In this paper, influence of crowding by inert particles on the geminate reaction kinetics is theoretically investigated. Time evolution equations for the survival probability of a geminate pair are derived from the master equation taking into account the correlation among all diffusing particles, and the results are compared with those obtained by Monte Carlo simulations. In general, excluded volume interactions by the inert particles slow down the diffusive motion of reactants. However, when the initial concentration of the inert particles is uniform and high, we show that additional influence of interference between reaction and correlated diffusion accelerates the transient decay of the survival probability in the diffusion-controlled limit. We also study the escape probability for a nonuniform initial distribution of the inert particles by taking the continuous limit in space. We show that reaction yield is increased when the reaction proceeds in the presence of a positive density gradient of the inert particles which inhibits the escape of reactants. The effect can be interpreted as a cage effect.

By building upon a Feynman-Kac formalism, we assess the distribution of the number of collisions in a given region for a broad class of discrete-time random walks in absorbing and nonabsorbing media. We derive the evolution equation for the generating function of the number of collisions, and we complete our analysis by examining the moments of the distribution and their relation to the walker equilibrium density. Some significant applications are discussed in detail: in particular, we revisit the gambler's ruin problem and generalize to random walks with absorption the arcsine law for the number of collisions on the half-line.

The generalized Gibbs ensemble introduced for describing few-body correlations in exactly solvable systems following a quantum quench is related to the nonergodic way in which operators sample, in the limit of infinite time after the quench, the quantum correlations present in the initial state. The nonergodicity of the correlations is thus shown analytically to imply the equivalence with the generalized Gibbs ensemble for quantum Ising and $XX$ spin chains as well as for the Luttinger model the thermodynamic limit, and for a broad class of initial states and correlation functions of both local and nonlocal operators.

We examine the effects of memory and different updating paradigms in a game-theoretic model of competitive learning, where agents are influenced in their choice of strategy by both the choices made by, and the consequent success rates of, their immediate neighbors. We apply parallel and sequential updates in all possible combinations to the two competing rules and find, typically, that the phase diagram of the model consists of a disordered phase separating two ordered phases at coexistence. A major result is that the corresponding critical exponents belong to the generalized universality class of the voter model. When the two strategies are distinct but not too different, we find the expected linear-response behavior as a function of their difference. Finally, we look at the extreme situation when a superior strategy, accompanied by a short memory of earlier outcomes, is pitted against its inverse; interestingly, we find that a long memory of earlier outcomes can occasionally compensate for the choice of a globally inferior strategy.

From microscopic models, a Langevin equation can, in general, be derived only as an approximation. Two possible conditions to validate this approximation are studied. One is, for a linear Langevin equation, that the frequency of the Fourier transform should be close to the natural frequency of the system. The other is by the assumption of “slow” variables. We test this method by comparison with an exactly soluble model and point out its limitations. We base our discussion on two approaches. The first is a direct, elementary treatment of Senitzky. The second is via a generalized Langevin equation as an intermediate step.

The Green's function method developed previously [S. B. Chernyshuk and B. I. Lev, Phys. Rev. E 81, 041701 (2010)] is used to describe elastic interactions between axially symmetric colloidal particles in a nematic cell in the presence of an external electric or magnetic field. Formulas for dipole-dipole, dipole-quadrupole, and quadrupole-quadrupole interactions in the homeotropic and planar nematic cells with parallel and perpendicular field orientations are obtained. A set of predictions has been made: (1) The deconfinement effect for dipole particles in the homeotropic nematic cell when an electric field is approaching its Freedericksz threshold value $E\Rightarrow E_t$. This means cancellation of the confinement effect found in [M. Vilfan et al., Phys. Rev. Lett. 101, 237801 (2008)] near the Freedericksz transition. In the planar nematic cell this deconfinement effect exists for both dipole and quadrupole particles and depends on the field orientation as well as on the sign of dielectric anisotropy $\Delta \varepsilon$. (2) The effect of tunable stabilization of the particles is predicted. The equilibrium distance between two particles, which are attracted along the electric field parallel to the planes of a homeotropic nematic cell with $\Delta \varepsilon <0$, depends on the strength of the field. (3) Attraction and repulsion zones for all elastic interactions are changed dramatically under the action of the external field.

We study the propagation of waves in quasi-one-dimensional finite periodic systems whose classical (ray) dynamics is diffusive. By considering a random matrix model for a chain of $L$ identical chaotic cavities, we show that its average conductance as a function of $L$ displays an ohmic behavior even though the system has no disorder. This behavior, with an average conductance decay $N/L$, where $N$ is the number of propagating modes in the leads that connect the cavities, holds for $1\ll L\lesssim \sqrt{N}.$ After this regime, the average conductance saturates at a value of $\mathcal{O}\left(\sqrt{N}\right)$ given by the average number of propagating Bloch modes $\langle N_B\rangle$ of the infinite chain. We also study the weak localization correction and conductance distribution, and characterize its behavior as the system undergoes the transition from diffusive to Bloch ballistic. These predictions are tested in a periodic cosine waveguide.

We study the coupling of bouncing-ball modes to chaotic modes in two-dimensional billiards with two parallel boundary segments. Analytically, we predict the corresponding decay rates using the fictitious integrable system approach. Agreement with numerically determined rates is found for the stadium and the cosine billiard. We use this result to predict the asymptotic behavior of the counting function $N_{\text{bb}}\left(E\right)\sim E^{\delta }$. For the stadium billiard we find agreement with the previous result $\delta =3/4$. For the cosine billiard we derive $\delta =5/8$, which is confirmed numerically and is well below the previously predicted upper bound $\delta =9/10$.

Spreading of evaporative liquid drops in a thin porous layer has been studied. The entire spreading process can be divided into three distinct phases according to the change of the wetted porous region size. The first phase is characterized by the expansion of the wetted porous region and shrinking of the liquid drop. Contact line pinning is observed in the wetted porous region in the second phase even with the liquid drop totally absorbed into the porous layer. The third phase sees the shrinkage of the wetted porous region until it is not observable. Based on these observations, a model is devised to simulate the spreading of a liquid drop under the studied conditions. Partial differential equations are used to describe the relation between liquid drop volume and other important parameters of a fluid flow, including maximum wetted region diameter achieved, time taken to reach each spreading process phase, and evaporation rate. Calculated results are in good agreement with the experimental data.

We present a numerical study of the evolution of height distributions (HDs) obtained in interface growth models belonging to the Kardar-Parisi-Zhang (KPZ) universality class. The growth is done on an initially flat substrate. The HDs obtained for all investigated models are very well fitted by the theoretically predicted Gaussian orthogonal ensemble (GOE) distribution. The first cumulant has a shift that vanishes as $t^{-1/3}$, while the cumulants of order $2\le n\le 4$ converge to GOE as $t^{-2/3}$ or faster, behaviors previously observed in other KPZ systems. These results yield evidences for the universality of the GOE distribution in KPZ growth on flat substrates. Finally, we further show that the surfaces are described by the Airy${}_1$ process.

With this work we investigate the stationary nonequilibrium density matrix of current carrying nonequilibrium steady states of in-between quantum systems that are connected to reservoirs. We describe the analytical procedure to obtain the explicit result for the reduced density matrix of quantum transport when the system, the connecting reservoirs, and the system-reservoir interactions are described by quadratic Hamiltonians. Our procedure is detailed for both electronic transport described by the tight-binding Hamiltonian and for phonon transport described by harmonic Hamiltonians. For the special case of weak system-reservoir couplings, a more detailed description of the steady-state density matrix is obtained. Several paradigm transport setups for interelectrode electron transport and low-dimensional phonon heat flux are elucidated.

The efficiency at maximum power output of linear irreversible Carnot-like heat engines is investigated based on the assumption that the rate of irreversible entropy production of the working substance in each “isothermal” process is a quadratic form of the heat exchange rate between the working substance and the reservoir. It is found that the maximum power output corresponds to minimizing the irreversible entropy production in two isothermal processes of the Carnot-like cycle, and that the efficiency at maximum power output has the form ${\eta }_{mP}={\eta }_C/(2-\gamma {\eta }_C)$, where ${\eta }_C$ is the Carnot efficiency, while $\gamma$ depends on the heat transfer coefficients between the working substance and two reservoirs. The value of ${\eta }_{mP}$ is bounded between ${\eta }_{-}\equiv {\eta }_C/2$ and ${\eta }_{+}\equiv {\eta }_C/(2-{\eta }_C)$. These results are consistent with those obtained by Chen and Yan [J. Chem. Phys. 90, 3740 (1989)] based on the endoreversible assumption, those obtained by Esposito et al. [Phys. Rev. Lett. 105, 150603 (2010)] based on the low-dissipation assumption, and those obtained by Schmiedl and Seifert [Europhys. Lett. 81, 20003 (2008)] for stochastic heat engines which in fact also satisfy the low-dissipation assumption. Additionally, we find that the endoreversible assumption happens to hold for Carnot-like heat engines operating at the maximum power output based on our fundamental assumption, and that the Carnot-like heat engines that we focused on do not strictly satisfy the low-dissipation assumption, which implies that the low-dissipation assumption or our fundamental assumption is a sufficient but non-necessary condition for the validity of ${\eta }_{mP}={\eta }_C/(2-\gamma {\eta }_C)$ as well as the existence of two bounds, ${\eta }_{-}\equiv {\eta }_C/2$ and ${\eta }_{+}\equiv {\eta }_C/(2-{\eta }_C)$.

We reinvestigate the Deterministic Lattice Gas introduced as a paradigmatic model of the $1/f$ spectra [Phys. Rev. Lett. 64, 3103 (1990)] arising according to the self-organized criticality scenario. We demonstrate that the density fluctuations exhibit an unexpected dependence on systems size and relate the finding to effective Langevin equations. The low-density behavior is controlled by the critical properties of the gas at the absorbing state phase transition. We also show that the deterministic lattice gas is in the Manna universality class of absorbing state phase transitions. This is in contrast to expectations in the literature that suggested that the entirely deterministic nature of the dynamics would put the model in a different universality class. To our knowledge this is the first fully deterministic member of the Manna universality class.

We have calculated the lowest energy quantized breather excitations of both the $\beta$ and the $\alpha$ Fermi-Pasta-Ulam monoatomic lattices and the diatomic $\beta$ lattice within the ladder approximation. While the classical breather excitations form continua, the quantized breather excitations form a discrete hierarchy labeled by a quantum number $n$. Although the number of phonons is not conserved, the breather excitations correspond to multiple bound states of phonons. The $n=2$ breather spectra are composed of resonances in the two-phonon continuum and of discrete branches of infinitely long-lived excitations. The nonlinear attributes of these excitations become more pronounced at elevated temperatures. The calculated $n=2$ breather and the resonance of the monoatomic $\beta$ lattice hybridize and exchange identity at the zone boundary and are in reasonable agreement with the results of previous calculations using the number-conserving approximation. However, by contrast, the breather spectrum of the $\alpha$ monoatomic lattice couples resonantly with the single-phonon spectrum and cannot be calculated within a number-conserving approximation. Furthermore, we show that for sufficiently strong nonlinearity, the $\alpha$ lattice breathers can be observed directly through the single-phonon inelastic neutron-scattering spectrum. As the temperature is increased, the single-phonon dispersion relation for the $\alpha$ lattice becomes progressively softer as the lattice instability is approached. For the diatomic $\beta$ lattice, it is found that there are three distinct branches of $n=2$ breather dispersion relations, which are associated with three distinct two-phonon continua. The two-phonon excitations form three distinct continua: One continuum corresponds to the motion of two independent acoustic phonons, another to the motion of two independent optic phonons, and the last continuum is formed by propagation of two phonons that are one of each character. Each breather dispersion relation is split off the top from of its associated continuum and remains within the forbidden gaps between the continua. The energy splittings from the top of the continua rapidly increase, and the dispersions rapidly decrease with the decreasing energy widths of the associated continua. This finding is in agreement with recent observations of sharp branches of nonlinear vibrational modes in NaI through inelastic neutron-scattering measurements. Furthermore, since the band widths of the various continua successively narrow as the magnitude of their characteristic excitation energies increase, the finding is also in agreement the theoretical prediction that breather excitations in discrete lattices should be localized in the classical limit.

We study the impact of an intruder on a dense granular material. The process of impact and interaction between the intruder and the granular particles is modeled using discrete element simulations in two spatial dimensions. In the first part of the paper we discuss how the intruder's dynamics depends on (1) the intruder's properties, including its size, shape and composition, (2) the properties of the grains, including friction, polydispersity, structural order, and elasticity, and (3) the properties of the system, including its size and gravitational field. It is found that polydispersity and related structural order, and frictional properties of the granular particles, play a crucial role in determining impact dynamics. In the second part of the paper we consider the response of the granular system itself. We discuss the force networks that develop, including their topological evolution. The influence of friction and structural order on force propagation, including the transition from hyperbolic-like to elastic-like behavior is discussed, as well as the affine and nonaffine components of the grain dynamics. Several broad observations include the following: tangential forces between granular particles are found to play a crucial role in determining impact dynamics; both force networks and particle dynamics are correlated with the dynamics of the intruder itself.

Phase transitions of aqueous colloidal dispersions of charged platelike particles of niobate nanosheets were investigated as a function of the aspect ratio ($r_{\mathrm{asp}}$) and particle volume concentration (${\phi }_{\mathrm{p}}$) by means of small-angle neutron scattering and small-angle x-ray scattering. The results elucidated the following three pieces of evidence: (1) the macroscopic phase separation of the dispersions into an isotropic phase and a liquid crystalline (LC) phase under the conditions of (a) varying $r_{\mathrm{asp}}$ (1.3$\times$10${}^{-4}$ ≤ $r_{\mathrm{asp}}$ ≤ 2.5$\times$10${}^{-3}$) at a constant ${\phi }_{\mathrm{p}}$ $=$ 0.01 and (b) varying ${\phi }_{\mathrm{p}}$ (0.01 ≤ ${\phi }_{\mathrm{p}}$ ≤ 0.025) at a constant $r_{\mathrm{asp}}$ $=$ 2.5$\times$10${}^{-3}$, a mechanism of which is proposed in the text, where $r_{\mathrm{asp}}$ ≡ $d$/$\overline{L}$, with $d$ and $\overline{L}$ being thickness and the average lateral size of the plates, respectively; (2) the $r_{\mathrm{asp}}$-induced phase transition of the LC phase from a nematic phase to a highly periodic layered phase, the line shapes of the scattering peaks of which were examined by Caillé's analysis, upon increasing $r_{\mathrm{asp}}$ under the condition (a); (3) the LC phase having remarkable concentration fluctuations of the particles which are totally unexpected for the conventional lyotropic molecular LC but which are anticipated to be general for the platelike colloidal particles.

We present part I in a two-part study of an open chaotic cavity shaped as a vase. The vase possesses an unstable periodic orbit in its neck. Trajectories passing through this orbit escape without return. For our analysis, we consider a family of trajectories launched from a point on the vase boundary. We imagine a vertical array of detectors past the unstable periodic orbit and, for each escaping trajectory, record the propagation time and the vertical detector position. We find that the escape time exhibits a complicated recursive structure. This recursive structure is explored in part I of our study. We present an approximation to the Helmholtz equation for waves escaping the vase. By choosing a set of detector points, we interpolate trajectories connecting the source to the different detector points. We use these interpolated classical trajectories to construct the solution to the wave equation at a detector point. Finally, we construct a plot of the detector position versus the escape time and compare this graph to the results of an experiment using classical ultrasound waves. We find that generally the classical trajectories organize the escaping ultrasound waves.

We present part II of a study of chaotic escape from an open two-dimensional vase-shaped cavity. A surface of section reveals that the chaotic dynamics is controlled by a homoclinic tangle, the union of stable and unstable manifolds attached to a hyperbolic fixed point. Furthermore, the surface of section rectifies escape-time graphs into sequences of escape segments; each sequence is called an epistrophe. Some of the escape segments (and therefore some of the epistrophes) are forced by the topology of the dynamics of the homoclinic tangle. These topologically forced structures can be predicted using the method called homotopic lobe dynamics (HLD). HLD takes a finite length of the unstable manifold and a judiciously altered topology and returns a set of symbolic dynamical equations that encode the folding and stretching of the unstable manifold. We present three applications of this method to three different lengths of the unstable manifold. Using each set of dynamical equations, we compute minimal sets of escape segments associated with the unstable manifold, and minimal sets associated with a burst of trajectories emanating from a point on the vase's boundary. The topological theory predicts most of the early escape segments that are found in numerical computations.

Density gradients across a reaction front can lead to convective fluid motion. Stable fronts require a heavier fluid on top of a lighter one to generate convective fluid motion. On the other hand, unstable fronts can be stabilized with an opposing density gradient, where the lighter fluid is on top. In this case, we can have a stable flat front without convection or a steady convective front of a given wavelength near the onset of convection. The fronts are described with the Kuramoto-Sivashinsky equation coupled to hydrodynamics governed by Darcy's law. We obtain a dispersion relation between growth rates and perturbation wave numbers in the presence of a density discontinuity accross the front. We also analyze the effects of this density change in the transition to chaos.

We study synchronization of sinusoidally coupled phase oscillators on networks with modular structure and a large number of oscillators in each community. Of particular interest is the hierarchy of local and global synchrony, i.e., synchrony within and between communities, respectively. Using the recent ansatz of Ott and Antonsen [Chaos 18, 037113 (2008)], we find that the degree of local synchrony can be determined from a set of coupled low-dimensional equations. If the number of communities in the network is large, a low-dimensional description of global synchrony can be also found. Using these results, we study bifurcations between different types of synchrony. We find that, depending on the relative strength of local and global coupling, the transition to synchrony in the network can be mediated by local or global effects.