We analyze the effect of a time-dependent external field on non-Markovian migration described by the continuous time random walk (CTRW) approach. The rigorous method of treating the problem is proposed which is based on the Markovian representations of the CTRW approach and field modulation. With the use of this method we derive the non-Markovian stochastic Liouville equation (SLE), that describes the effect of this field, and thoroughly analyze the relation of the derived SLE with equations proposed earlier. This SLE is applied to the case of subdiffusive migration in which the exact formulas for the first and second moments of spatial distribution are obtained. In the case of oscillating external field they predict unusual dependence of the first moment on oscillation phase and anomalous time behavior of field dependent contribution to the dispersion which agree with results of earlier works. Anomalous time dependence is also found in the case of a fluctuating field. The specific features of this time dependence are analyzed in detail.

We study the effect of a non-Gaussian noise on interstate switching activated primarily by Gaussian noise. Even weak non-Gaussian noise can strongly change the switching rate. The effect is determined by all moments of the noise distribution. It is expressed in a closed form in terms of the noise characteristic functional. The analytical results are compared with the results of simulations for an overdamped system driven by white Gaussian noise and a Poisson noise. Switching induced by a purely Poisson noise is also discussed.

Recently, a quantum-mechanical proof of the increase of Boltzmann entropy in quantum systems that are coupled to an external classical source of work has been given. Here we illustrate this result by applying it to a forced quantum harmonic oscillator. We show plots of the actual temporal evolution of work and entropy for various forcing protocols. We note that entropy and work can be partially or even fully returned to the source, although both work and entropy balances are non-negative at all times in accordance with the minimal work principle and the Clausius principle, respectively. A necessary condition for the increase of entropy is that the initial distribution is decreasing (e.g., canonical). We show evidence that for a nondecreasing distribution (e.g., microcanonical), the quantum expectation of entropy may decrease slightly. Interestingly, the classical expectation of entropy cannot decrease, irrespective of the initial distribution, in the forced harmonic oscillator.

The properties of solid states, biophysical materials, neuronal circuits, and equilibrium states of a many-body system can be studied by using techniques in statistical physics. It has been common practice to represent a system composed of binary state units by using an Ising spin network where each unit has symmetric $\{-1,1\}$ states. However, the asymmetry or symmetry of the binary states of the units can affect the property and ergodicity of the system, but better understanding of the quantitative difference is still needed. We compare systems of binary units with symmetric or asymmetric states. The network has spatially modulated interaction with quenched randomness. We can bridge the Ising spin network and McCulloch-Pitts neuron network and analyze the stability of the system via replica method by introducing an interpolating parameter. The effects of the asymmetry states affect the multistability of the system and the stability of replica-symmetry solutions.

Diffusion of an overdamped Brownian particle on a symmetric periodic substrate is investigated in the presence of pulsated perturbations of two kinds: (i) Stepwise lateral displacements (flashing substrate) and (ii) instantaneous tilts (shot noise). Pulses are applied, as it is often observed, in either periodic or random sequences with assigned mean (bias) and average waiting time (time constant). For a given bias, both the diffusion coefficient and the mobility of the particle can be greatly enhanced by tuning the time constant. Moreover, also depending on the time constant, the mobility can grow negative in (i) or exceed unity in (ii). We term this phenomenon resonant transport.

This experimental study is focused on the process of bubble breakup in steadily sheared foams, at constant shear rate or constant shear stress. Two different types of surfactants were used and glycerol was added to the aqueous phase, to check how the bubble breakup depends on the surface modulus and on bulk viscosity of the foaming solutions. The experiments show that bubble breakup in foams occurs above a well defined critical dimensionless stress, ${\tilde{\tau }}_{\mathrm{CR}}\equiv ({\tau }_{\mathrm{CR}}R∕\sigma )\approx 0.40$, which is independent of surfactant used, solution viscosity, and bubble volume fraction (varied between 92 and 98 %). Here ${\tau }_{\mathrm{CR}}$ is the dimensional shear stress, above which a bubble with radius $R$ and surface tension $\sigma$ would break in sheared foam. The value of the critical stress experimentally found by us ${\tilde{\tau }}_{\mathrm{CR}}\approx 0.40$, is about two orders of magnitude lower than the critical stress for breakup of single bubbles in sheared Newtonian liquids, ${\tilde{\tau }}_{\mathrm{CR}}\approx 25$. This large difference in the critical stress is explained by the strong interaction between neighboring bubbles in densely populated foams, which facilitates bubble subdivision into smaller bubbles. A strong effect of bubble polydispersity on the kinetics of bubble breakup (at similar mean bubble size) was observed and explained. Experiments were also performed with hexadecane-in-water emulsions of drop volume fraction 83% $⩽\Phi ⩽95\%$ to study drop breakup in concentrated emulsions. Qualitatively similar behavior was observed to that of foams, with the critical dimensionless stress for drop breakup being lower, ${\tilde{\tau }}_{\mathrm{CR}}\approx 0.15$, and practically independent of the drop volume fraction and viscosity ratio (varied between 0.01 and 1). This critical stress is by several times lower than the critical stress for breakage of single drops in sheared Newtonian fluids at comparable viscosity ratio, which evidences for facilitated drop subdivision in concentrated emulsions. To explain the measured low values of the critical stress, a different type of capillary instability of the breaking bubbles and drops in concentrated foams and emulsions is proposed and discussed.

Positron annihilation lifetime spectroscopy (PALS) was used to study the microstructure of the free volume in the temperature range between $103\mathrm{K}$ and $393\mathrm{K}$ in phenylphthalein-dimethylether (PDE), a low-molecular-weight glass former. Using the routine LIFETIME9.0, the ortho-positronium ($o$-Ps) lifetime distribution was analyzed, and from this, the volume distribution $g_n\left(v_h\right)$ of subnanometer-size holes was calculated. From a comparison of PALS and specific volume data, the number density and the volume fraction of holes were estimated. These free-volume data, as a function of temperature, were used to test the validity of the Cohen-Turnbull (CT) free-volume theory. It was found that the structural relaxation from dielectric spectroscopy can be described by the CT theory after introducing a corrected free volume $(V_{\mathrm{f}}-\Delta V)$, where $\Delta V=0.014{\mathrm{cm}}^3∕\mathrm{g}$. The extended free-volume theory of Cohen and Grest can be fitted to the dielectric-relaxation and free-volume data, but the parameters of both fits are not consistent. PDE shows some peculiar features. The “knee” in the $o$-Ps lifetime expansion and crossover in temperature dependence of the frequency of the primary dielectric relaxation process occur at different temperatures. In addition, the change in the Vogel-Fulcher-Tammann parameters at $T_B∕T_g=1.1$ has no observable effect on the mean free volume $⟨v_h⟩$ (or $V_f$). The size of the smallest representative freely fluctuating subsystem, $⟨V_{\mathrm{SV}}⟩$ estimated from the standard deviation ${\sigma }_h$ of $g_n\left(v_h\right)$, decreases from $4.1{\mathrm{nm}}^3\text{to}2.6{\mathrm{nm}}^3$ when the temperature increases from $T∕T_g=1.0$ to 1.15. Correspondingly, the length of dynamic heterogeneity, $\xi ={⟨V_{\mathrm{VS}}⟩}^{1∕3}$, decreases from $1.6\mathrm{nm}\text{to}1.4\mathrm{nm}$. It is concluded that at $T∕T_g\approx 1.10=T_B∕T_g$ the system transforms from a heterogeneous to a homogeneous (true) liquid.

In this paper we present an investigation into the calculation of the Frank elastic constants of hard platelets via molecular simulation and virial expansion beyond second order. Monte Carlo simulations were carried out and director fluctuations measured as a function of wave vector $\mathit{k}$, giving the elastic constants through a fit in the low-$k$ limit. Additionally, the virial expansion coefficients of the elastic constants up to sixth order were calculated, and the validity of the theory determined by comparison with the simulation results. The simulation results are also compared with experimental measurements on colloidal suspensions of platelike particles.

Systems with global symmetry group $O\left(2\right)$ experience topological transition in the two-dimensional space. But there is controversy about such a transition for systems with global symmetry group $O\left(3\right)$. As an example of the latter case, we study the Lebwohl-Lasher model for the two-dimensional liquid crystal, using three different methods independent of the proper values of possible critical exponents. Namely, we analyze the at-equilibrium order parameter distribution function with (1) the hyperscaling relation; (2) the first-scaling collapse for the probability distribution function; and (3) the Binder’s cumulant. We give strong evidence for definite lack of a line of critical points at low temperatures in the Lebwohl-Lasher model, contrary to conclusions of a number of previous numerical studies.

We study information processing in a peripheral sensory receptor system which possesses spontaneous dynamics with two distinct rhythms. Such organization was found in the electrosensory system of paddlefish and is represented by two distinct and unidirectionally coupled oscillators, resulting in biperiodic spontaneous firing patterns of sensory neurons. We use computational modeling to elucidate the functional role of spontaneous oscillations in conveying information from sensory periphery to the brain. We show that biperiodic organization resulting in nonrenewal statistics of background neuronal activity leads to significant improvement in information transfer through the system as compared to an equivalent renewal model.

Multicommunity population systems may reach a consensus state where the fractions of each species in different communities agree on a common value. In this paper, by analyzing the evolutionary dynamics based on an extended replicator equation incorporating community effects, the consensus problem of population systems with $n$ communities is studied. In particular, the simple case of two communities is investigated in detail. In general, for $n$ communities, a sufficient and necessary condition for population systems to reach a consensus of coexistent state is provided. Regarding the population dynamics for the four different types of games, whether the population systems can achieve consensus is determined. The dynamics of community-structured populations shows richer features than nonstructured populations, and some nontrivial phenomena arising from different community-structured population systems are illustrated with concrete numerical examples.

We measure the transmission and reflection amplitudes of microwaves in a resonator coupled to two antennas at room temperature in the regime of weakly overlapping resonances and in a frequency range of $3–16\mathrm{GHz}$. Below $10.1\mathrm{GHz}$ the resonator simulates a chaotic quantum system. The distribution of the elements of the scattering matrix $S$ is not Gaussian. The Fourier coefficients of $S$ are used for a best fit of the autocorrelation function of $S$ to a theoretical expression based on random-matrix theory. We find very good agreement below but not above $10.1\mathrm{GHz}$.

Mutual information between the time series of two dynamical elements measures how well their activities are coordinated. In a network of interacting elements, the average mutual information over all pairs of elements $I$ is a global measure of the correlation between the elements’ dynamics. Local topological features in the network have been shown to affect $I$. Here we define a generalized clustering coefficient $C_p$ and show that this quantity captures the effects of local structures on the global dynamics of networks. Using random Boolean networks (RBNs) as models of networks of interacting elements, we show that the variation of $⟨I⟩$ ($I$ averaged over an ensemble of RBNs with the number of nodes $N$ and average connectivity $k$) with $N$ and $k$ is caused by the variation of $⟨C_p⟩$. Also, the variability of $I$ between RBNs with equal $N$ and $k$ is due to their distinct values of $C_p$. Consequently, we propose a rewiring method to generate ensembles of BNs, from ordinary RBNs, with fixed values of $C_p$ up to order 5, while maintaining in- and out-degree distributions. Using this methodology, the dependency of $⟨C_p⟩$ on $N$ and $k$ and the variability of $I$ for RBNs with equal $N$ and $k$ are shown to disappear in RBNs with $C_p$ set to zero. The $⟨I⟩$ of ensembles of RBNs with fixed, nonzero $C_p$ values, also becomes almost independent of $N$ and $k$. In addition, it is shown that $⟨C_p⟩$ exhibits a power-law dependence on $N$ in ordinary RBNs, suggesting that the $C_p$ affects even relatively large networks. The method of generating networks with fixed $C_p$ values is useful to generate networks with small $N$ whose dynamics have the same properties as those of large scale networks, or to generate ensembles of networks with the same $C_p$ as some specific network, and thus comparable dynamics. These results show how a system’s dynamics is constrained by its local structure, suggesting that the local topology of biological networks might be shaped by selection, for example, towards optimizing the coordination between its components.

Aging phenomena in the plastic response of amorphous solids are studied within the theory of shear transformation zones (STZs), which describes the kinetic rearrangement of localized defects in response to external stress. To account for the slow, nonequilibrium dynamics after a quench below the glass transition temperature, two possible models are considered. In the first model, transition rates between the internal states of STZs decrease with time, while in the second model aging occurs due to the relaxation of an effective temperature that determines the number density of STZs and other out-of-equilibium degrees of freedom. It is shown that for reasonable choices of parameters, both models capture qualitatively typical aging features seen in computer simulations and experiments: (i) compliance curves measured for different waiting times $t_{\mathrm{w}}$ after the quench can be superimposed, when the observation times are rescaled with relaxation times $\propto t_{\mathrm{w}}^{\mu }$, $0<\mu ⩽1$, and (ii) stress-strain curves show a stationary plateau stress independent of $t_{\mathrm{w}}$ and a peak stress that increases logarithmically with both $t_{\mathrm{w}}$ and the strain rate. Trends of the aging behavior with the quench temperature are also discussed.

Chaotic dynamical systems with two or more attractors lying on invariant subspaces may, provided certain mathematical conditions are fulfilled, exhibit intermingled basins of attraction: Each basin is riddled with holes belonging to basins of the other attractors. In order to investigate the occurrence of such phenomenon in dynamical systems of ecological interest (two-species competition with extinction) we have characterized quantitatively the intermingled basins using periodic-orbit theory and scaling laws. The latter results agree with a theoretical prediction from a stochastic model, and also with an exact result for the scaling exponent we derived for the specific class of models investigated. We discuss the consequences of the scaling laws in terms of the predictability of a final state (extinction of either species) in an ecological experiment.

In a recent paper we presented a stochastic Green function (SGF) algorithm, which has the properties of being general and easy to apply to any lattice Hamiltonian of the form $\widehat{\mathcal{H}}=\widehat{\mathcal{V}}-\widehat{\mathcal{T}}$, where $\widehat{\mathcal{V}}$ is diagonal in the chosen occupation number basis and $\widehat{\mathcal{T}}$ has only positive matrix elements. We propose here a modified version of the update scheme that keeps the simplicity and generality of the original SGF algorithm, and significantly enhances its efficiency.

Subdiffusion is an important physical phenomenon observed in many systems. However, numerical techniques to study it, especially when coupled to reactions, are lacking. In this paper, we develop an efficient Monte Carlo algorithm based on the Gillespie algorithm and the continuous-time random walk to simulate reaction-subdiffusion systems. Using this algorithm, we investigate Turing pattern formation in the Schnakenberg model with subdiffusion. First, we show that, as the system becomes more subdiffusive, the homogeneous state becomes more difficult to destablize and Turing patterns form less easily. Second, we show that, as the number of particles in the system decreases, the magnitude of fluctuations increases and again the Turing patterns form less easily. Third, we show that, as the system becomes more subdiffusive, the ratio between the two diffusive constants must be higher in order to observe Turing patterns. Finally, we also carry out linear stability analysis to validate the results obtained from our algorithm.

We demonstrate that, in general, only for fluid flows in which the gradient of the strain rate is constant or zero can the classical Navier-Stokes equations with constant transport coefficients be considered exact. This is typical of two of the most common types of flow: Couette and Poiseuille. For more complicated flow fields in which the streaming velocity involves higher order nonlinear terms, the use of nonlocal constitutive equations gives an exact description of the flow. These constitutive equations involve nonlocal transport kernels. For momentum transport we demonstrate that nonlocality will be significant for any particular flow field if the even moments of the nonlocal viscosity kernel are non-negligible. This corresponds to the condition that the strain rate varies appreciably over the width of the kernel in real space. Such conditions are likely to be dominant for nanofluidic flows.

The coupled activated dynamics in dense mixtures of repulsive and sticky hard spheres is studied using stochastic nonlinear Langevin equation theory. The effective free energy surface, barriers, saddle point trajectories, and mean first passage times depend in a rich manner on mixture composition, (high) total volume fraction, and attractive interaction strength. In general, there are three types of saddle point trajectories or relaxation pathways: a pure sticky or pure repulsive particle displacement keeping the other species localized, and a cooperative motion involving repulsive and attractive particle displacements. The barrier for activated hopping usually increases with the ratio of sticky to repulsive particle displacement. However, at intermediate values of the displacement ratio it can attain a broad plateau value, and can even exhibit a local maximum, and hence nonmonotonic behavior, at high sticky particle mixture compositions if the attraction strength is modest. The mean first passage, or hopping, times are computed using multidimensional Kramers theory. In most cases the hopping time trends reflect the behavior of the barrier height, especially as the sticky particle attraction strengths become large. However, there are dramatic exceptions associated with cooperative repulsive and attractive particle trajectories where the barriers are high but a greatly enhanced number of such trajectories exist near the saddle point.

Signaling events in eukaryotic cells are often guided by a scaffolding protein. Scaffold proteins assemble multiple proteins into a spatially localized signaling complex and exert numerous physical effects on signaling pathways. To study these effects, we consider a minimal, three-state kinetic model of scaffold-mediated kinase activation. We first introduce and apply a path summation technique to obtain approximate solutions to a single molecule master equation that governs protein kinase activation. We then consider exact numerical solutions. We comment on when this approximation is appropriate and then use this analysis to illustrate the competition of processes occurring at many time scales that are involved in signal transduction in the presence of a scaffold protein. We find that our minimal model captures how scaffold concentration can influence the times over which signaling is distributed in kinase cascades. For a range of scaffold concentrations, scaffolds allow for signaling to be distributed over multiple decades. The findings are consistent with recent experiments and simulation data. These results provide a framework and offer a mechanism for understanding how scaffold proteins can influence the shape of the waiting time distribution of kinase activation and effectively broaden the times over which protein kinases are activated in the course of cell signaling.