The relaxation dynamics of the one-dimensional totally asymmetric simple exclusion process on a ring is considered in the case of step initial condition. Analyzing the time evolution of the local particle densities and currents by the Bethe ansatz method, we examine their full relaxation dynamics. As a result, we observe peculiar behaviors, such as the emergence of a ripple in the density profile and the existence of the excessive particle currents. Moreover, by making a finite-size scaling analysis of the asymptotic amplitudes of the local densities and currents, we find the scaling exponents with respect to the total number of sites to be $-3/2$ and $-1$, respectively.

Recent reports [N. Jia and S. Ma, Phys. Rev. E 79, 031115 (2009); T. Neumann and P. Wagner, Phys. Rev. E 80, 013101 (2009)] have different opinions on the exact analytical solution of the inflow in the Nagel-Schreckenberg model with expanded left boundary condition. In the current study, the different implementations of the “expanded left boundary” are proven to cause the confliction. Detailed analyses show that both reports are reasonable, depending on whether the rule “clear the minisystem first” is applied.

Exploring the World Wide Web has become one of the key issues in information science, specifically in view of its application to the PageRank-like algorithms used in search engines. The random walk approach has been employed to study such a problem. The probability of return to the origin (RTO) of random walks is inversely related to how information can be accessed during random surfing. We find analytically that the RTO probability for a given starting node shows a crossover from a slow to a fast decay behavior with time and the crossover time increases with the degree of the starting node. We remark that the RTO probability becomes almost constant in the early-time regime as the degree exponent approaches two. This result indicates that a random surfer can be effectively trapped at the hub and supports the necessity of the random jump strategy empirically used in the Google's search engine.

Two routes to phase-locking in the optically injected laser system are investigated both involving limit cycles where the phase of the slave laser is unlocked but is nevertheless bounded. We use an experimental phase-resolving technique to unambiguously demonstrate the phenomenon via explicit phasors for the slave laser electric field. Theoretical considerations show that for locking mechanisms involving Hopf bifurcations, such limit cycles of bounded phase are generic. For weakly damped devices, such as quantum well lasers, this can involve an excited resonance at the relaxation oscillation frequency. For highly damped devices there is no such excitation but the bounded phase behavior must persist. Phasor portraits for other regimes are also obtained including a chaotic regime.

The matter-wave solutions of Bose-Einstein condensates with three-body interaction are examined through the one-dimensional Gross-Pitaevskii equation. By using a modified lens-type transformation and a further extension of the tanh-function method we obtain the exact analytical solutions which describe the propagation of kink-shaped solitons, anti-kink-shaped solitons, and other families of solitary waves. We realize that the shape of a kink solitary wave depends on both the scattering length and the parameter of atomic exchange with the substrate. The stability of the solitary waves is examined using analytical and numerical methods. Our results can also be applied to nonlinear optics in the presence of cubic-quintic media.

Wave billiards which are chaotic in the geometrical limit are known to support nongeneric spatially localized modes called scar modes. The interaction of the scar modes with gain has been recently investigated in optics in microcavity lasers and vertical-cavity surface-emitting lasers. Exploiting the localization properties of scar modes in their wave-analogous phase-space representation, we report experimental results of scar mode selection by gain in a doped D-shaped optical fiber.

An outstanding idea originally introduced by Greenberg is to investigate whether there is equivalence between intermediate statistics, which may be different from anyonic statistics, and $q$-deformed particle algebra. Also, a model to be studied for addressing such an idea could possibly provide us some new consequences about the interactions of particles as well as their internal structures. Motivated mainly by this idea, in this work, we consider a $q$-deformed Fermi gas model whose statistical properties enable us to effectively study interpolating statistics. Starting with a generalized Fermi-Dirac distribution function, we derive several thermostatistical functions of a gas of these deformed fermions in the thermodynamical limit. We study the high-temperature behavior of the system by analyzing the effects of $q$ deformation on the most important thermostatistical characteristics of the system such as the entropy, specific heat, and equation of state. It is shown that such a deformed fermion model in two and three spatial dimensions exhibits the interpolating statistics in a specific interval of the model deformation parameter 0 < $q$ < 1. In particular, for two and three spatial dimensions, it is found from the behavior of the third virial coefficient of the model that the deformation parameter $q$ interpolates completely between attractive and repulsive systems, including the free boson and fermion cases. From the results obtained in this work, we conclude that such a model could provide much physical insight into some interacting theories of fermions, and could be useful to further study the particle systems with intermediate statistics.

We report a mechanism in which self-assembly propagates spontaneously in a continuous medium, enabling the delivery of local order information to distance. In a large stable system a locally self-assembled structure as a precursor destabilizes its surrounding areas through a dipole interaction. The newly formed structures inherit the same order information from the precursor and further activate the self-assembly of their neighbors. This process causes spatial extension of self-assembly and replication of the order, producing extremely long-range ordered superlattice without defects.

A general formulation of stochastic thermodynamics is presented for open systems exchanging energy and particles with multiple reservoirs. By introducing a partition in terms of “mesostates” (e.g., sets of “microstates”), the consequence on the thermodynamic description of the system is studied in detail. When microstates within mesostates rapidly thermalize, the entire structure of the microscopic theory is recovered at the mesostate level. This is not the case when these microstates remain out of equilibrium, leading to additional contributions to the entropy balance. Some of our results are illustrated for a model of two coupled quantum dots.

Extensive kinetic Monte Carlo simulations are presented for the Wolf-Villain model in $(1+1)$ dimensions. Asymptotic dynamic scaling is found for lattice sizes $L⩾2048$. The exponents obtained from our simulations, $\alpha =0.50\pm 0.02$ and $\beta =0.25\pm 0.02$, are in excellent agreement with the exact values $\alpha =1/2$ and $\beta =1/4$ for the one-dimensional Edwards-Wilkinson equation. Our findings explain the widespread discrepancies of previous reports for exponents of the Wolf-Villain model in $(1+1)$ dimensions, and the results are also consistent with the theoretical predictions of López et al. [J. M. López, M. Castro, and R. Gallego, Phys. Rev. Lett. 94, 166103 (2005)].

There are some hydrodynamic equations that, while their parent kinetic equation satisfies fundamental mechanical properties, appear themselves to violate mechanical or thermodynamic properties. This paper aims to shed some light on the source of this problem. Starting with diffusive volume hydrodynamic models, the microscopic temporal and spatial scales are first separated at the kinetic level from the macroscopic scales at the hydrodynamic level. Then, we consider Klimontovich's spatial stochastic version of the Boltzmann kinetic equation and show that, for small local Knudsen numbers, the stochastic term vanishes and the kinetic equation becomes the Boltzmann equation. The collision integral dominates in the small local Knudsen number regime, which is associated with the exact traditional continuum limit. We find a subdomain of the continuum range, which the conventional Knudsen number classification does not account for appropriately. In this subdomain, it is possible to obtain a fully mechanically consistent volume (or mass) diffusion model that satisfies the second law of thermodynamics on the grounds of extended non-local-equilibrium thermodynamics.

By numerical simulations, it is illustrated that a magnetic dipole with a flexible tail behaves as a swimmer in AC magnetic fields. The behavior of the swimmer on long time scales is analyzed and it is shown that due to the flexibility of the tail two kinds of torques arise, the first is responsible for the orientation of the swimmer perpendicularly to the AC field and the second drags the filament in the direction of the rotating field. Due to this, circular trajectories of the swimmer are possible; however, these are unstable. The self-propulsion velocity of this swimmer is higher than the velocities of other magnetic microdevices for comparable values of the magnetoelastic number.

Conservation equations governed by a nonlocal interaction potential generate aggregates from an initial uniform distribution of particles. We address the evolution and formation of these aggregating steady states when the interaction potential has both attractive and repulsive singularities. Currently, no existence theory for such potentials is available. We develop and compare two complementary solution methods, a continuous pseudoinverse method and a discrete stochastic lattice approach, and formally show a connection between the two. Interesting aggregation patterns involving multiple peaks for a simple doubly singular attractive-repulsive potential are determined. For a swarming Morse potential, characteristic slow-fast dynamics in the scaled inverse energy is observed in the evolution to steady state in both the continuous and discrete approaches. The discrete approach is found to be remarkably robust to modifications in movement rules, related to the potential function. The comparable evolution dynamics and steady states of the discrete model with the continuum model suggest that the discrete stochastic approach is a promising way of probing aggregation patterns arising from two- and three-dimensional nonlocal interaction conservation equations.

Recently, it was found by Schneider et al. [Proc. Natl. Acad. Sci. USA 108, 3838 (2011)], using simulations, that scale-free networks with “onion structure” are very robust against targeted high degree attacks. The onion structure is a network where nodes with almost the same degree are connected. Motivated by this work, we propose and analyze, based on analytical considerations, an onionlike candidate for a nearly optimal structure against simultaneous random and targeted high degree node attacks. The nearly optimal structure can be viewed as a set of hierarchically interconnected random regular graphs,the degrees and populations of whose nodes are specified by the degree distribution. This network structure exhibits an extremely assortative degree-degree correlation and has a close relationship to the “onion structure.” After deriving a set of exact expressions that enable us to calculate the critical percolation threshold and the giant component of a correlated network for an arbitrary type of node removal, we apply the theory to the cases of random scale-free networks that are highly vulnerable against targeted high degree node removal. Our results show that this vulnerability can be significantly reduced by implementing this onionlike type of degree-degree correlation without much undermining the almost complete robustness against random node removal. We also investigate in detail the robustness enhancement due to assortative degree-degree correlation by introducing a joint degree-degree probability matrix that interpolates between an uncorrelated network structure and the onionlike structure proposed here by tuning a single control parameter. The optimal values of the control parameter that maximize the robustness against simultaneous random and targeted attacks are also determined. Our analytical calculations are supported by numerical simulations.

Chains of charged dust particles are observed aligned with a subsonic ion flow. These chains are found in dilute regions, near the midplane of a parallel-plate radio-frequency plasma under microgravity conditions. The argon ion flow speed near these chains was estimated to be of order ${10}^2$ m/s, corresponding to an ion acoustic Mach number $M<0.1$. The chains were observed to be stable in both the longitudinal and transverse directions. This stability suggests that there is a transverse restoring force. The transverse components of the ion-drag force or electrostatic wake-field forces could provide such a stabilizing effect. The chain appears to terminate with a final dust particle that is located in a dilute region; this observation suggests a possible attractive force in the longitudinal direction in the presence of a subsonic ion flow.

We experimentally investigate the micro-origin of the absence of trough trapping in nonlinear traveling dust acoustic waves self-excited by the downward ion flow in the dissipative dusty plasma. The wave forms of dust density, the drag force from the background neutrals, ions, and dusts, and the effective potential energy for dusts are constructed by tracking dust motion and measuring the velocity and the position-dependent forces. The tilted washboard type potential wave form with a slight phase lead to the dust density wave form is obtained. It provides sufficient kinetic energy to compensate drag dissipation and move dusts from the dust density trough to the crest front. The dusts with sufficient energy overcome the downward pushing by the crest front, climb over the crest, and sustain the oscillatory motion with upward drift. Those dusts with insufficient energy to climb over the potential barrier of the crest are trapped in and move downward with the crest front, until kicked upward by fluctuation. The upward neutral dominated drag force prevents them from sliding down the potential energy hill at the crest front and further oscillating in the trough. It leads to the absence of trough trapping.

We investigate two-dimensional (2D) ordinary and gap solitons in the 2D and the quasi-one-dimensional parity-time ($\mathcal{PT}$) linear lattice potentials. The stability diagrams for both versions of $\mathcal{PT}$ potentials are given. Particularly, we find that 2D gap solitons with self-attractive nonlinearity may exist in the $\mathcal{PT}$ lattice, but they are unstable due to the collapse instability.

We present a supersymmetric formulation of Markov processes, represented by a family of Langevin equations with multiplicative white noise. The hidden symmetry encodes equilibrium properties such as fluctuation-dissipation relations. The formulation does not depend on the particular prescription to define the Wiener integral. In this way, different equilibrium distributions, reached at long times for each prescription, can be formally treated on the same footing.