We propose to describe correlations in classical and quantum systems in terms of full counting statistics of a suitably chosen discrete observable. The method is illustrated with two exactly solvable examples: the classical one-dimensional Ising model and the quantum spin-1/2 $XY$ chain. For the one-dimensional Ising model, our method results in a phase diagram with two phases distinguishable by the long-distance behavior of the Jordan-Wigner strings. For the anisotropic spin-1/2 $XY$ chain in a transverse magnetic field, we compute the full counting statistics of the magnetization and use it to classify quantum phases of the chain. The method, in this case, reproduces the previously known phase diagram. We also discuss the relation between our approach and the Lee-Yang theory of zeros of the partition function.

We consider the “Touch and Stop” cluster growth percolation (CGP) model on the two-dimensional square lattice. A key parameter in the model is the fraction $p$ of occupied “seed” sites that act as nucleation centers from which a particular cluster growth procedure is started. Here, we consider two growth styles: rhombic and disk-shaped cluster growth. For intermediate values of $p$ the final state, attained by the growth procedure, exhibits a cluster of occupied sites that span the entire lattice. Using numerical simulations we investigate the percolation probability and the order parameter and perform a finite-size scaling analysis for lattices of side length up to $L=1024$ in order to carefully determine the critical exponents that govern the respective transition. In contrast to previous studies, reported in Tsakiris et al. [Phys. Rev. E 82, 041108 (2010)], we find strong numerical evidence that the CGP model is in the standard percolation universality class.

We report an experimental study on the transition between a disordered liquidlike state and an ordered solidlike one, in a collection of magnetically interacting macroscopic grains. A monolayer of magnetized particles is vibrated vertically at a moderate density. At high excitation a disordered, liquidlike state is observed. When the driving dimensionless acceleration $\Gamma$ is quasistatically reduced, clusters of ordered grains grow below a critical value, ${\Gamma }_c$. These clusters have a well-defined hexagonal and compact structure. If the driving is subsequently increased, these clusters remain stable up to a higher critical value, ${\Gamma }_l$. Thus, the solid-liquid transition exhibits a hysteresis cycle. However, the lower onset ${\Gamma }_c$ is not well defined as it depends strongly on the acceleration ramp speed and also on the magnetic interaction strength. Metastability is observed when the driving is rapidly quenched from high acceleration, $\Gamma >{\Gamma }_l$, to a low final excitation, ${\Gamma }_q$. After this quench, solid clusters nucleate after a time lag, ${\tau }_o$, either immediately (${\tau }_o=0$) or after some time lag (${\tau }_o>0$) that can vary from seconds up to several hundreds of seconds. The immediate growth occurs below a particular acceleration value, ${\Gamma }_s$ ($\lesssim {\Gamma }_c$). In all cases, for $t\ge {\tau }_o$ a solid cluster's temporal growth can be phenomenologically described by a stretched exponential law. The evolution of the parameters of this law as a function of ${\Gamma }_q$ is presented and the values of fitted parameters are discussed.

Within the harmonic approximation, we analytically determine the elastic-mediated interaction between colloidal nanoparticles adsorbed on the surface of smectic films under the influence of an external field. Both cases of free-standing films and films deposited over a solid substrate are considered. We show that the asymptotic decay ($1/R$ in free-standing and exponential in deposited films) is not altered by the external field. However, the external field plays distinct roles according to the film configuration, the interparticle distance, the film thickness, and the surface tension at the film-gas interface. We provide a detailed discussion under the light of the distinct mechanisms controlling the undulations of the surface layer.

We investigate thickness and surface anchoring strength influence on pitch transitions in a planar cholesteric liquid crystal layer. The cholesteric-nematic transition is also investigated. We assume planar boundary conditions, with strong anchoring strength at one interface and weak anchoring strength at the other. The surface anchoring energy we consider to describe the deviation of the surface twist angle from the easy axis induced by a bulk deformation is a parabolic potential or Rapini and Papoular periodic potential, respectively. We show that under strain, all pitch transitions take place at a critical thickness that is equal to the quarter of the natural cholesteric pitch. The latter result does not depend on the anchoring strength, the particular surface potential, or material properties. The twist angle on the limiting surface characterized by weak anchoring varies with strain either by slipping and or in a discontinuous manner according to the thickness of the sample. The position of the bifurcation point depends only on the ratio of the extrapolation length over the layer thickness, but its value is model dependent. Multistability and multiplicity of the transition are discussed.

We consider the evolution of large but finite populations on arbitrary fitness landscapes. We describe the evolutionary process by a Markov-Moran process. We show that to $O(1/N)$, the time-averaged fitness is lower for the finite population than it is for the infinite population. We also show that fluctuations in the number of individuals for a given genotype can be proportional to a power of the inverse of the mutation rate. Finally, we show that the probability for the system to take a given path through the fitness landscape can be nonmonotonic in system size.

With the aim of furthering the explanation of iridescence in Morpho butterflies, we developed an optical model based on the finite-element (FE) method, taking more accurately into account the exact morphology of the wing, origin of iridescence. We modeled the photonic structure of a basal scale of the Morpho rhetenor wing as a three-dimensional object, infinite in one direction, with a shape copied from a TEM image, and made out of a slightly absorbing dielectric material. Periodic boundary conditions were used in the FE method to model the wing periodic structure and perfectly matched layers permitted the free-space scattering computation. Our results are twofold: first, we verified on a simpler structure, that our model yields the same result as the rigorous coupled wave analysis (RCWA), and second, we demonstrated that it is necessary to assume an absorption gradient in the true structure, to account for experimental reflectivity measured on a real wing.

Diffusion is one of the main transport processes that occur inside cells determining the spatial and time distribution of relevant action molecules. In most cases these molecules not only diffuse but also interact with others as they get transported. When these interactions occur faster than diffusion the resulting transport can be characterized by “effective diffusion coefficients” that depend on both the reaction rates and the “free” diffusion coefficients. Fluorescence correlation spectroscopy (FCS) gives information on effective rather than free diffusion coefficients under this condition. In the present paper we investigate what coefficients can be drawn from FCS experiments for a wide range of values of the ratio of reaction to diffusion time scales, using different fitting functions. We find that the effective coefficients can be inferred with relatively small errors even when the condition of fast reactions does not exactly hold. Since the diffusion time scale depends on the size of the observation volume and the reaction time scale depends on concentrations, we also discuss how by changing either one or the other property one can switch between the two limits and extract more information on the system under study.

Some small birds typically clap their wings ventrally, particularly during hovering. To investigate this phenomenon, we analyzed the kinematic motion and wake flow field of two passerine species that hover with the same flapping frequency. For these two birds, the ventral clap is classified as direct and cupping. Japanese White-eyes undertake a direct clap via their hand wings, whereas Gouldian Finches undertake a cupping clap with one wing overlaying the other. As a result of their morphological limitation, birds of both greater size and wing span cup their wings to increase the wing speed during a ventral clap because of the larger wing loading. This morphological limitation leads also to a structural discrepancy of the wake flow fields between these two passerine species. At the instant of clapping, the direct clap induces a downward air velocity 1.68 times and generates a weight-normalized lift force 1.14 times that for the cupping clap. The direct clap produces a small upward jet and a pair of counter-rotating vortices, both of which abate the transient lift at the instant of clapping, but they are not engendered by the cupping clap. The aerodynamic mechanisms generated with a ventral clap help the small birds to avoid abrupt body swinging at the instant of clapping so as to maintain their visual stability during hovering.

When prepared in the liquid-liquid coexistence region, the four-component lipid system distearoyl-phospha-tidylcholine–dioleoyl-phosphatidylcholine–palmitoyl,oleoyl-phosphatidylcholine–cholesterol (DSPC-DOPC-POPC-Cholesterol), with certain ratios of DOPC and POPC, shows striking modulated phase patterns on the surface of giant unilamellar vesicles (GUVs). In this simulation study, we show that the morphology of these patterns can be explained by the competition of line tension (which tends to favor large round domains) and curvature, as specified by the Helfrich energy functional. In this study we use a Monte-Carlo simulation on the surface of a GUV to determine the equilibrium shape and phase morphology. We find that the patterns arising from these competing interactions very closely approximate those observed, that the patterned morphologies represent thermodynamically stable configurations, and that the geometric nature of these patterns is closely tied to the relative and absolute values of the model parameters.

Interactions between oscillators can be investigated with standard tools of time series analysis. However, these methods are insensitive to the directionality of the coupling, i.e., the asymmetry of the interactions. An elegant alternative was proposed by Rosenblum and collaborators [M. G. Rosenblum, L. Cimponeriu, A. Bezerianos, A. Patzak, and R. Mrowka, Phys. Rev. E 65, 041909 (2002); M. G. Rosenblum and A. S. Pikovsky, Phys. Rev. E 64, 045202 (2001)] which consists in fitting the empirical phases to a generic model of two weakly coupled phase oscillators. This allows one to obtain the interaction functions defining the coupling and its directionality. A limitation of this approach is that a solution always exists in the least-squares sense, even in the absence of coupling. To preclude spurious results, we propose a three-step protocol: (1) Determine if a statistical dependency exists in the data by evaluating the mutual information of the phases; (2) if so, compute the interaction functions of the oscillators; and (3) validate the empirical oscillator model by comparing the joint probability of the phases obtained from simulating the model with that of the empirical phases. We apply this protocol to a model of two coupled Stuart-Landau oscillators and show that it reliably detects genuine coupling. We also apply this protocol to investigate cardiorespiratory coupling in anesthetized rats. We observe reciprocal coupling between respiration and heartbeat and that the influence of respiration on the heartbeat is generally much stronger than vice versa. In addition, we find that the vagus nerve mediates coupling in both directions.

We consider a fitness model assumed to generate simple graphs with a power-law heavy-tailed degree sequence, $P\left(k\right)\propto k^{-1-\alpha }$ with $0<\alpha <1$, in which the corresponding distributions do not possess a mean. We discuss the situations in which the model is used to produce a multigraph and examine what happens if the multiple edges are merged to a single one and thus a simple graph is built. We give the relation between the (normalized) fitness parameter $r$ and the expected degree $\nu$ of a node and show analytically that it possesses nontrivial intermediate and final asymptotic behaviors. We show that the model produces $P\left(k\right)\propto k^{-2}$ for large values of $k$ independent of $\alpha$. Our analytical findings are confirmed by numerical simulations.

Information management services on networks, such as search and dissemination, play a key role in any large-scale distributed system. One of the most desirable features of these services is the maximization of the coverage, i.e., the number of distinctly visited nodes under constraints of network resources as well as time. However, redundant visits of nodes by different message packets (modeled, e.g., as walkers) initiated by the underlying algorithms for these services cause wastage of network resources. In this work, using results from analytical studies done in the past on a $K$-random-walk-based algorithm, we identify that redundancy quickly increases with an increase in the density of the walkers. Based on this postulate, we design a very simple distributed algorithm which dynamically estimates the density of the walkers and thereby carefully proliferates walkers in sparse regions. We use extensive computer simulations to test our algorithm in various kinds of network topologies whereby we find it to be performing particularly well in networks that are highly clustered as well as sparse.

In this paper we investigate the effect of slowly-varying parameters on the energy transfer in a weakly coupled system. For definiteness, we consider a system of two nonlinear oscillators, in which the directly excited first oscillator with constant parameter is attached to the oscillator with slowly time-varying frequency. It is proved that the equations of the slow passage through resonance in this system are identical to the equations of nonlinear Landau-Zener (LZ) tunneling. Three types of dynamical behavior are distinguished, namely, quasilinear, moderately nonlinear, and strongly nonlinear ones. Quasilinear systems exhibit a gradual energy transfer from the excited to the attached oscillator, while moderately nonlinear systems are characterized by an abrupt transition from the energy localization on the excited oscillator to the localization on the attached oscillator. In strongly nonlinear systems, the transition from the energy localization to strong energy exchange between the oscillators is revealed. Explicit approximate solutions describing the transient processes in moderately and strongly nonlinear systems are suggested. Correctness of the constructed approximations is confirmed by numerical results. The results presented in this paper, in addition to providing an analytical framework for understanding the transient dynamics, suggest an approximate procedure for solving the nonlinear LZ problem with arbitrary initial conditions over a finite time-interval.

A paradigm for optimal state-space reconstruction with nonuniform time delays is proposed. A comparison based on a diffeomorphic measure and a smoothness cost function shows that the proposed methodology achieves a better reconstruction compared to a reconstruction based on time delays that are multiples of the first minimum of mutual information. It is also shown how the proposed methodology is a more reliable approach to determining the embedding dimension.

Dispersive shock waves (DSWs) are physically important phenomena that occur in systems dominated by weak dispersion and weak nonlinearity. The Korteweg–de Vries (KdV) equation is the universal model for systems with weak dispersion and weak, quadratic nonlinearity. Here we show that the long-time-asymptotic solution of the KdV equation for general, steplike data is a single-phase DSW; this DSW is the “largest” possible DSW based on the boundary data. We find this asymptotic solution using the inverse scattering transform and matched-asymptotic expansions. So while multistep data evolve to have multiphase dynamics at intermediate times, these interacting DSWs eventually merge to form a single-phase DSW at large time.

The Verbaarschot-Weidenmüller-Zirnbauer (VWZ) model is believed to correctly represent the correlations of two $S$-matrix elements for an open quantum chaotic system, but the solution has considerable complexity and is presently only accessed numerically. Here a procedure is developed to deduce its features over the full range of the parameter space in a transparent and simple analytical form preserving accuracy to a considerable degree. The bulk of the VWZ correlations are described by the Gorin-Seligman expression for the two-amplitude correlations of the Ericson-Gorin-Seligman model. The structure of the remaining correction factors for correlation functions is discussed with special emphasis of the rôle of the level correlation hole both for inelastic and elastic correlations.

Using only dimensional considerations, Monin and Obukhov proposed a “universal” stability correction function ${\varphi }_c\left(\zeta \right)$ that accounts for distortions caused by thermal stratification to the mean scalar concentration profile in the atmospheric surface layer when the flow is stationary, planar homogeneous, fully turbulent, and lacking any subsidence. For nearly 6 decades, their analysis provided the basic framework for almost all operational models and data interpretation in the lower atmosphere. However, the canonical shape of ${\varphi }_c\left(\zeta \right)$ and the departure from the Reynold's analogy continue to defy theoretical explanation. Here, the basic processes governing the scalar-velocity cospectrum, including buoyancy and the scaling laws describing the velocity and temperature spectra, are considered via a simplified cospectral budget. The solution to this cospectral budget is then used to derive ${\varphi }_c\left(\zeta \right)$, thereby establishing a link between the energetics of turbulent velocity and scalar concentration fluctuations and the bulk flow describing the mean scalar concentration profile. The resulting theory explains all the canonical features of ${\varphi }_c\left(\zeta \right)$, including the onset of power laws for various stability regimes and their concomitant exponents, as well as the causes of departure from Reynold's analogy.

Anisotropic superhydrophobic surfaces have the potential to greatly reduce drag and enhance mixing phenomena in microfluidic devices. Recent work has focused mostly on cases of superhydrophobic stripes. Here, we analyze a relevant situation of cosine variation of the local slip length. We derive approximate formulas for maximal (longitudinal) and minimal (transverse) directional effective slip lengths that are in good agreement with the exact numerical solution and lattice-Boltzmann simulations. Compared to the case of superhydrophobic stripes, the cosine texture can provide a very large effective slip. However, the difference between eigenvalues of the slip-length tensor is smaller, indicating that the flow is less anisotropic.

A free-energy lattice Boltzmann approach has been used to perform simulations of liquid penetration into random porous media. We focus our study on the effects of microstructures, particularly microtopography, on liquid penetration driven by capillary force and external pressure. For this purpose we set up a model structure that consists of a network of interconnected capillaries with varying pore geometries. The results showed that the discontinuities in the solid-surface curvature, as are present as corners on the capillary surfaces, have strong influences on liquid penetration through their pinning effects and interactions with local geometry.