An algorithm to calculate the density of states, based on the well-known Wang-Landau method, is introduced. Independent random walks are performed in different restricted ranges of energy, and the resultant density of states is modified by a function of time, $F\left(t\right)\propto t^{-1}$, for large time. As a consequence, the calculated density of state, $g_m(E,t)$, approaches asymptotically the exact value $g_{\mathit{ex}}\left(E\right)$ as $\propto t^{-1∕2}$, avoiding the saturation of the error. It is also shown that the growth of the interface of the energy histogram belongs to the random deposition universality class.

The adsorption-desorption phenomenon of neutral particles dissolved in an isotropic fluid is investigated by using a nonsingular kernel in the kinetic equation at the limiting surfaces. To account for the relevance of a memory effect, three types of kernels in the kinetic equation are considered. Similar kernels have been used to investigate nonexponential relaxation including several contexts such as dielectric relaxation, diffusion-controlled relaxation in liquids, liquid crystals, and amorphous polymers. A suitable choice for a temporal kernel can account for the relative importance of physisorption or chemisorption, according to the time scale governing the adsorption phenomena, and can be the key mechanism to understand the specific roles of both processes. By using a general procedure, the time evolution of the density of particles is determined in closed analytical form. The analysis is relevant in the description of the adsorption phenomena in general.

We study the creep rupture of viscoelastic fiber bundles under uniaxial constant tensile loading, assuming global load sharing (GLS) for the redistribution of load following fiber failure. We consider loading paths such that the stress raises to a value ${\sigma }_0$ under a time-independent loading (negligible creep strain) and remains fixed thereafter. Motivated by experimental observations, we introduce an “effective” strain controlled failure criterion to incorporate damage into the system, thus damage is distributed over time. In addition, when a “limit” value for the effective stress is reached, failure of the remaining alive fibers is instantaneous. This enables us to show both analytically and numerically that creep rupture occurs for external loads above a critical value that is less than the static fracture bundle’s strength in accordance with experimental observations. An analytical expression for this critical load is given. For stress levels below the critical value, the system suffers only partial failure since the deformation tends to a stationary solution for which the effective stress is below the limit value giving rise to an infinite lifetime. On the other hand, if the time-independent loading process ends in the softening regime, the deformation of the system monotonically increases in time resulting in global failure at finite time irrespectively of the applied load. Moreover, the applied model is found to be consistent with the experimentally observed increase of the creep rupture displacement with decreasing steady external load (above the critical value).

One-variable thermostats are studied as a generalization of the Nosé-Hoover method, which is aimed at achieving Gibbs’ canonical distribution while conserving the time reversibility. A condition for equations of motion for the system with the thermostats is derived in the form of a partial differential equation. Solutions of this equation constitute a family of thermostats including the Nosé-Hoover method as the minimal solution. It is shown that the one-variable thermostat coupled with the one-dimensional harmonic oscillator loses its ergodicity with large enough relaxation time. The present result suggests that multivariable thermostats are required to assure the ergodicity and to work as a heat bath.

Acoustic measurements of aqueous foams show three distinct radiation mechanisms that contribute to the sound pressure field: oscillations of a bubble surface that precede popping due to the instability of thin liquid film, impulsive radiation due to bursts of bubbles, and oscillations from neighboring bubbles excited by a burst bubble. The movies captured by a fast camera confirm that the bubbles adjacent to a breaking bubble oscillate under the influence of the pressure generated by the burst bubble. The spectra of resulting transient sounds fall in the range of $2–8\mathrm{kHz}$ and those from bubble oscillations correlate well with the bubble size.

We investigate the effect of interactions between inclusions on the coarsening behavior of elastically inhomogeneous multiphase systems with lattice misfit using a recently introduced two-dimensional multiscale model based on the classical time-dependent density-functional theory. We show that spontaneous shape changes are very efficient in limiting the impact of the interactions on the chemical potential of inclusions. For this reason, the interactions between isolated pairs of inclusions are unable to significantly affect coarsening. At higher volume fraction, the efficiency of shape changes drops and major shifts of the chemical potential are observed; these are shown to be strong enough to counteract capillarity. For example, we show that sufficient confinement by neighboring inclusions causes inverse coarsening and we provide illustrations of this. We also examine the effect of interface elasticity in the presence of interactions. We demonstrate that elasticity induces kinetic faceting and gives rise to oscillations in the chemical potential of the inclusions. This is shown to lead to the stabilization of microstructures composed of inclusions of various sizes. Finally, we propose a simple modified Lifshitz-Slyozov-Wagner model for assessing the effect of interactions on coarsening. The results are shown to be in excellent agreement with experiment.

Through phase plane analysis of a class of two-dimensional spiking and bursting neuron models, covering some of the most popular map-based neuron models, we show that there exists a trade-off between the sensitivity of the neuron to steady external stimulation and its resonance properties, and how this trade-off may be tuned by the neutral or asymptotic character of the slow variable. Implications of the results for the suprathreshold behavior of the neurons, both by themselves and as part of networks, are presented in different regimes of interest, such as the excitable, regular spiking, and bursting regimes. These results establish a consistent link between single-neuron parameters and resulting network dynamics, and will hopefully be useful as a guide for modeling.

We report an experimental study on transient membrane permeabilization of single living bovine aortic endothelial cells (BAEC) by tightly focused femtosecond near-infrared laser pulses. The membrane permeabilization of the BAEC cells was studied as a function of the incident laser intensity. The rate of dye uptake by the cells was analyzed using time-lapse imaging. We found that membrane permeabilization occurs for laser intensities higher than $4.0\times {10}^{12}\mathrm{W}∕{\mathrm{cm}}^2$. For laser intensity above $3.3\times {10}^{13}\mathrm{W}∕{\mathrm{cm}}^2$ the cell disintegrates. Within these two limits the rate of dye uptake increases logarithmically with increasing laser intensity. This functional dependence is explained by considering the Gaussian intensity distribution across the laser focal spot. Cell membrane permeabilization is explained by the creation of a plasma within the laser focal spot. The physical understanding of the relationship between dye uptake, pore characteristics, and laser intensity allows control of the concentrations of molecules delivered into cells through the control of pore characteristics.

We study the mechanical properties of semiflexible polymers when the contour length of the polymer is comparable to its persistence length. We compute the exact average end-to-end distance and shape of the polymer for different boundary conditions, and show that boundary effects can lead to significant deviations from the well-known long-polymer results. We also consider the case of stretching a uniformly charged biopolymer by an electric field, for which we compute the average extension and the average shape, which is shown to be trumpetlike. Our results also apply to long biopolymers when thermal fluctuations have been smoothed out by a large applied field or force.

A popular approach for describing the structure of many complex networks focuses on graph theoretic properties that characterize their large-scale connectivity. While it is generally recognized that such descriptions based on aggregate statistics do not uniquely characterize a particular graph and also that many such statistical features are interdependent, the relationship between competing descriptions is not entirely understood. This paper lends perspective on this problem by showing how the degree sequence and other constraints (e.g., connectedness, no self-loops or parallel edges) on a particular graph play a primary role in dictating many features, including its correlation structure. Building on recent work, we show how a simple structural metric characterizes key differences between graphs having the same degree sequence. More broadly, we show how the (often implicit) choice of a background set against which to measure graph features has serious implications for the interpretation and comparability of graph theoretic descriptions.

We study the problem of controlling a general complex network toward an assigned synchronous evolution by means of a pinning control strategy. We define the pinning controllability of the network in terms of the spectral properties of an extended network topology. The roles of the control and coupling gains, as well as of the number of pinned nodes, are also discussed.

The inverse energy cascade in two-dimensional Navier-Stokes turbulence is examined in the quasisteady regime, with small-scale, band-limited forcing at scale $k_f^{-1}$, with particular attention to the influence of forcing Reynolds number Re on the energy distribution at large scales. The strength of the inverse energy cascade, or fraction of energy input that is transferred to larger scales, increases monotonically toward unity with increasing $\mathrm{Re}\propto k_{\max }^2∕k_f^2$, where $k_{\max }$ is the maximum resolved wave number. Moreover, as Re increases beyond a critical value, for which a direct enstrophy cascade to small scales is first realized, the energy spectrum in the energy-cascading range steepens from a $k^{-5∕3}$ to $k^{-2}$ dependence. The steepening is interpreted as the result of a greater tendency for coherent vortex formation in cases when forcing scales are adequately resolved. In spectral space, it is associated with nonlocality of the inverse energy transfer.

In this study, existing primary stability boundary data for flow between concentric cylinders, for the broad range of radius and rotation ratios examined, were found to be self-similar in a properly chosen parameter space. The experimental results for the primary transitions to both Taylor vortex flow and spiral vortex flow collapsed onto a single curve using a combination of variables technique, for both counter-rotating and co-rotating cylinders. The curves were then empirically fit, yielding explicit analytic formulas for the critical Reynolds number for any radius ratio $\left(\eta \right)$ and rotation ratio $\left(\mu \right)$. For counter-rotating flows, the primary critical Reynolds number is determined by a single variable: the ratio of the nodal gap fraction to a known function of the radius ratio. The existence and influence of a nodal surface is shown experimentally for $\mu \cong -1.7$. For co-rotating flows, the important scaled variable was found to be the radius ratio divided by the nodal radius ratio. Comparisons of the resulting explicit stability formulas were made to existing analytic stability expressions and experimental data. Excellent quantitative agreement was found with data across the entire parameter space.

The effects of a feedback with multiple time delays on noise-induced dynamics are studied in a nonlinear system close to the Hopf instability. We show analytically and numerically that such a feedback creates two distinct time scales, which can be tuned independently by the feedback parameters. In this way, the coherence of noise-induced oscillations can be drastically improved, and an arbitrarily large correlation of oscillations can be achieved without inducing a bifurcation. This opens up new perspectives for control of stochastic dynamical systems.

Thermophoresis, akin to thermal diffusion in simple fluid mixtures, consists of particle drift induced by a temperature gradient. Notwithstanding its practical interest, the dependence of thermophoretic effects on particle size $R$ is still theoretically and experimentally debated. By performing measurements of water-in-oil microemulsion droplets with tunable size, we show that the thermal diffusion coefficient, at least for a suspension of small particles in a nonpolar solvent, does not appreciably depend on $R$.

Concentrated bacterial suspensions spontaneously develop transient spatiotemporal patterns of coherent locomotion whose correlation lengths greatly exceed the size of individual organisms. Continuum models have indicated that a state of uniform swimming order is linearly unstable at finite wavelengths, but have not addressed the nonlinear dynamics of the coherent state, with its biological implications for mixing, transport, and intercellular communication. We investigate a specific model incorporating hydrodynamic interactions in thin-film geometries and show by numerical studies that it displays large scale persistently recurring vortices, as actually observed.

We study the barrier crossing of a particle driven by white symmetric Lévy noise of index $\alpha$ and intensity $D$ for three different generic types of potentials: (a) a bistable potential, (b) a metastable potential, and (c) a truncated harmonic potential. For the low noise intensity regime we recover the previously proposed algebraic dependence on $D$ of the characteristic escape time, $T_{\mathrm{esc}}\simeq C\left(\alpha \right)∕D^{\mu \left(\alpha \right)}$, where $C\left(\alpha \right)$ is a coefficient. It is shown that the exponent $\mu \left(\alpha \right)$ remains approximately constant, $\mu \approx 1$ for $0<\alpha <2$; at $\alpha =2$ the power-law form of $T_{\mathrm{esc}}$ changes into the known exponential dependence on $1∕D$; it exhibits a divergencelike behavior as $\alpha$ approaches 2. In this regime we observe a monotonous increase of the escape time $T_{\mathrm{esc}}$ with increasing $\alpha$ (keeping the noise intensity $D$ constant). The probability density of the escape time decays exponentially. In addition, for low noise intensities the escape times correspond to barrier crossing by multiple Lévy steps. For high noise intensities, the escape time curves collapse for all values of $\alpha$. At intermediate noise intensities, the escape time exhibits nonmonotonic dependence on the index $\alpha$, while still retaining the exponential form of the escape time density.

A closed form expression for the propagator is derived, in terms of modified Bessel functions, for the Fokker-Planck equation for a physically important generalization of the Ornstein-Uhlenbeck process where the diffusion constant $D\left(p\right)$ is a function of the momentum. The closed form is found for the general case $D\left(p\right)\sim {\mid p\mid }^{-\alpha }$ where $\alpha ⩾0$ and leads to the standard Gaussian form for $\alpha =0$. The propagator for the specific case $D\left(p\right)\sim {\mid p\mid }^{-1}$ is used to derive analytic expressions for probability distributions and correlation coefficients. An exact expression is found for the constant of proportionality for the anomalous diffusion of the mean-square displacement of a particle at short times.

Using multispeckle x-ray photon correlation spectroscopy, we have measured the slow, wave-vector-dependent dynamics of concentrated, disordered nanoemulsions composed of silicone oil droplets in water. The intermediate scattering function possesses a compressed exponential line shape and a relaxation time that varies inversely with wave vector. We interpret this dynamics as strain in response to local stress relaxation. The motion includes a transient component whose characteristic velocity decays exponentially with time following a mechanical perturbation of the nanoemulsions and a second component whose characteristic velocity is essentially independent of time. The steady-state characteristic velocity is surprisingly insensitive to the droplet volume fraction in the concentrated regime, indicating that the strain motion is only weakly dependent on the droplet-droplet interactions.

Lateral diffusion on curved biological membranes has been studied theoretically and experimentally. However, how membrane geometries influence the diffusion process remains unclear. Here we show the significance of Gaussian curvature by numerically solving the diffusion equation in a geodesic polar coordinate system with regard to several types of surfaces including elliptic and hyperbolic paraboloids. On surfaces where Gaussian curvature has positive and negative values, diffusion is slower and faster than on the plane, respectively. The deviation from the normal diffusion on the plane tends to get larger as the absolute value of Gaussian curvature increases. Diffusion is anisotropic at a surface region where the normal curvature is anisotropic and Gaussian curvature has nonzero values. The anisotropy can be classified into several types according to whether diffusion is the fastest or the slowest in the principal directions. In the case of diffusion on spheroids, the limited area of a closed surface reduces the diffusion rate so greatly that the slowdown effects of positive values of Gaussian curvature are concealed. Analysis of the diffusion equation suggests that Gaussian curvature causes slowed or accelerated diffusion and anisotropic diffusion in any type of surface. Furthermore, it is discussed the degree to which Gaussian curvature influences diffusive phenomena taking place in real membranes through such effects. These results provide a different image of biological membranes that lateral diffusion of membrane molecules is usually anisotropic and the diffusion rate kaleidoscopically changes according to place.