In a previous paper [Phys. Rev. E 83, 051911 (2011)] we have shown that the results of a quantum-mechanical calculation of electronic energy transfer (EET) over aggregates of coupled monomers can be described also by a model of interacting classical electric dipoles in a weak-coupling approximation, which we referred to as the realistic coupling approximation (RCA). The method was illustrated by EET on a simple linear chain of molecules and also by energy transfer on an arrangement of monomers corresponding to that of the Fenna-Matthews-Olson (FMO) complex relevant for photosynthesis. The study was limited to electronic degrees of freedom, since this is the origin of coherent EET in the quantum case. Nevertheless, more realistic models of EET require the inclusion of the decohering effects of coupling to an environment, when the molecular aggregate becomes an open quantum system. Here we consider the quantum description of EET on a linear chain and on the FMO complex, incorporating environment coupling and constructing the classical version of the same systems in the density matrix formalism. The close agreement of the exact quantum and exact classical results in the RCA is demonstrated and justified analytically in the RCA. This lends further support to the conclusion that the coherence properties of EET in the FMO complex are evident at the classical level and should not be ascribed as solely due to quantum effects.

In this work we study a modified version of the majority-vote model with noise. In particular, we consider a random diluted square lattice wherein a site is empty with a probability $r$. In order to analyze the critical behavior of the model, we perform Monte Carlo simulations on lattices with linear sizes up to $L=140$. By means of a finite-size scaling analysis we estimate the critical noises $q_c$ and the critical ratios $\beta /\nu$, $\gamma /\nu$, and $1/\nu$ for some values of the probability $r$. Our results suggest that the critical exponents are different from those of the original model ($r=0$), but they are $r$ independent ($r>0$). In addition, if we consider that agents can diffuse through the lattice, the exponents remain the same, suggesting a new universality class for the majority-vote model with noise. Based on the numerical data, we may conjecture that the values of the exponents in this universality class are $\beta \sim 0.45$, $\gamma \sim 1.1$, and $\nu \sim 1.0$, which satisfy the scaling relation $2\beta +\gamma =d\nu =2$.

We establish a quantum Otto engine (QOE) of a two-level atom, which is confined in a one-dimensional (1D) harmonic trap and is coupled to single-mode radiation fields. Besides two adiabatic processes, the QOE cycle consists of two isochoric processes, along one of which the two-level atom as the working substance interacts with a single-mode radiation field. Based on the semigroup approach, we derive the time for completing any adiabatic process and then present a performance analysis of the heat engine model. Furthermore, we generalize the results to the performance optimization for a QOE of a single two-level atom trapped in a 1D power-law potential. Our result shows that the efficiency at maximum power output is dependent on the trap exponent $\theta$ but is independent of the energy spectrum index $\sigma$.

Transport phenomena in a one-dimensional system of interacting particles is studied. This system is embedded in a periodic and left-right asymmetric potential driven by a force periodic in time and space. When the density (number of particles per site) is an integer, directional current of the particles is collective; that is, it involves the whole system since all the sites are equivalents. On the other hand, when the system has a defect, a new localized or noncollective current appears due to the migration of defects from one site to another. We show here how this “defective” (defects generated) current can be controlled by white noise.

Successive vertical vibrations can cause a granular pack to rearrange and move to more and more dense configurations. The dilation of the pack that occurs during the vibrations is important to these rearrangements and the resulting compaction of the system. This paper presents an experimental study in which a confining force is used to limit the amount of dilation of the pack. These experiments show that the compaction is greatly reduced in the presence of a confining force. Systems with different shaking accelerations and different confining forces compact in the same way if the amount of dilation is the same. Under large confining forces, there is very little dilation. The resulting compaction when dilation is inhibited is very slow and may approach a final packing fraction of approximately 0.6, consistent with ideas of a critical packing fraction for the onset of dilation.

This paper shows that negative coefficients of normal restitution occur inevitably when the interaction force between colliding particles is finite. We derive an explicit criterion showing that for any set of material properties there is always a collision geometry leading to negative restitution coefficients. While from a phenomenological point of view, negative coefficients of normal restitution appear rather artificial, this phenomenon is generic and implies an important overlooked limitation of the widely used hard sphere model. The criterion is explicitly applied to two paradigmatic situations: for the linear dashpot model and for viscoelastic particles. In addition, we show that for frictional particles the phenomenon is less pronounced than for smooth spheres.

The unsteady growth of ammonium chloride dendrites during crystallization from an aqueous solution in a thin capillary is experimentally investigated. The dependence of the crystal area $S$ on the time $t$ for various sectors located along primary branches and side branches is measured. The hypothesis that the ratio between the area change and the area itself [$S^{\prime }\left(t\right)/S\left(t\right)$] is one and the same for different but simultaneously growing parts of an unsteady dendrite is advanced and confirmed. This conclusion allows a curve to be proposed to describe the evolution of the dendrite area (or its part), with the form $S\left(t\right)=\mathrm{const}t{}^a\exp (-bt)$, where $a$ and $b$ are the parameters whose values are determined in the paper. The nondimensionalization of $S$($t$) and $S^{\prime }\left(t\right)/S\left(t\right)$ (using the full dendrite growth time) produces simple one-parameter functions that depend on a single parameter $a$ (which is presumably associated only with the physical and chemical characteristics of the crystallized system and, in our case, is equal to $1.7\pm 0.2$).

Short-term changes in efficacy have been postulated to enhance the ability of synapses to transmit information between neurons, and within neuronal networks. Even at the level of connections between single neurons, direct confirmation of this simple conjecture has proven elusive. By combining paired-cell recordings, realistic synaptic modeling, and information theory, we provide evidence that short-term plasticity can not only improve, but also reduce information transfer between neurons. We focus on a concrete example in rat neocortex, but our results may generalize to other systems. When information is contained in the timings of individual spikes, we find that facilitation, depression, and recovery affect information transmission in proportion to their impacts upon the probability of neurotransmitter release. When information is instead conveyed by mean spike rate only, the influences of short-term plasticity critically depend on the range of spike frequencies that the target network can distinguish (its effective dynamic range). Our results suggest that to efficiently transmit information, the brain must match synaptic type, coding strategy, and network connectivity during development and behavior.

We investigate different dynamical regimes of the neuronal network in the CA3 area of the hippocampus. The proposed neuronal circuit includes two fast- and two slowly spiking cells which are interconnected by means of dynamical synapses. On the individual level, each neuron is modeled by FitzHugh-Nagumo equations. Three basic rhythmic patterns are observed: the gamma rhythm in which the fast neurons are uniformly spiking, the theta rhythm in which the individual spikes are separated by quiet epochs, and the theta-gamma rhythm with repeated patches of spikes. We analyze the influence of asymmetry of synaptic strengths on the synchronization in the network and demonstrate that strong asymmetry reduces the variety of available dynamical states. The model network exhibits multistability; this results in the occurrence of hysteresis in dependence on the conductances of individual connections. We show that switching between different rhythmic patterns in the network depends on the degree of synchronization between the slow cells.

Elements of networks interact in many ways, so modeling them with graphs requires multiple types of edges (or network layers). Here we show that such multiplex networks are generically more vulnerable to global cascades than simplex networks. We generalize the threshold cascade model [Watts, Proc. Natl. Acad. Sci. USA 99, 5766 (2002)] to multiplex networks, in which a node activates if a sufficiently large fraction of neighbors in any layer are active. We show that both combining layers (i.e., realizing other interactions play a role) and splitting a network into layers (i.e., recognizing distinct kinds of interactions) facilitate cascades. Notably, layers unsusceptible to global cascades can cooperatively achieve them if coupled. On one hand, this suggests fundamental limitations on predicting cascades without full knowledge of a system's multiplexity; on the other hand, it offers feasible means to control cascades by introducing or removing sparse layers in an existing network.

We present an approximated maximum likelihood method for the multifractal random walk processes of [E. Bacry et al., Phys. Rev. E 64, 026103 (2001)]. The likelihood is computed using a Laplace approximation and a truncation in the dependency structure for the latent volatility. The procedure is implemented as a package in the r computer language. Its performance is tested on synthetic data and compared to an inference approach based on the generalized method of moments. The method is applied to estimate parameters for various financial stock indices.

We analyze the dissipative dynamics of a particle governed by a two-dimensional generalized Langevin equation with coupled fractional Gaussian noise and white noise in its respective coordinates, assuming the lowest-order coupling form. Two situations are studied: In the first the particle is free from external force and in the second the particle is subject to a two-dimensional harmonic potential. We derive the general expressions for the mean values, variances, and velocity autocorrelation function and evaluate their temporal evolutions via the numerical Laplace inversion technique. Through the analytical results of the short-time and long-time behaviors, we also explicitly elucidate the effects of fluctuation correlation coupling and interoscillator coupling on the dynamic behaviors of the particle. It is shown that in both situations the couplings do not affect the short-time behavior of self-diffusions in each coordinate, and the subdiffusive and normal diffusive features of these processes resemble those in a one-dimensional system with fractional Gaussian noise and white noise, respectively. However, over a long time period, the fluctuation correlation extends the characteristic time scales for the self-diffusions of a free particle; while only the interoscillator coupling induces a retardation of the relaxation processes of a bounded particle toward equilibrium. Moreover, both couplings generate a cross diffusion, whose long-time approximation has two possible forms, the selection of which depends on the relevant time scales of self-diffusions in each coordinate.

We have calculated the joint probability distribution function for random reverse-cyclic matrices and shown that it is related to an $N$-body exactly solvable model. We refer to this well-known model potential as a screened harmonic oscillator. The connection enables us to obtain all the correlations among the particle positions moving in a screened harmonic potential. The density of nontrivial eigenvalues of this ensemble is found to be of the Wigner form and admits a hole at the origin, in contrast to the semicircle law of the Gaussian orthogonal ensemble of random matrices. The spacing distributions assume different forms ranging from Gaussian-like to Wigner.

We study the efficiency at maximum power of two coupled heat engines, using thermoelectric generators (TEGs) as engines. Assuming that the heat and electric charge fluxes in the TEGs are strongly coupled, we simulate numerically the dependence of the behavior of the global system on the electrical load resistance of each generator in order to obtain the working condition that permits maximization of the output power. It turns out that this condition is not unique. We derive a simple analytic expression giving the relation between the electrical load resistance of each generator permitting output power maximization. We then focus on the efficiency at maximum power (EMP) of the whole system to demonstrate that the Curzon-Ahlborn efficiency may not always be recovered: The EMP varies with the specific working conditions of each generator but remains in the range predicted by irreversible thermodynamics theory. We discuss our results in light of nonideal Carnot engine behavior.

We consider the dynamics of $Q$ learning in two-player two-action games with a Boltzmann exploration mechanism. For any nonzero exploration rate the dynamics is dissipative, which guarantees that agent strategies converge to rest points that are generally different from the game's Nash equlibria (NEs). We provide a comprehensive characterization of the rest point structure for different games and examine the sensitivity of this structure with respect to the noise due to exploration. Our results indicate that for a class of games with multiple NEs the asymptotic behavior of learning dynamics can undergo drastic changes at critical exploration rates. Furthermore, we demonstrate that, for certain games with a single NE, it is possible to have additional rest points (not corresponding to any NE) that persist for a finite range of the exploration rates and disappear when the exploration rates of both players tend to zero.

We estimate the expected behavior of the quantum model of a heat engine when we have incomplete information about external macroscopic parameters such as the magnetic field controlling the intrinsic energy scales of the working medium. We explicitly derive the prior probability distribution for these unknown parameters $a_i(i=1,2)$. Based on a few simple assumptions, the prior probability distribution is found to be of the form $\Pi \left(a_i\right)\propto 1/a_i$. By calculating the expected values of various physical quantities related to this engine, we find that the expected behavior of the quantum model exhibits thermodynamiclike features. This leads us to a surprising proposal that incomplete information quantified as an appropriate prior distribution can lead us to expect classical thermodynamic behavior in quantum models.

Competitive adsorption of counterions of multiple species to charged surfaces is studied by a size-effect-included mean-field theory and Monte Carlo (MC) simulations. The mean-field electrostatic free-energy functional of ionic concentrations, constrained by Poisson's equation, is numerically minimized by an augmented Lagrangian multiplier method. Unrestricted primitive models and canonical ensemble MC simulations with the Metropolis criterion are used to predict the ionic distributions around a charged surface. It is found that, for a low surface charge density, the adsorption of ions with a higher valence is preferable, agreeing with existing studies. For a highly charged surface, both the mean-field theory and the MC simulations demonstrate that the counterions bind tightly around the charged surface, resulting in a stratification of counterions of different species. The competition between mixed entropy and electrostatic energetics leads to a compromise that the ionic species with a higher valence-to-volume ratio has a larger probability to form the first layer of stratification. In particular, the MC simulations confirm the crucial role of ionic valence-to-volume ratios in the competitive adsorption to charged surfaces that had been previously predicted by the mean-field theory. The charge inversion for ionic systems with salt is predicted by the MC simulations but not by the mean-field theory. This work provides a better understanding of competitive adsorption of counterions to charged surfaces and calls for further studies on the ionic size effect with application to large-scale biomolecular modeling.

Through a combination of theory, numerical simulation, and experiment, we investigate the motion of magnetic beads on the surface of a magnetic ratchet driven by multifrequency fields. Here, we focus on the influence of static forcing terms, which were not included in previous models, and we derive analytical models that show why the static forcing terms are responsible for inducing beads of two different sizes to move in opposite directions on the same ratchet potential. We begin our analysis with the simplest possible forcing model, and we show that the main effect of the static forcing terms is to delay the phase of flux reversal. From there, we move onto the full analysis and theoretically derive the phase range for which opposite motion among two different bead types is achieved. Based on these theoretical results, we conduct experimental investigations that explore the effects of bead size and static forcing coefficient on the direction of bead motion, which confirm most of the expected trends. These results shed light both on past experimental work both by ourselves and others, as well as elucidate the more general multiplexing capabilities of ratchets.