The study of liquid dynamics at mesoscopic scales is still strewn with difficulty due to limitations in theory and experiment. Historically, significant attention has been given to the analysis of space-time correlation functions and their frequency-Fourier transforms at a few discrete wave numbers. The massive computing power afforded by modern high performance computing clusters and the advent of a wide-angle neutron spin-echo spectrometer, however, have unlocked a more intuitive and fruitful approach to this problem. Using molecular dynamics simulations, here we demonstrate the benefits of spatiotemporally mapping intermediate scattering functions on a dense grid of correlation times and wave numbers. Four model systems are investigated: a Lennard-Jones liquid, a coarse-grained bead-spring polymer, a molten sodium chloride, and a poly(ethylene oxide) melt. We show that the spatiotemporal mapping approach is particularly useful for elucidating the mesoscopic dynamics in these liquids, where several underlying mechanisms, such as molecular relaxations, hydrodynamic modes, and nonhydrodynamic excitations, are potentially at play. Compared to the traditional method, direct visualization of density space-time correlation functions on two-dimensional color maps permits appraisals of complicated dynamical behavior at mesoscales in a global manner. For example, the scaling relations between space and time for different types of molecular motions can be straightforwardly identified on these plots, without any model-dependent analysis. Additionally, we show how theoretical ideas regarding collective mesoscopic dynamics, such as the classical hydrodynamic theory, the convolution approximation, and a recently proposed phenomenological model, can be discussed in terms of the global features of spatiotemporal maps of intermediate scattering functions. The new perspective offered by the spatiotemporal mapping method should prove useful for the study of liquid dynamics in general.

The emergence of surface patterns on the surfaces of compliant materials subject to plowing wear is a complex problem which can be quantitatively characterized, e.g., on polymer surfaces scraped by an atomic force microscope (AFM) tip. Here we explore the applicability of a phenomenological model recently introduced to describe this phenomenon. Based on the competition between the viscoplastic indentation and the elastic shear stress caused by the tip, the model is able to reproduce the wavy features (ripples) observed when the tip is scanned along a series of parallel lines. For low values of the driving velocity $v$ and the spacing $b$ between scan lines, the existence of dotted areas formed by variously oriented pit alignments is observed. Moreover, coexistence of rippled with dotted domains is also observed at suitable parameter values. The formation process of the ripples is also described in detail. The amplitude, period, and orientation of these features are estimated numerically for different values of $v$ and $b$ parameters. We have also revisited the formation of the wavy patterns formed when a single line is scanned, and derived an equation which correctly describes their period and depth, and the static friction as well. This equation is not applicable when several lines are scanned one after the other and the ripples emerge as result of a cooperative process which involves the scanning of several lines.

The framework of transition state theory (TST) provides a powerful way for analyzing the dynamics of physical and chemical reactions. While TST has already been successfully used to obtain reaction rates for systems with a single time-dependent saddle point, multiple driven saddles have proven challenging because of their fractal-like phase space structure. This paper presents the construction of an approximately recrossing-free dividing surface based on the normally hyperbolic invariant manifold in a time-dependent two-saddle model system. Based on this, multiple methods for obtaining instantaneous (time-resolved) decay rates of the underlying activated complex are presented and their results discussed.

Fluctuation theorems impose fundamental bounds in the statistics of the entropy production with the second law of thermodynamics being the most famous. Using information theory, we quantify the information of entropy production and find an upper tight bound as a function of its mean from the strong detailed fluctuation theorem. The bound is given in terms of a maximal distribution, a member of the exponential family with nonlinear argument. We show that the entropy produced by heat transfer using a bosonic mode at weak coupling reproduces the maximal distribution in a limiting case. The upper bound is extended to the continuous domain and verified for the heat transfer using a levitated nanoparticle. Finally, we show that a composition of qubit swap engines satisfies a particular case of the maximal distribution regardless of its size.

In this paper, we study the inhomogeneity of chaotic sea properties far from islands in billiardlike systems and its influence on distributions of particle's return times. A visibly homogeneous chaotic sea at certain parameters has a nontrivial internal structure, in particular, being divided into two chaotic phases with different properties. These phases are not separated by any obstacles, neither in phase nor in configuration spaces, and are partially overlaying. The emergence of a chaotic sea structure may be explained by the existence of remnants of integrable behavior, like sites of regular trajectories of broken islands of stability built into the chaotic sea. In the case of such chaotic seas, we find distributions of return times with two main sites of exponential decay.

The spreading dynamics of infectious diseases is determined by the interplay between geography and population mixing. There is homogeneous mixing at the local level and human mobility between distant populations. Here I model spatial location as a type and the population mixing by intra- and intertype mixing patterns. Using the theory of multitype branching process, I calculate the expected number of new infections as a function of time. In one dimension the analysis is reduced to the eigenvalue problem of a tridiagonal Teoplitz matrix. In $d$ dimensions I take advantage of the graph cartesian product to construct the eigenvalues and eigenvectors from the eigenvalue problem in 1 one dimension. Using numerical simulations I uncover a transition from linear to multitype mixing exponential growth with increasing the population size. Given that most countries are characterized by a network of cities with more than 100 000 habitants, I conclude that the multitype mixing approximation should be the prevailing scenario.

Extreme events are rare and sudden abnormal deviations of the system's behavior from a typical state. Statistical analysis reveals that if the time series contains extreme events, its distribution has a heavy tail. In dynamical systems, extreme events often occur due to developing instability preceded by noise amplification. Here, we apply this theory to analyze generalized epileptic seizures in the human brain. First, we demonstrate that the time series of electroencephalogram (EEG) spectral power in a frequency band of 1–5 Hz obeys a heavy-tailed distribution, confirming the presence of extreme events. Second, we report that noise on EEG signals gradually increases before the seizure onset. Thus, we hypothesize that generalized epileptic seizures in humans are the extreme events emerging from instability accompanied by preictal noise amplification similar to other dynamical systems.

Revealing the structural features of a complex system from the observed collective dynamics is a fundamental problem in network science. To compute the various topological descriptors commonly used to characterize the structure of a complex system (e.g., the degree, the clustering coefficient, etc.), it is usually necessary to completely reconstruct the network of relations between the subsystems. Several methods are available to detect the existence of interactions between the nodes of a network. By observing some physical quantities through time, the structural relationships are inferred using various discriminating statistics (e.g., correlations, mutual information, etc.). In this setting, the uncertainty about the existence of the edges is reflected in the uncertainty about the topological descriptors. In this study, we propose a methodological framework to evaluate this uncertainty, replacing the topological descriptors, even at the level of a single node, with appropriate probability distributions, eluding the reconstruction phase. Our theoretical framework agrees with the numerical experiments performed on a large set of synthetic and real-world networks. Our results provide a grounded framework for the analysis and the interpretation of widely used topological descriptors, such as degree centrality, clustering, and clusters, in scenarios in which the existence of network connectivity is statistically inferred or when the probabilities of existence ${\pi }_{ij}$ of the edges are known. To this purpose, we also provide a simple and mathematically grounded process to transform the discriminating statistics into the probabilities ${\pi }_{ij}$.

Recreational fishing is a highly socioecological process. Although recreational fisheries are self-regulating and resilient, changing anthropogenic pressure drives these fisheries to overharvest and collapse. Here, we evaluate the effect of demographic and environmental stochasticity for a social-ecological two-species fish model. In the presence of noise, we find that an increase in harvesting rate drives a critical transition from high-yield–low-price fisheries to low-yield–high-price fisheries. To calculate stochastic trajectories for demographic noise, we derive the master equation corresponding to the model and perform a Monte Carlo simulation. Moreover, the analysis of the probabilistic potential and mean first-passage time reveals the resilience of alternative steady states. We also describe the efficacy of a few generic indicators in forecasting sudden transitions. Furthermore, we show that incorporating social norms on the model allows a moderate fish density to maintain despite higher harvesting rates. Overall, our study highlights the occurrence of critical transitions in a stochastic social-ecological model and suggests ways to mitigate them.

Using video microscopy and simulations, we study the long-time diffusion of colloidal tracers in a wide range of model porous media composed of frozen colloidal matrices with different structures. We found that the diffusion coefficient of a tracer can be quantitatively determined by the structures of porous media. In particular, a universal scaling relation exists between the dimensionless diffusion coefficient of the tracer and the structural entropy of the system. This universal scaling relation is an extension of the scaling law previously discovered for the diffusion of colloidal particles in fluctuating media.

The combined effects of external electric, magnetic, and Aharonov-Bohm (AB) flux fields on the two-dimensional hydrogen atom embedded in both Debye and quantum plasmas modeled by the more general exponential cosine Coulomb (MGECSC) potential are investigated using the general analytic approach, namely the homotopy analysis method (HAM). The analytical convergent solutions are obtained for the ground state as well as excited states at both weak and strong intensity of the external fields. The influence of the screening parameters on the quantum levels are exhaustively explored in the presence of three external fields. It is worth emphasizing that our analytical HAM results have 4–10 digits of accuracy in comparison with the numerical results. In the framework of the HAM method, there is no any small parameter different from the perturbation. Owing to this advantage, the convergent accurate solutions always can be obtained by the HAM approach even for the strong external fields. There is no limit to the value of the parameters or the strength of the external fields. It is also observed that the combined effects of the external fields play an important role on the interaction potential profile and the applied external magnetic field is the most dominant in the hydrogen atomic system. Also note that the combined effect of the fields is stronger than individual effects in both Debye and quantum plasmas. The findings obtained by the HAM-based approach in this study shed substantial light on the more complicated problems in plasmas for the atomic systems or molecular physics.

Granger causality (GC) is a statistical notion of causal influence based on prediction via linear vector autoregression. For Gaussian variables it is equivalent to transfer entropy, an information-theoretic measure of time-directed information transfer between jointly dependent processes. We exploit such equivalence and calculate exactly the local Granger causality, i.e., the profile of the information transferred from the driver to the target process at each discrete time point; in this frame, GC is the average of its local version. We show that the variability of the local GC around its mean relates to the interplay between driver and innovation (autoregressive noise) processes, and it may reveal transient instances of information transfer not detectable from its average values. Our approach offers a robust and computationally fast method to follow the information transfer along the time history of linear stochastic processes, as well as of nonlinear complex systems studied in the Gaussian approximation.

The groundbreaking investigation by Deutsch [Phys. Rev. A 43, 2046 (1991)] of how a closed many-body quantum system approaches thermal equilibrium is revisited. It is shown how to carry out some important steps that were missing in that paper. Moreover, the class of admitted systems is extended considerably.

Epithelial cell tissues have a slow relaxation dynamics resembling that of supercooled liquids. Yet, they also have distinguishing features. These include an extended short-time subdiffusive transient, as observed in some experiments and recent studies of model systems, and a sub-Arrhenius dependence of the relaxation time on temperature, as reported in numerical studies. Here we demonstrate that the anomalous glassy dynamics of epithelial tissues originates from the emergence of a fractal-like energy landscape, particles becoming virtually free to diffuse in specific phase space directions up to a small distance. Furthermore, we clarify that the stiffness of the cells tunes this anomalous behavior, tissues of stiff cells having conventional glassy relaxation dynamics.

The linear evolution of the incompressible Rayleigh-Taylor instability for the interface between an elastic-plastic slab medium and a lighter semi-infinite ideal fluid beneath the slab is developed for the case in which slab is attached to a rigid wall at the top surface. The theory yields the maps for the stability in the space determined by the initial perturbation amplitude and wavelength, as well as for the transition boundary from the elastic to the plastic regimes for arbitrary thicknesses of the slab and density contrasts between the media. In particular, an approximate but very accurate scaling law is found for the minimum initial perturbation amplitude required for instability and for the corresponding perturbation wavelength at which it occurs. These results allows for an interpretation of the recent experiments by Maimouni et al. [Phys. Rev. Lett. 116, 154502 (2016)].

We propose a model for demixing of two species by assuming a density-dependent effective diffusion coefficient of the particles. Both sorts of microswimmers diffuse as active overdamped Brownian particles with a noise intensity that is determined by the surrounding density of the respective other species within a sensing radius $r_s$. A higher concentration of the first (second) sort will enlarge the diffusion and, in consequence, the intensity of the noise experienced by the second (first) sort. Numerical and analytical investigations of steady states of the macroscopic equations prove the demixing of particles due to this reciprocally concentration-dependent diffusivity. An ambiguity of the numerical integration scheme for the purely local model ($r_s\to 0$) is resolved by considering nonvanishing sensing radii in a nonlocal model with $r_s>0$.

We study the dynamics of random walks hopping on homogeneous hypercubic lattices and multiplying at a fertile site. In one and two dimensions, the total number $\mathcal{N}\left(t\right)$ of walkers grows exponentially at a Malthusian rate depending on the dimensionality and the multiplication rate $\mu$ at the fertile site. When $d>d_c=2$, the number of walkers may remain finite forever for any $\mu$; it surely remains finite when $\mu \le {\mu }_d$. We determine ${\mu }_d$ and show that $\langle \mathcal{N}\left(t\right)\rangle$ grows exponentially if $\mu >{\mu }_d$. The distribution of the total number of walkers remains broad when $d\le 2$, and also when $d>2$ and $\mu >{\mu }_d$. We compute $\langle {\mathcal{N}}^m\rangle$ explicitly for small $m$, and show how to determine higher moments. In the critical regime, $\langle \mathcal{N}\rangle$ grows as $\sqrt{t}$ for $d=3$, $t/lnt$ for $d=4$, and $t$ for $d>4$. Higher moments grow anomalously, $\langle {\mathcal{N}}^m\rangle \sim {\langle \mathcal{N}\rangle }^{2m-1}$, in the critical regime; the growth is normal, $\langle {\mathcal{N}}^m\rangle \sim {\langle \mathcal{N}\rangle }^m$, in the exponential phase. The distribution of the number of walkers in the critical regime is asymptotically stationary and universal, viz., it is independent of the spatial dimension. Interactions between walkers may drastically change the behavior. For random walks with exclusion, if $d>2$, there is again a critical multiplication rate, above which $\langle \mathcal{N}\left(t\right)\rangle$ grows linearly (not exponentially) in time; when $d\le d_c=2$, the leading behavior is independent on $\mu$ and $\langle \mathcal{N}\left(t\right)\rangle$ exhibits a sublinear growth.

We present a model of contact process on Domany-Kinzel cellular automata with a geometrical disorder. In the 1D model, each site is connected to two nearest neighbors which are either on the left or the right. The system is always attracted to an absorbing state with algebraic decay of average density with a continuously varying complex exponent. The log-periodic oscillations are imposed over and above the usual power law and are clearly evident as $p\to 1$. This effect is purely due to an underlying topology because all sites have the same infection probability $p$ and there is no disorder in the infection rate. An extension of this model to two and three dimensions leads to similar results. This may be a common feature in systems where quenched disorder leads to effective fragmentation of the lattice.

By directly using the probability formulas of quantum trajectories, we construct an auxiliary open quantum system for a periodically driven open quantum system whose dynamics is governed by the Floquet quantum master equation. This auxiliary system can generate a quantum trajectory ensemble that is consistent with the canonical quantum trajectory ensemble. We find that, at a long time limit, though the Lindblad operators are modified, the coherent dynamics of the auxiliary system is the same as that of the original system. A periodically driven two-level quantum system is used to illustrate this construction.