Brownian particles in random potentials show an extended regime of subdiffusive dynamics at intermediate times. The asymptotic diffusive behavior is often established at very long times and thus cannot be accessed in experiments or simulations. For the case of one-dimensional random potentials with Gaussian distributed energies, we present a detailed analysis of experimental and simulation data. It is shown that the asymptotic long-time diffusion coefficient can be related to the behavior at intermediate times, namely, the minimum of the exponent that characterizes subdiffusion and hence corresponds to the maximum degree of subdiffusion. As a consequence, investigating only the dynamics at intermediate times is sufficient to predict the order of magnitude of the long-time diffusion coefficient and the time scale at which the crossover from subdiffusion to diffusion occurs, i.e., when the long-time diffusive regime and hence thermal equilibrium is established. Inversely, theoretical predictions derived for the asymptotic long-time behavior can be used to quantitatively characterize the intermediate behavior, which hardly has been studied so far.

Molecular dynamics simulations with varying damping are used to examine the effects of inertia and spatial dimension on sheared disordered solids in the athermal quasistatic limit. In all cases the distribution of avalanche sizes follows a power law over at least three orders of magnitude in dissipated energy or stress drop. Scaling exponents are determined using finite-size scaling for systems with ${10}^3$–${10}^6$ particles. Three distinct universality classes are identified corresponding to overdamped and underdamped limits, as well as a crossover damping that separates the two regimes. For each universality class, the exponent describing the avalanche distributions is the same in two and three dimensions. The spatial extent of plastic deformation is proportional to the energy dissipated in an avalanche. Both rise much more rapidly with system size in the underdamped limit where inertia is important. Inertia also lowers the mean energy of configurations sampled by the system and leads to an excess of large events like that seen in earthquake distributions for individual faults. The distribution of stress values during shear narrows to zero with increasing system size and may provide useful information about the size of elemental events in experimental systems. For overdamped and crossover systems the stress variation scales inversely with the square root of the system size. For underdamped systems the variation is determined by the size of the largest events.

Using high-speed confocal microscopy, we measure the particle positions in a colloidal suspension under large-amplitude oscillatory shear. Using the particle positions, we quantify the in situ anisotropy of the pair-correlation function, a measure of the Brownian stress. From these data we find two distinct types of responses as the system crosses over from equilibrium to far-from-equilibrium states. The first is a nonlinear amplitude saturation that arises from shear-induced advection, while the second is a linear frequency saturation due to competition between suspension relaxation and shear rate. In spite of their different underlying mechanisms, we show that all the data can be scaled onto a master curve that spans the equilibrium and far-from-equilibrium regimes, linking small-amplitude oscillatory to continuous shear. This observation illustrates a colloidal analog of the Cox-Merz rule and its microscopic underpinning. Brownian dynamics simulations show that interparticle interactions are sufficient for generating both experimentally observed saturations.

The phase behavior of hard boardlike biaxial particles of relative dimensions close to the clamitic to discotic crossover is explored by means of Monte Carlo molecular simulations. Transitions between two distinct biaxial nematic phases as well as transitions from a biaxial nematic to a uniaxial Sm-$A$ phase are obtained. The formation of anisotropic supramolecular assemblies is demonstrated and is quantified by means of rotationally invariant pair correlation functions.

Synfire chains are thought to underlie precisely timed sequences of spikes observed in various brain regions and across species. How they are formed is not understood. Here we analyze self-organization of synfire chains through the spike-timing dependent plasticity (STDP) of the synapses, axon remodeling, and potentiation decay of synaptic weights in networks of neurons driven by noisy external inputs and subject to dominant feedback inhibition. Potentiation decay is the gradual, activity-independent reduction of synaptic weights over time. We show that potentiation decay enables a dynamic and statistically stable network connectivity when neurons spike spontaneously. Periodic stimulation of a subset of neurons leads to formation of synfire chains through a random recruitment process, which terminates when the chain connects to itself and forms a loop. We demonstrate that chain length distributions depend on the potentiation decay. Fast potentiation decay leads to long chains with wide distributions, while slow potentiation decay leads to short chains with narrow distributions. We suggest that the potentiation decay, which corresponds to the decay of early long-term potentiation of synapses, is an important synaptic plasticity rule in regulating formation of neural circuity through STDP.

We present experimental and theoretical arguments, at the single-neuron level, suggesting that neuronal response fluctuations reflect a process that positions the neuron near a transition point that separates excitable and unexcitable phases. This view is supported by the dynamical properties of the system as observed in experiments on isolated cultured cortical neurons, as well as by a theoretical mapping between the constructs of self-organized criticality and membrane excitability biophysics.

We study the interaction of phase singularities with homogeneous Neumann boundaries in one, two, and three spatial dimensions for the complex Ginzburg-Landau equation. The existence of a boundary-induced drift attractor, well known for spiral waves in two spatial dimensions, is demonstrated for scroll waves in three spatial dimensions. We find that a cylindrical Neumann boundary can lock a scroll ring, thus preventing the collapse of its closed filament.

We examine the connectivity fluctuations across networks obtained when the horizontal visibility (HV) algorithm is used on trajectories generated by nonlinear circle maps at the quasiperiodic transition to chaos. The resultant HV graph is highly anomalous as the degrees fluctuate at all scales with amplitude that increases with the size of the network. We determine families of Pesin-like identities between entropy growth rates and generalized graph-theoretical Lyapunov exponents. An irrational winding number with pure periodic continued fraction characterizes each family. We illustrate our results for the so-called golden, silver, and bronze numbers.

It is of fundamental significance, especially with regard to application, to fully understand the flow behavior of unsteady natural convection boundary layers on a vertical plate heated by a time-dependent heat flux. Such an understanding is currently scarce. In this paper, the scaling analysis by Lin et al.  [Phys. Rev. E 79, 066313 (2009)] using a simple three-region structure for the unsteady natural convection boundary layer of a homogeneous Newtonian fluid with $\mathrm{Pr}>1$ under isothermal heating was substantially extended for the case when the heating is due to a time-varying sinusoidal heat flux. A series of scalings was developed for the thermal boundary thickness, the plate temperature, the viscous boundary thicknesses, and the maximum vertical velocity within the boundary layer, which are the major parameters representing the flow behavior, in terms of the governing parameters of the flow, i.e., the Rayleigh number Ra, the Prandtl number Pr, and the dimensionless natural frequency $f_n$ of the time-varying sinusoidal heat flux, at the start-up stage, at the transition time scale which represents the ending of the start-up stage and the beginning of the transitional stage of the boundary-layer development, and at the quasi-steady stage. These scalings were validated by comparison to 10 full numerical solutions of the governing equations with Ra, Pr, and $f_n$ in the ranges ${10}^6\le \mathrm{Ra}\le {10}^9$, $3\le \mathrm{Pr}\le 100$, and $0.01\le f_n\le 0.1$ and were shown in general to provide an accurate description of the flow at different development stages, except for high-Pr runs in which a further, although weak, Pr dependence is present, which cannot be accurately predicted by the current scaling analysis using the simple three-region structure, attributed to the non-boundary-layer nature of the velocity field with high-Pr fluids. Some scalings at the transition time scale and at the quasi-steady stage also produce noticeable deviations from the numerical results when $f_n$ is reduced, indicating that there may be a further $f_n$ dependence of the scalings which also cannot be accurately predicted by the current scaling analysis.

We present a signed measure analysis of compressible Hall magnetohydrodynamic turbulence with an external guide field. Signed measure analysis allows us to characterize the scaling behavior of the sign-oscillating flow structures and their geometrical properties (fractal dimensions of structures). A reduced numerical model, valid when a strong guide magnetic field is present, is used here. In order to discuss the effect of the Hall term, different values for the ion skin depth are considered in the simulations. Results show that as the Hall term is increased, the fractal dimension of the current and vorticity sheets decreases. This observation, together with previous analysis of the same fields, provides a comprehensive description of the effect of the Hall force on the formation of structures. Two main processes are identified, namely, the widening and unraveling of the sheets.

Transport properties in random and scale-free (SF) networks are studied by analyzing the betweenness centrality (BC) distribution $P\left(B\right)$ in the minimum spanning trees (MSTs) and infinite incipient percolation clusters (IIPCs) of the networks. It is found that $P\left(B\right)$ in MSTs scales as $P\left(B\right)\sim B^{-\delta }$. The obtained values of $\delta$ are classified into two different categories, $\delta \simeq 1.6$ and $\delta \simeq 2.0$. Using the mapping between BC and the branch size of tree structures, it is proved that $\delta$ in MSTs which are close to critical trees is 1.6. In contrast, $\delta$ in MSTs which are supercritical trees is shown to be 2.0. We also find $\delta =1.5$ in IIPCs, which is a natural result because IIPC is physically critical. Based on the results in MSTs, a physical reason why $\delta \ge 2$ in the original networks is suggested.

When a drop impacts a pool of liquid it entraps a thin disk of air under its center. This disk contracts rapidly into a bubble to minimize surface energy. Herein we use ultra-high-speed imaging to measure the contraction speed of this disk when the drop and pool are of different liquids. For miscible liquids the contraction rate is governed by the weaker of the two surface tensions. Some undulations are observed on the edge of the disk for a water drop impacting a pool of water, but not on a pool of lower surface tension. Similar results are observed for a pair of immiscible liquids.

We consider the distribution of the duration time, the time elapsed since it began, of a diffusion process given its present position, under the assumption that the process began at the origin. For unbiased diffusion, the distribution does not exist (it is identically zero) for one- and two-dimensional systems. We find the explicit expression for the distribution for three and higher dimensions and discuss the behavior of the duration time statistics: we find that the expected duration time exists only for dimensions five and higher, whereas the variance becomes finite for seven dimensions and above. We then turn to the case of biased diffusion. The drift velocity introduces a new time scale and the resulting statistics arise from the interplay of the diffusive time scale and the drift time scale. For these systems all the moments exist and explicit expressions are presented and discussed for the expected duration time and its variance for all dimensions.

We investigate the electrostatic contribution to the lipid membrane mechanical parameters: tension, bending rigidity, spontaneous curvature, and flexocoefficient, using an approach where stress in the membrane is explicitly balanced. Our model includes an applied electrostatic potential as well as a charge distribution in the membrane. We apply our theory to membranes having surface charges and electric dipoles at the surface.

By considering the discrete nonlinear Schrödinger model with dipole-dipole interactions for dipolar condensate, the existence, the types, the stability, and the dynamics of the localized modes in a nonlinear lattice are discussed. It is found that the contact interaction and the dipole-dipole interactions play important roles in determining the existence, the type, and the stability of the localized modes. Because of the coupled effects of the contact interaction and the dipole-dipole interactions, rich localized modes and their stability nature can exist: when the contact interaction is larger and the dipole-dipole interactions is smaller, a discrete bright breather occurs. In this case, while the on-site interaction can stabilize the discrete breather, the dipole-dipole interactions will destabilize the discrete breather; when both the contact interaction and the dipole-dipole interactions are larger, a discrete kink appears. In this case, both the on-site interaction and the dipole-dipole interactions can stabilize the discrete kink, but the discrete kink is more unstable than the ordinary discrete breather. The predicted results provide a deep insight into the dynamics of blocking, filtering, and transfer of the norm in nonlinear lattices for dipolar condensates.

Extending the well-known Thomas-Fermi $Z$-scaling laws to the Coulomb coupling parameter, we investigate the stabilization of the ionic coupling in isochoric heating [Clérouin et al., Phys. Rev. E 87, 061101 (2013)]. This stabilization is restricted to a domain in atomic number $Z$, temperature, and density, including strong limitations on high couplings, that can only be obtained for high-$Z$ elements. Contact is made with recent isochoric heating experiments. The consequences for corresponding states with respect to ionic coupling are also quantified via orbital free molecular dynamics simulations. This opens avenues for future isochoric heating experiments.

In this work we will use digital images to compute the entropy dependence on temperature of a nematic lyotropic sample. The set of images comprehend the entire temperature range between a reentrant nematic isotropic phase transition, at a low temperature, and a usual nematic isotropic phase transition at a higher temperature. We will show that, inside the nematic phase, the image entropy profile agrees accurately with the entropy given by the Maier-Saupe model. As far as we know, this is the first time that the entropy of a lyotropic nematic phase is evaluated by this method, which introduces a way to measure their macroscopic variables. Namely, being that the entropy is a thermodynamical potential, this result implies that digital images can be used to compute mean values of nematic random variables.

We design nonlinear functions for the transmission of a small signal with non-Gaussian noise and perform experiments to characterize their responses. Using statistical design theory [A. Ichiki and Y. Tadokoro, Phys. Rev. E 87, 012124 (2013)], a static nonlinear function is estimated from the probability density function of the given noise in order to maximize the signal-to-noise ratio of the output. Using an electronic system that implements the optimized nonlinear function, we confirm the recovery of a small signal from a signal with non-Gaussian noise. In our experiment, the non-Gaussian noise is a mixture of Gaussian noises. A similar technique is also applied to the optimization of the threshold value of the function. We find that, for non-Gaussian noise, the response of the optimized nonlinear systems is better than that of the linear system.