We show that a large class of pulse-coupled oscillators converge with high probability from random initial conditions on a large class of graphs with time delays. Our analysis combines previous local convergence results, probabilistic network analysis, and a classification scheme for type-II phase response curves to produce rigorous lower bounds for convergence probabilities based on network density. These results suggest methods for the analysis of pulse-coupled oscillators, and provide insights into the balance of excitation and inhibition in the operation of biological type-II phase response curves and also the design of decentralized and minimal clock synchronization schemes in sensor nets.

For a flowing, self-oscillating medium, we study the competition between traveling flow-distributed-oscillation waves excited by periodic driving at the upstream boundary and bulk oscillations originating downstream from the boundary. As previously observed in the case of stationary driving, we find that there is a region in parameter space where boundary-driven traveling waves of sufficiently high amplitude can impose themselves on the entire medium despite the presence of an absolute instability, which otherwise tends to block information from upstream. For sufficiently low flow rates, however, the imposed waves are arrested at a nonlinear blocking transition. Unlike the stationary case, we find that the region of imposed waves extends well into regions where, according to the linear approximation, there should be no traveling waves at all. This suggests that the extinction of the traveling waves is analogous to a subcritical Hopf bifurcation.

A random walk scheme, consisting of alternating phases of regular Brownian motion and Lévy walks, is proposed as a model for run-and-tumble bacterial motion. Within the continuous-time random walk approach we obtain the long-time and short-time behavior of the mean squared displacement of the walker as depending on the properties of the dwelling time distribution in each phase. Depending on these distributions, normal diffusion, superdiffusion, and ballistic spreading may arise.

In this work, we introduce two spatiotemporal colored bounded noises, based on the zero-dimensional Cai-Lin and Tsallis-Borland noises. Then we study and characterize the dependence of the defined stochastic processes on both a temporal correlation parameter $\tau$ and a spatial coupling parameter $\lambda$. In particular, we found that varying $\lambda$ may induce a transition of the distribution of the noise from bimodality to unimodality. With the aim of investigating the role played by bounded noises in nonlinear dynamical systems, we analyze the behavior of the real Ginzburg-Landau time-varying model additively perturbed by such noises. The observed phase transition phenomenology is quite different from that observed when the perturbations are unbounded. In particular, we observed an inverse order-to-disorder transition and a reentrant transition, with dependence on the specific type of bounded noise.

We consider the formation of finite-size domains in lipid bilayers consisting of saturated and hybrid lipids. First, we describe a monolayer model that includes a coupling between a compositional scalar field and a two-dimensional vectorial order parameter. Such a coupling yields an effective two-dimensional microemulsion free energy for the lipid monolayer, and its characteristic length of compositional modulations can be considered as the origin of finite-size domains in biological membranes. Next, we consider a coupled bilayer composed of two modulated monolayers and discuss the static and dynamic properties of concentration fluctuations above the transition temperature. We also investigate the micro-phase separation below the transition temperature and compare the micro-phase separated structures with statics and dynamics of concentration fluctuations above the transition.

We investigate the physical meaning of quantum superposition states between reactants and products in electron transfer reactions. We show that such superpositions are strongly suppressed and, to leading orders of perturbation theory, do not pertain in electron transfer reactions. This is because of the intermediate manifold of states separating the reactants from the products. We provide an intuitive description of these considerations with Feynman diagrams. We also discuss the relation of such quantum coherences to understanding the fundamental quantum dynamics of spin-selective radical-ion-pair reactions.

Catastrophes of all kinds can be roughly defined as short-duration, large-amplitude events following and followed by long periods of “ripening.” Major earthquakes surely belong to the class of “catastrophic” events. Because of the space-time scales involved, an experimental approach is often difficult, not to say impossible, however desirable it could be. Described in this article is a “laboratory” setup that yields data of a type that is amenable to theoretical methods of prediction. Observations are made of a critical slowing down in the noisy signal of a solder wire creeping under constant stress. This effect is shown to be a fair signal of the forthcoming catastrophe in two separate dynamical models. The first is an “abstract” model in which a time-dependent quantity drifts slowly but makes quick jumps from time to time. The second is a realistic physical model for the collective motion of dislocations (the Ananthakrishna set of equations for unstable creep). Hope thus exists that similar changes in the response to noise could forewarn catastrophes in other situations, where such precursor effects should manifest early enough.

The mean rate of energy dissipation $\langle \varepsilon \rangle$ per unit mass of turbulence is often written in the form of $\langle \varepsilon \rangle =C_u{\langle u^2\rangle }^{3/2}/L_u$, where the root-mean-square velocity fluctuation ${\langle u^2\rangle }^{1/2}$ and the velocity correlation length $L_u$ are parameters of the energy-containing large scales. However, the dimensionless coefficient $C_u$ is known to depend on the flow configuration that is to induce the turbulence. We define the correlation length $L_{u^2}$ of the local energy $u^2$, study $C_{u^2}=\langle \varepsilon \rangle L_{u^2}/{\langle u^2\rangle }^{3/2}$ with experimental data of several flows, and find that $C_{u^2}$ does not depend on the flow configuration. Not $L_u$ but $L_{u^2}$ could serve universally as the typical size of the energy-containing eddies, so that ${\langle u^2\rangle }^{3/2}/L_{u^2}$ is proportional to the rate at which the kinetic energy is removed from those eddies and is eventually dissipated into heat. The independence from the flow configuration is also found for the two-point correlations and so on when $L_{u^2}$ is used to normalize the scale.

In a recent paper [Yiotis et al., Phys. Rev. E 85, 046308 (2012)] we developed a model for the drying of porous media in the presence of gravity. It incorporated effects of corner film flow, internal and external mass transfer, and the effect of gravity. Analytical results were derived when gravity opposes drying and hence leads to a stable percolation drying front. In this paper, we test the theory using laboratory experiments. A series of isothermal drying experiments in glass bead packings saturated with volatile hydrocarbons is conducted. The transparent glass cells containing the packing allow for the visual monitoring of the phase distribution patterns below the surface, including the formation of liquid films, as the gaseous phase invades the pore space, and for the control of the thickness of the diffusive mass boundary layer over the packing. The experimental results agree very well with theory, provided that the latter is generalized to account for the effects of corner roundness in the film region (which was neglected in the theoretical part). We demonstrate the existence of an early constant rate period (CRP), which lasts as long as the films saturate the surface of the packing, and of a subsequent falling rate period (FRP), which begins practically after the detachment of the film tips from the external surface. During the CRP, the process is controlled by diffusion within the stagnant gaseous phase in the upper part of the cells, yielding a Stefan tube problem solution. During the FRP, the process is controlled by diffusion within the packing, with a drying rate inversely proportional to the observed position of the film tips in the cell. Theoretical and experimental results compare favorably for a specific value of the roundness of the films, which is found to be constant and equal to 0.2 for various conditions, and verify the theoretical dependence on the capillary ${\mathrm{Ca}}_f$, Bond $\mathrm{Bo},$ and Sherwood $\mathrm{Sh}$ numbers.

A coarse-grained lattice Metropolis Monte Carlo (CG-MMC) method is presented for simulating fluid systems described by standard molecular force fields. First, a thermodynamically consistent coarse-grained interaction potential is obtained numerically and automatically from a continuous force field such as Lennard-Jones. The coarse-grained potential then is used to drive CG-MMC simulations of vapor-liquid equilibrium in Lennard-Jones, square-well, and simple point charge water systems. The CG-MMC predicts vapor-liquid phase envelopes, as well as the particle density distributions in both the liquid and vapor phases, in excellent agreement with full-resolution Monte Carlo simulations, at a fraction of the computational cost.

For any translation-invariant quantum lattice system with a symmetry group $G$, we propose a practical and universal construction of order parameters which identify quantum phase transitions with symmetry-breaking order. They are defined in terms of the fidelity between a ground state and its symmetry-transformed counterpart, and are computed through tensor network representations of the ground-state wave function. To illustrate our scheme, we consider three quantum systems on an infinite lattice in one spatial dimension, namely, the quantum Ising model in a transverse magnetic field, the quantum spin-$\frac{1}{2}$$XYX$ model in an external magnetic field, and the quantum spin-1 $XXZ$ model with single-ion anisotropy. All these models have symmetry group ${\mathbb{Z}}_2$ and exhibit broken-symmetry phases. We also discuss the role of the order parameters in identifying factorized states.

We study a layer of grains atop a plate which oscillates sinusoidally in the direction of gravity, using three-dimensional, time-dependent numerical solutions of continuum equations to Navier-Stokes order as well as hard-sphere molecular dynamics simulations. For high accelerational amplitudes of the plate, the layer exhibits a steady-state “density inversion” in which a high-density portion of the layer is supported by a lower-density portion. At low accelerational amplitudes, the layer exhibits oscillatory time dependence that is strongly correlated to the motion of the plate. We show that continuum simulations yield results consistent with molecular dynamics results in both regimes.

Recently Wang et al. [Phys. Rev. Lett. 104, 027801 (2010)] reported the discovery of a novel multilayer phase in polar liquid crystals. The phase was unambiguously assigned to a six-layer antiferroelectric structure (Sm-$C_{d6}^{*}$) by resonant x-ray diffraction. This discovery lead to essential progress in understanding the nature of polar phases. However, more recently, Chandani et al. [Liq. Cryst. 38, 663 (2011)] in the same material clearly identified the novel phase as a ferrielectric five-layer structure (Sm-$C_{d5}^{*}$) by the electric-field-induced birefringence. This contradiction seemed to be a mystery. In this paper we show that the two experiments are in agreement. Phenomenological Landau theory of the phase transitions shows that both phases (Sm-$C_{d6}^{*}$ and Sm-$C_{d5}^{*}$) exist and transform into each other in a relatively low electric field.

The virial expansion method is applied within a harmonic approximation to an interacting $N$-body system of identical fermions. We compute the canonical partition functions for two and three particles to get the two lowest orders in the expansion. The energy spectrum is carefully interpolated to reproduce ground-state properties at low temperature and the noninteracting high-temperature limit of constant virial coefficients. This resembles the smearing of shell effects in finite systems with increasing temperature. Numerical results are discussed for the second and third virial coefficients as functions of dimension, temperature, interaction, and transition temperature between low- and high-energy limits.

We consider heat transfer between two thermal reservoirs mediated by a quantum system using the generalized quantum Langevin equation. The thermal reservoirs are treated as ensembles of oscillators within the framework of the Drude-Ullersma model. General expressions for the heat current and thermal conductance are obtained for arbitrary coupling strength between the reservoirs and the mediator and for different temperature regimes. As an application of these results we discuss the origin of Fourier's law in a chain of large but finite subsystems coupled to each other by the quantum mediators. We also address a question of anomalously large heat current between the scanning tunneling microscope (STM) tip and substrate found in a recent experiment. The question of minimum thermal conductivity is revisited in the framework of scaling theory as a potential application of the developed approach.

For highly charged dielectric surfaces, the asymptotic structure underlying electrokinetic phenomena in the thin-double-layer limit reshuffles. The large counterion concentration near the surface, associated with the Boltzmann distribution in the diffuse layer, supports appreciable tangential fluxes appearing as effective surface currents in a macroscale description. Their inevitable nonuniformity gives rise in turn to comparable transverse currents, which, for logarithmically large zeta potentials, modify the electrokinetic transport in the electroneutral bulk. To date, this mechanism has been studied only using a weak-field linearization. We present here a generic thin-double-layer analysis of the electrokinetic transport about highly charged dielectric solids, which is not restricted to weak fields. We identify the counterion concentration amplification with the emergence of an internal boundary layer—within the diffuse part of the double layer—characterized by distinct scaling of ionic concentrations and electric field. In this multiscale description, surface conduction is conveniently localized within the internal layer. Our systematic scheme thus avoids the cumbersome procedure of retaining small asymptotic terms which change their magnitude at large zeta potentials. The electrokinetic transport predicted by the resulting macroscale model is inherently accompanied by bulk concentration polarization, which in turn results in nonlinear bulk transport. A novel fundamental subtlety associated with this intrinsic feature, overlooked in the weak-field approximation, has to do with the ambiguity of the “particle zeta potential” concept: In general, even uniformly charged surfaces are characterized by a nonuniform zeta-potential distribution. This impairs the need for a careful identification of the dimensionless number representing the transition to large zeta potentials.

We study closed liquid membranes that segregate into three phases due to differences in the chemical and physical properties of its components. The shape and in-plane membrane arrangement of the phases are coupled through phase-specific bending energies and line tensions. We use simulated annealing Monte Carlo simulations to find low-energy structures, allowing both phase arrangement and membrane shape to relax. The three-phase system is the simplest one in which there are multiple interface pairs, allowing us to analyze interfacial preferences and pairwise distinct line tensions. We observe the system's preference for interface pairs that maximize differences in spontaneous curvature. From a pattern selection perspective, this acts as an effective attraction between phases of most disparate spontaneous curvature. We show that this effective attraction is robust enough to persist even when the interface between these phases is the most penalized by line tension. This effect is driven by geometry and not by any explicit component-component interaction.

We explore mode locking of spontaneous oscillations of saccular hair cell bundles to periodic mechanical deflections. A simple dynamic systems framework is presented that captures the main features of the experimentally observed behavior in the form of an Arnold tongue. We propose that the phase-locking transition can proceed via different bifurcations. At low stimulus amplitudes $F$, the transition to mode locking as a function of the stimulus frequency $\omega$ has the character of a saddle-node bifurcation on an invariant circle. At higher stimulus amplitudes, the mode-locking transition has the character of a supercritical Andronov-Hopf bifurcation.

We use a standard discrete-time linear Gaussian model to analyze the information storage capability of individual nodes in complex networks, given the network structure and link weights. In particular, we investigate the role of two- and three-node motifs in contributing to local information storage. We show analytically that directed feedback and feedforward loop motifs are the dominant contributors to information storage capability, with their weighted motif counts locally positively correlated to storage capability. We also reveal the direct local relationship between clustering coefficient(s) and information storage. These results explain the dynamical importance of clustered structure and offer an explanation for the prevalence of these motifs in biological and artificial networks.

The local density of states (LDOS) is a distribution that characterizes the effects of perturbations on quantum systems. Recently, a semiclassical theory was proposed for the LDOS of chaotic billiards and maps. This theory predicts that the LDOS is a Breit-Wigner distribution independent of the perturbation strength and also gives a semiclassical expression for the LDOS width. Here, we test the validity of such an approximation in quantum maps by varying the degree of chaoticity, the region in phase space where the perturbation is applied, and the intensity of the perturbation. We show that for highly chaotic maps or strong perturbations the semiclassical theory of the LDOS is accurate to describe the quantum distribution. Moreover, the width of the LDOS is also well represented for its semiclassical expression in the case of mixed classical dynamics.