We present a simplified description for spin-dependent electronic transport in honeycomb-lattice structures with spin-orbit interactions, using generalizations of the stochastic nonequilibrium model known as the totally asymmetric simple exclusion process. Mean field theory and numerical simulations are used to study currents, density profiles, and current polarization in quasi-one-dimensional systems with open boundaries, and externally imposed particle injection ($\alpha$) and ejection ($\beta$) rates. We investigate the influence of allowing for double site occupancy, according to Pauli's exclusion principle, on the behavior of the quantities of interest. We find that double occupancy shows strong signatures for specific combinations of rates, namely high $\alpha$ and low $\beta$, but otherwise its effects are quantitatively suppressed. Comments are made on the possible relevance of the present results to experiments on suitably doped graphenelike structures.

Statistical properties of the one-dimensional spring-block (Burridge-Knopoff) model of earthquakes obeying the rate- and state-dependent friction law are studied by extensive computer simulations. The quantities computed include the magnitude distribution, the rupture-length distribution, the main shock recurrence-time distribution, the seismic-time correlations before and after the main shock, the mean slip amount, and the mean stress drop at the main shock, etc. Events of the model can be classified into two distinct categories. One tends to be unilateral with its epicenter located at the rim of the rupture zone of the preceding event, while the other tends to be bilateral with enhanced “characteristic” features resembling the so-called “asperity.” For both types of events, the distribution of the rupture length $L_r$ exhibits an exponential behavior at larger sizes, $\approx exp[-L_r/L_0]$ with a characteristic “seismic correlation length” $L_0$. The mean slip as well as the mean stress drop tends to be rupture-length independent for larger events. The continuum limit of the model is examined, where the model is found to exhibit pronounced characteristic features. In the continuum limit, the characteristic rupture length $L_0$ is estimated to be $\sim 100$ [km]. This means that, even in a hypothetical homogenous infinite fault, events cannot be indefinitely large in the exponential sense, the upper limit being of order $\sim {10}^3$ kilometers. Implications to real seismicity are discussed.

We consider Landau-Zener tunneling of solitons in a weakly coupled two-channel system, for this purpose we construct a simple mechanical system using two weakly coupled chains of nonlinear oscillators with gradually decreasing (first chain) and increasing (second chain) masses. The model allows us to consider soliton propagation and Landau-Zener tunneling between the chains. It is shown that soliton tunneling characteristics become drastically dependent on its amplitude in nonlinear regime. The validity of the developed tunneling theory is justified via comparison with direct numerical simulations on oscillator ladder system.

Canards are special solutions to ordinary differential equations that follow invariant repelling slow manifolds for long time intervals. In realistic biophysical single-cell models, canards are responsible for several complex neural rhythms observed experimentally, but their existence and role in spatially extended systems is largely unexplored. We identify and describe a type of coherent structure in which a spatial pattern displays temporal canard behavior. Using interfacial dynamics and geometric singular perturbation theory, we classify spatiotemporal canards and give conditions for the existence of folded-saddle and folded-node canards. We find that spatiotemporal canards are robust to changes in the synaptic connectivity and firing rate. The theory correctly predicts the existence of spatiotemporal canards with octahedral symmetry in a neural field model posed on the unit sphere.

The current fluctuations of a driven resistor-inductor-diode circuit are investigated here looking for signatures of critical behavior monitored by the driving frequency. The experimentally obtained time series of the voltage drop across the resistor (as directly proportional to the current flowing through the circuit) were analyzed by means of the method of critical fluctuations in analogy to thermal critical systems. Intermittent criticality was revealed for a critical frequency band signifying the transition between the normal rectifier phase in the low frequencies and a full-wave conducting, capacitorlike phase in the high frequencies. The transition possesses critical characteristics with a characteristic exponent $p_l=1.65$. A fractal analysis in terms of the rescale range ($R/\phantom{RS}S$) and detrended fluctuation analysis methods yielded results fully compatible with the critical dynamics analysis. Suggestions for the interpretation of the observed behavior in terms of $p\text{−}n$ junction operation are discussed.

The shape equation and linking conditions for a vesicle with two phase domains are derived. We refine the conjecture on the general neck condition for the limit shape of a budding vesicle proposed by Jülicher and Lipowsky [Phys. Rev. Lett. 70, 2964 (1993); Phys. Rev. E 53, 2670 (1996)], and then we use the shape equation and linking conditions to prove that this conjecture holds not only for axisymmetric budding vesicles, but also for asymmetric ones. Our study reveals that the mean curvature at any point on the membrane segments adjacent to the neck satisfies the general neck condition for the limit shape of a budding vesicle when the length scale of the membrane segments is much larger than the characteristic size of the neck but still much smaller than the characteristic size of the vesicle.

We present an optimal detrended fluctuation analysis (DFA) and apply it to evaluate the local roughness exponent in nonequilibrium surface growth models with mounded morphology. Our method consists in analyzing the height fluctuations computing the shortest distance of each point of the profile to a detrending curve that fits the surface within the investigated interval. We compare the optimal DFA (ODFA) with both the standard DFA and nondetrended analysis. We validate the ODFA method considering a one-dimensional model in the Kardar-Parisi-Zhang universality class starting from a mounded initial condition. We applied the methods to the Clarke-Vvedensky (CV) model in $2+1$ dimensions with thermally activated surface diffusion and absence of step barriers. It is expected that this model belongs to the nonlinear molecular beam epitaxy (nMBE) universality class. However, an explicit observation of the roughness exponent in agreement with the nMBE class was still missing. The effective roughness exponent obtained with ODFA agrees with the value expected for the nMBE class, whereas using the other methods it does not agree. We also characterize the transient anomalous scaling of the CV model and obtained that the corresponding exponent is in agreement with the value reported for other nMBE models with weaker corrections to the scaling.

One of the well-known problems of hydrodynamics is studied: the problem of classification of vortex knots for ideal fluid flows. In the literature there are known Moffatt statements that all torus knots $K_{m,n}$ for all rational numbers $m/n$ ($0<m/n<\infty$) are realized as vortex knots for each one of the considered axisymmetric fluid flows. We prove that actually such a uniformity does not exist because it does not correspond to the facts. Namely, we derive a complete classification of all vortex knots realized for the fluid flows studied by Moffatt and demonstrate that the real structure of vortex knots is much more rich because the sets of mutually nonisotopic vortex knots realized for different axisymmetric fluid flows are all different. An exact formula for the limit of the hydrodynamic safety factor $q_h$ at a vortex axis is derived for arbitrary axisymmetric fluid equilibria. Another exact formula is obtained for the limit of the magnetohydrodynamics safety factor $q$ at a magnetic axis for the general axisymmetric plasma equilibria.

By means of hybrid multiparticle collsion–particle-in-cell (MPC-PIC) simulations we study the dynamical scaling of energy and density correlations at equilibrium in moderately coupled two-dimensional (2D) and quasi-one-dimensional (1D) plasmas. We find that the predictions of nonlinear fluctuating hydrodynamics for the structure factors of density and energy fluctuations in 1D systems with three global conservation laws hold true also for 2D systems that are more extended along one of the two spatial dimensions. Moreover, from the analysis of the equilibrium energy correlators and density structure factors of both 1D and 2D neutral plasmas, we find that neglecting the contribution of the fluctuations of the vanishing self-consistent electrostatic fields overestimates the interval of frequencies over which the anomalous transport is observed. Such violations of the expected scaling in the currents correlation are found in different regimes, hindering the observation of the asymptotic scaling predicted by the theory.

The role of spatial resolution of the electron gyroradius in electrostatic particle-in-cell (PIC) simulations is studied. It is demonstrated that resolving the gyroradius is crucial for simulations of strongly magnetized plasmas and that nonresolving it results in substantial anisotropic heating of electrons. The numerical heating can, in some cases, be suppressed by the higher-order weighting to the grid, but it cannot be avoided. Possible mechanisms behind this numerical heating are discussed. The study is carried out with a fully three dimensional electrostatic PIC code with an external magnetic and electric fields.

A generalized phase-space kinetic Boltzmann equation for highly nonequilibrium charged particle transport via localized and delocalized states is used to develop continuity, momentum, and energy balance equations, accounting explicitly for scattering, trapping and detrapping, and recombination loss processes. Analytic expressions detail the effect of these microscopic processes on mobility and diffusivity. Generalized Einstein relations (GER) are developed that enable the anisotropic nature of diffusion to be determined in terms of the measured field dependence of the mobility. Interesting phenomena such as negative differential conductivity and recombination heating and cooling are shown to arise from recombination loss processes and the localized and delocalized nature of transport. Fractional transport emerges naturally within this framework through the appropriate choice of divergent mean waiting time distributions for localized states, and fractional generalizations of the GER and mobility are presented. Signature impacts on time-of-flight current transients of recombination loss processes via both localized and delocalized states are presented.

The combination of bistability and noise is ubiquitous in complex systems, from biology to social interactions, and has important implications for their functioning and resilience. Here we use a simple three-state dynamical process, in which nodes go from one pole to another through an intermediate state, to show that noise can induce polarization switching in bistable systems if dynamical correlations are significant. In large, fully connected networks, where dynamical correlations can be neglected, increasing noise yields a collapse of bistability to an unpolarized configuration where the three possible states of the nodes are equally likely. In contrast, increased noise induces abrupt and irreversible polarization switching in sparsely connected networks. In multiplexes, where each layer can have a different polarization tendency, one layer is dominant and progressively imposes its polarization state on the other, offsetting or promoting the ability of noise to switch its polarization. Overall, we show that the interplay of noise and dynamical correlations can yield discontinuous transitions between extremes, which cannot be explained by a simple mean-field description.

We study extensively the forget-remember mechanism (FRM) for message spreading, originally introduced in Eur. Phys. J. B 62, 247 (2008). The freedom of specifying forget-remember functions governing the FRM can enrich the spreading dynamics to a very large extent. The master equation is derived for describing the FRM dynamics. By applying the mean field techniques, we have shown how the steady states can be reached under certain conditions, which agrees well with the Monte Carlo simulations. The distributions of forget and remember times can be explicitly given when the forget-remember functions take linear or exponential forms, which might shed some light on understanding the temporal nature of diseases like flu. For time-dependent FRM there is an epidemic threshold related to the FRM parameters. We have proven that the mean field critical transmissibility for the SIS model and the critical transmissibility for the SIR model are the lower and the the upper bounds of the critical transmissibility for the FRM model, respectively.

We study the rheology of suspensions of ice crystals at moderate to high volume fractions in a sucrose solution in which they are partially soluble, a model system for a wide class of crystal mushes or slurries. Under step changes in shear rate, the viscosity changes to a relaxed value over several minutes, in a manner well fitted by a single exponential. The behavior of the relaxed viscosity is power-law shear thinning with shear rate, with an exponent of $-1.76\pm 0.25$, so that shear stress falls with increasing shear rate. On longer time scales, the crystals ripen (leading to a falling viscosity) so that the mean radius increases with time to the power $0.14\pm 0.07$. We speculate that this unusually small exponent is due to the interaction of classical ripening dynamics with abrasion or breakup under flow. We compare the rheological behavior to mechanistic models based on flow-induced aggregation and breakup of crystal clusters, finding that the exponents can be predicted from liquid phase sintering and breakup by brittle fracture.

We study a complex plasma under microgravity conditions that is first stabilized with an oscillating electric field. Once the stabilization is stopped, the so-called heartbeat instability develops. We study how the kinetic energy spectrum changes during and after the onset of the instability and compare with the double cascade predicted by Kraichnan and Leith for two-dimensional turbulence. The onset of the instability manifests clearly in the ratio of the reduced rates of cascade of energy and enstrophy and in the power-law exponents of the energy spectra.

We modify the path integral representation of exciton transport in open quantum systems such that an exact description of the quantum fluctuations around the classical evolution of the system is possible. As a consequence, the time evolution of the system observables is obtained by calculating the average of a stochastic difference equation which is weighted with a product of pseudoprobability density functions. From the exact equation of motion one can clearly identify the terms that are also present if we apply the truncated Wigner approximation. This description of the problem is used as a basis for the derivation of a new approximation, whose validity goes beyond the truncated Wigner approximation. To demonstrate this we apply the formalism to a donor-acceptor transport model.

Adaptation is a crucial biological function possessed by many sensory systems. In this paper, we show that the fluctuation-dissipation theorem (FDT) serves as an ideal mathematical tool to study adaptation. With the aid of the nonequilibrium FDT developed by Seifert and Speck [Europhys. Lett. 89, 10007 (2010)], we demonstrate the nonequilibrium nature of adaptation in bacterial chemotaxis. We further show that nonequilibrium is a necessary condition for adaptation even beyond the linear response regime using the spectral theory of generator matrices. In particular, the results of this paper are irrelevant to the specific functional forms of the model parameters. This suggests that the nonequilibrium nature of adaptation is a topological property, rather than a geometric property, of the underlying biochemical reaction network.

The random-field Ising model is one of the few disordered systems where the perturbative renormalization group can be carried out to all orders of perturbation theory. This analysis predicts dimensional reduction, i.e., that the critical properties of the random-field Ising model in $D$ dimensions are identical to those of the pure Ising ferromagnet in $D-2$ dimensions. It is well known that dimensional reduction is not true in three dimensions, thus invalidating the perturbative renormalization group prediction. Here, we report high-precision numerical simulations of the 5D random-field Ising model at zero temperature. We illustrate universality by comparing different probability distributions for the random fields. We compute all the relevant critical exponents (including the critical slowing down exponent for the ground-state finding algorithm), as well as several other renormalization-group invariants. The estimated values of the critical exponents of the 5D random-field Ising model are statistically compatible to those of the pure 3D Ising ferromagnet. These results support the restoration of dimensional reduction at $D=5$. We thus conclude that the failure of the perturbative renormalization group is a low-dimensional phenomenon. We close our contribution by comparing universal quantities for the random-field problem at dimensions $3\le D<6$ to their values in the pure Ising model at $D-2$ dimensions, and we provide a clear verification of the Rushbrooke equality at all studied dimensions.

We investigate a Deffuant model on a ring by introducing two modifications: the repelling mechanism and the circular opinions. The repelling mechanism drives the opinions of two individuals away from each other and the circular opinions are defined on a circle. We find that the repelling mechanism tends to polarize the opinions of adjacent individuals and the circular opinions bring up a spatiotemporal pattern in which all individuals take different opinions but the opinion difference between two neighboring individuals tends to zero in the limit of the population size. In the Deffuant model with both repelling mechanism and the circular opinions, opinion dynamics depends on both the bounded confidence and the convergence rate. The interplay between the repelling mechanism and the circular opinion may give rise to time-dependent opinion dynamics.