The Ehrenfest-time scale in quantum transport separates essentially classical propagation from wave interference and here we consider its effect on the transmission and reflection through quantum dots. In particular, we calculate the Ehrenfest-time dependence of the next-to-leading-order quantum corrections to the transmission and reflection for dc and ac transport and check that our results are consistent with current conservation relations. Looking as well at spectral statistics in closed systems, we finally demonstrate how the contributions analyzed here imply changes in the calculation, given by Brouwer et al. [Phys. Rev. E 74, 066208 (2006)], of the next-to-leading order of the spectral form factor. Our semiclassical result coincides with the result obtained by Tian and Larkin [Phys. Rev. B 70, 035305 (2004)] by field-theoretical methods.

We provide a comprehensive view of various phase transitions in random $K$-satisfiability problems solved by stochastic-local-search algorithms. In particular, we focus on the finite-size scaling (FSS) exponent, which is mathematically important and practically useful in analyzing finite systems. Using the FSS theory of nonequilibrium absorbing phase transitions, we show that the density of unsatisfied clauses clearly indicates the transition from the solvable (absorbing) phase to the unsolvable (active) phase as varying the noise parameter and the density of constraints. Based on the solution clustering (percolation-type) argument, we conjecture two possible values of the FSS exponent, which are confirmed reasonably well in numerical simulations for $2\le K\le 3$.

We demonstrate that the geometry of a data cloud is computable on multiple scales without prior knowledge about its structure. We show that the concepts of “time” and “temperature” are beneficial for constructing a hierarchical geometry based on local information provided by a similarity measure. We design two devices for construction of this hierarchy. Along the time axis, a regulated random walk incorporated with recurrence-time dynamics detects information about the number of clusters and the corresponding cluster membership of individual data nodes. Along the temperature axis we build the geometric hierarchy of a data cloud, which consists of only a few phase transitions. The base level of the hierarchy especially exhibits the intrinsic data structure. At each chosen temperature, we form an ensemble matrix that summarizes information extracted from many regulated random walks. This device constitutes the basis for constructing one corresponding level of the hierarchy by means of spectral clustering. We illustrate the construction of such geometric hierarchies using simulated and real data.

Starting from a stochastic two-dimensional process we studied the transformation of points in disks and squares following a protocol according to which at any step the island size increases proportionally to the corresponding Voronoi tessera. Two interaction mechanisms among islands have been dealt with: coalescence and impingement. We studied the evolution of the island density and of the island size distribution functions, in dependence on island collision mechanisms for both Poissonian and correlated spatial distributions of points. The island size distribution functions have been found to be invariant with the fraction of transformed phase for a given stochastic process. The $n\left(\Theta \right)$ curve describing the island decay has been found to be independent of the shape (apart from high correlation degrees) and interaction mechanism.

$N$ searchers are sent out by a source in order to locate a fixed object which is at a finite distance $D$, but the search space is infinite and $D$ would be in general unknown. Each of the searchers has a finite random lifetime, and may be subject to destruction or failures, and it moves independently of other searchers, and at intermediate locations some partial random information may be available about which way to go. When a searcher is destroyed or disabled, or when it “dies naturally,” after some time the source becomes aware of this and it sends out another searcher, which proceeds similarly to the one that it replaces. The search ends when one of the searchers finds the object being sought. We use $N$ coupled Brownian motions to derive a closed form expression for the average search time as a function of $D$ which will depend on the parameters of the problem: the number of searchers, the average lifetime of searchers, the routing uncertainty, and the failure or destruction rate of searchers. We also examine the cost in terms of the total energy that is expended in the search.

If the work per cycle of a quantum heat engine is averaged over an appropriate prior distribution for an external parameter $a$, the work becomes optimal at Curzon-Ahlborn (CA) efficiency. More general priors of the form $\Pi \left(a\right)\propto 1/a^{\gamma }$ yield optimal work at an efficiency which stays close to CA value, in particular near equilibrium the efficiency scales as one-half of the Carnot value. This feature is analogous to the one recently observed in literature for certain models of finite-time thermodynamics. Further, the use of Bayes’ theorem implies that the work estimated with posterior probabilities also bears close analogy with the classical formula. These findings suggest that the notion of prior information can be used to reveal thermodynamic features in quantum systems, thus pointing to a connection between thermodynamic behavior and the concept of information.

At temperatures between $7.5°\text{C}$ and $20°\text{C}$ as well as $26°\text{C}$ and $40°\text{C}$ we have recorded the densities and specific heat at constant pressure for critical mixtures of polystyrene in cyclohexane. The degrees of polymerization were $N=288$ (critical temperature $T_c=9.77°\text{C}$) and $N=6242$ $\left(T_c=27.56°\text{C}\right)$, respectively. In the two-phase regime a series of reproducible events exists in the specific-heat traces, indicating the existence of nonequilibrium intermediate states as likely resulting from an oscillatory instability of droplet formation. In the one-phase region the critical contribution to the heat capacity follows power law with critical exponent $\alpha =0.11$ compatible with Ising-like criticality. At larger $N$, however, the critical amplitude of the heat capacity is noticeably smaller than at lower degree of polymerization. This finding may be taken as an indication of different effects from competing mesoscale lengths: the radius of gyration of the polymer and the fluctuation correlation length of the mixture. The density traces reveal marginal deviations from simple linear temperature dependencies. If these deviations are analyzed in terms of critical contributions, different signs in the amplitude result, in conformity with the signs in the pressure dependence of the critical temperature. The absolute values of the amplitudes, however, are substantially larger than predicted from the critical amplitudes of the heat capacities.

We study analytically and numerically a one-dimensional model of interacting line defects (steps) fluctuating on a vicinal crystal. Our goal is to formulate and validate analytical techniques for approximately solving systems of coupled nonlinear stochastic differential equations (SDEs) governing fluctuations in surface motion. In our analytical approach, the starting point is the Burton-Cabrera-Frank (BCF) model by which step motion is driven by diffusion of adsorbed atoms on terraces and atom attachment-detachment at steps. The step energy accounts for entropic and nearest-neighbor elastic-dipole interactions. By including Gaussian white noise to the equations of motion for terrace widths, we formulate large systems of SDEs under different choices of diffusion coefficients for the noise. We simplify this description via (i) perturbation theory and linearization of the step interactions and, alternatively, (ii) a mean-field (MF) approximation whereby widths of adjacent terraces are replaced by a self-consistent field but nonlinearities in step interactions are retained. We derive simplified formulas for the time-dependent terrace-width distribution (TWD) and its steady-state limit. Our MF analytical predictions for the TWD compare favorably with kinetic Monte Carlo simulations under the addition of a suitably conservative white noise in the BCF equations.

We study the cooperative dynamics of Brownian motors moving along a one-dimensional track when an external load is applied to the leading motor, mimicking molecular motors pulling on membrane-bound cargoes in intracellular traffic. Due to the asymmetric loading, self-organized motor clusters form spontaneously. We model the motors with a two-state noise-driven ratchet formulation and study analytically and numerically the collective velocity-force and efficiency-force curves resulting from mutual interactions, mostly hard-core repulsion and weak (nonbinding) attraction. We analyze different parameter regimes including the limits of weak noise, mean-field behavior, rigid coupling, and large numbers of motors, for the different interactions. We present a general framework to classify and quantify cooperativity. We show that asymmetric loading leads generically to enhanced cooperativity beyond the simple superposition of the effects of individual motors. For weakly attracting interactions, the cooperativity is mostly enhanced, including highly coordinated motion of motors and complex nonmonotonic velocity-force curves, leading to self-regulated clusters. The dynamical scenario is enriched by resonances associated to commensurability of different length scales. Large clusters exhibit synchronized dynamics and bidirectional motion. Biological implications are discussed.

A wide variety of subharmonic $n$-phase cluster patterns was observed in experiments with spatially extended chemical and electrochemical oscillators. These patterns cannot be captured with a phase model. We demonstrate that the introduction of a nonlinear global coupling (NGC) in the complex Ginzburg-Landau equation has subharmonic cluster pattern solutions in wide parameter ranges. The NGC introduces a conservation law for the oscillatory state of the homogeneous mode, which describes the strong oscillations of the mean field in the experiments. We show that the NGC causes a pronounced 2:1 self-resonance on any spatial inhomogeneity, leading to two-phase subharmonic clustering, as well as additional higher resonances. Nonequilibrium Ising-Bloch transitions occur as the coupling strength is varied.

A localized source of buoyancy flux in a nonreactive fluid medium creates a plume. The flux can be provided by either heat, a compositional difference between the fluid comprising the plume and its surroundings, or a combination of both. For autocatalytic plumes produced by the iodate-arsenous acid reaction, however, buoyancy is produced along the entire reacting interface between the plume and its surroundings. Buoyancy production at the moving interface drives fluid motion, which in turn generates flow that advects the reaction front. As a consequence of this interplay between fluid flow and chemical reaction, autocatalytic plumes exhibit a rich dynamics during their ascent through the reactant medium. One of the more interesting dynamical features is the production of an accelerating vortical plume head that in certain cases pinches-off and detaches from the upwelling conduit. After pinch-off, a new plume head forms in the conduit below, and this can lead to multiple generations of plume heads for a single plume initiation. We investigated the pinch-off process using both experimentation and simulation. Experiments were performed using various concentrations of glycerol, in which it was found that repeated pinch-off occurs exclusively in a specific concentration range. Autocatalytic plume simulations revealed that pinch-off is triggered by the appearance of accelerating flow in the plume conduit.

We consider a $\left(1+1\right)$-dimensional ballistic deposition process with next-nearest-neighbor interactions, which belongs to the Kardar-Parisi-Zhang (KPZ) universality class. The focus of our analysis is on the properties of structures appearing in the bulk of a growing aggregate: a forest of independent clusters separated by “crevices.” Competition for growth (mutual screening) between different clusters results in “thinning” of this forest, i.e., the number density $c\left(h\right)$ of clusters decreases with the height $h$ of the pattern. For the discrete stochastic equation describing the process we introduce a variational formulation similar to that used for the randomly forced continuous Burgers equation. This allows us to identify the “clusters” and crevices with minimizers and shocks in the Burgers turbulence. Capitalizing on the ideas developed for the latter process, we find that $c\left(h\right)\sim h^{-\alpha }$ with $\alpha =2/3$. We compute also scaling laws that characterize the ballistic deposition patterns in the bulk: the law of transversal fluctuations of cluster boundaries and the size distribution of clusters. It turns out that the intercluster interface is superdiffusive: the corresponding exponent is twice as large as the KPZ exponent for the surface of the aggregate. Finally we introduce a probabilistic concept of ballistic growth, dubbed the “hairy” Airy process in view of its distinctive geometric features. Its statistical properties are analyzed numerically.

We study pattern formation processes in anisotropic system governed by the Kuramoto-Sivashinsky equation with multiplicative noise as a generalization of the Bradley-Harper model for ripple formation induced by ion bombardment. For both linear and nonlinear systems we study noise-induced effects at ripple formation and discuss scaling behavior of the surface growth and roughness characteristics. It was found that the secondary parameters of the ion beam (beam profile and variations of an incidence angle) can crucially change the topology of patterns and the corresponding dynamics.

By combining the force-extension relation of single semiflexible polymers with a Langevin equation to capture the dissipative dynamics of chains moving through a viscous medium we study the dynamical response of cross-linked biopolymer materials. We find that at low frequencies the network deformations are highly nonaffine, and show a low plateau in the modulus. At higher frequencies, this nonaffinity decreases while the elastic modulus increases. With increasing frequency, more and more nonaffine network relaxation modes are suppressed, resulting in a stiffening. This effect is fundamentally different from the high-frequency stiffening due to the single-filament relaxation modes [F. Gittes and F. C. MacKintosh, Phys. Rev. E 58, R1241 (1998)], not only in terms of its mechanism but also in its resultant scaling: $G^{\prime }\left(\omega \right)\sim {\omega }^{\alpha }$ with $\alpha >3/4$. This may determine nonlinear material properties at low, physiologically relevant frequencies.

The relaxation dynamics of 1,2-propanediol-–1,3-propanediol mixtures is studied in supercooled liquid regions across a wide composition range. The composition dependences of liquid fragility and nonexponential parameter ${\beta }_{KWW}$ are presented in the hydrogen-bonded mixtures with ideal mixing. The fragility index and glass transition temperature are shown to develop inversely with ${\beta }_{KWW}$, in analogy to the dynamic behaviors in mixtures of van der Waals liquids. Negative mixing effects on liquid fragility and ${\beta }_{KWW}$ are observed, and the strongest dependence of ${\beta }_{KWW}$ on relaxation dynamics is revealed at the equimolar concentration. The glass formation in isomeric liquids is also addressed.

Recently online communities have attracted great interest and have become an important medium of information exchange between users. The aim of this work is to introduce a simple model of the evolution of online communities. This model describes (a) the time evolution of users’ activity in a web service, e.g., the time evolution of the number of online friends or written posts, (b) the time evolution of the degree distribution of a social network, and (c) the time evolution of the number of active users of a web service. In the second part of the paper we investigate the influence of the users’ lifespan (i.e., the total time in which they are active in an online community) on the process of rumor propagation in evolving social networks. Viral marketing is an important application of such method of information propagation.

We derive analytic solutions for the potential and field in a one-dimensional system of masses or charges with periodic boundary conditions, in other words, Ewald sums for one dimension. We also provide a set of tools for exploring the system evolution and show that it is possible to construct an efficient algorithm for carrying out simulations. In the cosmological setting we show that two approaches for satisfying periodic boundary conditions—one overly specified and the other completely general—provide a nearly identical clustering evolution until the number of clusters becomes small, at which time the influence of any size-dependent boundary cannot be ignored. Finally, we compare the results with other recent work with the hope to provide clarification over differences these issues have induced.

Noisy scattering dynamics in the randomly driven Hénon-Heiles oscillator is investigated when the energy is above the threshold to permit particles to escape from the scattering region. First, some basic simulation procedures are briefly introduced and the fractal exit basins appear to be robust when the bounded noisy excitation is imposed on the oscillator. Second, several key fractal characteristics of the sample basin boundaries, such as the delay-time function and the uncertainty dimension, are estimated from which this oscillator is found to be structurally unstable against the bounded noisy excitation. Moreover, the stable and unstable manifolds of some sample chaotic invariant sets are estimated and illustrated in a special two-dimensional Poincaré section. Lastly, several previous methods are developed to identify three arbitrarily chosen noisy scattering time series of the randomly driven Hénon-Heiles oscillator, from which the quasiperiodic-dominant and the chaotic-dominant dynamical behaviors are distinguished.

The zero surface tension fluid-fluid interface dynamics in a radial Hele-Shaw cell driven by both injection and rotation is studied by a conformal-mapping approach. The situation in which one of the fluids is inviscid and has negligible density is analyzed. When Coriolis force effects are ignored, exact solutions of the zero surface tension rotating Hele-Shaw problem with injection reveal suppression of cusp singularities for sufficiently high rotation rates. We study how the Coriolis force affects the time-dependent solutions of the problem, and the development of finite time singularities. By employing Richardson’s harmonic moments approach we obtain conformal maps which describe the time evolution of the fluid boundary. Our results demonstrate that the inertial Coriolis contribution plays an important role in determining the time for cusp formation. Moreover, it introduces a phase drift that makes the evolving patterns rotate. The Coriolis force acts against centrifugal effects, promoting (inhibiting) cusp breakdown if the more viscous and dense fluid lies outside (inside) the interface. Despite the presence of Coriolis effects, the occurrence of finger bending events has not been detected in the exact solutions.

The injection of a fluid into another of larger viscosity in a Hele-Shaw cell usually results in the formation of highly branched patterns. Despite the richness of these structures, in many practical situations such convoluted shapes are quite undesirable. In this Brief Report, we propose an efficient and easily reproducible way to restrain these instabilities based on a simple piecewise-constant pumping protocol. It results in a reduction in the size of the viscous fingers by one order of magnitude.