We provide a macroscale description of electrokinetic particle-electrode interactions at high frequencies, where chemical reactions at the electrodes are negligible. Using a thin-double-layer approximation, our starting point is the set of macroscale equations governing the “bounded” configuration comprising of a particle suspended between two electrodes, wherein the electrodes are governed by a capacitive charging condition and the imposed voltage is expressed as an integral constraint. In the large-cell limit the bounded model is transformed into an effectively equivalent “unbounded” model describing the interaction between the particle and a single electrode, where the imposed-voltage condition is manifested in a uniform field at infinity together with a Robin-type condition applying at the electrode. This condition, together with the standard no-flux condition applying at the particle surface, leads to a linear problem governing the electric potential in the fluid domain in which the dimensionless frequency $\omega$ of the applied voltage appears as a governing parameter. In the high-frequency limit $\omega \gg 1$ the flow is dominated by electro-osmotic slip at the particle surface, the contribution of electrode electro-osmosis being $O\left({\omega }^{-2}\right)$ small. That simplification allows for a convenient analytical investigation of the prevailing case where the clearance between the particle and the adjacent electrode is small. Use of tangent-sphere coordinates allows to calculate the electric and flows fields as integral Hankel transforms. At large distances from the particle, along the electrode, both fields decay with the fourth power of distance.

We study a strongly adsorbed flexible polyelectrolyte chain on tori. In this generalized Thomson problem, the patterns of the adsorbed chain are analyzed in the space of the toroidal coordinates and in terms of the orientation of each chain segment. Various patterns are found, including double spirals, disclination-like structures, Janus tori, and uniform wrappings, arising from the long-range electrostatic interaction and the toroidal geometry. Their broken mirror symmetry is quantitatively characterized by introducing an order parameter, an integral of the torsion. The uniform packing, which breaks the mirror symmetry the least, has the lowest value of the order parameter. In addition, it is found that the electrostatic energy of confined chains on tori conforms to a power law regardless of the screening effect in some typical cases studied. Furthermore, we study random walks on tori that generate chain configurations in the large screening limit or at large thermal fluctuation; some features associated with the toroidal geometry are discussed.

We use a stochastic Markovian dynamics approach to describe the spreading of vector-transmitted diseases, such as dengue, and the threshold of the disease. The coexistence space is composed of two structures representing the human and mosquito populations. The human population follows a susceptible-infected-recovered (SIR) type dynamics and the mosquito population follows a susceptible-infected-susceptible (SIS) type dynamics. The human infection is caused by infected mosquitoes and vice versa, so that the SIS and SIR dynamics are interconnected. We develop a truncation scheme to solve the evolution equations from which we get the threshold of the disease and the reproductive ratio. The threshold of the disease is also obtained by performing numerical simulations. We found that for certain values of the infection rates the spreading of the disease is impossible, for any death rate of infected mosquitoes.

A simple model for the force-dependent unwinding and rewinding rates of the nucleosome inner turn is constructed and quantitatively compared to the results of recent measurements [A. H. Mack et al., J. Mol. Biol. 423, 687 (2012)]. First, a coarse-grained model for the histone-DNA free-energy landscape that incorporates both an elastic free-energy barrier and specific histone-DNA bonds is developed. Next, a theoretical expression for the rate of transitions across a piecewise linear free-energy landscape with multiple minima and maxima is presented. Then, the model free-energy landscape, approximated as a piecewise linear function, and the theoretical expression for the transition rates are combined to construct a model for the force-dependent unwinding and rewinding rates of the nucleosome inner turn. Least-mean-squares fitting of the model rates to the rates observed in recent experiments rates demonstrates that this model is able to well describe the force-dependent unwinding and rewinding rates of the nucleosome inner turn, observed in the recent experiments, except at the highest forces studied, where an additional ad hoc term is required to describe the data, which may be interpreted as an indication of an alternate high-force nucleosome disassembly pathway, that bypasses simple unwinding. The good agreement between the measurements and the model at lower forces demonstrates that both specific histone-DNA contacts and an elastic free-energy barrier play essential roles for nucleosome winding and unwinding, and quantifies their relative contributions.

A variation of the Brownian ratchet mechanism for the force generated by the combination of the random motion and the ratchet structure is proposed and simulated with granular chains moving randomly on periodic ratchet plates. The present mechanism differs from the flashing ratchet model of the kinesin-microtubule molecular motor. When the bead chain bounces against the periodic ratchet, the chain as a whole will gain an impulse in the direction of the long side (the side with smaller slope). The observed behaviors of the simulating system, including (i) the force-velocity relation, (ii) the stall force as a function of the number of chains, (iii) the increase of velocity with the excitation, and (iv) the appearance of steps at low velocity and its distribution function, are similar to the corresponding ones of the kinesin-microtubule system.

An extension of the Truscott-Brindley model [Bull. Math. Biol. 56, 981 (1994)] is derived to account for the effect of demographic fluctuations. In the presence of seasonal forcing and sufficiently shallow water conditions, the fluctuations induced by the discreteness of the zooplankton component appear sufficient to cause switching between the bloom and no-bloom cycles predicted at the mean-field level by the model. The destabilization persists in the thermodynamic limit of a water basin infinitely extended in the horizontal direction.

Recent work has revealed a law governing flux fluctuation and the average flux in complex dynamical systems. We establish the universality of this flux-fluctuation law through the following steps: (i) We derive the law in a more general setting, showing that it depends on a single parameter characterizing the external driving; (ii) we conduct extensive numerical computations using distinct external driving, different network topologies, and multiple traffic routing strategies; and (iii) we analyze data from an actual vehicle traffic system in a major city in China to lend more credence to the universality of the flux-fluctuation law. Additional factors considered include flux fluctuation on links, window size effect, and hidden topological structures such as nodal degree correlation. Besides its fundamental importance in complex systems, the flux-fluctuation law can be used to infer certain intrinsic property of the system for potential applications such as control of complex systems for improved performance.

Contrarian behavior is a kind of self-organization in complex adaptive systems (CASs). Here we report the existence of a transition point in a model resource-allocation CAS with contrarian behavior by using human experiments, computer simulations, and theoretical analysis. The resource ratio and system predictability serve as the tuning parameter and order parameter, respectively. The transition point helps to reveal the positive or negative role of contrarian behavior. This finding is in contrast to the common belief that contrarian behavior always has a positive role in resource allocation, say, stabilizing resource allocation by shrinking the redundancy or the lack of resources. It is further shown that resource allocation can be optimized at the transition point by adding an appropriate size of contrarians. This work is also expected to be of value to some other fields ranging from management and social science to ecology and evolution.

The basic ingredients in a semiclassical theory are the classical invariant objects serving as a support for quantization. Recent studies, mainly obtained on quantum maps, have led to the commonly accepted belief that the classical repeller—the set of nonescaping orbits in the future and past evolution—is the object that suitably plays this role in open scattering systems. In this paper we present numerical evidence warning that this may not always be the case. For this purpose we study recently introduced families of tribaker maps [L. Ermann, G. G. Carlo, J. M. Pedrosa, and M. Saraceno, Phys. Rev. E 85, 066204 (2012)], which share the same asymptotic properties but differ in their short-time behavior. We have found that although the eigenvalue distribution of the evolution operator of these maps follows the fractal Weyl law prediction, the theory of short periodic orbits for open maps fails to describe the resonance eigenfunctions of some of them. This is a strong indication that new elements must be included in the semiclassical description of open quantum systems. We provide an interpretation of the results in order to have hints about them.

We measure the swimming speed of a cylindrical version of Taylor's swimming sheet in viscoelastic fluids, and find that depending on the rheology, the speed can either increase or decrease relative to the speed in a Newtonian viscous fluid. The swimming stroke of the sheet is a prescribed propagating wave that travels along the sheet in the azimuthal direction. The measurements are performed with the sheet immersed in a fluid inside a cylindrical tank under torque-free conditions. Swimming speeds in the Newtonian case are found to be consistent with calculations using the Stokes equation. A faster swimming speed is found in a viscoelastic fluid that has a viscosity independent of shear rate. By contrast, a slower swimming speed is found with more complex shear-thinning viscoelastic fluids which have multiple relaxation time scales as well. These results are compared with calculations with Oldroyd-B fluids which find a decreasing swimming speed with Deborah number given by the product of the fluid elastic relaxation time scale and the driving frequency.

We investigate the dynamics of a special group of runaway electrons which possibly play an important role in toroidal fusion devices. Starting from the torus center they are accelerated by a toroidal electric field and are hence forced to move across the toroidal magnetic field into regions with rising poloidal field in order to compensate for the centrifugal forces. Can such particles finally form a tight beam of relativistic runaways in the outboard region or is this prevented due to the perpendicular momentum they gain by passing the toroidal field? Since neither the energy nor the magnetic momentum of the particles is conserved this question has been treated by invoking the relativistic equations of motion. It turns out, however, that the problem can be essentially simplified since, apart from the centrifugal forces associated with the toroidal motion, the inertia forces are negligible. The resulting first order equation can be solved analytically. From the solution it is concluded that the formation of narrow runaway beams with diameters in the range of micrometers and very small pitch angles ($v_{\perp }/v_{\left|\right|}<{10}^{-6}$) appears feasible. Such electrons would perform low-frequency oscillations about three to four orders of magnitude lower than the gyrofrequency in the toroidal field. When passing the maximum poloidal magnetic field strength they are suddenly lost from the plasma region.

We present a master equation approach to the study of the bulk-mediated surface diffusion mechanism in a three-dimensional confined domain. The proposed scheme allowed us to evaluate analytically a number of magnitudes that were used to characterize the efficiency of the bulk-mediated surface transport mechanism, for instance, the mean escape time from the domain, and the mean number of distinct visited sites on the confined domain boundary.

In this paper we consider a stochastic process that may experience random reset events which suddenly bring the system to the starting value and analyze the relevant statistical magnitudes. We focus our attention on monotonic continuous-time random walks with a constant drift: The process increases between the reset events, either by the effect of the random jumps, or by the action of the deterministic drift. As a result of all these combined factors interesting properties emerge, like the existence (for any drift strength) of a stationary transition probability density function, or the faculty of the model to reproduce power-law-like behavior. General formulas for two extreme statistics, the survival probability, and the mean exit time are also derived. To corroborate in an independent way the results of the paper, Monte Carlo methods were used. These numerical estimations are in full agreement with the analytical predictions.

The position of an invasion front, propagating into an unstable state, fluctuates because of the shot noise coming from the discreteness of reacting particles and stochastic character of the reactions and diffusion. A recent macroscopic theory [Meerson and Sasorov, Phys. Rev. E 84, 030101(R) (2011)] yields the probability of observing, during a long time, an unusually slow front. The theory is formulated as an effective Hamiltonian mechanics which operates with the density field and the conjugate “momentum” field. Further, the theory assumes that the most probable density field history of an unusually slow front represents, up to small corrections, a traveling front solution of the Hamilton equations. Here we verify this assumption by solving the Hamilton equations numerically for models belonging to the directed percolation universality class.

The thermalization phenomenon and many-body quantum statistical properties are studied on the example of several observables in isolated spin-chain systems, both integrable and generic nonintegrable. While diagonal matrix elements for nonintegrable models comply with the eigenstate thermalization hypothesis, the integrable systems show evident deviations and similarity to properties of noninteracting many-fermion models. The finite-size scaling reveals that the crossover between the two regimes is given by a scale closely related to the scattering length. Low-frequency off-diagonal matrix elements related to dc transport quantities also follow in a generic system a behavior analogous to the eigenstate thermalization hypothesis, however, unrelated to one of the diagonal matrix elements.

We study the stationary probability distribution of a system driven by shot noise. We find that both in the overdamped and underdamped regime, the coordinate distribution displays power-law singularities in its central part. For sufficiently low rate of noise pulses they correspond to distribution peaks. We find the positions of the peaks and the corresponding exponents. In the underdamped regime the peak positions are given by a geometric progression. The energy distribution in this case also displays multiple peaks with positions given by a geomet-ric progression. Such structure is a signature of the shot-noise induced fluctuations. The analytical results are in excellent agreement with numerical simulations.

We present a study of the bend angle distribution of semiflexible polymers of short and intermediate lengths within the wormlike chain model. This enables us to calculate the elastic response of a stiff molecule to a bending moment. Our results go beyond the Hookean regime and explore the nonlinear elastic behavior of a single molecule. We present analytical formulas for the bend angle distribution and for the moment-angle relation. Our analytical study is compared against numerical Monte Carlo simulations. The functional forms derived here can be applied to fluorescence microscopic studies on actin and DNA. Our results are relevant to recent studies of “kinks” and cyclization in short and intermediate length DNA strands.

Critical adsorption of a lattice self-avoiding bond fluctuation polymer chain confined between two parallel impenetrable surfaces is studied using the Monte Carlo method. The dependence of the mean contact number $\langle M\rangle$ on the temperature $T$ and on the chain length $N$ is simulated for a polymer-surface interaction $E=-1$. A critical adsorption of the polymer is found at $T_c=1.65$ for large surface separation distance $D>N^{\nu }b$, whereas no critical adsorption is observed for small distance $D<N^{\nu }b$, where ν ≈ 0.58 is the Flory exponent and $b$ is the mean bond length. The critical adsorption point $T_c=1.65$ is the same as that of a grafted polymer. Normal diffusion is observed for the confined polymer; however, the diffusion rate is dependent on the temperature and surface separation distance.

Dynamical behaviors of the competitive Lotka-Volterra system even for 3 species are not fully understood. In this paper, we study this problem from the perspective of the Lyapunov function. We construct explicitly the Lyapunov function using three examples of the competitive Lotka-Volterra system for the whole state space: $\left(1\right)$ the general 2-species case, $\left(2\right)$ a 3-species model, and $\left(3\right)$ the model of May-Leonard. The basins of attraction for these examples are demonstrated, including cases with bistability and cyclical behavior. The first two examples are the generalized gradient system, where the energy dissipation may not follow the gradient of the Lyapunov function. In addition, under a new type of stochastic interpretation, the Lyapunov function also leads to the Boltzmann-Gibbs distribution on the final steady state when multiplicative noise is added.

An asymptotic approach is utilized in order to obtain a unified description of the propagated field dynamics due to an input Gaussian-modulated harmonic wave of arbitrary initial pulse width in a linear, causally dispersive gain medium, described by the single resonance Lorentz model. The asymptotic method of analysis is applied on the unified, exact integral representation of the propagated field, which is characterized by a unified complex phase function that depends upon the input field and gain medium parameters as well as upon the propagation distance in the medium. In order to apply the asymptotic method, an analysis of the evolution of the saddle point locations, which depend upon the dispersive properties of the gain medium, the temporal width, and the carrier frequency of the input Gaussian pulse as well as upon the propagation distance and of the topography of the real part of the unified phase function in the complex $\omega$ plane, must be performed. Upon the subsequent numerical application of the asymptotic method, the predictions of the unified asymptotic approach are found to be in exceptional agreement with the respective results of a purely numerical experiment for all considered initial pulse widths and lead to a unified model of Gaussian pulse propagation in a gain Lorentzian medium. According to this model, the propagated field is composed of pulse components, each being due to the asymptotic contribution of a respective relevant saddle point of the unified phase function. The instantaneous angular frequency of oscillation and the stationary point(s) of the envelope of each such pulse component are then obtained from the real and imaginary parts, respectively, of the corresponding relevant saddle point as it evolves in the complex $\omega$ plane. This theoretical approach may then yield particularly useful physical insights into attosecond pulse propagation.