We demonstrate optical waveguiding in recently discovered free-standing bent-core liquid-crystal filaments. The bent-core liquid-crystal molecules in air self-assemble into a cylindrical geometry that is “solidlike” along the radial direction of the filament and liquid in the axial direction of the filament. These filaments are unique not only because they are fluids, but also because they are anisotropic. For this reason, their waveguiding properties not predictable need to be characterized. The light power transmitted through the filament was found to be independent of temperature from $180°\text{C}$ to near room temperature. Initial defects of newly pulled filaments were found to self-anneal, thus leaving defect-free fibers, where light scattering was found to be insignificant. The absorbance was found to be strongly wavelength dependent in the visible regime and relatively small in the infrared range. A self-assembled optical waveguide with self-annealing fluid properties may have promising applications in optical communications or in optical microchips.

We discuss a modification to random matrix theory (RMT) eigenstate statistics that systematically takes into account the nonuniversal short-time behavior of chaotic systems. The method avoids diagonalization of the Hamiltonian, instead requiring only knowledge of short-time dynamics for a chaotic system or ensemble of similar systems. Standard RMT and semiclassical predictions are recovered in the limits of zero Ehrenfest time and infinite Heisenberg time, respectively. As examples, we discuss wave-function autocorrelations and cross correlations and show how the approach leads to a significant improvement in the accuracy for simple chaotic systems where comparison can be made with brute-force diagonalization.

Using a semiclassical ansatz we analytically predict for the fidelity of $\delta$-kicked rotors the occurrence of revivals and the disappearance of intermediate revival peaks arising from the breaking of a symmetry in the initial conditions. A numerical verification of the predicted effects is given and experimental ramifications are discussed.

The exact mean time between encounters of a given particle in a system consisting of many particles undergoing random walks in discrete time is calculated, on both regular and complex networks. Analytical results are obtained both for independent walkers, where any number of walkers can occupy the same site, and for walkers with an exclusion interaction, when no site can contain more than one walker. These analytical results are then compared with numerical simulations, showing very good agreement.

We investigate a Hamiltonian model of networks. The model is a mirror formulation of the $XY$ model (hence the name)—instead of letting the $XY$ spins vary, keeping the coupling topology static, we keep the spins conserved and sample different underlying networks. Our numerical simulations show complex scaling behaviors with various exponents as the system grows and temperature approaches zero, but no finite-temperature universal critical behavior. The ground-state and low-order excitations for sparse, finite graphs are a fragmented set of isolated network clusters. Configurations of higher energy are typically more connected. The connected networks of lowest energy are stretched out giving the network large average distances. For the finite sizes we investigate, there are three regions—a low-energy regime of fragmented networks, an intermediate regime of stretched-out networks, and a high-energy regime of compact, disordered topologies. Scaling up the system size, the borders between these regimes approach zero temperature algebraically, but different network-structural quantities approach their $T=0$ values with different exponents. We argue this is a, perhaps rare, example of a statistical-physics model where finite sizes show a more interesting behavior than the thermodynamic limit.

The problem of a film flowing down an inclined porous layer is considered. The fully developed basic flow is driven by gravitation. A careful linear instability analysis is carried out. We use Darcy’s law to describe the porous layer and solve the coupling equations of the fluid and the porous medium rather than the decoupled equations of the one-sided model used in previous works. The eigenvalue problem is solved by means of a Chebyshev collocation method. We compare the instability of the two-sided model with the results of the one-sided model. The result reveals a porous mode instability which is completely neglected in previous works. For a falling film on an inclined porous plane there are three instability modes, i.e., the surface mode, the shear mode, and the porous mode. We also study the influences of the depth ratio $\widehat{d}$, the Darcy number $\delta$, and the Beavers-Joseph coefficient ${\alpha }_{BJ}$ on the instability of the system.

Numerical simulations of spontaneous flame acceleration are performed within the problem of flame transition to detonation in two-dimensional channels. The acceleration is studied in the extremely wide range of flame front velocity changing by 3 orders of magnitude during the process. Flame accelerates from realistically small initial velocity (with Mach number about ${10}^{-3}$) to supersonic speed in the reference frame of the tube walls. It is shown that flame acceleration undergoes three distinctive stages: (1) initial exponential acceleration in the quasi-isobaric regime, (2) almost linear increase in the flame speed to supersonic values, and (3) saturation to a stationary high-speed deflagration velocity. The saturation velocity of deflagration may be correlated with the Chapman-Jouguet deflagration speed. The acceleration develops according to the Shelkin mechanism. Results on the exponential flame acceleration agree well with previous theoretical and numerical studies. The saturation velocity is in line with previous experimental results. Transition of flame acceleration regime from the exponential to the linear one, and then to the constant velocity, happens because of gas compression both ahead and behind the flame front.

A class of algorithms in discrete space and continuous time for Brownian first-passage-time estimation is considered. A simple algorithm is derived that yields exact mean first-passage times (MFPTs) for linear potentials in one dimension, regardless of the lattice spacing. When applied to nonlinear potentials and/or higher spatial dimensions, numerical evidence suggests that this algorithm yields MFPT estimates that either outperform or rival Langevin-based (discrete time and continuous space) estimates.

Based on a detailed experimental investigation in an aspect-ratio-4 rectangular cell in the range $3.7\times {10}^7\le \text{Ra}\le 3.7\times {10}^9$, we present evidence of possible scenarios of the long-term dynamics of large-scale circulations (LSC) in bounded large-aspect-ratio turbulent Rayleigh-Bénard convection. Karhunen-Loève analysis of instantaneous velocity fields from long-time particle image velocimetry measurements suggests two different states, but both appear to be produced by a single large-scale flow structure. The measurements provide a three-dimensional picture of LSC in the $\Gamma =4$ cell. A modified scaling relation between the LSC peak frequency ${\omega }_{\text{p}}$ and Ra is proposed.

We present a technique, which we call “etching,” which we use to study the harmonic measure of Fortuin-Kasteleyn clusters in the $Q$-state Potts model for $Q=1–4$. The harmonic measure is the probability distribution of random walkers diffusing onto the perimeter of a cluster. We use etching to study regions of clusters which are extremely unlikely to be hit by random walkers, having hitting probabilities down to ${10}^{-4600}$. We find good agreement between the theoretical predictions of Duplantier and our numerical results for the generalized dimension $D\left(q\right)$ including regions of small and negative $q$.

Using Monte Carlo simulations and a domain-wall theory, we discuss the effect of coupling several totally asymmetric simple exclusion processes (TASEPs) to a finite reservoir of particles. This simple model mimics directed biological transport processes in the presence of finite resources such as protein synthesis limited by a finite pool of ribosomes. If all TASEPs have equal length, we find behavior which is analogous to a single TASEP coupled to a finite pool. For the more generic case of chains with different lengths, several unanticipated regimes emerge. A generalized domain-wall theory captures our findings in good agreement with simulation results.

Non-Markovian stochastic Langevin-like equations of motion are compared to their corresponding Markovian (local) approximations. The validity of the local approximation for these equations, when contrasted with the fully nonlocal ones, is analyzed in detail. The conditions for when the equation in a local form can be considered a good approximation are then explicitly specified. We study both the cases of additive and multiplicative noises, including system-dependent dissipation terms, according to the fluctuation-dissipation theorem.

In this paper, the accumulated payoff of each agent is regulated so as to reduce the heterogeneity of the distribution of all such payoffs. It is found that there exists an optimal regulation strength at which cooperation in the prisoner’s dilemma game is optimally promoted. If the heterogeneity is regulated to be either too weak or too strong, the promotive effect disappears and the evolution of cooperation may even be impaired if compared to the absence of the proposed regulatory mechanism. An explanation of the observed results is provided. In particular, it is found that cooperators on the spatial grid are not isolated but form compact clusters and that the distribution of these clusters is crucial for the promotion of cooperation. Our work provides insights into relations between the distribution of payoffs and the evolution of cooperative behavior in situations constituting a social dilemma.

We demonstrate that a finite bath fluctuation theorem of the Crooks type holds for systems that have been thermalized via weakly coupling them to a bath with energy independent finite specific heat. We show that this theorem reduces to the known canonical and microcanonical fluctuation theorems in the two respective limiting cases of infinite and vanishing specific heat of the bath. The result is elucidated by applying it to a two-dimensional hard disk colliding elastically with few other hard disks in a rectangular box with perfectly reflecting walls.

Chiral smectic liquid crystals exhibit a series of phases, including ferroelectric, antiferroelectric, and ferrielectric commensurate structures as well as an incommensurate $\text{Sm-}{C}_{\alpha }^{\ast }$ phase. We carried out an extension of the phenomenological model recently presented by Hamaneh and Taylor based on the distorted-clock model. The salient feature of this model is that it links the appearance of phases to a spontaneous microscopic twist: i.e., an increment $\alpha$ of the azimuthal angle from layer to layer. The balance between this twist and an orientational order parameter $J$ gives the effective phase. We introduce a second orientational order parameter $I$, which physical meaning comes from the macroscopic polarization; the effect of an applied electric is also studied. We derive phase diagrams and correlate them to our experimental results under field showing the sequence of phases versus temperature and electric field in some compounds.

It has been shown that a single standard linear integrate-and-fire (IF) neuron under a general time-dependent stimulus cannot possess chaotic dynamics despite the firing-reset discontinuity. Here we address the issue of whether conductance-based, pulsed-coupled network interactions can induce chaos in an IF neuronal ensemble. Using numerical methods, we demonstrate that all-to-all, homogeneously pulse-coupled IF neuronal networks can indeed give rise to chaotic dynamics under an external periodic current drive. We also provide a precise characterization of the largest Lyapunov exponent for these high dimensional nonsmooth dynamical systems. In addition, we present a stable and accurate numerical algorithm for evaluating the largest Lyapunov exponent, which can overcome difficulties encountered by traditional methods for these nonsmooth dynamical systems with degeneracy induced by, e.g., refractoriness of neurons.

We show that hemispherical dynamos can result from weak equatorial symmetry breaking of the flow in the interior of planets and stars. Using a model of spherical dynamo, we observe that the interaction between a dipolar and a quadrupolar mode can localize the magnetic field in only one hemisphere when the equatorial symmetry is broken. This process is shown to be related to the one that is responsible for reversals of the magnetic field. These seemingly very different behaviors are thus understood in a unified framework.

Two types of homogeneous surface nanobubble populations, created by different means, are analyzed statistically on both their sizes and spatial positions. In the first type (created by droplet deposition, case A) the bubble size $R$ is found to be distributed according to a generalized gamma law with a preferred radius $R^{\ast }=20\text{nm}$. The radial distribution function shows a preferred spacing at $\sim 5.5R^{\ast }$. These characteristics do not show up in comparable Monte Carlo simulated configurations of random packings of hard disks with the same size distribution and the same density, suggesting a structuring effect in the nanobubble formation process. The nanobubble size distribution of the second population type (created by ethanol-water exchange, case B) is a mixture of two clearly separated distributions, hence, with two preferred radii. The local ordering is less significant, due to the looser packing of the nanobubbles.

It is shown that using the similarity transformations, a set of three-dimensional $p\text{−}q$ nonlinear Schrödinger (NLS) equations with inhomogeneous coefficients can be reduced to one-dimensional stationary NLS equation with constant or varying coefficients, thus allowing for obtaining exact localized and periodic wave solutions. In the suggested reduction the original coordinates in the $\left(1+3\right)$ space are mapped into a set of one-parametric coordinate surfaces, whose parameter plays the role of the coordinate of the one-dimensional equation. We describe the algorithm of finding solutions and concentrate on power (linear and nonlinear) potentials presenting a number of case examples. Generalizations of the method are also discussed.

A thermal lattice Boltzmann (LB) model is presented for axisymmetric thermal flows in the incompressible limit. The model is based on the double-distribution-function LB method, which has attracted much attention since its emergence for its excellent numerical stability over the multispeed LB method. Compared with the existing axisymmetric thermal LB models, the present model is simpler and retains the inherent features of the standard LB method. Numerical simulations are carried out for the thermally developing laminar flows in circular ducts and the natural convection in an annulus between two coaxial vertical cylinders. The Nusselt number obtained from the simulations agrees well with the analytical solutions and/or the results reported in previous studies.