Experimental and theoretical studies of a smectic-$A$–hexatic-$B$ transition in freely suspended films of thickness $2–10\mu \mathrm{m}$ of the $n$-pentyl-$4^{\prime }-n$-pentanoyloxy-biphenyl-4-carboxylate (54COOBC) compound are presented. X-ray investigations revealed a discontinuous first-order transition into the hexatic phase. The temperature region of two-phase coexistence near the phase transition point diminishes with decreasing film thickness. The width of this temperature region as a function of the film thickness was derived on the basis of a Landau mean-field theory in the vicinity of a tricritical point (TCP). Close to TCP the surface hexatic-$B$ order penetrates anomalously deep into the film interior.

The $2\lambda$-O oscillatory mode of cellular solidification patterns is studied in thin samples of a succinonitrile-acrylonitrile transparent alloy. The origin and the nature of oscillations are revisited and discussed by combining experiment with three-dimensional phase-field numerical simulations. The existence domain of $2\lambda$-O oscillations and the evolution of their period with growth velocity are determined and compared. Simulations evidence transversal solute fluxes between neighboring cells as an essential feature of cell dynamics. A solute balance model in which transversal fluxes are crucial for oscillations recovers the emergence of a $2\lambda$-O mode and its period-velocity relationship. It thus confirms the fundamental role of transversal fluxes and provides a complete coherent description of the physical mechanisms of $2\lambda$-O oscillations. Parametric excitations are used to force $2\lambda$-O oscillations beyond their stability domain and highlight the nature of the underlying oscillator, especially its nonlinearity responsible for intermittent oscillations and complex behavior in the resonance band.

We present the equations for wicking in two- and three-dimensional porous media when liquid is evaporating through the wet front using the Green–Ampt saturated capillary flow model in polar and spherical geometries. The time-dependent behavior of two-dimensional wicking influenced by front interface evaporation manifests distinctly from the influence on wicking by normal surface evaporation. This is shown in several ways; notably, the first-order effects of the front evaporation, as considered via an evaporation-capillary number, is of a lower order in the front position than normal evaporation. Furthermore, the front evaporation-induced steady states of the front position and bulk velocity vary significantly with the dimensionality of the flow expansion in the porous domain; with respect to the dimensionality, the front position decreases while the bulk velocity increases.

We calculate the probability distribution function (PDF) of an overdamped Brownian particle moving in a periodic potential energy landscape $U\left(x\right)$. The PDF is found by solving the corresponding Smoluchowski diffusion equation. We derive the solution for any periodic even function $U\left(x\right)$ and demonstrate that it is asymptotically (at large time $t$) correct up to terms decaying faster than $\sim t^{-3/2}$. As part of the derivation, we also recover the Lifson-Jackson formula for the effective diffusion coefficient of the dynamics. The derived solution exhibits agreement with Langevin dynamics simulations when (1) the periodic length is much larger than the ballistic length of the dynamics, and (2) when the potential barrier $\mathrm{\Delta }U=max\left[U\right(x\left)\right]-min\left[U\right(x\left)\right]$ is not much larger than the thermal energy $k_{B}T$.

The elephant random walk is a history-dependent random walk. We study a class of interacting elephant random walks. Our model includes the exclusion process as a special case. By means of Monte Carlo simulations and mean-field arguments, we find that it exhibits a condensation phenomenon with a phase transition that is manifestly of first order. The transition point depends on the initial configuration.

A phase space boundary between transition and nontransition trajectories, similar to those observed in Hamiltonian systems with rank-1 saddles, is verified experimentally in a macroscopic system. We present a validation of the phase space flux across rank-1 saddles connecting adjacent potential wells, and we confirm the underlying phase space conduits that mediate the transition. Experimental regions of transition are found to agree with the theory to within 1%, suggesting the robustness of phase space conduits of transition in a broad array of two or more degrees of freedom experimental systems, despite the presence of small dissipation.

Irregularly sampled time series usually require data preprocessing before a desired time-series analysis can be applied. We propose an approach for distance measuring of pairs of data points which is directly applicable to irregularly sampled time series. In order to apply recurrence plot analysis to irregularly sampled time series, we use this approach and detect regime transitions in prototypical models and for an application from palaeoclimatatology. This approach might be useful for any method that is based on distance measuring, e.g., correlation sum or Lyapunov exponent estimation.

Most ionic liquids contain at least one rather complex ion species exhibiting a dipolar moment. In the present work, we provide a thorough evaluation of broadband dielectric spectra of 12 ionic liquids taking into account the often neglected reorientational dynamics of these ions. We confirm that this dynamics leads to a clear relaxational signature in the spectra, a fact that so far only was considered in few previous works. The obtained reorientational relaxation times are well consistent with earlier inelastic light-scattering and high-frequency dielectric investigations. Evaluating our dielectric spectra in terms of reorientational motions reveals a close coupling of the ion-rotation dynamics to the ionic charge transport in a broad temperature range from the low-viscosity liquid above room temperature deep into the high-viscosity supercooled state close to $T_g$. This coupling does not seem to be mediated by the viscosity but probably is of more direct nature, pointing to a revolving-door mechanism as also considered for plastic-crystalline ionic conductors. Our results show that the reorientational motion of the dipolar ions plays a significant and so far widely overlooked role for the ionic charge transport in ionic liquids.

Particle motion and correlations in fluids within confined domains promise to provide challenges and opportunities for experimental and theoretical studies. We report molecular dynamics simulations of a Lennard-Jones gas mimicking argon under partial confinement for a wide range of densities at a temperature of $300\mathrm{K}$. The isotropic behavior of velocity autocorrelation function (VACF) and mean squared displacement (MSD), seen in the bulk, breaks down due to partial confinement. A distinct trend emerges in the ${\text{VACF}}_{\perp }$ and ${\text{MSD}}_{\perp }$, corresponding to the confined direction, while the trends in ${\text{VACF}}_{\parallel }$ and ${\text{MSD}}_{\parallel }$, corresponding to the other two unconfined directions are seen to be unaffected by the confinement. ${\text{VACF}}_{\perp }$ displays a minimum, at short timescales, that correlates with the separation between the reflective walls. The effect of partial confinement on ${\text{MSD}}_{\perp }$ is seen to manifest as a transition from diffusive to subdiffusive motion with the transition time correlating with the minimum in the ${\text{VACF}}_{\perp }$. When compared to the trends shown by MSD and VACF in the bulk, the ${\text{MSD}}_{\perp }$ exhibits subdiffusive behavior, and the ${\text{VACF}}_{\perp }$ features rapid decay, suggesting that confinement suppresses the role of thermal fluctuations significantly. Repetitive wall-mediated collisions are identified to give rise to the minima in ${\text{VACF}}_{\perp }$ and in turn a characteristic frequency in its frequency spectrum. The strong linear relation between the minima in ${\text{VACF}}_{\perp }$ and wall-spacing suggests the existence of collective motion propagating at the speed of sound. These numerical experiments can offer interesting possibilities in the study of confined motion with observable consequences.

This paper presents a detailed analysis of the effect of a large external noise on the propagation of a front between two stable steady states. Noise affects one of the steady states or the thresholds. Significant differences with respect to the case of small noise intensity are carefully studied using a Langevin approach. The average effect of noise is modeled by means of an additional nonlinear term that enables an analysis of short-time and long-time behaviors. Nontrivial behaviors are numerically observed and analytically discussed: (i) Two symmetry breakings of the fluctuation-free stable states are observed and (ii) two fronts propagating in opposite directions are simultaneously observed and the propagation direction may be exchanged by changing the diffusion coefficient.

Much work has been devoted to studying percolation of networks and interdependent networks under varying levels of failures. Researchers have considered many different realistic network structures such as scale-free networks, spatial networks, and more. However, thus far no study has analyzed a system of hierarchical community structure of many networks. For example, infrastructure across cities is likely distributed with nodes tightly connected within small neighborhoods, somewhat less connected across the whole city, and even fewer connections between cities. Furthermore, while previous work identified interconnected nodes, those nodes with links outside their neighborhood, to be more likely to be attacked or to fail, in a hierarchical structure nodes can be interconnected in different layers (between neighborhoods, between cities, etc.). We consider here the case where the nodes with interconnections at the highest level of the hierarchy are most likely to fail, followed by those with interconnections at the next level, etc. This is because nodes at higher levels of the hierarchy have the longest links as well as having more flow passing through them. We develop an analytic solution for percolation of both single and interdependent networks of this structure and verify our theory through simulations. We find that, depending on the number of levels in the hierarchy, there may be multiple transitions in the giant component (fraction of connected nodes), as the network separates at the various levels. Our results show that these multiple jumps are a feature of hierarchical networks and can affect the vulnerability of infrastructure networks.

We use information geometry in which the local distance between models measures their distinguishability from data to quantify the flow of information under the renormalization group. We show that information about relevant parameters is preserved with distances along relevant directions maintained under flow. By contrast, irrelevant parameters become less distinguishable under the flow with distances along irrelevant directions contracting according to renormalization group exponents. We develop a covariant formalism to understand the contraction of the model manifold. We then apply our tools to understand the emergence of the diffusion equation and more general statistical systems described by a free energy. Our results give an information-theoretic justification of universality in terms of the flow of the model manifold under coarse graining.

Irving and Kirkwood [J. Irving and J. G. Kirkwood, The statistical mechanical theory of transport processes. IV. The equations of hydrodynamics, J. Chem. Phys. 18, 817 (1950)] derived the transport equations from the principles of classical statistical mechanics using the Dirac delta to define local densities. Thereby, formulas for fluxes were obtained in terms of molecular variables. The Irving and Kirkwood formalism has inspired numerous formulations. Many of the later developments, however, considered it more rigorous to replace the Dirac delta with a continuous volume-weighted averaging function and subsequently defined fluxes as a volume density. Although these volume-averaged flux formulas have dominated the literature for decades and are widely implemented in popular molecular dynamics (MD) software, they are a departure from the well-established physical concept of fluxes. In this paper, we review the historical developments that led to the unified physical concept of fluxes for transport phenomena. We then use MD simulations to show that these popular flux formulas conserve neither momentum nor energy, nor do they produce fluxes that are consistent with their physical definitions. We also use two different approaches to derive fluxes for general many-body potentials. The results of the formulation show that atomistic formulas for fluxes can be fully consistent with the physical definitions of fluxes and conservation laws.

The functionals of particle paths have diverse applications in physics, mathematics, hydrology, economics, and other fields. Under the framework of a continuous-time random walk, the equations governing the probability density functions (PDFs) of the functionals, including those of the paths of stochastic processes of normal diffusion, anomalous diffusion, and even diffusion with reaction, have been derived. Sometimes the stochastic processes in physics and chemistry are naturally described by Langevin equations. The Langevin picture has the advantage of studying the dynamics with an external force field and analyzing the effect of noise resulting from a fluctuating environment. We derive the equations governing the PDFs of the functionals of paths of the Langevin system with both space- and time-dependent force fields and arbitrary multiplicative noise, and the backward version is proposed for a system with arbitrary additive noise or multiplicative Gaussian white noise together with a force field. For the newly built equations, their applications in solving the PDFs of the occupation time and area under the trajectory curve are provided, and the results are confirmed by simulations.

We uncover a route from low-dimensional to high-dimensional chaos in nonsmooth dynamical systems as a bifurcation parameter is continuously varied. The striking feature is the existence of a finite parameter interval of periodic attractors in between the regimes of low- and high-dimensional chaos. That is, the emergence of high-dimensional chaos is preceded by the system's settling into a totally nonchaotic regime. This is characteristically distinct from the situation in smooth dynamical systems where high-dimensional chaos emerges directly and smoothly from low-dimensional chaos. We carry out an analysis to elucidate the underlying mechanism for the abrupt emergence and disappearance of the periodic attractors and provide strong numerical support for the typicality of the transition route in the pertinent two-dimensional parameter space. In view of the previous understanding that chaos is typically robust (i.e., without periodic windows) in nonsmooth dynamical systems, the occurrence of a parameter regime of periodic attractors between low- and high-dimensional chaos is unexpected. The finding has implications to applications where high-dimensional and robust chaos is desired.

The occurrence of new events in a system is typically driven by external causes and by previous events taking place inside the system. This is a general statement, applying to a range of situations including, more recently, to the activity of users in online social networks (OSNs). Here we develop a method for extracting from a series of posting times the relative contributions that are exogenous, e.g., news media, and endogenous, e.g., information cascade. The method is based on the fitting of a generalized linear model (GLM) equipped with a self-excitation mechanism. We test the method with synthetic data generated by a nonlinear Hawkes process, and apply it to a real time series of tweets with a given hashtag. In the empirical dataset, the estimated contributions of exogenous and endogenous volumes are close to the amounts of original tweets and retweets respectively. We conclude by discussing the possible applications of the method, for instance in online marketing.

Particulate matter, such as foams, emulsions, and granular materials, attain rigidity in a dense regime: the rigid phase can yield when a threshold force is applied. The rigidity transition in particulate matter exhibits bona fide scaling behavior near the transition point. However, a precise determination of exponents describing the rigidity transition has raised much controversy. Here we pinpoint the causes of the controversies. We then establish a conceptual framework to quantify the critical nature of the rigidity transition. Our results demonstrate that there is a spectrum of possible values for the critical exponents for which, without a robust framework, one cannot distinguish the genuine values of the exponents. Our approach is twofold: (1) a precise determination of the transition density using rheological measurements and (2) a matching rule that selects the critical exponents and rules out all other possibilities from the spectrum. This enables us to determine exponents with unprecedented accuracy and resolve the long-standing controversy over exponents of jamming. The generality of the approach paves the way to quantify the critical nature of many other types of rheological phase transitions such as those in oscillatory shearing.

In classical thermodynamics the entropy is an extensive quantity, i.e., the sum of the entropies of two subsystems in equilibrium with each other is equal to the entropy of the full system consisting of the two subsystems. The extensitivity of entropy has been questioned in the context of a theoretical foundation for the so-called $\kappa$ distributions, which describe plasma constituents with power-law velocity distributions. We demonstrate here, by employing the recently introduced regularized $\kappa$ distributions, that entropy can be defined as an extensive quantity even for such power-law-like distributions that truncate exponentially.

Results are presented from a basic heat transport experiment using a magnetized electron temperature filament that behaves as a thermal resonator. A small, crystal cathode injects low-energy electrons along the magnetic field into the afterglow of a large preexisting plasma forming a hot electron filament embedded in a colder plasma. A series of low amplitude, sinusoidal perturbations are added to the cathode discharge bias that create an oscillating heat source capable of driving thermal waves. Langmuir probe measurements demonstrate driven thermal oscillations and allow for the determination of the amplitude and parallel phase velocity of the thermal waves over a range of driver frequencies. The results conclusively show the presence of a thermal resonance and are used to verify the parallel thermal wave dispersion relation based on classical transport theory. A nonlinear transport code is used to verify the analysis procedure. This technique provides an alternative measure of the density normalized thermal conductivity, independent of the electron temperature.