The present work studies the Ghatak-Sherrington (GS) model in the presence of a magnetic random field (RF). Previous results obtained from the GS model without a RF suggest that disorder and frustration are the key ingredients to produce spontaneous inverse freezing (IF). However, in this model, the effects of disorder and frustration always appear combined. In that sense, the introduction of RF allows us to study the IF under the effects of a disorder which is not a source of frustration. The problem is solved within the one step replica symmetry approximation. The results show that the first order transition between the spin glass and the paramagnetic phases, which is related to the IF for a certain range of crystal field $D$, is gradually suppressed when the RF is increased.

This study presents molecular dynamics simulations on the segregation of binary mixtures in a high-velocity rotating drum. Depending on the ratio between the particle radius and density, similarities to the Brazil-nut effect and its reverse form are shown in the ringlike spin segregation patterns in radial direction. The smaller and heavier particles accumulated toward the drum wall, whereas the bigger and lighter particles accumulated toward the drum center. The effects of particle radius and density on the segregation states were quantified and the phase diagram of segregation in the ${\rho }_b/{\rho }_s$ - $r_b/r_s$ space was plotted. The observed phenomena can be explained by the combined percolation and the buoyancy effects.

Advances in nanopatterned surface fabrication have sparked an interest in studying surface topology effects on heat transfer across liquid-solid interfaces (LSIs). In this study, molecular dynamics (MD) simulations are conducted to examine the effects of surface nanopatterning on the thermal resistance across LSIs. It is shown that nanopatterning can strongly influence the wetting behavior and vibrational properties of a solid surface. The combination of these two factors has a direct effect on the degree of vibrational coupling between the adsorbed liquid and the solid surface. A strong correlation exists between this coupling and the resulting LSI thermal resistance.

The phase diagram for a lattice ring polymer under applied force, with variable solvent quality, for different topological knot states, is determined for the first time. In addition to eliminating pseudophases where the polymer is flattened into a single layer, it is found that nontrivial knots result in additional pseudophases under tensile force conditions.

The dynamics of birth-death processes with extinction points that are unstable in the deterministic average description has been extensively studied, mainly in the context of the stochastic transition from the mean-field attracting fixed point to the absorbing state. Here we study the opposite case of a small perturbation from the zero-population absorbing state. We show that such perturbations can grow beyond the mean-field attracting fixed point and then can collapse back into the absorbing state. Such dynamics can represent, for example, the fast growth of a pathogen and then its destruction by the immune system. We show that when the prey perturbation extinction probability is high, the loss of synchronization between the prey densities in different regions in space leads to two possible dynamic regimes: (a) a directed percolation regime based on the balance between regions escaping the absorbing state and regions absorbed into it, and (b) wave trains representing the transition of the entire space to the mean-field stable positive fixed point.

We propose a network reciprocity model in which an agent probabilistically adopts learning or teaching strategies. In the learning adaptation mechanism, an agent may copy a neighbor's strategy through Fermi pairwise comparison. The teaching adaptation mechanism involves an agent imposing its strategy on a neighbor. Our simulations reveal that the reciprocity is significantly affected by the frequency with which learning and teaching agents coexist in a network and by the structure of the network itself.

We study the dynamics of an active Brownian particle with a nonlinear friction function located in a spatial cubic potential. For strong but finite damping, the escape rate of the particle over the spatial potential barrier shows a nonmonotonic dependence on the noise intensity. We relate this behavior to the fact that the active particle escapes from a limit cycle rather than from a fixed point and that a certain amount of noise can stabilize the sojourn of the particle on this limit cycle.

A method is proposed to determine the carrier-envelope phase (CEP) of a relativistic few-cycle laser pulse via the frequency of the Thomson backscattering (TBS) light. We theoretically investigate the generation of a flying mirror when a few-cycle drive pulse with relativistic intensity interacts with a target combined with a thin and a thick foil. The frequency of the TBS light generated from the flying mirror shows a sensitive dependence on the CEP of the drive pulse. The obtained results are verified by one-dimensional particle-in-cell simulations and are explained by an analytical model.

Recently, it has been shown that large arrays of identical oscillators with nonlocal coupling can have a remarkable type of solutions that display a stationary macroscopic pattern of coexisting regions with coherent and incoherent motions, often called chimera states. Here, we present a detailed numerical study of the appearance of such solutions in two-dimensional arrays of coupled phase oscillators. We discover a variety of stationary patterns, including circular spots, stripe patterns, and patterns of multiple spirals. Here, stationarity means that, for increasing system size, the locally averaged phase distributions tend to the stationary profile given by the corresponding thermodynamic limit equation.

For a modified Kepler problem, we reexamine jumps in the saturation spectral rigidity and large oscillations of the level number variance with near zero minima. Earlier discrepancy between the periodic orbit theory and numerical calculation is cleared by a quantum mechanical calculation. A new class of radial periodic orbits is included establishing a complete correspondence between the periodic orbit theory and the quantum mechanical approach. We show that the diagonal approximation for the level density in the periodic orbit theory already gives a good fit with the numerical calculation. Even greater accuracy is achieved by considering coherent interference between the classical periodic orbits term and the Balian-Bloch term. This procedure produces improved results for the hard-wall rectangular billiards as well.

We study the clustering properties of inertial particles in a turbulent viscoelastic fluid. The investigation is carried out by means of direct numerical simulations of turbulence in the Oldroyd-B model. The effects of polymers on the small-scale properties of homogeneous turbulence are considered in relation with their consequences on clustering of particles, both lighter and heavier than the carrying fluid. We show that, depending on particle and flow parameters, polymers can either increase or decrease clustering.

An average modeling methodology under the lubrication approach is used to formulate a set of three coupled nonlinear partial differential equations based on the Nusselt scales. This system, known as the energy-integral method in literature, simplifies the Navier-Stokes equation at the first order and analyzes the dynamics of a thin sheet of fluid flowing over a topography with sinusoidally varying longitudinal furrows. Limiting cases of the linear stability results are mathematically discussed and the complete linear system is numerically handled by means of finite differences to approximate the eigenfunctions and their derivatives in a periodic domain. In a geometry which resembles a vertical shift of a topography, with the amplitude being equal to the shift length, it is found that such a geometry stabilizes the flow compared to its counterpart with no shift, such that the wave characteristics get affected. To confirm the stability results, a numerical investigation is performed.

Flow through the pores of granular materials has many instances in practice. Therefore, it is interesting to realize how some parameters, such as the shape of the particles affect the passing flow. Following the recent mathematical theory proposed by the authors, this paper deals with the issue of how tortuosity and permeability are influenced by the particle shape. Comparison of the results with the experimental data reveals the competency of the theory in predicting the impact of particle geometry.

Under investigation in this paper are the coupled nonlinear Schrödinger (CNLS) equations, which can be used to govern the optical-soliton propagation and interaction in such optical media as the multimode fibers, fiber arrays, and birefringent fibers. By taking the 3-CNLS equations as an example for the $N$-CNLS ones ($N⩾3$), we derive the analytic mixed-type two- and three-soliton solutions in more general forms than those obtained in the previous studies with the Hirota method and symbolic computation. With the choice of parameters for those soliton solutions, soliton interactions and complexes are investigated through the asymptotic and graphic analysis. Soliton interactions and complexes with the bound dark solitons in a mode or two modes are observed, including that (i) the two bright solitons display the breatherlike structures while the two dark ones stay parallel, (ii) the two bright and dark solitons all stay parallel, and (iii) the states of the bound solitons change from the breatherlike structures to the parallel one even with the distance between those solitons smaller than that before the interaction with the regular one soliton. Asymptotic analysis is also used to investigate the elastic and inelastic interactions between the bound solitons and the regular one soliton. Furthermore, some discussions are extended to the $N$-CNLS equations ($N>3$). Our results might be helpful in such applications as the soliton switch, optical computing, and soliton amplification in the nonlinear optics.

Mesoscopic models play an important role in our understanding of the deformation and flow of amorphous materials. One such description, based on the shear transformation zone theory, has recently been reformulated within a nonequilibrium thermodynamics framework and found to be consistent with it. We show here that a similar interpretation can be made for the soft glassy rheology (SGR) model. Conceptually this means that the “noise temperature” $x$, proposed phenomenologically in the SGR model to control the dynamics of a set of slow mesoscopic degrees of freedom, can consistently be interpreted as their actual thermodynamic temperature. (Because such modes are slow to equilibrate, this generally does not coincide with the temperature of the fast degrees of freedom and/or heat bath.) If one chooses to make this interpretation, the thermodynamic framework significantly constrains extensions of the SGR approach to models in which $x$ is a dynamical variable. We assess in this light some such extensions recently proposed in the context of shear banding.

Enßlin and Weig [Phys. Rev. E 82, 051112 (2010)] have introduced a “minimum Gibbs free energy” (MGFE) approach for estimation of the mean signal and signal uncertainty in Bayesian inference problems: it aims to combine the maximum a posteriori (MAP) and maximum entropy (ME) principles. We point out, however, that there are some important questions to be clarified before the new approach can be considered fully justified, and therefore able to be used with confidence. In particular, after obtaining a Gaussian approximation to the posterior in terms of the MGFE at some temperature $T$, this approximation should always be raised to the power of $T$ to yield a reliable estimate. In addition, we show explicitly that MGFE indeed incorporates the MAP principle, as well as the MDI (minimum discrimination information) approach, but not the well-known ME principle of Jaynes [E.T. Jaynes, Phys. Rev. 106, 620 (1957)]. We also illuminate some related issues and resolve apparent discrepancies. Finally, we investigate the performance of MGFE estimation for different values of $T$, and we discuss the advantages and shortcomings of the approach.

We endorse the comment on our recent paper [Enßlin and Weig, Phys. Rev. E 82, 051112 (2010)] by Iatsenko, Stefanovska, and McClintock [Phys. Rev. E 85, 033101 (2012)], and we try to clarify the origin of the apparent controversy on two issues. The aim of the minimal Gibbs free energy approach to provide a signal estimate is not affected by their Comment. However, if one wants to extend the method to also infer the a posteriori signal uncertainty, any tempering of the posterior has to be undone at the end of the calculations, as they correctly point out. Furthermore, a distinction is made here between maximum entropy, the maximum entropy principle, and the so-called maximum entropy method in imaging, hopefully clarifying further the second issue of their Comment.

We study the onset of chaos and statistical relaxation in two isolated dynamical quantum systems of interacting spins 1/2, one of which is integrable and the other chaotic. Our approach to identifying the emergence of chaos is based on the level of delocalization of the eigenstates with respect to the energy shell, the latter being determined by the interaction strength between particles or quasiparticles. We also discuss how the onset of chaos may be anticipated by a careful analysis of the Hamiltonian matrices, even before diagonalization. We find that despite differences between the two models, their relaxation processes following a quench are very similar and can be described analytically with a theory previously developed for systems with two-body random interactions. Our results imply that global features of statistical relaxation depend on the degree of spread of the eigenstates within the energy shell and may happen to both integrable and nonintegrable systems.

The interaction of laser pulses of picosecond duration and terawatt to petawatt power accelerated for the very fast undistorted plasma blocks for deuterium DD or deuterium tritium fast ignition is investigated. Based on the direct and instant conversion of laser energy into mechanical motion by nonlinear (ponderomotive) forces, any thermal pressure generation is delayed by the collision process. Following the studying of the classical collision frequency, it is found that the quantum modified collision at higher energies results in a correction by about 15$\%$ reduction of the delay.