Chemical reaction networks which exhibit strong fluctuations are common in microscopic systems in which reactants appear in low copy numbers. The analysis of these networks requires stochastic methods, which come in two forms: direct integration of the master equation and Monte Carlo simulations. The master equation becomes infeasible for large networks because the number of equations increases exponentially with the number of reactive species. Monte Carlo methods, which are more efficient in integrating over the exponentially large phase space, also become impractical due to the large amounts of noisy data that need to be stored and analyzed. The recently introduced multiplane method [A. Lipshtat and O. Biham, Phys. Rev. Lett. 93, 170601 (2004)] is an efficient framework for the stochastic analysis of large reaction networks. It is a dimensional reduction method, based on the master equation, which provides a dramatic reduction in the number of equations without compromising the accuracy of the results. The reduction is achieved by breaking the network into a set of maximal fully connected subnetworks (maximal cliques). A separate master equation is written for the reduced probability distribution associated with each clique, with suitable coupling terms between them. This method is highly efficient in the case of sparse networks, in which the maximal cliques tend to be small. However, in dense networks some of the cliques may be rather large and the dimensional reduction is not as effective. Furthermore, the derivation of the multiplane equations from the master equation is tedious and difficult. Here we present the reduced-multiplane method in which the maximal cliques are broken down to the fundamental two-vertex cliques. The number of equations is further reduced, making the method highly efficient even for dense networks. Moreover, the equations take a simpler form, which can be easily constructed using a diagrammatic procedure, for any desired network architecture. It is shown that the method provides accurate results for the population sizes of the reactive species and their reaction rates.

A method is presented for system identification of spatially extended systems with structural inhomogeneities of local dynamics and additional long-range links. The proposed identification procedure is based on steady-state stabilization and is illustrated with an inhomogeneous two-dimensional grid of coupled FitzHugh-Nagumo models.

This paper examines particle trapping and release in confined microvortex flows, including those near a solid surface due to variations in the electrokinetic slip velocity and those at a liquid-gas interface due to an external momentum source. We derive a general analytical solution for a two-dimensional microvortex flow within a semicircular cap. We also use a bifurcation theory on the kinetic equation of particles under various velocity and force fields to delineate the conditions for a vortex trap, a point trap, a limit cycle trap, and the selective sorting of the particles into different traps. In the presence of only divergence-free forces on suspended particles, we find that two parameters, such as those related to Stokes drag, gravity, and flow vorticity, are sufficient to classify all the trap topologies for a given slip velocity distribution. We also show that nondivergence-free forces such as nonuniform repulsion or attraction can capture suspended particles in one trap and selectively sort a binary suspension into different traps.

A two-dimensional particle-in-cell (PIC) model is proposed to study the wake field and stopping power induced by a nonrelativistic charged particle moving perpendicular to the external magnetic field in two-component plasmas. The effects of the magnetic field on the wake potential and the stopping due to the polarization of both the plasma ions and electrons are discussed. The velocity fields of plasma ions and electrons are investigated, respectively, in the weak and strong magnetic field cases. Our simulation results show that in the case of weak magnetic field and high ion velocity, the wakes exhibit typical V-shaped cone structures and the opening cone angles decrease with the increasing ion velocity. As the magnetic field becomes strong, the wakes lose their typical V-shaped structures and become highly asymmetrical. Similar results can be obtained in the case of low ion velocity and strong magnetic field. In addition, stopping power is calculated and compared with previous one-dimensional and full three-dimensional PIC results.

We investigate the asymptotic state of time-periodic quantum systems with regular and chaotic Floquet states weakly coupled to a heat bath. The asymptotic occupation probabilities of these two types of states follow fundamentally different distributions. Among regular states the probability decreases from the state in the center of a regular island to the outermost state by orders of magnitude, while chaotic states have almost equal probabilities. We derive an analytical expression for the occupations of regular states of kicked systems, which depends on the winding numbers of the regular tori and the parameters temperature and driving frequency. For a constant winding number within a regular island it simplifies to Boltzmann-like weights $\text{exp}\left(-{\beta }_{\text{eff}}{E}_m^{\text{reg}}\right)$, similar to time-independent systems. For this we introduce the regular energies $E_m^{\text{reg}}$ of the quantizing tori and an effective winding-number-dependent temperature $1/{\beta }_{\text{eff}}$, different from the actual bath temperature. Furthermore, the occupations of other typical Floquet states in a mixed phase space are studied, i.e., regular states on nonlinear resonances, beach states, and hierarchical states, giving rise to distinct features in the occupation distribution. Avoided crossings involving a regular state lead to drastic consequences for the entire set of occupations. We introduce a simplified rate model whose analytical solutions describe these occupation changes quite accurately.

Strategy changes are an essential part of evolutionary games. Here, we introduce a simple rule that, depending on the value of a single parameter $w$, influences the selection of players that are considered as potential sources of the new strategy. For positive $w$ players with high payoffs will be considered more likely, while for negative $w$ the opposite holds. Setting $w$ equal to zero returns the frequently adopted random selection of the opponent. We find that increasing the probability of adopting the strategy from the fittest player within reach, i.e., setting $w$ positive, promotes the evolution of cooperation. The robustness of this observation is tested against different levels of uncertainty in the strategy adoption process and for different interaction networks. Since the evolution to widespread defection is tightly associated with cooperators having a lower fitness than defectors, the fact that positive values of $w$ facilitate cooperation is quite surprising. We show that the results can be explained by means of a negative feedback effect that increases the vulnerability of defectors although initially increasing their survivability. Moreover, we demonstrate that the introduction of $w$ effectively alters the interaction network and thus also the impact of uncertainty by strategy adoptions on the evolution of cooperation.

We show that, in dimension higher than one, heat diffusion and viscosity cannot arrest thermal collapse in a freely evolving dilute granular gas, even in the absence of gravity. Thermal collapse involves a finite-time blowup of the gas density. It was predicted earlier in ideal, Euler hydrodynamics of dilute granular gases in the absence of gravity, and in nonideal, Navier-Stokes granular hydrodynamics in the presence of gravity. We determine, analytically and numerically, the dynamic scaling laws that characterize the gas flow close to collapse. We also investigate bifurcations of a freely evolving dilute granular gas in circular and wedge-shaped containers. Our results imply that, in general, thermal collapse can only be arrested when the gas density becomes comparable with the close-packing density of grains. This provides a natural explanation to the formation of densely packed clusters of particles in a variety of initially dilute granular flows.

In this paper, the flow of dense suspensions of monodisperse spheres in wall-bounded channels is studied using a mesoscopic numerical model based on the dissipative particle dynamics (DPD) technique. Experimental observations [for instance, L. Isa et al., Phys. Rev. Lett. 98, 198305 (2007)] have confirmed that understanding the relevant physics of this problem requires probing at the mesoscopic level to account for the particle scale behavior. The DPD-based approach presented here enables us to explore various aspects of suspension flow at the particle scale. The yielding behavior of the suspensions is studied using macroscopic stress components calculated from the particle level. The relationship between various normal and shear stress components at the yielding plane is presented and discussed. It is seen that in dense suspensions, yielding is characterized by a strong dependence on all the stress components: ${\tau }_{xx}$, ${\tau }_{xy}$, and ${\tau }_{yy}$. It is also seen that different stress components have different length-scale dependencies. While the normal stress in the flow direction, ${\tau }_{xx}$, depends on macroscopic parameters such as the driving force, ${\tau }_{yy}$, the normal stress transverse to the flow, depends on particle level parameters and is independent of the driving force. Wall topologies with characteristic dimensions on the order of the suspension particle size have a strong effect on the flow characteristics and the stress components.

Polymer nanocomposites, materials combining polymers and inorganic components such as nanosized crystallites or nanoparticles have attracted significant attention in recent years. A successful strategy for designing polymer nanocomposites is polymer functionalization via attaching functional groups with specific affinity for the inorganic component. In this paper, a systematic investigation by molecular dynamics of polymer functionalization for design of composites combining nanosize crystallites with multiblock polymers in solution is presented. It is shown that functionalization is an example of active self-assembly, where the resulting polymer nanocomposite exhibits a different type of order than the original pure polymer system (without inorganic components). Optimal polymer architectures and concentrations are identified appropriate for different applications, alongside an in-depth analysis on the origin and stability of the resulting phases as well as its experimental implications.

Spike-timing-dependent plasticity (STDP) has been shown to generate a synaptic weight structure that is determined by the timing of the pre- and postsynaptic spikes at the synapse. In this paper it is shown under what conditions a neuron stimulated by several pools of delta-correlated inputs encodes this input structure in its resulting weight structure. The analysis is carried out using Poisson neurons with weight-dependent STDP. The learning dynamics induced by STDP leads to both stabilization of the input weights and competition between the weights for a broad range of learning parameters. The results demonstrate how weight-dependent STDP can generate multimodal stable asymptotic distributions of the synaptic weights.

Diverse self-sustained oscillatory patterns and their mechanisms in small-world networks (SWNs) of excitable nodes are studied. Spatiotemporal patterns of SWNs are sensitive to long-range connection probability $P$ and coupling intensity $D$. By varying $P$ in wide range with fixed $D$, we observe totally six types of asymptotic states: pure spiral waves, pure self-sustained target waves, patterns of mixtured spirals and target waves, pseudospiral turbulence, synchronizing oscillations, and rest state. The parameter conditions for all these states are specified, and the mechanisms of these states are heuristically explained. In particular, the mechanism of emergence and annihilation of synchronizing oscillations is explained by using the shortest path length analysis.

We investigate various dynamic structure factors for harmonic and anharmonic chains. For harmonic chains with mass disorder we find some unexpected features, such as a fine structure contributing to a central peak, which is present also in the spatial spectra of the eigenfunctions. These results are contrasted with structure factors of Lyapunov modes obtained for the disordered Lennard-Jones chain. For this nonlinear system the static and the dynamic Lyapunov structure factors show opposite trends in their temperature dependence.

We examine a generalized FitzHugh-Nagumo (FHN) type model with modified excitability derived from the diffusive Morris-Lecar equations for neuronal activity. We obtain exact analytic solutions in the form of traveling waves using a piecewise linear approximation for the activator and inhibitor reaction terms. We study the existence and stability of waves and find that the inhibitor species exhibits different types of wave forms (fronts and pulses), while the activator wave maintains the usual kink (front) shape. The nonequilibrium Ising-Bloch bifurcation for the wave speed that occurs in the FHN model, where the control parameter is the ratio of inhibitor to activator time scales, persists when the strength of the inhibitor nonlinearity is taken as the bifurcation parameter.

The present paper deals with the two-dimensional numerical simulation of gaseous flow and heat transfer in planar microchannel and nanochannel with different wall temperatures in transitional regime $0.1\le \text{Kn}\le 1$. An atomistic molecular simulation method is used known as thermal lattice-Boltzmann method. The results of simulation are presented in four cases corresponding to the Fourier flow, shear-driven flow (Couette flow), pressure-driven flow (Poiseuille flow), and mixed shear–pressure-driven flow in the developing and fully developed regions. The mixed shear–pressure-driven flow is divided into two subcases with shear stress and pressure gradient acting in the same and the opposite directions. Normalized temperature and velocity profiles across the channel, distribution of local wall Nusselt number, and friction coefficient are illustrated. Using this method, nonlinear pressure distribution in the streamwise direction, reduction in mass flow rate, $C_f\text{Re}$, and Nu by increasing the Knudsen number are studied. It is seen that for Couette flow, Nu over the hotter plate is greater than the cooler plate, but for the pressure-driven flow with stationary wall temperature dependency of viscosity and thermal conductivity causes this trend to be reversed. The reversed flow appearance in the velocity profile is captured in the case of opposite shear–pressure-driven flow.

Dust produced in tokamaks is an important issue for fusion. Dust particles can introduce health and safety issues when in the same time can have an impact on reactor performance. Apart from the associated problems there are also potential benefits that make the better understanding of their behavior important. In this work the dust transport code Dust in TOKamakS will be used to explore the effect that variations in the plasma background and the physical model, describing the plasma-dust interaction, have on their predicted trajectories.

We study the dynamics of a thin film over a substrate heated from below in a framework of a strongly nonlinear one-dimensional Cahn-Hilliard equation. The evolution leads to a fractalization into smaller and smaller scales. We demonstrate that a primitive element in the appearing hierarchical structure is a dissipative compacton. Both direct simulations and the analysis of a self-similar solution show that the compactons appear at superexponentially decreasing scales, which means vanishing dimension of the fractal.

We obtain the exact nonequilibrium work generating function (NEWGF) for a small system consisting of a massive Brownian particle connected to internal and external springs. The external work is provided to the system for a finite-time interval. The Jarzynski equality, obtained in this case directly from the NEWGF, is shown to be valid for the present model, in an exact way regardless of the rate of external work.

We analyze a pair of diffusion equations which are derived in the infinite system-size limit from a microscopic, individual based, stochastic model. Deviations from the conventional Fickian picture are found which ultimately relate to the depletion of resources on which the particles rely. The macroscopic equations are studied both analytically and numerically, and are shown to yield anomalous diffusion which does not follow a power law with time, as is frequently assumed when fitting data for such phenomena. These anomalies are here understood within a consistent dynamical picture which applies to a wide range of physical and biological systems, underlining the need for clearly defined mechanisms which are systematically analyzed to give definite predictions.

We investigate the propagation and scattering of highly nonlinear waves in disordered granular chains composed of diatomic (two-mass) units of spheres that interact via Hertzian contact. Using ideas from statistical mechanics, we consider each diatomic unit to be a “spin,” so that a granular chain can be viewed as a spin chain composed of units that are each oriented in one of two possible ways. Experiments and numerical simulations both reveal the existence of two different mechanisms of wave propagation: in low-disorder chains, we observe the propagation of a solitary pulse with exponentially decaying amplitude. Beyond a critical level of disorder, the wave amplitude instead decays as a power law, and the wave transmission becomes insensitive to the level of disorder. We characterize the spatiotemporal structure of the wave in both propagation regimes and propose a simple theoretical interpretation for a transition between the two regimes. Our investigation suggests that an elastic spin chain can be used as a model system to investigate the role of heterogeneities in the propagation of highly nonlinear waves.

Crystal nucleation and growth processes induced by an externally applied shear strain in a model metallic glass are studied by means of nonequilibrium molecular dynamics simulations, in a range of temperatures. We observe that the nucleation-growth process takes place after a transient, induction regime. The critical cluster size and the lag-time associated with this induction period are determined from a mean first-passage time analysis. The laws that describe the cluster-growth process are studied as a function of temperature and strain rate. A theoretical model for crystallization kinetics that includes the time dependence for nucleation and cluster growth is developed within the framework of the Kolmogorov-Johnson-Mehl-Avrami scenario and is compared with the molecular dynamics data. Scalings for the cluster-growth laws and for the crystallization kinetics are also proposed and tested. The observed nucleation rates are found to display a nonmonotonic strain rate dependency.