In this paper we present a biorealistic model for the first part of the early vision of processing by incorporating memristive nanodevices. The architecture of the proposed network is based on the organization and functioning of the outer plexiform layer (OPL) in the vertebrate retina. We demonstrate that memristive devices are indeed a valuable building block for neuromorphic architectures, as their highly nonlinear and adaptive response could be exploited for establishing ultradense networks with dynamics similar to that of their biological counterparts. We particularly show that hexagonal memristive grids can be employed for faithfully emulating the smoothing effect occurring in the OPL to enhance the dynamic range of the system. In addition, we employ a memristor-based thresholding scheme for detecting the edges of grayscale images, while the proposed system is also evaluated for its adaptation and fault tolerance capacity against different light or noise conditions as well as its distinct device yields.

Fluctuation-dissipation theorems can be used to predict characteristics of noise from characteristics of the macroscopic response of a system. In the case of gene networks, feedback control determines the “network rigidity,” defined as resistance to slow external changes. We propose an effective Fokker-Planck equation that relates gene expression noise to topology and to time scales of the gene network. We distinguish between two situations referred to as normal and inverted time hierarchies. The noise can be buffered by network feedback in the first situation, whereas it can be topology independent in the latter.

We study the shape and texture of finite domains comprising chiral or achiral molecules carrying tilt, embedded in a two-dimensional surface or membrane, using a combination of simulations and exact variational calculations. We find a variety of shapes and textures including rectangular-shaped domains and a spontaneously broken chiral texture, when the molecules are achiral. We show that chiral tilt domains nucleating in a region of two-phase coexistence repel each other, thereby preventing coalescence and further growth. Our work principally addresses observations of domains in multicomponent giant unilamellar vesicles. It may also be relevant in the study of domains in phospholipid monolayers, nucleating domains of Sm-C${}^{*}$ in Sm-A films, and chiral emulsions in Sm-A films, in situations where we can ignore dipolar interactions.

Electronic transport through chaotic quantum dots exhibits universal, system-independent properties, consistent with random-matrix theory. The quantum transport can also be rooted, via the semiclassical approximation, in sums over the classical scattering trajectories. Correlations between such trajectories can be organized diagrammatically and have been shown to yield universal answers for some observables. Here, we develop the general combinatorial treatment of the semiclassical diagrams, through a connection to factorizations of permutations. We show agreement between the semiclassical and random matrix approaches to the moments of the transmission eigenvalues. The result is valid for all moments to all orders of the expansion in inverse channel number for all three main symmetry classes (with and without time-reversal symmetry and spin-orbit interaction) and extends to nonlinear statistics. This finally explains the applicability of random-matrix theory to chaotic quantum transport in terms of the underlying dynamics as well as providing semiclassical access to the probability density of the transmission eigenvalues.

In our busy lives, almost all of us have to walk with a cup of coffee. While often we spill the drink, this familiar phenomenon has never been explored systematically. Here we report on the results of an experimental study of the conditions under which coffee spills for various walking speeds and initial liquid levels in the cup. These observations are analyzed from the dynamical systems and fluid mechanics viewpoints as well as with the help of a model developed here. Particularities of the common cup sizes, the coffee properties, and the biomechanics of walking proved to be responsible for the spilling phenomenon. The studied problem represents an example of the interplay between the complex motion of a cup, due to the biomechanics of a walking individual, and the low-viscosity-liquid dynamics in it.

For the nonlinear Shrödinger equation with disorder it was found numerically that in some regime of the parameters Anderson localization is destroyed and subdiffusion takes place for a long time interval. It was argued that the nonlinear term acts as random noise. In the present work, the properties of this effective noise are studied numerically. Some assumptions made in earlier work were verified, and fine details were obtained. The dependence of various quantities on the localization length of the linear problem were computed. A scenario for the possible breakdown of the theory for a very long time is outlined.

Based on the soliton solution on a continuous wave background for an integrable Hirota equation, the reduction mechanism and the characteristics of the Peregrine rogue wave in the propagation of femtosecond pulses of optical fiber are discussed. The results show that there exist two processes of the formation of the Peregrine rogue wave: one is the localized process of the continuous wave background, and the other is the reduction process of the periodization of the bright soliton. The characteristics of the Peregrine rogue wave are exhibited by strong temporal and spatial localization. Also, various initial excitations of the Peregrine rogue wave are performed and the results show that the Peregrine rogue wave can be excited by a small localized (single peak) perturbation pulse of the continuous wave background, even for the nonintegrable case. The numerical simulations show that the Peregrine rogue wave is unstable. Finally, through a realistic example, the influence of the self-frequency shift to the dynamics of the Peregrine rogue wave is discussed. The results show that in the absence of the self-frequency shift, the Peregrine rogue wave can split into several subpulses; however, when the self-frequency shift is considered, the Peregrine rogue wave no longer splits and exhibits mainly a peak changing and an increasing evolution property of the field amplitude.

We report on a granular experiment that produces multiple quasiperiodic pattern solutions in a rotating flat container filled with a bidisperse mixture of grains. The observed dynamics show a pronounced spatiotemporally periodic drift of segregated patterns. In the course of long experiment durations, the system switches between different states that appear to be stable oscillatory solutions over many periods. In the long-term limit, the system does not tend toward a stationary state. The results complement and extend previous observations in cylindrical geometries, and represent a challenge for modeling and theoretical description.

We study a model of two-dimensional interacting monomers which has two symmetric absorbing states and exhibits two kinds of phase transition; one is an order-disorder transition and the other is an absorbing phase transition. Our focus is around the order-disorder transition, and we investigate whether this transition is described by the critical exponents of the two-dimensional Ising model. By analyzing the relaxation dynamics of “staggered magnetization,” the finite-size scaling, and the behavior of the magnetization in the presence of a symmetry-breaking field, we show that this model should belong to the Ising universality class. Our results along with the universality hypothesis support the idea that the order-disorder transition in two-dimensional models with two symmetric absorbing states is of the Ising universality class, contrary to the recent claim [K. Nam et al., J. Stat. Mech.: Theory Exp. (2011) L06001]. Furthermore, we illustrate that the Binder cumulant could be a misleading guide to the critical point in these systems.

We propose a kinetic mechanism of electrochemical interactions. We assume fast formation and recombination of electron donors ${\mathcal{D}}^{-}$ and acceptors ${\mathcal{A}}^{+}$ on electrode surfaces. These mediators are continuously formed in the electrode matter by thermal fluctuations. The mediators ${\mathcal{D}}^{-}$ and ${\mathcal{A}}^{+}$, chemically equivalent to the electrode metal, enter electrochemical interactions on the electrode surfaces. Electrochemical dynamics and current-voltage characteristics of a selected electrochemical system are studied. Our results are in good qualitative agreement with those given by the classical Butler-Volmer kinetics. The proposed model can be used to study fast electrochemical processes in microsystems and nanosystems that are often out of the thermal equilibrium. Moreover, the kinetic mechanism operates only with the surface concentrations of chemical reactants and local electric potentials, which facilitates the study of electrochemical systems with indefinable bulk.

We consider the class of short rate interest rate models for which the short rate is proportional to the exponential of a Gaussian Markov process $x\left(t\right)$ in the terminal measure $r\left(t\right)=a\left(t\right)\exp \left[x\right(t\left)\right]$. These models include the Black-Derman-Toy and Black-Karasinski models in the terminal measure. We show that such interest rate models are equivalent to lattice gases with attractive two-body interaction, $V(t_1,t_2)=-\text{Cov}[x\left(t_1\right),x\left(t_2\right)]$. We consider in some detail the Black-Karasinski model with $x\left(t\right)$ as an Ornstein-Uhlenbeck process, and show that it is similar to a lattice gas model considered by Kac and Helfand, with attractive long-range two-body interactions, $V(x,y)=-\alpha (e^{-\gamma |x-y|}-e^{-\gamma (x+y)})$. An explicit solution for the model is given as a sum over the states of the lattice gas, which is used to show that the model has a phase transition similar to that found previously in the Black-Derman-Toy model in the terminal measure.

We investigate the Schelling model of social segregation, formulated as an intrinsically nonequilibrium system, in which the agents occupy districts (or patches) rather than sites on a grid. We show that this allows the equations governing the dynamical behavior of the model to be derived. Analysis of these equations reveals a jamming transition in the regime of low-vacancy density, and inclusion of a spatial dimension in the model leads to a pattern forming instability. Both of these phenomena exhibit unusual characteristics which may be studied through our approach.

We study the position fluctuations of interacting particles aligned in a finite cell that avoid any crossing in equilibrium with a thermal bath. The focus is put on the influence of the confining force directed along the cell length. We show that the system may be modeled as a 1D chain of particles with identical masses, linked with linear springs of varying spring constants. The confining force may be accounted for by linear springs linked to the walls. When the confining force range is increased toward the inside of the chain, a paradoxical behavior is exhibited. The outermost particles fluctuations are enhanced, whereas those of the inner particles are reduced. A minimum of fluctuations is observed at a distance of the cell extremities that scales linearly with the confining force range. Those features are in very good agreement with the model. Moreover, the simulations exhibit an asymmetry in their fluctuations which is an anharmonic effect. It is characterized by the measurement of the skewness, which is found to be strictly positive for the outer particles when the confining force is short ranged.

We show that a quenched and relaxed completely integrable system is hardly distinguishable from the corresponding generalized Gibbs ensemble in a dynamical sense. To be specific, the response of the quenched and relaxed system to a second quench can be accurately reproduced by using the generalized Gibbs ensemble as a substitute. Remarkably, as demonstrated with the transverse Ising model and the hard-core bosons in one dimension, not only the steady values but even the transient, relaxation dynamics of the physical variables can be accurately reproduced by using the generalized Gibbs ensemble as a pseudoinitial state. This result is an important complement to the previously established result that a quenched and relaxed system is hardly distinguishable from the generalized Gibbs ensemble in a static sense. The relevance of the generalized Gibbs ensemble in the nonequilibrium dynamics of completely integrable systems is then greatly strengthened.

Estimations of an underlying rate from data points are inevitably disturbed by the irregular occurrence of events. Proper estimation methods are designed to avoid overfitting by discounting the irregular occurrence of data, and to determine a constant rate from irregular data derived from a constant probability distribution. However, it can occur that rapid or small fluctuations in the underlying density are undetectable when the data are sparse. For an estimation method, the maximum degree of undetectable rate fluctuations is uniquely determined as a phase transition, when considering an infinitely long series of events drawn from a fluctuating density. In this study, we analytically examine an optimized histogram and a Bayesian rate estimator with respect to their detectability of rate fluctuation, and determine whether their detectable-undetectable phase transition points are given by an identical formula defining a degree of fluctuation in an underlying rate. In addition, we numerically examine the variational Bayes hidden Markov model in its detectability of rate fluctuation, and determine whether the numerically obtained transition point is comparable to those of the other two methods. Such consistency among these three principled methods suggests the presence of a theoretical limit for detecting rate fluctuations.

Based on the difference between a spanning cluster and a wrapping cluster, an alternative criterion for testing wrapping percolation is provided for two-dimensional lattices. By following the Newman-Ziff method, the finite size scalings of estimates for percolation thresholds are given. The results are consistent with those from Machta's method.

Using a Markov chain approach we rederive the exact density functional for hard-rod mixtures on a one-dimensional lattice, which forms the basis of the lattice fundamental measure theory. The transition probability in the Markov chain depends on a set of occupation numbers, which reflects the property of a zero-dimensional cavity to hold at most one particle. For given mean occupation numbers (density profile), an exact expression for the equilibrium distribution of microstates is obtained, which means an expression for the unique external potential that generates the density profile in equilibrium. By considering the rod ends to fall onto lattice sites, the mixture is always additive.

Spiral waves subjected to an external periodic force exhibit very rich spatiotemporal dynamics including resonance attractors. In previous research, the modulation was mainly described as additional induced flow in the system, and a theory has been developed based on reducing the spiral wave dynamics to a low-dimensional map. In this paper, another perspective for study of the resonance attractors is suggested. The periodic modulation of excitability is directly described by the time dependence of the parameters. This approach gives us nice results that are well consistent with the experiments. Additionally, when we force the spiral with a frequency larger than its intrinsic frequency, another branch of spiral meandering with qualitatively different properties is observed. Full resonances are also clearly indicated. Furthermore, a kinetic model for spiral movement suggested in our previous paper is applied to this case. The theoretical results are in good quantitative agreement with numerical simulations. The model could be widely used in different excitable systems.

We theoretically explore the eigenstates of a coupled $p$:$q$ commensurate harmonic oscillator with SU(2) coupling interactions under the canonical transformation. The spatial patterns of the high-order eigenstates are found to be markedly localized on Lissajous figures from single to multiple periodic orbits. Controlling the pumping size in large-Fresnel-number degenerate cavities, we have experimentally observed the laser transverse modes that display the wave patterns to be analogous to the derived eigenstates.