We perform simulations of random Ising models defined over small-world networks and we check the validity and the level of approximation of a recently proposed effective field theory. Simulations confirm a rich scenario with the presence of multicritical points with first- or second-order phase transitions. In particular, for second-order phase transitions, independent of the dimension $d_0$ of the underlying lattice, the exact predictions of the theory in the paramagnetic regions, such as the location of critical surfaces and correlation functions, are verified. Quite interestingly, we verify that the Edwards-Anderson model with $d_0=2$ is not thermodynamically stable under graph noise.

We examine birth-death processes with state dependent transition probabilities and at least one absorbing boundary. In evolution, this describes selection acting on two different types in a finite population where reproductive events occur successively. If the two types have equal fitness the system performs a random walk. If one type has a fitness advantage it is favored by selection, which introduces a bias (asymmetry) in the transition probabilities. How long does it take until advantageous mutants have invaded and taken over? Surprisingly, we find that the average time of such a process can increase, even if the mutant type always has a fitness advantage. We discuss this finding for the Moran process and develop a simplified model which allows a more intuitive understanding. We show that this effect can occur for weak but nonvanishing bias (selection) in the state dependent transition rates and infer the scaling with system size. We also address the Wright-Fisher model commonly used in population genetics, which shows that this stochastic slowdown is not restricted to birth-death processes.

We propose a model for the passage between metastable states of mind dynamics. As changing points we use the rapid transition processes simultaneously detectable in EEG signals related to different cortical areas. Our model consists of a non-Poissonian intermittent process, which signals that the brain is in a condition of complexity, upon which a Poisson process is superimposed. We provide an analytical solution for the waiting-time distribution for the model, which is well obeyed by physiological data. Although the role of the Poisson process remains unexplained, the model is able to reproduce many behaviors reported in literature, although they seem contradictory.

We develop a generalization of the Black-Cox structural model of default risk. The extended model captures uncertainty related to firm’s ability to avoid default even if company’s liabilities momentarily exceeding its assets. Diffusion in a linear potential with the radiation boundary condition is used to mimic a company’s default process. The exact solution of the corresponding Fokker-Planck equation allows for derivation of analytical expressions for the cumulative probability of default and the relevant hazard rate. Obtained closed formulas fit well the historical data on global corporate defaults and demonstrate the split behavior of credit spreads for bonds of companies in different categories of speculative-grade ratings with varying time to maturity. Introduction of the finite rate of default at the boundary improves valuation of credit risk for short time horizons, which is the key advantage of the proposed model. We also consider the influence of uncertainty in the initial distance to the default barrier on the outcome of the model and demonstrate that this additional source of incomplete information may be responsible for nonzero credit spreads for bonds with very short time to maturity.

Linear magnetohydrodynamic instabilities are studied analytically in the case of unbounded inviscid and electrically conducting flows that are submitted to both rotation and precession with shear in an external magnetic field. For given rotation and precession the possible configurations of the shear and of the magnetic field and their interplay are imposed by the “admissibility” condition (i.e., the base flow must be a solution of the magnetohydrodynamic Euler equations): we show that an “admissible” basic magnetic field must align with the basic absolute vorticity. For these flows with elliptical streamlines due to precession we undertake an analytical stability analysis for the corresponding Floquet system, by using an asymptotic expansion into the small parameter $\epsilon$ (ratio of precession to rotation frequencies) by a method first developed in the magnetoelliptical instabilities study by Lebovitz and Zweibel [Astrophys. J. 609, 301 (2004)]. The present stability analysis is performed into a suitable frame that is obtained by a systematic change of variables guided by symmetry and the existence of invariants of motion. The obtained Floquet system depends on three parameters: $\epsilon$, $\eta$ (ratio of the cyclotron frequency to the rotation frequency) and $\chi =\text{cos}\alpha$, with $\alpha$ being a characteristic angle which, for circular streamlines, $\epsilon =0$, identifies with the angle between the wave vector and the axis of the solid body rotation. We look at the various (centrifugal or precessional) resonant couplings between the three present modes: hydrodynamical (inertial), magnetic (Alfvén), and mixed (magnetoinertial) modes by computing analytically to leading order in $\epsilon$ the instabilities by estimating their threshold, growth rate, and maximum growth rate and their bandwidths as functions of $\epsilon$, $\eta$, and $\chi$. We show that the subharmonic “magnetic” mode appears only for $\eta >\sqrt{5}/2$ and at large $\eta$ $\left(⪢1\right)$ the maximal growth rate of both the “hydrodynamic” and magnetic modes approaches $\epsilon /2$, while the one of the subharmonic “mixed” mode approaches zero.

We study two-dimensional soliton-soliton vector pairs in media with self-focusing nonlinearities and defocusing cross interactions. The general properties of the stationary states and their stability are investigated. The different scenarios of instability are observed using numerical simulations. The quasistable propagation regime of the high-power vector solitons is revealed.

The detrending moving average (DMA) algorithm is a widely used technique to quantify the long-term correlations of nonstationary time series and the long-range correlations of fractal surfaces, which contains a parameter $\theta$ determining the position of the detrending window. We develop multifractal detrending moving average (MFDMA) algorithms for the analysis of one-dimensional multifractal measures and higher-dimensional multifractals, which is a generalization of the DMA method. The performance of the one-dimensional and two-dimensional MFDMA methods is investigated using synthetic multifractal measures with analytical solutions for backward $\left(\theta =0\right)$, centered $\left(\theta =0.5\right)$, and forward $\left(\theta =1\right)$ detrending windows. We find that the estimated multifractal scaling exponent $\tau \left(q\right)$ and the singularity spectrum $f\left(\alpha \right)$ are in good agreement with the theoretical values. In addition, the backward MFDMA method has the best performance, which provides the most accurate estimates of the scaling exponents with lowest error bars, while the centered MFDMA method has the worse performance. It is found that the backward MFDMA algorithm also outperforms the multifractal detrended fluctuation analysis. The one-dimensional backward MFDMA method is applied to analyzing the time series of Shanghai Stock Exchange Composite Index and its multifractal nature is confirmed.

We continue the study of a particle (atom, molecule) undergoing an unbiased random walk on the Sierpinski gasket, and obtain for the gasket and tower the eigenvalue spectrum of the associated stochastic master equation. Analytic expressions for recurrence relations among the eigenvalues are derived. The recurrence relations obtained are compared with those determined for two Euclidean lattices, the closed chain with an absorbing site and a finite chain with an absorbing site at one end. We check and confirm the internal consistency between the smallest eigenvalue and the mean walklength in each of the cases studied. Attention is drawn to the relevance of the results obtained to a problem of electron transfer in proteins.

Local and global persistence exponents associated with zero-temperature quenched dynamics of two-dimensional $XY$ model and three-dimensional Heisenberg model have been estimated using numerical simulations. The method of block persistence has been used to find the global and local exponents simultaneously (in a single simulation). Temperature universality of both the exponents for three-dimensional Heisenberg model has been confirmed by simulating the stochastic (with noise) version of the equation of motion. The noise amplitudes added were small enough to retain the dynamics below criticality. In the second part of our work we have studied scaling associated with correlated persistence sites in the three-dimensional Heisenberg model in the later stages of the dynamics. The relevant length scale associated with correlated persistent sites was found to behave in a manner similar to the dynamic length scale associated with the phase ordering dynamics.

We analyze the slow glassy structural relaxation as measured through collective and tagged-particle density correlation functions obtained from Brownian dynamics simulations for a polydisperse system of quasi-hard spheres in the framework of the mode-coupling theory (MCT) of the glass transition. Asymptotic analyses show good agreement for the collective dynamics when polydispersity effects are taken into account in a multicomponent calculation, but qualitative disagreement at small $q$ when the system is treated as effectively monodisperse. The origin of the different small-$q$ behavior is attributed to the interplay between interdiffusion processes and structural relaxation. Numerical solutions of the MCT equations are obtained taking properly binned partial static structure factors from the simulations as input. Accounting for a shift in the critical density, the collective density correlation functions are well described by the theory at all densities investigated in the simulations, with quantitative agreement best around the maxima of the static structure factor and worst around its minima. A parameter-free comparison of the tagged-particle dynamics however reveals large quantitative errors for small wave numbers that are connected to the well-known decoupling of self-diffusion from structural relaxation and to dynamical heterogeneities. While deviations from MCT behavior are clearly seen in the tagged-particle quantities for densities close to and on the liquid side of the MCT glass transition, no such deviations are seen in the collective dynamics.

We investigate the tight packing of nematic polymers inside a confining hard sphere. We model the polymer via the continuum Frank elastic free energy augmented by a simple density dependent part as well as by taking proper care of the connectivity of the polymer chains when compared with simple nematics. The free energy ansatz is capable of describing an orientational ordering transition within the sample between an isotropic polymer solution and a polymer nematic phase. We solve the Euler-Lagrange equations numerically with the appropriate boundary conditions for the director and density field and investigate the orientation and density profile within a sphere. Two important parameters of the solution are the exact locations of the beginning and the end of the polymer chain. Pending on their spatial distribution and the actual size of the hard sphere enclosure we can get a plethora of various configurations of the chain exhibiting different defect geometry.

Cavitation in glassy polymers is known to result from highly triaxial states of local stress and the presence of impurities. Understanding of cavitation, particularly void nucleation, is important as cavities are precursors to crazes, which in turn lead to fracture. In this work we study the early stages of void nucleation in glassy amorphous polymers by imposing, in well designed molecular dynamics simulations, highly triaxial states of stress on ensembles of entangled linear macromolecular chains and monitoring the evolution of the entanglement network. Our results demonstrate that deformation induced disentanglement and rearrangement of topological constraints along individual chains play an important role in the early stages of void nucleation. Even in the glassy state, deformation causes significant changes in the rheological constraints on a chain though the number of interchain binary contacts may not change much.

The thermodynamic scaling idea enables an elegant description of relaxation dynamics near the glass transition and provides a linkage between thermodynamics and molecular dynamics of supercooled liquids. A lot of effort has been put into finding functions, $f\left(T^{-1}{V}^{-\gamma }\right)$, which can scale dynamical quantities such as relaxation time, viscosity, and diffusion coefficient. Within the trend, Papathanassiou [A. N. Papathanassiou, Phys. Rev. E 79, 032501 (2009)] has recently derived a new scaling function for the reduced diffusion coefficient. In this Comment, we report that this scaling function is not sufficiently grounded, because it is based on some scaled equation of state which predicts significantly different values of the scaling exponent $\gamma$ from volumetric data in comparison with those found from the scaling of relaxation or viscosity data. Moreover, we would like to point out that any scaling function $f$ cannot be straightforwardly formulated on the basis of any equation of state which yields the scaling exponent $\gamma$ different from that used to scale the dynamic quantity.

The expansion of a plasma slab into a vacuum is studied using one-dimensional and two-dimensional particle-in-cell simulations. As electrons transfer their longitudinal kinetic energy to ions during the expansion, the electron temperature becomes anisotropic. Once this anisotropy exceeds a threshold value, it drives the Weibel instability, leading to magnetic fields in the megagauss range. These fields induce energy transfer between the longitudinal and transverses directions, which influences the expansion. The impact of a cold electron population on this phenomenon is also investigated.

We analyze the dynamics of heterogeneous granular particles immersed in a bath of thermalized particles, which are candidates for granular motors, with a mechanical approach. We first apply the method to the previously introduced asymmetric piston and show that it gives the exact drift velocity in the Brownian limit. We also obtain results for the efficiency of the motor and compare with numerical simulations. Finally, we introduce a chiral rotor model and discuss opportunities for observing a real granular motor.

We investigate hydrodynamic noise in a dilute granular gas during the homogeneous cooling state, by means of a proper application of the direct simulation Monte Carlo (DSMC) algorithm. The DSMC includes a source of randomization which is not present in molecular dynamics (MD) for inelastic hard disks. Notwithstanding this difference, a fair quantitative agreement is found, including a violation of the fluctuation-dissipation relation for the noise amplitude of the same order observed in MD. This study suggests that deterministic collision dynamics is not an essential ingredient to reproduce, up to a good degree of approximation, hydrodynamic fluctuations in dilute granular gases.

We study pulse propagation in one-dimensional chains of spherical granules decorated with small randomly sized granules placed between bigger monodisperse ones. Such “designer chains” are of interest in efforts to control the behavior of the pulse so as to optimize its propagation or attenuation, depending on the desired application. We show that a recently proposed effective description of simple decorated chains can be extended to predict pulse properties in chains decorated with small granules of randomly chosen radii. Furthermore, we also show that the binary-collision approximation can again be used to provide analytic results for this system.

The Rayleigh-Brillouin light scattering is studied in the glass-forming picoline with emphasis to the temperature dependence of the Landau-Placzek ratio. It was found that the Landau-Placzek ratio is in good agreement with the theoretical prediction at $T>T_A$, where $T_A$ is the temperature of transition from an Arrhenius-like to a non-Arrhenius behavior for the $\alpha$-relaxation time dependence on temperature. Below $T_A$ the Landau-Placzek ratio exceeds significantly the theoretical prediction. The finding is interpreted as the evidence of the locally favored structures, which presence in an equilibrium glass-forming liquid below $T_A$.

A sublimating vicinal crystal surface can undergo a step bunching instability when the attachment-detachment kinetics is asymmetric, in the sense of a normal Ehrlich-Schwoebel effect. Here we investigate this instability in a model that takes into account the subtle interplay between sublimation and step-step interactions, which breaks the volume-conserving character of the dynamics assumed in previous work. On the basis of a systematically derived continuum equation for the surface profile, we argue that the nonconservative terms pose a limitation on the size of emerging step bunches. This conclusion is supported by extensive simulations of the discrete step dynamics, which show breakup of large bunches into smaller ones as well as arrested coarsening and periodic oscillations between states with different numbers of bunches.

Thalamocortical (TC) neurones are known to express the low-voltage activated, inactivating ${\text{Ca}}^{2+}$ current $I_{\text{T}}$. The triggering of this current underlies the generation of low threshold ${\text{Ca}}^{2+}$ potentials that may evoke single or bursts of action potentials. Moreover, this current can contribute to an intrinsic slow $\left(<1\text{Hz}\right)$ oscillation whose rhythm is partly determined by the steady state component of $I_{\text{T}}$ and its interaction with a leak current. This steady state, or window current as it is so often called, has received relatively little theoretical attention despite its importance in determining the electroresponsiveness and input-output relationship of TC neurones. In this paper, we introduce an integrate-and-fire spiking neuron model that includes a biophysically realistic model of $I_{\text{T}}$. We briefly review the subthreshold bifurcation diagram of this model with constant current injection before moving on to consider its response to periodic forcing. Direct numerical simulations show that as well as the expected mode-locked responses there are regions of parameter space that support chaotic behavior. To reveal the mechanism by which the window current generates a chaotic response to periodic forcing we consider a piecewise linear caricature of the dynamics for the gating variables in the model of $I_{\text{T}}$. This model can be analyzed in closed form and is shown to support an unstable set of periodic orbits. Trajectories are repelled from these organizing centers until they reach the threshold for firing. By determining the condition for a grazing bifurcation (at the border between a spiking and nonspiking event) we show how knowledge of the unstable periodic orbits (existence and stability) can be combined with the grazing condition to determine an effective one-dimensional map that captures the essentials of the chaotic behavior. This map is discontinuous and has strong similarities with the universal limit mapping in grazing bifurcations derived in the context of impacting mechanical systems [A. B. Nordmark, Phys. Rev. E 55, 266 (1997)].