We consider enhanced diffusion for Brownian motion on a tilted periodic potential. Expressing the effective diffusion in terms of the eigenvalue band structure, we establish a connection between band gaps in the eigenspectrum and enhanced diffusion. We explain this connection for a simple cosine potential with a linear force and then generalize to more complicated potentials including one-dimensional potentials with multiple frequency components and nonseparable multidimensional potentials. We find that potentials with multiple band gaps in the eigenspectrum can lead to multiple maxima or broadening of the force-diffusion curve. These features are likely to be observable in experiments.

Very recently, To et al. have experimentally explored granular flow in a cylindrical silo, with a bottom wall that rotates horizontally with respect to the lateral wall [Phys. Rev. E 100, 012906 (2019)]. Here we numerically reproduce their experimental findings, in particular, the peculiar behavior of the mass flow rate $Q$ as a function of the frequency of rotation $f$. Namely, we find that for small outlet diameters $D$ the flow rate increased with $f$, while for larger $D$ a nonmonotonic behavior is confirmed. Furthermore, using a coarse-graining technique, we compute the macroscopic density, momentum, and the stress tensor fields. These results show conclusively that changes in the discharge process are directly related to changes in the flow pattern from funnel flow to mass flow. Moreover, by decomposing the mass flux (linear momentum field) at the orifice into two main factors, macroscopic velocity and density fields, we obtain that the nonmonotonic behavior of the linear momentum is caused by density changes rather than by changes in the macroscopic velocity. In addition, by analyzing the spatial distribution of the kinetic stress, we find that for small orifices increasing rotational shear enhances the mean kinetic pressure $\langle p^k\rangle$ and the system dilatancy. This reduces the stability of the arches, and, consequently, the volumetric flow rate increases monotonically. For large orifices, however, we detected that $\langle p^k\rangle$ changes nonmonotonically, which might explain the nonmonotonic behavior of $Q$ when varying the rotational shear.

This work investigates dense packings of congruent hard infinitesimally thin circular arcs in the two-dimensional Euclidean space. It focuses on those denotable as major whose subtended angle $\theta \in \left(\pi ,2\pi \right]$. Differently than those denotable as minor whose subtended angle $\theta \in \left[0,\pi \right]$, it is impossible for two hard infinitesimally thin circular arcs with $\theta \in \left(\pi ,2\pi \right]$ to arbitrarily closely approach once they are arranged in a configuration, e.g., on top of one another, replicable ad infinitum without introducing any overlap. This makes these hard concave particles, in spite of being infinitesimally thin, most densely pack with a finite number density. This raises the question as to what are these densest packings and what is the number density that they achieve. Supported by Monte Carlo numerical simulations, this work shows that one can analytically construct compact closed circular groups of hard major circular arcs in which a specific, $\theta$-dependent, number of them (counter) clockwise intertwine. These compact closed circular groups then arrange on a triangular lattice. These analytically constructed densest-known packings are compared to corresponding results of Monte Carlo numerical simulations to assess whether they can spontaneously turn up.

Under an external acoustic field, particles experience radiation forces that bring them to certain trapping locations, such as pressure or velocity nodes for the case of plane standing wave. Due to acoustical interactions, particles form clusters on reaching those trapping locations. In this work, by using the far-field evaluation of scattered fields, a generalized force potential is formulated that gives both the primary and interaction forces for particles with size much smaller than the wavelength (Rayleigh limit). The generalized potential for the primary force is the same as the Gorkov's potential. The interaction potential and forces between a pair of particles at the zero-primary-force locations are studied for the two cases of planar and nonplanar (Bessel) standing waves. It was found that the interaction forces are predominantly dependent on the product of the external acoustic field and the scattered fields from the adjacent particles. Besides the line formation, other cluster shapes are shown to be plausible for three solid particles agglomerating under a plane standing wave. The mutual interaction force between particles of different material properties was found to be not equal and opposite in general, suggesting that they do not form an action and reaction pair. From the interaction patterns due to the nonplanar field of a Bessel standing wave, it is inferred that many cluster configurations are possible since particles near the stable trapping locations attract each other from more than one direction. The advantage of using the generalized force potential is that it provides physical insight for the acoustical manipulation of small particles in any external field with arbitrary wave front, such as those used in acoustic holography.

The lattice Boltzmann (LB) approach is presented for the near-field thermal radiation (including the contributions of the propagating and evanescent waves). The radiative transfer equations in the medium and on the interface are derived for the propagating and evanescent waves from the Maxwell equations, respectively. The Chapman-Enskog analysis is adopted to derive the LB model to recover the radiative transfer equation. The scattering parameter coefficient η is proposed to demonstrate the wave behavior of photons on the interface between medium and vacuum. The numerical tests are implemented to solve the near-field radiative heat transfer between two slabs by using the proposed LB approach. The accuracy of the LB model can be improved by increasing the resolution of the wave-number space. By comparing with the benchmark of analytical solutions, the proposed numerical approach enables computing the near-field thermal radiation with good accuracy and exhibits promising applications in dealing with complicated near-field thermal radiation processes.

We report a formula for the dry adiabatic lapse rate that depends on the compressibility factor and the adiabatic curves. Then, to take into account the nonideal behavior of the gases, we consider molecules that can move, rotate, and vibrate and the information of molecular interactions through the virial coefficients. We deduce the compressibility factor in its virial expansion form and the adiabatic curves within the virial expansion up to any order. With this information and to illustrate the mentioned formula, we write the lapse rate for the ideal gas, and the virial expansion up to the second and third coefficient cases. To figure out the role of the virial coefficients and vibrations, under different atmospheric conditions, we calculate the lapse rate for Earth, Mars, Venus, Titan, and the exoplanet Gl 581d. Furthermore, for each one we consider three models in the virial expansion: van der Waals, square-well, and hard-sphere. Also, when possible, we compare our results to the experimental data. Finally, we remark that for Venus and Titan, which are under extreme conditions of pressure or temperature, our calculations are in good agreement with the observed values, in some instances.

We study a distribution of times of the first arrivals to absorbing targets in turbulent diffusion, which is due to a multiplicative noise. Two examples of dynamical systems with a multiplicative noise are studied. The first one is a random process according to inhomogeneous diffusion, which is also known as a geometric Brownian motion in the Black-Scholes model. The second model is due to a random processes on a two-dimensional comb, where inhomogeneous advection is possible only along the backbone, while Brownian diffusion takes place inside the branches. It is shown that in both cases turbulent diffusion takes place as the one-dimensional random process with the log-normal distribution in the presence of absorbing targets, which are characterized by the Lévy-Smirnov distribution for the first hitting times.

We calculate the ground-state energy density $\epsilon \left(g\right)$ for the one-dimensional $N$-state quantum clock model up to order 18, where $g$ is the coupling and $N=3,4,5,...,10,20$. Using methods based on the Padé approximation, we extract the singular structure of ${\epsilon }^{″}\left(g\right)$ or $\epsilon \left(g\right)$. They correspond to the specific heat and free energy of the classical two-dimensional (2D) clock model. We find that, for $N=3,4$, there is a single critical point at $g_c=1$. The heat capacity exponent of the corresponding 2D classical model is $\alpha =0.34\pm 0.01$ for $N=3$, and $\alpha =-0.01\pm 0.01$ for $N=4$. For $N>4$, there are two exponential singularities related by $g_{c1}=1/g_{c2}$, and $\epsilon \left(g\right)$ behaves as $A{e}^{-\frac{c}{|g_c{-g|}^{\sigma }}}+\text{analytic}\text{terms}$ near $g_c$. The exponent $\sigma$ gradually grows from 0.2 to 0.5 as $N$ increases from 5 to 9, and it stabilizes at 0.5 when $N>9$. The phase transitions exhibited in these models should be generalizations of the Kosterlitz-Thouless transition, which has $\sigma =0.5$.

We show that it is possible to have nonzero ergotropy in the steady states of an open quantum system consisting of qubits that are collectively coupled to a thermal bath at a finite temperature. The dynamics of our model leads the qubits into a steady state that has coherences in the energy eigenbasis when the system consists of more than a single qubit. We observe that even though the system does not have inverted populations, it is possible to extract work from the coherences and we analytically show that in the high-temperature limit, ergotropy per unit energy is equal to the $l_1$ norm of coherence for the two-qubit case. Further, we analyze the scaling of coherence and ergotropy as a function of the number of qubits in the system for different initial states. Our results demonstrate that one can design a quantum battery that is charged by a dissipative thermal bath in the weak-coupling regime.

We revisit the problem of the reduction of the three-dimensional (3D) dynamics of Bose-Einstein condensates, under the action of strong confinement in one direction ($z$), to a 2D mean-field equation. We address this problem for the confining potential with a singular term, viz., $V_z\left(z\right)=2z^2+{\zeta }^2/z^2$, with constant $\zeta$. A quantum phase transition is induced by the latter term, between the ground state (GS) of the harmonic oscillator and the 3D condensate split in two parallel noninteracting layers, which is a manifestation of the “superselection” effect. A realization of the respective physical setting is proposed, making use of resonant coupling to an optical field, with the resonance detuning modulated along $z$. The reduction of the full 3D Gross-Pitaevskii equation (GPE) to the 2D nonpolynomial Schrödinger equation (NPSE) is based on the factorized ansatz, with the $z$ -dependent multiplier represented by an exact GS solution of the 1D Schrödinger equation with potential $V_z\left(z\right)$. For both repulsive and attractive signs of the nonlinearity, the 2D NPSE produces GS and vortex states, that are virtually indistinguishable from the respective numerical solutions provided by full 3D GPE. In the case of the self-attraction, the threshold for the onset of the collapse, predicted by the 2D NPSE, is also virtually identical to its counterpart obtained from the 3D equation. In the same case, stability and instability of vortices with topological charge $S=1$, 2, and 3 are considered in detail. Thus, the procedure of the spatial-dimension reduction, 3D $\to$ 2D, produces very accurate results, and it may be used in other settings.

An alternative method for the calculation of excited chaotic eigenfunctions in arbitrary energy windows is presented. We demonstrate the feasibility of using wave functions localized on unstable periodic orbits as efficient basis sets for this task in classically chaotic systems. The number of required localized wave functions is only of the order of the ratio $t_H/t_E$, with $t_H$ the Heisenberg time and $t_E$ the Ehrenfest time. As an illustration, we present convincing results for a coupled two-dimensional quartic oscillator with chaotic dynamics.

We recently argued that a self-propelled particle is formally equivalent to a system consisting of two subsystems coupled by a nonreciprocal interaction [Phys. Rev. E 100, 050603(R) (2019)]. Here, we show that this nonreciprocal coupling allows us to extract useful work from a single self-propelled particle maintained at constant temperature, by using an aligning interaction to control correlations between the particle's position and self-propulsion.

Diffusion of particles carried by Poiseuille flow of the surrounding solvent in a three-dimensional (3D) tube of varying diameter is considered. We revisit our mapping technique [F. Slanina and P. Kalinay, Phys. Rev. E 100, 032606 (2019)], projecting the corresponding 3D advection-diffusion equation onto the longitudinal coordinate and generating an effective one-dimensional modified Fick-Jacobs (or Smoluchowski) equation. A different scaling of the transverse forces by a small auxiliary parameter $\epsilon$ is used here. It results in a recurrence scheme enabling us to derive the corrections of the effective diffusion coefficient and the averaged driving force up to higher orders in $\epsilon$. The new scaling also preserves symmetries of the stationary solution in any order of $\epsilon$. Finally we show that Reguera-Rubí's formula, widely applied for description of diffusion in corrugated tubes, can be systematically corrected by the strength of the flow $Q$; we give here the first two terms in the form of closed analytic formulas.

The equilibrium structure and the dispersion relations of collective excitations in trilayer Yukawa systems in the strongly coupled liquid regime are examined. The equilibrium correlations reveal a variety of structures in the liquid phase, reminiscent of the corresponding structures in the solid phase. At small layer separation substitutional disorder becomes the governing feature. Theoretical dispersion relations are obtained by applying the quasilocalized charge approximation (QLCA) formalism, while numerical data are generated by microcanonical molecular dynamics simulations. The dispersions and polarizations of the collective excitations obtained through both of these methods are compared and discussed in detail. We find that the QLCA method is, in general, very satisfactory, but that there are phenomena not covered by the QLCA. In particular, by analyzing the dynamical longitudinal and transverse current fluctuation spectra we discover the existence of a structure not related to the collective mode spectra. This also provides insight into the long-standing problem of the gap frequency discrepancy, observed in strongly coupled layered systems in earlier studies.

In this paper, a perturbation theory of thermal rectification is developed for a thermal system where an effective thermal conductivity throughout the system can be identified and changes smoothly and slightly. This theory provides an analytical formula of the thermal rectification ratio with rigorous mathematical derivations and physical assumptions. The physical meanings and limitations of the present theory are discussed in detail. Furthermore, a physical relationship among the thermal rectification, system length, temperature difference, and thermal conductivity is built. It reveals the linear relationship between the thermal rectification ratio and temperature difference. Also, the size dependence of the thermal rectification relies on the specific form of the thermal conductivity. In addition, several previous experimental and numerical observations are well explained by this theory.

We report on the experimental investigation of the dependence of the elastic enhancement, i.e., enhancement of scattering in the backward direction over scattering in other directions, of a wave-chaotic system with partially violated time-reversal ($\mathcal{T}$) invariance on its openness. The elastic enhancement factor is a characteristic of quantum chaotic scattering which is of particular importance in experiments, like compound-nuclear reactions, where only cross sections, i.e., the moduli of the associated scattering matrix elements, are accessible. In the experiment a quantum billiard with the shape of a quarter bow tie, which generates a chaotic dynamics, is emulated by a flat microwave cavity. Partial $\mathcal{T}$-invariance violation of varying strength $0\le \xi \lesssim 1$ is induced by two magnetized ferrites. The openness is controlled by increasing the number $M$ of open channels, $2\le M\le 9$, while keeping the internal absorption unchanged. We investigate the elastic enhancement as function of $\xi$ and find that for a fixed $M$ it decreases with increasing $\mathcal{T}$-invariance violation, whereas it increases with increasing openness beyond a certain value of $\xi \gtrsim 0.2$. The latter result is surprising because it is opposite to that observed in systems with preserved $\mathcal{T}$invariance ($\xi =0$). We come to the conclusion that the effect of $\mathcal{T}$-invariance violation on the elastic enhancement then dominates over the openness, which is crucial for experiments which rely on enhanced backscattering, since, generally, a decrease of the openness is unfeasible. Motivated by these experimental results, we performed theoretical investigations based on random matrix theory which confirm our findings.

Considering the theory of electromagnetic waves from the Maxwell's equations, we introduce a ($3+1$)-dimensionsal cubic-quintic complex Ginzburg-Landau equation describing the dynamics of dissipative light bullets in nonlinear metamaterials. The model equation, which is derived beyond the slowly varying envelope approximation, includes the effects of diffraction, dispersion, loss, gain, cubic, and quintic nonlinearities, as well as cubic and quintic self-steepening effects. The modulational instability of the plane waves is studied both theoretically, using the linear stability analysis, and numerically, using direct simulations of the Fourier space of the proposed nonlinear wave equation, based on the Drude model. The linear theory predicts instability for any amplitude of the primary wave. Also, in the linear stability analysis, self-steepening effects of different orders are confronted and one discusses their effects on the behavior of the gain spectrum under both normal and anomalous group-velocity dispersion regimes. Analytical results are equally confronted to direct numerical simulations and fully agree with the predictions from the gain spectra. Modulational instability is manifested by clusters of solitons and multihump and dromion-like structures, whose emergence and features depend not only on system parameters, such as the cubic and quintic self-steepening coefficients, but also on the propagation distance under a suitable balance between nonlinear and dispersive effects.

Evidence is mounting that the race of living organisms for adaptation to the chemicals synthesized by their neighbors may drive community structures. Here, an ecoevolutionary model for community assembly through resource competition, toxin-mediated interactions (allelopathy), and evolutionary branching is investigated. We found that stable communities with increasing biodiversity can emerge at weak allelopathic suppression, but strong chemical warfare drastically impairs diversity. For successive invasion events, the allelopathic interaction networks exhibit, respectively, Gaussian and Weibull degree distributions at weak and strong allelopathy. For the branching process dynamics, degrees scale as power laws truncated by stretched exponentials in both regimes. In addition, allelochemical interactions tend to be arranged in modules with low clustering coefficients and disassortative behavior to ensure community stability. So, in a homogeneous environment, species-rich communities can be assembled only at the context of a weak biochemical warfare between organisms, and even under this regime species interact with only a few others.