial structures. Among them, the city is a representative system and its morphology has attracted much attention. While most existing studies have been devoted to individual dynamics and focused on the proximity of specific areas of a city, we here pay attention to the city as a complex system, where interactions between individuals give rise to emergent properties. Specifically, analyzing the big data on every building in Seoul City, we specify the relevant interactions among constituents and probe the emergence of complex land use patterns. In particular, based on the empirical observations, we illustrate that interactions between land uses are frustrated, which serves as a basic postulate of the theory of urban morphology. We examine this conjecture with the help of a layered Ising-type model and disclose that the actual land use pattern emerges at the criticality of the system in the presence of heterogeneously distributed fields. It is also remarked that our model, allowing quantitative predictions, can easily be applied to other cities around the world.

We formulate a theory of the effects of long-range interactions on the surface tension and spontaneous curvature of proteinaceous shells based on the general Deryaguin-Landau-Verwey-Overbeek mesoscale approach to colloid stability. We derive the full renormalization formulas for the elastic properties of the shell and consider in detail the renormalization of the spontaneous curvature as a function of the corresponding Hamaker coefficient, inner and outer capsid charges, and bathing solution properties. The renormalized spontaneous curvature is found to be a nonmonotonic function of several parameters describing the system.

When European starlings come together to form a flock, the distribution of their individual velocities narrows around the mean velocity of the flock. We argue that, in a broad class of models for the joint distribution of positions and velocities, this narrowing generates an entropic effect that opposes the cohesion of the flock. The strength of this effect depends strongly on the nature of the interactions among birds: If birds are coupled to a fixed number of neighbors, the entropic forces are weak, while if they couple to all other birds within a fixed distance, the entropic effects are sufficient to tear a flock apart.