We numerically study the critical behavior of the one-dimensional $XY$ model of the size $N$ with variable interaction range $L$. As expected, the standard local order parameter of the magnetization is shown to well detect the mean-field-type transition which occurs at any nonzero value of $L/N$. The system is particularly interesting since the underlying one-dimensional structure allows us to study the topological excitation of the winding number across the whole system even though the system shares the mean-field transition with the globally coupled system. We propose a nonlocal order parameter based on the width of the winding number distribution which exhibits a clear signature of the transition nature of the system.

The prevalence of heterogeneous nucleation in nature was explained qualitatively by the classical theory for heterogeneous nucleation established over more than 60 years ago, but the quantitative validity and the key conclusions of the theory have remained unconfirmed. Employing the forward flux sampling method and the coarse-grained water model (mW), we explicitly computed the heterogeneous ice nucleation rates in the supercooled water on a graphitic surface at various temperatures. The independently calculated ice nucleation rates were found to fit well according to the classical theory for heterogeneous nucleation. The fitting procedure further yields the estimate of the potency factor, which measures the ratio of the heterogeneous nucleation barrier to the homogeneous nucleation barrier. Remarkably, the estimated potency factor agrees quantitatively with the volumetric ratio of the critical nuclei between the heterogeneous and homogeneous nucleation. Our numerical study thus provides a strong support to the quantitative power of the theory and allows understanding ice nucleation behaviors under the most relevant freezing conditions.

The Gaussian chain model is the classical description of a polymeric chain, which provides analytical results regarding end-to-end distance, the distribution of segments around the mass center of a chain, coarse-grained interactions between two chains and effective interactions in binary mixtures. This hierarchy of results can be calculated thanks to the $\alpha$ stability of the Gaussian distribution. In this paper we show that it is possible to generalize the model of Gaussian chain to the entire class of $\alpha$-stable distributions, obtaining the analogous hierarchy of results expressed by the analytical closed-form formulas in the Fourier space. This allows us to establish the $\alpha$-stable chain model. We begin with reviewing the applications of Levy flights in the context of polymer sciences, which include: chains described by the heavy-tailed distributions of persistence length; polymers adsorbed to the surface; and the chains driven by a noise with power-law spatial correlations. Further, we derive the distribution of segments around the mass center of the $\alpha$-stable chain and construct the coarse-grained interaction potential between two chains. These results are employed to discuss the model of binary mixture consisting of the $\alpha$-stable chains. In what follows, we establish the spinodal decomposition condition generalized to the mixtures of the $\alpha$-stable polymers. This condition is further applied to compare the on-surface phase separation of adsorbed polymers (which are known to be described with heavy-tailed statistics) with the phase separation condition in the bulk. Finally, we predict the four different scenarios of simultaneous mixing and demixing in the two- and three-dimensional systems.

The quantum ratchet current is studied in the parameter space of the dissipative kicked rotor model coupled to a zero-temperature quantum environment. We show that vacuum fluctuations blur the generic isoperiodic stable structures found in the classical case. Such structures tend to survive when a measure of statistical dependence between the quantum and classical currents are displayed in the parameter space. In addition, we show that quantum fluctuations can be used to overcome transport barriers in the phase space. Related quantum ratchet current activation regions are spotted in the parameter space. Results are discussed based on quantum, semiclassical, and classical calculations. While the semiclassical dynamics involves vacuum fluctuations, the classical map is driven by thermal noise.

Forecasting a time series from multivariate predictors constitutes a challenging problem, especially using model-free approaches. Most techniques, such as nearest-neighbor prediction, quickly suffer from the curse of dimensionality and overfitting for more than a few predictors which has limited their application mostly to the univariate case. Therefore, selection strategies are needed that harness the available information as efficiently as possible. Since often the right combination of predictors matters, ideally all subsets of possible predictors should be tested for their predictive power, but the exponentially growing number of combinations makes such an approach computationally prohibitive. Here a prediction scheme that overcomes this strong limitation is introduced utilizing a causal preselection step which drastically reduces the number of possible predictors to the most predictive set of causal drivers making a globally optimal search scheme tractable. The information-theoretic optimality is derived and practical selection criteria are discussed. As demonstrated for multivariate nonlinear stochastic delay processes, the optimal scheme can even be less computationally expensive than commonly used suboptimal schemes like forward selection. The method suggests a general framework to apply the optimal model-free approach to select variables and subsequently fit a model to further improve a prediction or learn statistical dependencies. The performance of this framework is illustrated on a climatological index of El Niño Southern Oscillation.

We study the transient behavior in coupled dissipative dynamical systems based on the linear analysis around the steady state. We find that the transient time is minimized at a specific set of system parameters and show that at this parameter set, two eigenvalues and two eigenvectors of the Jacobian matrix coalesce at the same time; this degenerate point is called the exceptional point. For the case of coupled limit-cycle oscillators, we investigate the transient behavior into the amplitude death state, and clarify that the exceptional point is associated with a critical point of frequency locking, as well as the transition of the envelope oscillation.

We formulate a smoothed-particle hydrodynamics numerical method, traditionally used for the Euler equations for fluid dynamics in the context of astrophysical simulations, to solve the nonlinear Schrödinger equation in the Madelung formulation. The probability density of the wave function is discretized into moving particles, whose properties are smoothed by a kernel function. The traditional fluid pressure is replaced by a quantum pressure tensor, for which a robust discretization is found. We demonstrate our numerical method on a variety of numerical test problems involving the simple harmonic oscillator, soliton-soliton collision, Bose-Einstein condensates, collapsing singularities, and dark matter halos governed by the Gross-Pitaevskii-Poisson equation. Our method is conservative, applicable to unbounded domains, and is automatically adaptive in its resolution, making it well suited to study problems with collapsing solutions.

In a recent work, a new numerical method (the lifespan method) has been introduced to study the critical properties of epidemic processes on complex networks [M. Boguñá, C. Castellano, and R. Pastor-Satorras, Phys. Rev. Lett. 111, 068701 (2013)]. Here, we present a detailed analysis of the viability of this method for the study of the critical properties of generic absorbing-state phase transitions in lattices. Focusing on the well-understood case of the contact process, we develop a finite-size scaling theory to measure the critical point and its associated critical exponents. We show the validity of the method by studying numerically the contact process on a one-dimensional lattice and comparing the findings of the lifespan method with the standard quasistationary method. We find that the lifespan method gives results that are perfectly compatible with those of quasistationary simulations and with analytical results. Our observations confirm that the lifespan method is a fully legitimate tool for the study of the critical properties of absorbing phase transitions in regular lattices.

We present a composite generalized Langevin equation as a unified framework for bridging the hydrodynamic, Brownian, and adhesive spring forces associated with a nanoparticle at different positions from a wall, namely, a bulklike regime, a near-wall regime, and a lubrication regime. The particle velocity autocorrelation function dictates the dynamical interplay between the aforementioned forces, and our proposed methodology successfully captures the well-known hydrodynamic long-time tail with context-dependent scaling exponents and oscillatory behavior due to the binding interaction. Employing the reactive flux formalism, we analyze the effect of hydrodynamic variables on the particle trajectory and characterize the transient kinetics of a particle crossing a predefined milestone. The results suggest that both wall-hydrodynamic interactions and adhesion strength impact the particle kinetics.

Catalytically active colloids maintain nonequilibrium conditions in which they produce and deplete chemicals and hence effectively act as sources and sinks of molecules. While individual colloids that are symmetrically coated do not exhibit any form of dynamical activity, the concentration fields resulting from their chemical activity decay as $1/r$ and produce gradients that attract or repel other colloids depending on their surface chemistry and ambient variables. This results in a nonequilibrium analog of ionic systems, but with the remarkable novel feature of action-reaction symmetry breaking. We study solutions of such chemically active colloids in dilute conditions when they join up to form molecules via generalized ionic bonds and discuss how we can achieve structures with time-dependent functionality. In particular, we study a molecule that adopts a spontaneous oscillatory pattern of conformations and another that exhibits a run-and-tumble dynamics similar to bacteria. Our study shows that catalytically active colloids could be used for designing self-assembled structures that possess dynamical functionalities that are determined by their prescribed three-dimensional structures, a strategy that follows the design principle of proteins.

Boiling crisis is a transition between nucleate and film boiling. It occurs at a threshold value of the heat flux from the heater called CHF (critical heat flux). Usually, boiling crisis studies are hindered by the high CHF and short transition duration (below 1 ms). Here we report on experiments in hydrogen near its liquid-vapor critical point, in which the CHF is low and the dynamics slow enough to be resolved. As under such conditions the surface tension is very small, the experiments are carried out in the reduced gravity to preserve the conventional bubble geometry. Weightlessness is created artificially in two-phase hydrogen by compensating gravity with magnetic forces. We were able to reveal the fractal structure of the contour of the percolating cluster of the dry areas at the heater that precedes the boiling crisis. We provide a direct statistical analysis of dry spot areas that confirms the boiling crisis at zero gravity as a scale-free phenomenon. It was observed that, in agreement with theoretical predictions, saturated boiling CHF tends to zero (within the precision of our thermal control system) in zero gravity, which suggests that the boiling crisis may be observed at any heat flux provided the experiment lasts long enough.

We report a comprehensive study of the flow of liquid triggered by injecting a droplet into a liquid foam microchannel, also called a Plateau border. This drop-injected experiment reveals an intricate dynamics for the liquid redistribution, with two contrasting regimes observed, ruled either by inertia or viscosity. We devoted a previous study [A. Cohen et al., Phys. Rev. Lett. 112, 218303 (2014)] to the inertial imbibition regime, unexpected at such small length scales. Here we report other features of interest of the drop-injected experiment, related to the coalescence of the droplet with the liquid microchannel, to both the inertial and viscous regimes, and to the occurrence of liquid flow through the soap films as well as effects of the interfacial rheology. The transition between the two regimes is investigated and qualitatively accounted for. The relevance of our results to liquid foam drainage is tackled by considering the flow of liquid at the nodes of the network of interconnected microchannels. Extensions of our study to liquid foams are discussed.

A method to estimate the index of refraction in warm and hot dense matter is proposed. This method combines the Kubo-Greenwood approach, Maxwell equations, and existing codes that calculate photoabsorption and photoemission coefficients in warm and hot dense plasmas. An effective electrical conductivity is calculated from existing opacity codes from which the index of refraction is derived. Illustrations are shown on specific examples.

An efficient and simple approach of measuring the absolute free energy as a function of temperature for spin lattice models using a two-stage parallel tempering Monte Carlo and the free energy perturbation method is discussed and the results are compared with those of population annealing Monte Carlo using the three-dimensional Edwards-Anderson Ising spin glass model as benchmark tests. This approach requires little modification of regular parallel tempering Monte Carlo codes with also little overhead. Numerical results show that parallel tempering, even though using a much less number of temperatures than population annealing, can nevertheless equally efficiently measure the absolute free energy by simulating each temperature for longer times.

We investigate the rate of thermalization of local operators in the one-dimensional anisotropic antiferromagnetic Heisenberg model with next-nearest neighbor interactions that break integrability. This is done by calculating the scaling of the difference of the diagonal and canonical thermal ensemble values as a function of system size, and by directly calculating the time evolution of the expectation values of the operators with the Chebyshev polynomial expansion. Spatial and spin symmetry is exploited and the Hamiltonian is divided into subsectors according to their symmetry. The rate of thermalization depends on the proximity to the integrable limit. When integrability is weakly broken thermalization is slow, and becomes faster the stronger the next-nearest neighbor interaction is. Three different regimes for the rate of thermalization with respect to the strength of the integrability breaking parameter are identified. These are shown to be directly connected with the relative strength of the low and higher energy difference off-diagonal operator matrix elements in the symmetry eigenbasis of the Hamiltonian. Close to the integrable limit the off-diagonal matrix elements peak at higher energies and high-frequency fluctuations are important and slow down thermalization. Away from the integrable limit a strong low-energy peak gradually develops that takes over the higher frequency fluctuations and leads to quicker thermalization.

The nonextensive entropic measure proposed by Tsallis [C. Tsallis, J. Stat. Phys. 52, 479 (1988)] introduces a parameter, $q$, which is not defined but rather must be determined. The value of $q$ is typically determined from a piece of data and then fixed over the range of interest. On the other hand, from a phenomenological viewpoint, there are instances in which $q$ cannot be treated as a constant. We present two distinct approaches for determining $q$ depending on the form of the equations of constraint for the particular system. In the first case the equations of constraint for the operator $\widehat{O}$ can be written as $\mathrm{Tr}\left(F^q\widehat{O}\right)=C$, where $C$ may be an explicit function of the distribution function $F$. We show that in this case one can solve an equivalent maxent problem which yields $q$ as a function of the corresponding Lagrange multiplier. As an illustration the exact solution of the static generalized Fokker-Planck equation (GFPE) is obtained from maxent with the Tsallis enropy. As in the case where $C$ is a constant, if $q$ is treated as a variable within the maxent framework the entropic measure is maximized trivially for all values of $q$. Therefore $q$ must be determined from existing data. In the second case an additional equation of constraint exists which cannot be brought into the above form. In this case the additional equation of constraint may be used to determine the fixed value of $q$.

The family of $q$-Gaussian and $q$-exponential probability densities fit the statistical behavior of diverse complex self-similar nonequilibrium systems. These distributions, independently of the underlying dynamics, can rigorously be obtained by maximizing Tsallis “nonextensive” entropy under appropriate constraints, as well as from superstatistical models. In this paper we provide an alternative and complementary scheme for deriving these objects. We show that $q$-Gaussian and $q$-exponential random variables can always be expressed as a function of two statistically independent gamma random variables with the same scale parameter. Their shape index determines the complexity $q$ parameter. This result also allows us to define an extended family of asymmetric $q$-Gaussian and modified $q$-exponential densities, which reduce to the standard ones when the shape parameters are the same. Furthermore, we demonstrate that a simple change of variables always allows relating any of these distributions with a beta stochastic variable. The extended distributions are applied in the statistical description of different complex dynamics such as log-return signals in financial markets and motion of point defects in a fluid flow.

We present a simple paradigm for detection of an immobile target by a space-time coupled random walker with a finite lifetime. The motion of the walker is characterized by linear displacements at a fixed speed and exponentially distributed duration, interrupted by random changes in the direction of motion and resumption of motion in the new direction with the same speed. We call these walkers “mortal creepers.” A mortal creeper may die at any time during its motion according to an exponential decay law characterized by a finite mean death rate ${\omega }_m$. While still alive, the creeper has a finite mean frequency $\omega$ of change of the direction of motion. In particular, we consider the efficiency of the target search process, characterized by the probability that the creeper will eventually detect the target. Analytic results confirmed by numerical results show that there is an ${\omega }_m$-dependent optimal frequency $\omega ={\omega }_{\mathrm{opt}}$ that maximizes the probability of eventual target detection. We work primarily in one-dimensional $\left(d=1\right)$ domains and examine the role of initial conditions and of finite domain sizes. Numerical results in $d=2$ domains confirm the existence of an optimal frequency of change of direction, thereby suggesting that the observed effects are robust to changes in dimensionality. In the $d=1$ case, explicit expressions for the probability of target detection in the long time limit are given. In the case of an infinite domain, we compute the detection probability for arbitrary times and study its early- and late-time behavior. We further consider the survival probability of the target in the presence of many independent creepers beginning their motion at the same location and at the same time. We also consider a version of the standard “target problem” in which many creepers start at random locations at the same time.

We discuss relaxation and aging processes in the one- and two-dimensional $ABC$ models. In these driven diffusive systems of three particle types, biased exchanges in one direction yield a coarsening process characterized in the long-time limit by a logarithmic growth of ordered domains that take the form of stripes. From the time-dependent length, derived from the equal-time spatial correlator, and from the mean displacement of individual particles different regimes in the formation and growth of these domains can be identified. Analysis of two-times correlation and response functions reveals dynamical scaling in the asymptotic logarithmic growth regime as well as complicated finite-time and finite-size effects in the early and intermediate time regimes.