We investigate occupation time statistics for random walks on a comb with ramified teeth. This is achieved through the relation between the occupation time and the first passage times. Statistics of occupation times in half space follows Lamperti's distribution, i.e., the generalized arcsine law holds. Transitions between different behaviors are observed, which are controlled by the size of the backbone and teeth of the comb, as well as bias. Occupation time on a nonsimply connected domain is analyzed with a mean-field theory and numerical simulations. In that case, the generalized arcsine law is not valid.

We describe a method to obtain the reduced density matrix (RDM) correct up to second order in system-bath coupling in nonequilibrium steady-state situations. The RDM is obtained via a scheme based on analytic continuation, using the time-local Redfield-like quantum master equation, which was earlier used by the same authors [J. Chem. Phys. 136, 194110 (2012)] to obtain the correct thermal equilibrium description. This nonequilibrium modified Redfield solution is then corroborated with the exact RDM obtained via the nonequilibrium Green's function technique for the quantum harmonic oscillator. Lastly, the scheme is compared to different quantum master equations (QMEs), namely the time-local Redfield-like and the Lindblad-like QMEs, in order to illustrate the differences between each of these approaches.

In lattice systems, the effects of optical phonons on heat transport are usually neglected due to their relatively small group velocities compared with acoustic phonons, or even assumed to be negative because introducing optical phonons may simultaneously reduce the group velocities of acoustic phonons. In order to well understand the role played by optical phonons, we propose a one-dimensional anharmonic lattice model with alternating interactions, where the optical phonons can be conveniently tuned. We find that in contrast to previous studies, the optical phonons (in coordination with the nonlinearities) can enhance heat transport in the thermodynamical limit, suggesting that optical phonons can also play an active role. The underlying mechanism is related to the effects of two kinds of nonlinear excitations, i.e., the optical and the gap discrete breathers (DBs). These DBs release energy and in turn facilitate heat transport.

Using quasiexact numerical density-matrix renormalization-group techniques we calculate the critical Casimir force for a two-dimensional (2D) Ising strip with equal strong surface fields, along the thermodynamic paths corresponding to the fixed nonzero bulk field $h\ne 0$. Using the Derjaguin approximation we also determine the critical Casimir force and its potential for two disks. We find that varying the temperature along the isofields lying between the bulk coexistence and the capillary condensation critical point leads to a dramatic increase of the critical Casimir interactions with a qualitatively different functional dependence on the temperature than along $h=0$. These findings might be of relevance for biomembranes, whose heterogeneity is recently interpreted as being connected with a critical behavior belonging to the 2D Ising universality class.

In this work, we report the kinetics of ordering occurring at the water-air interface of Laponite dispersions. Propagation of such ordering into the bulk and its relaxation dynamics were systematically studied through light scattering measurements. Depolarization ratio $D_p$, which accounted for the optical anisotropy, was measured as a function of depth from the interface and aging of the samples. The extent of spatial ordering was found to be several decades larger than the typical particle size. Spatial ordering originated from the interface and percolated into the bulk with aging time $t_w$. Growth in $D_p$ with waiting time was found to follow power-law behavior given as $D_p\sim t_w^n$, with $n$ increasing from 0.1 to 4 as one moved away from the interface into the bulk. $D_p$ decreased exponentially with depth $h$ given as $D_p\sim e^{-(h/h_0)}$, where $h_0$ is the decay length, increasing from 0.4 to 0.75 mm with aging time. Dynamic structure factor measurements performed on the samples at various aging times, depths, and temperatures yielded two distinct relaxation times: one fast mode followed by a slow mode. The fast mode remained invariant while slow mode relaxation time followed an exponential decay with depth. This study indicated that the arrested phase nucleated from the interface and propagated into the bulk, which was not observed when the surface was insulated with a layer of hydrophobic liquid. Dilution of the concentrated samples destroyed the aforesaid ordering and made the dispersion homogeneous implying the ordered state was a glass.

The “constitutive equation”–free scale-bridging method connecting nonequilibrium molecular dynamics and continuum fluid mechanics, that had hitherto been applied only to a parallel-plates geometry, is extended to study the flow of a polymer melt in a cylindrical pipe subject to a velocity in the direction parallel to the cylinder's axis. The system, initially at rest, is given a velocity at the cylinder's surface, and the evolution of the velocity profile within the fluid is studied, along with the time taken for the velocity to propagate toward the cylinder's axis. The said time of propagation is found to increase with the boundary velocity—a fact in contrast with the case of a Newtonian fluid for which the time of propagation is expected to be independent of the boundary velocity. For a fixed value of the boundary velocity, the propagation time is found to increase with the cylinder radius according to a power law with an exponent that is smaller than the corresponding exponent for a Newtonian fluid. For the lower values of the boundary velocity and the lower values of the radius studied, a velocity overshoot is observed at the cylinder's axis—a manifestation of elastic behavior of the fluid.

The possibility to extract properties of an interface between two immiscible liquids, e.g., electrolyte solutions or polyelectrolyte multilayers, by means of impedance spectroscopy is investigated theoretically within a dynamic density-functional theory which is equivalent to the Nernst-Planck-Poisson theory. An approach based on a two-step fitting procedure of an equivalent circuit to impedance spectra is proposed which allows us to uniquely separate bulk and interfacial elements. Moreover, the proposed method avoids overfitting of the bulk properties of the two liquids in contact and underfitting of the interfacial properties, as they might occur for standard one-step procedures. The key idea is to determine the bulk elements of the equivalent circuit in a first step by fitting corresponding subcircuits to the spectra of uniform electrolyte solutions, and afterwards fitting the full equivalent circuit with fixed bulk elements to the impedance spectrum containing the interface. This approach is exemplified for an equivalent circuit which leads to a physically intuitive qualitative behavior as well as to quantitatively realistic values of the interfacial elements. The proposed method is robust such that it can be expected to be applicable to a wide class of systems with liquid-liquid interfaces.

In biology, we frequently observe different species existing within the same environment. For example, there are many cell types in a tumour, or different animal species may occupy a given habitat. In modeling interactions between such species, we often make use of the mean-field approximation, whereby spatial correlations between the locations of individuals are neglected. Whilst this approximation holds in certain situations, this is not always the case, and care must be taken to ensure the mean-field approximation is only used in appropriate settings. In circumstances where the mean-field approximation is unsuitable, we need to include information on the spatial distributions of individuals, which is not a simple task. In this paper, we provide a method that overcomes many of the failures of the mean-field approximation for an on-lattice volume-excluding birth-death-movement process with multiple species. We explicitly take into account spatial information on the distribution of individuals by including partial differential equation descriptions of lattice site occupancy correlations. We demonstrate how to derive these equations for the multispecies case and show results specific to a two-species problem. We compare averaged discrete results to both the mean-field approximation and our improved method, which incorporates spatial correlations. We note that the mean-field approximation fails dramatically in some cases, predicting very different behavior from that seen upon averaging multiple realizations of the discrete system. In contrast, our improved method provides excellent agreement with the averaged discrete behavior in all cases, thus providing a more reliable modeling framework. Furthermore, our method is tractable as the resulting partial differential equations can be solved efficiently using standard numerical techniques.

The properties of double-stranded DNA and other chiral molecules depend on the local geometry, i.e., on curvature and torsion, yet the paths of closed chain molecules are globally restricted by topology. When both of these characteristics are to be incorporated in the description of circular chain molecules, e.g., plasmids, it is shown to have implications for the total positive curvature integral. For small circular micro-DNAs it follows as a consequence of Fenchel's inequality that there must exist a minimum length for the circular plasmids to be double stranded. It also follows that all circular micro-DNAs longer than the minimum length must be concave, a result that is consistent with typical atomic force microscopy images of plasmids. Predictions for the total positive curvature of circular micro-DNAs are given as a function of length, and comparisons with circular DNAs from the literature are presented.

The phenomenon of quantum localization in classically chaotic eigenstates is one of the main issues in quantum chaos (or wave chaos), and thus plays an important role in general quantum mechanics or even in general wave mechanics. In this work we propose two different localization measures characterizing the degree of quantum localization, and study their relation to another fundamental aspect of quantum chaos, namely the (energy) spectral statistics. Our approach and method is quite general, and we apply it to billiard systems. One of the signatures of the localization of chaotic eigenstates is a fractional power-law repulsion between the nearest energy levels in the sense that the probability density to find successive levels on a distance $S$ goes like $\propto$$S^{\beta }$ for small $S$, where $0\le \beta \le 1$, and $\beta =1$ corresponds to completely extended states. We show that there is a clear functional relation between the exponent $\beta$ and the two different localization measures. One is based on the information entropy and the other one on the correlation properties of the Husimi functions. We show that the two definitions are surprisingly linearly equivalent. The approach is applied in the case of a mixed-type billiard system [M. Robnik, J. Phys. A: Math. Gen. 16, 3971 (1983)], in which the separation of regular and chaotic eigenstates is performed.

Integrable models of resonant interaction of two or more waves in 1+1 dimensions are known to be of applicative interest in several areas. Here we consider a system of three coupled wave equations which includes as special cases the vector nonlinear Schrödinger equations and the equations describing the resonant interaction of three waves. The Darboux-Dressing construction of soliton solutions is applied under the condition that the solutions have rational, or mixed rational-exponential, dependence on coordinates. Our algebraic construction relies on the use of nilpotent matrices and their Jordan form. We systematically search for all bounded rational (mixed rational-exponential) solutions and find a broad family of such solutions of the three wave resonant interaction equations.

We consider dynamics and turbulent interaction of whistler modes within the framework of inertialess electron magnetohydrodynamics (EMHD). We argue that there is no energy principle in EMHD: any stationary closed configuration is neutrally stable. On the other hand, the relaxation principle, the long term evolution of a weakly dissipative system towards Taylor-Beltrami state, remains valid in EMHD. We consider the turbulent cascade of whistler modes. We show that (i) harmonic whistlers are exact nonlinear solutions; (ii) collinear whistlers do not interact (including counterpropagating); (iii) waves with the same value of the wave vector $k_1=k_2$ do not interact; (iv) whistler modes have a dispersion that allows a three-wave decay, including into a zero frequency mode; (v) the three-wave interaction effectively couples modes with highly different wave numbers and propagation angles. In addition, linear interaction of a whistler with a single zero mode can lead to spatially divergent structures via parametric instability. All these properties are drastically different from MHD, so that the qualitative properties of the Alfvén turbulence can not be transferred to the EMHD turbulence. We derive the Hamiltonian formulation of EMHD, and using Bogoliubov transformation reduce it to the canonical form; we calculate the matrix elements for the three-wave interaction of whistlers. We solve numerically the kinetic equation and show that, generally, the EMHD cascade develops within a broad range of angles, while transiently it may show anisotropic, nearly two-dimensional structures. Development of a cascade depends on the forcing (nonuniversal) and often fails to reach a steady state. Analytical estimates predict the spectrum of magnetic fluctuations for the quasi-isotropic cascade $\propto k^{-2}$. The cascade remains weak (not critically balanced). The cascade is UV local, while the infrared locality is weakly (logarithmically) violated.

A generalized inhomogeneous Gardner model with an external force term is investigated which can govern the soliton propagation and interaction in the vicinity of the negative ion critical density for certain plasmas or of equal layer depths for stratified fluids. Integrable aspects including the Lax pair and the $\Gamma$-Riccati-type Bäcklund transformation ($\Gamma$-R BT) are presented under the Painlevé conditions. By virtue of the $\Gamma$-R BT, analytic one- or two-soliton-like solutions with the inhomogeneous coefficients, external force term, eigenvalue in the Lax pair, and another parameter are obtained. Analytic analysis and graphic illustration imply that (1) the amplitude of a soliton is influenced by the quadratic and cubic nonlinear coefficients, the linear-damping coefficient, and the aforementioned eigenvalue; (2) the solitonic velocity is “controlled” by the inhomogeneous coefficients, the external force term, and the aforementioned eigenvalue and parameter; (3) the solitonic background is affected by the linear-damping coefficient, the external force term and the aforementioned parameter; and (4) the possibility of solitonic infection is dominated by the difference between eigenvalues.

We consider a general diffusion process that is force-free and the corresponding Fokker-Planck equation with an arbitrary diffusion coefficient. A propagator for the Fokker-Planck equation of the Stratonovich form is obtained based on random walks. The characteristics of the solution are analyzed.

We demonstrate by quantitative experimental measurements that metamaterials with anisotropic properties can be used in the context of water waves to produce a reflectionless bent waveguide. The anisotropic medium consists in a bathymetry with subwavelength layered structure that shifts the wave in the direction of the waveguide bending (10${}^{\circ }$, 20${}^{\circ }$, and 30${}^{\circ }$). The waveguide filled with such metamaterial is tested experimentally and compared to a reference empty bent waveguide. The experimental method used to characterize the wave field allows for space-time resolved measurements of water elevation. Results show the efficiency of the shifter. Modal treatment of the experimental data confirms that the metamaterial prevents higher modes from being excited in the waveguide.

The dc electric field effect on the anomalous exponent of the hopping conduction in the disorder model is investigated. First, we explain the model and derive an analytical expression of the effective waiting time for the general case. We show that the exponent depends on the external field. Then we focus on a one-dimensional system in order to illustrate the features of the anomalous exponent. We derive approximate expressions of the anomalous exponent of the system analytically. For the case of a weak field, the anomalous exponent is consistent with that of diffusive systems. This is consistent with the treatments of Barkai et al. [Phys. Rev. E 63, 046118 (2001)] and our result supports their theory. On the other hand, for the case of a strong field and a strong disorder, the time evolution of the exponent clearly differs from that in the weak field. The exponent is consistent with the well-known expression of the anomalous exponent in the multiple trapping model at mesoscopic time scales. In the long-time limit, a transition of the anomalous exponent to the same value of the weak field occurs. These findings are verified by the Monte Carlo simulation.

We show by numerical simulations that the presence of nonlinear velocity-dependent friction forces can induce a finite net drift in the stochastic motion of a particle in contact with an equilibrium thermal bath and in an asymmetric periodic spatial potential. In particular, we study the Kramers equation for a particle subjected to Coulomb friction, namely a constant force acting in the direction opposite to the particle's velocity. We characterize the nonequilibrium irreversible dynamics by studying the generalized fluctuation-dissipation relation for this ratchet model driven by Coulomb friction.

Collective motion in actively propelled particle systems is triggered on the very local scale by nucleation of coherently moving units consisting of just a handful of particles. These units grow and merge over time, ending up in a long-range ordered, coherently moving state. So far, there exists no bottom-up understanding of how the microscopic dynamics and interactions between the constituents are related to the system's ordering instability. In this paper, we study a class of models for propelled colloids allowing an explicit treatment of the microscopic details of the collision process. Specifically, the model equations are Newtonian equations of motion with separate force terms for particles' driving, dissipation, and interaction forces. Focusing on dilute particle systems, we analyze the binary scattering behavior for these models and determine—based on the microscopic dynamics—the corresponding “collision rule,” i.e., the mapping of precollisional velocities and impact parameter on postcollisional velocities. By studying binary scattering we also find that the considered models for active colloids share the same principle for parallel alignment: The first incoming particle (with respect to the center of collision) is aligned to the second particle as a result of the encounter. This behavior distinctively differs from alignment in nondriven dissipative gases. Moreover, the obtained collision rule lends itself as a starting point to apply kinetic theory for propelled particle systems in order to determine the phase boundary to a long-range ordered, coherently moving state. The microscopic origin of the collision rule offers the opportunity to quantitatively scrutinize the predictions of kinetic theory for propelled particle systems through direct comparison with multiparticle simulations. We identify local precursor correlations at the onset of collective motion to constitute the essential determinant for a qualitative and quantitative validity of kinetic theory. In conclusion, our “renormalized” approach clearly indicates that the framework of kinetic theory is flexible enough to accommodate the complex behavior of soft active colloids and allows a bottom-up understanding of how the microscopic dynamics of binary collisions relates to the system's behavior on large length and time scales.

We use Brownian dynamics (BD) simulations to study the ionic conduction and valence selectivity of a generic electrostatic model of a biological ion channel as functions of the fixed charge $Q_f$ at its selectivity filter. We are thus able to reconcile the discrete calcium conduction bands recently revealed in our BD simulations, M0 ($Q_f=1e$), M1 (3$e$), M2 (5$e$), with a set of sodium conduction bands L0 (0.5$e$), L1 (1.5$e$), thereby obtaining a completed pattern of conduction and selectivity bands vs $Q_f$ for the sodium-calcium channels family. An increase of $Q_f$ leads to an increase of calcium selectivity: L0 (sodium-selective, nonblocking channel) $\to$ M0 (nonselective channel) $\to$ L1 (sodium-selective channel with divalent block) $\to$ M1 (calcium-selective channel exhibiting the anomalous mole fraction effect). We create a consistent identification scheme where the L0 band is putatively identified with the eukaryotic sodium channel The scheme created is able to account for the experimentally observed mutation-induced transformations between nonselective channels, sodium-selective channels, and calcium-selective channels, which we interpret as transitions between different rows of the identification table. By considering the potential energy changes during permeation, we show explicitly that the multi-ion conduction bands of calcium and sodium channels arise as the result of resonant barrierless conduction. The pattern of periodic conduction bands is explained on the basis of sequential neutralization taking account of self-energy, as $Q_f(z,i)=ze(1/2+i)$, where $i$ is the order of the band and $z$ is the valence of the ion. Our results confirm the crucial influence of electrostatic interactions on conduction and on the Ca${}^{2+}/$Na${}^{+}$ valence selectivity of calcium and sodium ion channels. The model and results could be also applicable to biomimetic nanopores with charged walls.

We consider statistics of electronic transport in chaotic cavities where time-reversal symmetry is broken and one of the leads is weakly nonideal; that is, it contains tunnel barriers characterized by tunneling probabilities ${\Gamma }_i$. Using symmetric function expansions and a generalized Selberg integral, we develop a systematic perturbation theory in $1-{\Gamma }_i$ valid for an arbitrary number of channels and obtain explicit formulas up to second order for the average and variance of the conductance and for the average shot noise. Higher moments of the conductance are considered to leading order.