The neurons of the neocortex show ∼1-Hz synchronized transitions between an active up state and a quiescent down state. The up-down state transitions are highly coherent over large sections of the cortex, yet they are accompanied by pronounced, incoherent noise. We propose a simple model for the up-down state oscillations that allows analysis by straightforward dynamical systems theory. An essential feature is a nonuniform network geometry composed of groups of excitatory and inhibitory neurons with strong coupling inside a group and weak coupling between groups. The enhanced deterministic noise of the up state appears as the natural result of the proximity of a partial synchronization transition. The synchronization transition takes place as a function of the long-range synaptic strength linking different groups of neurons.

Spike-timing-dependent plasticity (STDP) is an important driving force of self-organization in neural systems. With properly chosen input signals, STDP can yield a synaptic pruning process, whose functional role needs to be further investigated. We explore this issue from an information theoretic standpoint. Temporally correlated stimuli are introduced to neurons of an input layer. Then synapses on the dendrite, and thus the receptive field, of an output neuron are refined by STDP. The mutual information between input and output spike trains is calculated with the context tree method. The results show that synapse removal can enhance information transfer, i.e., that “less can be more” under certain constraints that stress the balance between potentiation and depression dictated by the parameters of the STDP rule, as well as the temporal scale of the input correlation.

A model of fractal continuum flow employing local fractional differential operators is suggested. The generalizations of the Green-Gauss divergence and Reynolds transport theorems for a fractal continuum are suggested. The fundamental conservation laws and hydrodynamic equations for an anisotropic fractal continuum flow are derived. Some physical implications of the long-range correlations in the fractal continuum flow are briefly discussed. It is noteworthy to point out that the fractal (quasi)metric defined in this paper implies that the flow of an isotropic fractal continuum obeying the Mandelbrot rule of thumb for intersection is governed by conventional hydrodynamic equations.

Many networks are dynamic in that their topology changes rapidly—on the same time scale as the communications of interest between network nodes. Examples are the human contact networks involved in the transmission of disease, ad hoc radio networks between moving vehicles, and the transactions between principals in a market. While we have good models of static networks, so far these have been lacking for the dynamic case. In this paper we present a simple but powerful model, the time-ordered graph, which reduces a dynamic network to a static network with directed flows. This enables us to extend network properties such as vertex degree, closeness, and betweenness centrality metrics in a very natural way to the dynamic case. We then demonstrate how our model applies to a number of interesting edge cases, such as where the network connectivity depends on a small number of highly mobile vertices or edges, and show that our centrality definition allows us to track the evolution of connectivity. Finally we apply our model and techniques to two real-world dynamic graphs of human contact networks and then discuss the implication of temporal centrality metrics in the real world.

Many complex systems have been shown to share universal properties of organization, such as scale independence, modularity, and self-similarity. We borrow tools from statistical physics in order to study structural preferential attachment (SPA), a recently proposed growth principle for the emergence of the aforementioned properties. We study the corresponding stochastic process in terms of its time evolution, its asymptotic behavior, and the scaling properties of its statistical steady state. Moreover, approximations are introduced to facilitate the modeling of real systems, mainly complex networks, using SPA. Finally, we investigate a particular behavior observed in the stochastic process, the peloton dynamics, and show how it predicts some features of real growing systems using prose samples as an example.

Thermal strongly collisional dusty plasma is studied. The electrical neutrality of the plasma suggests that the gas phase has some electrostatic energy when the plasma contains charged dust grains. The value of this energy determines the interphase interaction and ionization balance in the plasma. Proceeding from this, a new method of calculation of the dust grains’ charges in plasmas with any number of ions (down to zero) has been proposed. The correspondence between the theory and the experimental data is demonstrated.

An average atom model for dense ionized fluids that includes ion correlations is presented. The model assumes spherical symmetry and is based on density functional theory, the integral equations for uniform fluids, and a variational principle applied to the grand potential. Starting from density functional theory for a mixture of classical ions and quantum mechanical electrons, an approximate grand potential is developed, with an external field being created by a central nucleus fixed at the origin. Minimization of this grand potential with respect to electron and ion densities is carried out, resulting in equations for effective interaction potentials. A third condition resulting from minimizing the grand potential with respect to the average ion charge determines the noninteracting electron chemical potential. This system is coupled to a system of point ions and electrons with an ion fixed at the origin, and a closed set of equations is obtained. Solution of these equations results in a self-consistent electronic and ionic structure for the plasma as well as the average ionization, which is continuous as a function of temperature and density. Other average atom models are recovered by application of simplifying assumptions.

The determinant representation of the $n$-fold Darboux transformation of the Hirota equation is given. Based on our analysis, the 1-soliton, 2-soliton, and breathers solutions are given explicitly. Further, the first order rogue wave solutions are given by a Taylor expansion of the breather solutions. In particular, the explicit formula of the rogue wave has several parameters, which is more general than earlier reported results and thus provides a systematic way to tune experimentally the rogue waves by choosing different values for them.

This paper develops a reduced-order equivalent-structure based model for polystyrene in a rigid body molecular dynamics framework. In general, a coarse-grained model for polymers is obtained by replacing a group of chemically connected atoms by an effective particle and deriving a coarse-grained interaction potential that reproduces the structure and dynamics at the desired length and time scale. In the current model, a detailed ($\sim 16$ atoms) polystyrene monomer referred to as basic structural element (BSE) is replaced by an equivalent model with spherical backbone particles and an ellipsoidal particle that represents the styrene sidegroup. The governing principals of this homogenization is based on the mass, centroid, angular momentum, and energy equivalence between the detailed and the proposed reduced-order model. The bonded interactions parameters are readily obtained in the optimization of the equivalent structure from the detailed representation. The nonbonded interactions are treated separately. In order to capture the stereochemistry of the polystyrene molecule, an anisotropic biaxial nonbonded interaction potential function known as RE-squared (RE2) interaction has been used between pairs of ellipsoidal and/or spherical particles in the system. The required calibration of the nonbonded parameters is carried out by matching with the experimental density and the local structure using radial distribution function. This homogenization process scales up the modeling system size significantly as the higher frequency motions like -C-H- vibrations and sidegroup movements are suppressed. The accuracy of the model is established by comparing fine-scale simulation with explicit representations.

We define and study a class of resource allocation processes where $gN$ agents, by repeatedly visiting $N$ resources, try to converge to an optimal configuration where each resource is occupied by at most one agent. The process exhibits a phase transition, as the density $g$ of agents grows, from an absorbing to an active phase. In the latter, even if the number of resources is in principle enough for all agents ($g<1$), the system never settles to a frozen configuration. We recast these processes in terms of zero-range interacting particles, studying analytically the mean field dynamics and investigating numerically the phase transition in finite dimensions. We find a good agreement with the critical exponents of the stochastic fixed-energy sandpile. The lack of coordination in the active phase also leads to a nontrivial faster-is-slower effect.

We describe a method to compute thermodynamic quantities in the harmonic approximation for identical bosons and fermions in an external confining field. We use the canonical partition function where only energies and their degeneracies enter. The number of states of given energy and symmetry is found by separating the center-of-mass motion, and by counting the remaining states of given symmetry and excitation energy of the relative motion. The oscillator frequencies that enter the harmonic Hamiltonian can be derived from realistic model parameters, and the method corresponds to an effective interaction approach based on harmonic interactions. To demonstrate the method, we apply it to systems in two dimensions. Numerical calculations are compared to a brute force method, which is considerably more computationally intensive.

We use confocal microscopy to study the three-dimensional (3D) structure of colloidal crystals formed by poly($N$-isopropylacrylamide)-co-(acrylic acid) microgels of diameter 1.0–1.5 $\mu$m. The confocal images are tracked to locate particle positions in 3D, which are used to compute pair-correlation functions $g$($r$), bond order parameters, and structure factors $s$($q$). We find that the structure remains fcc for a range of charge, size, and concentration of the particles. When the particles are weakly attractive and are at low concentrations, polycrystalline solids result. In addition, owing to the compressibility of the colloids, the crystals display remarkable structural stability when subjected to external stress.

Chain-expansion processes from knotted globules have been measured for poly(methyl methacrylate) (PMMA) in the mixed solvent tert-butyl alcohol (TBA) $+$ water (2.5 vol $\%$) by static light scattering. The solution was quenched from the $\Theta$ temperature of 41.5 ${}^{\circ }$C to 37.0 ${}^{\circ }$C, aged there for a time period $t_{\mathrm{p},}$ and then returned rapidly to the $\Theta$ temperature. The chain-expansion process was determined as a time evolution of the expansion factor ${\alpha }^2$ after the temperature increase. The measurement was carried out by changing the aging time $t_{\mathrm{p}}$ from 240 to 7200 min, and the molecular weight from $M_{\mathrm{w}}$ $=$ 4.0 $\times$ 10${}^6$ to 1.5 $\times$ 10${}^7$, by taking advantage of the extremely slow chain aggregation in the solution. The chain-expansion process obtained for $M_{\mathrm{w}}$ $=$ 1.22 $\times$ 10${}^7$ became slow with increasing $t_{\mathrm{p}}$, which revealed the knot formation in single globules. The characteristic time of the chain expansion from globules aged for $t_{\mathrm{p}}$ $=$ 7200 min was found to depend on the molecular weight as $M_{\mathrm{w}}^{2.7}$. This exponent, which is close to 3, demonstrated a disentanglement process due to self-reptation. The present data were compared with the previous data of the chain expansion from compact globules aged at 25.0 ${}^{\circ }$C. The comparison made at $M_{\mathrm{w}}$ $=$ 1.22 $\times$ 10${}^7$ and at the same values of $t_{\mathrm{p}}$ revealed that the chain expansion from the globules aged at 25.0 ${}^{\circ }$C was much faster than that from the globules at 37.0 ${}^{\circ }$C, indicating a lower knot density in the more compact globules. It was conjectured that the knot formation due to self-reptation would be suppressed in a compact globule because an entire conformational change required by knot formation would become difficult to occur in the confined space of high segment concentration, particularly for a long polymer chain. The chain collapse of PMMA in the mixed solvent has been observed to occur extremely slowly at the later stage. This slow process was explained by the suppressed self-reptation.

Heart rate variability (HRV) contains important information about the modulation of the cardiovascular system. Various methods of nonlinear dynamics (e.g., estimating Lyapunov exponents) and complexity measures (e.g., correlation dimension or entropies) have been applied to HRV analysis. Permutation entropy, which was proposed recently, has been widely used in many fields due to its conceptual and computational simplicity. It maps a time series onto a symbolic sequence of permutation ranks. The original permutation entropy assumes the time series under study has a continuous distribution, thus equal values are rare and can be ignored by ranking them according to their order of emergence, or broken by adding small random perturbations to ensure every symbol in a sequence is different. However, when the observed time series is digitized with lower resolution leading to a greater number of equal values, or the equalities represent certain characteristic sequential patterns of the system, it may not be rational to simply ignore or break them. In the present paper, a modified permutation entropy is proposed that, by mapping the equal value onto the same symbol (rank), allows for a more accurate characterization of system states. The application of the modified permutation entropy to the analysis of HRV is investigated using clinically collected data. Results show that modified permutation entropy can greatly improve the ability to distinguish the HRV signals under different physiological and pathological conditions. It can characterize the complexity of HRV more effectively than the original permutation entropy.

We experimentally investigate the thermocapillary migration induced by local laser heating of the advancing front of a growing droplet confined in a microfluidic channel. When heating implies an effective increase in interfacial tension, the laser behaves as a “soft door” whose stiffness can be tuned via the optical parameters (beam power and waist). The light-driven thermocapillary velocity of a growing droplet, which opposes the basic flow, is characterized for different types of fluid injection, either pressure or flow rate driven, and various channel aspect ratios. Measurements are interpreted using a simplified model for the temperature gradient at the interface, based on a purely diffusive, three-layer system. Considering the mean temperature gradient, we demonstrate that the classical large-scale temperature gradient behavior is retrieved in the opposite case when the thermal gradient length scale is smaller than the droplet size. We also demonstrate that the thermocapillary velocity is proportional to the smallest droplet curvature imposed by the channel confinement. This suggests that the thermocapillary velocity is in fact proportional to the mean temperature gradient and to the largest interface curvature radius, which both coincide with the imposed one and the spherical droplet radius in large-scale and unconfined situations. Furthermore, as used surfactant concentrations are largely above the critical micelle concentration, we propose a possible explanation, relying on state-of-the-art considerations on high-concentration surfactant-covered interfaces for the observed effective increase in interfacial tension with temperature. We also propose a mechanism for explaining the blocking effect at the scaling-law level. This mechanism involves the temporal evolution of hydrodynamic and thermocapillary forces, based on experimental observations. We finally show that this optocapillary interaction with a microfluidic droplet generator allows for controlling either the flow rate (valve) or the droplet size (sampler), depending on the imposed fluid injection conditions.

We analyze the statistical properties of three-dimensional (3D) turbulence in a rotating fluid. To this end we introduce a generating functional to study the statistical properties of the velocity field $\mathit{v}$. We obtain the master equation from the Navier-Stokes equation in a rotating frame and thence a set of exact hierarchical equations for the velocity structure functions for arbitrary angular velocity $\mathit{\Omega }$. In particular we obtain the differential forms for the analogs of the well-known von Karman-Howarth relation for 3D fluid turbulence. We examine their behavior in the limit of large rotation. Our results clearly suggest dissimilar statistical behavior and scaling along directions parallel and perpendicular to $\mathit{\Omega }$. The hierarchical relations yield strong evidence that the nature of the flows for large rotation is not identical to pure two-dimensional flows. To complement these results, by using an effective model in the small-$\Omega$ limit, within a one-loop approximation, we show that the equal-time correlation of the velocity components parallel to $\mathit{\Omega }$ displays Kolmogorov scaling $q^{-5/3}$ wherein as for all other components, the equal-time correlators scale as $q^{-3}$ in the inertial range where $\mathit{q}$ is a wave vector in 3D. Our results are generally testable in experiments and/or direct numerical simulations of the Navier-Stokes equation in a rotating frame.

We elucidate a nonconserved relaxational nonequilibrium dynamics of a O(2) symmetric model. We drive the system out of equilibrium by introducing a nonzero noise cross correlation of amplitude $D_{\times }$ in a stochastic Langevin description of the system, while maintaining the O(2) symmetry of the order parameter space. By performing dynamic renormalization group calculations in a field-theoretic set up, we analyze the ensuing nonequilibrium steady states and evaluate the scaling exponents near the critical point, which now depend explicitly on $D_{\times }$. Since the latter remains unrenormalized, we obtain universality classes varying continuously with $D_{\times }$. More interestingly, by changing $D_{\times }$ continuously from zero, we can make our system move away from its equilibrium behavior (i.e., when $D_{\times }=0$) continuously and incrementally.

We investigate both analytically and numerically the renormalization group equations in two-dimensional (2D) $Z\left(N\right)$ vector models. The position of the critical points of the two phase transitions for $N>4$ is established and the critical index $\nu$ is computed. For $N=7$ and 17 the critical points are located by Monte Carlo simulations, and some of the corresponding critical indices are determined. The behavior of the helicity modulus is studied for $N=5$, 7, and 17. Using these and other available Monte Carlo data we discuss the scaling of the critical points with $N$ and some other open theoretical problems.

In this work the critical indices $\beta$, $\gamma$, and $\nu$ for a three-dimensional (3D) hardcore cylinder composite system with short-range interaction have been obtained. In contrast to the 2D stick system and the 3D hardcore cylinder system, the determined critical exponents do not belong to the same universality class as the lattice percolation, although they obey the common hyperscaling relation for a 3D system. It is observed that the value of the correlation length exponent is compatible with the predictions of the mean field theory. It is also shown that, by using the Alexander-Orbach conjuncture, the relation between the conductivity and the correlation length critical exponents has a typical value for a 3D lattice system.

An improvement of Weinberg's quasiparticle method for solving general one-dimensional integral equations is presented. The method uses simple auxiliary Sturmian functions for positive or negative energies, and corrects iteratively for the truncation errors of the Sturmian expansion of the solution. Numerical examples are given for the solution of the Lippmann-Schwinger integral equation for the scattering of a particle from a potential with a repulsive core. An accuracy of $1:{10}^6$ is achieved after 14 iterations, and $1:{10}^{10}$ after 20 iterations. The calculations are carried out in configuration space with an accuracy of $1:{10}^{11}$ by using a spectral expansion method in terms of Chebyshev polynomials. The method can be extended to solving a Schrödinger equation with Coulomb and/or nonlocal potentials.