We report that the accuracy of predicting the occurrence time of the next earthquake is significantly enhanced by observing the latest rate of earthquake occurrences. The observation period that minimizes the temporal uncertainty of the next occurrence is on the order of 10 hours. This result is independent of the threshold magnitude and is consistent across different geographic areas. This time scale is much shorter than the months or years that have previously been considered characteristic of seismic activities.

A modified Mott-Smith method for predicting the one-dimensional shock wave solution at very high Mach numbers is constructed by developing a system of fluid dynamics equations. The predicted shock solutions in a gas of Maxwell molecules, a hard-sphere gas, and in argon using the newly proposed formalism are compared with the experimental data, direct-simulation Monte Carlo (DSMC) solution, and other solutions computed from some existing theories for Mach numbers $M<50$. In the limit of an infinitely large Mach number, the predicted shock profiles are also compared with the DSMC solution. The density, temperature and heat flux profiles calculated at different Mach numbers have been shown to have good agreement with the experimental and DSMC solutions.

The nonlinear oscillator $\mathrm{x¨}+(2m+3)x^{2m+1}\mathrm{ẋ}+x+x^{4m+3}=0,$ with $m$ a non-negative integer, is known to have a center in the origin, in a neighborhood of which are isochronous orbits, i.e., orbits with fixed period, not dependent on the amplitude. Here, we show that this oscillator can be explicitly integrated, and that its phase space can be completely characterized.

We propose a master equation approach to investigate the transition function and the escape dynamics of a general damping particle in a metastable potential. The transition function in the master equation is obtained analytically from the Langevin dynamics. We apply it to the oscillating barrier problem, in which the potential is structured by a harmonic potential smoothly linking with an inverse harmonic one, and thus both the barrier height and the curvature of potential change periodically with time. We use a Monte Carlo method to simulate the master equation and then calculate a time-dependent escape rate. This can decrease the coarse grain and save more computing time in comparison with the Langevin simulation. Our result has shown that there is a resonant activation phenomenon for the escape rate in the underdamped case.

The distribution of the transmission coefficient $T$ of a long system with a correlated Gaussian disorder is studied analytically and numerically in terms of the generalized Lyapunov exponent (LE) and the cumulants of ln $T$. The effect of the disorder correlations on these quantities is considered in weak, moderate, and strong disorder for different models of correlation. Scaling relations between the cumulants of ln $T$ are obtained. The cumulants are treated analytically within the semiclassical approximation in strong disorder and numerically for an arbitrary strength of the disorder. A small correlation scale approximation is developed for calculation of the generalized LE in a general correlated disorder. An essential effect of the disorder correlations on the transmission statistics is found. In particular, obtained relations between the cumulants and between them and the generalized LE show that, beyond weak disorder, transmission fluctuations and deviation of their distribution from the log-normal form (in a long but finite system) are greatly enhanced due to the disorder correlations. Parametric dependence of these effects upon the correlation scale is presented.

This paper deals with extinction of an isolated population caused by intrinsic noise. We model the population dynamics in a “refuge” as a Markov process which involves births and deaths on discrete lattice sites and random migrations between neighboring sites. In extinction scenario I, the zero population size is a repelling fixed point of the on-site deterministic dynamics. In extinction scenario II, the zero population size is an attracting fixed point, corresponding to what is known in ecology as the Allee effect. Assuming a large population size, we develop a WKB (Wentzel-Kramers-Brillouin) approximation to the master equation. The resulting Hamilton’s equations encode the most probable path of the population toward extinction and the mean time to extinction. In the fast-migration limit these equations coincide, up to a canonical transformation, with those obtained, in a different way, by Elgart and Kamenev [Phys. Rev. E 70, 041106 (2004)]. We classify possible regimes of population extinction with and without an Allee effect and for different types of refuge, and solve several examples analytically and numerically. For a very strong Allee effect, the extinction problem can be mapped into the overdamped limit of the theory of homogeneous nucleation due to Langer [Ann. Phys. (NY) 54, 258 (1969)]. In this regime, and for very long systems, we predict an optimal refuge size that maximizes the mean time to extinction.

Interacting systems with $K$ driven particle species on an open chain or chains that are coupled at the ends to boundary reservoirs with fixed particle densities are considered. We classify discontinuous and continuous phase transitions that are driven by adiabatic change of boundary conditions. We build minimal paths along which any given boundary-driven phase transition (BDPT) is observed and we reveal kinetic mechanisms governing these transitions. Combining minimal paths, we can drive the system from a stationary state with all positive characteristic speeds to a state with all negative characteristic speeds, by means of adiabatic changes of the boundary conditions. We show that along such composite paths, one generically encounters $Z$ discontinuous and $2(K-Z)$ continuous BDPT’s, with $Z$ taking values $0⩽Z⩽K$ depending on the path. As model examples, we consider solvable exclusion processes with product measure states and $K=1,2,3$ particle species and a nonsolvable two-way traffic model. Our findings are confirmed by numerical integration of hydrodynamic limit equations and by Monte Carlo simulations. Results extend straightforwardly to a wide class of driven diffusive systems with several conserved particle species.

Heat conduction through the Frenkel-Kontorova lattices is numerically investigated in the presence of a deformable substrate potential. It is found that the deformation of the substrate potential has a strong influence on heat conduction. The thermal conductivity as a function of the shape parameter is nonmonotonic. The deformation can enhance thermal conductivity greatly, and there exists an optimal deformable value at which thermal conductivity takes its maximum. Remarkably, we also find that the deformation can facilitate the appearance of the negative differential thermal resistance.

The densest local packings of $N$ three-dimensional identical nonoverlapping spheres within a radius $R_{\min }(N)$ of a fixed central sphere of the same size are obtained for selected values of $N$ up to $N=1054$. In the predecessor to this paper [A. B. Hopkins, F. H. Stillinger, and S. Torquato, Phys. Rev. E 81, 041305 (2010)], we described our method for finding the putative densest packings of $N$ spheres in $d$-dimensional Euclidean space ${\mathbb{R}}^d$ and presented those packings in ${\mathbb{R}}^2$ for values of $N$ up to $N=348$. Here we analyze the properties and characteristics of the densest local packings in ${\mathbb{R}}^3$ and employ knowledge of the $R_{\min }(N)$, using methods applicable in any $d$, to construct both a realizability condition for pair correlation functions of sphere packings and an upper bound on the maximal density of infinite sphere packings. In ${\mathbb{R}}^3$, we find wide variability in the densest local packings, including a multitude of packing symmetries such as perfect tetrahedral and imperfect icosahedral symmetry. We compare the densest local packings of $N$ spheres near a central sphere to minimal-energy configurations of $N+1$ points interacting with short-range repulsive and long-range attractive pair potentials, e.g., 12–6 Lennard-Jones, and find that they are in general completely different, a result that has possible implications for nucleation theory. We also compare the densest local packings to finite subsets of stacking variants of the densest infinite packings in ${\mathbb{R}}^3$ (the Barlow packings) and find that the densest local packings are almost always most similar as measured by a similarity metric, to the subsets of Barlow packings with the smallest number of coordination shells measured about a single central sphere, e.g., a subset of the fcc Barlow packing. Additionally, we observe that the densest local packings are dominated by the dense arrangement of spheres with centers at distance $R_{\min }(N)$. In particular, we find two “maracas” packings at $N=77$ and $N=93$, each consisting of a few unjammed spheres free to rattle within a “husk” composed of the maximal number of spheres that can be packed with centers at respective $R_{\min }(N)$.

We probe the dependence of the low-velocity drag force in granular materials on the effective gravitational acceleration ($g_{\mathrm{eff}}$) through studies of spherical granular materials saturated within fluids of varying density. We vary $g_{\mathrm{eff}}$ by a factor of 20, and we find that the granular drag is proportional to $g_{\mathrm{eff}}$, i.e. that the granular drag, $F_{\mathrm{probe}}$, on a vertical cylinder follows the expected relation $F_{\mathrm{probe}}=\eta {\rho }_{\mathrm{grain}}{g}_{\mathrm{eff}}{d}_{\mathrm{probe}}{h}_{\mathrm{probe}}^2$ where the drag is related to the probe's depth of insertion, $h_{\mathrm{probe}}$; the probe's diameter, $d_{\mathrm{probe}}$; the grain material's density, ${\rho }_{\mathrm{grain}}$; and a dimensionless constant, $\eta$. The dimensionless constant shows no systematic variation over four orders of magnitude in effective grain weight, demonstrating that the relation holds over that entire range to within the precision of our data.

We describe a random bond network with fluctuating mechanical constraints for which structural and dynamical length scales are explicitly defined and can be compared with the observable properties of the system. The constraints give well-defined individual structures, describing rigid clusters of particles, and there are distinct structural changes between different configurations. In addition, unambiguous unconstrained motions, including extended collective motions, can be defined within each configuration of constraints. By considering fluctuations of bonds in the network, we can analyze the relaxation of a simple model amorphous material subject to randomly arranged mechanical constraints. The lengths of the collective motions are obtained directly and compared with both the relaxation kinetics and the susceptibility ${\chi }_4$. Above percolation, the latter quantity is shown to decrease with increasing degree of constraint, a behavior linked, in this paper, to the presence of overconstraint in the network at bond densities beyond the percolation point. Our model system, despite a propensity for highly collective motions, shows that an increasing timescale for relaxation can be accompanied by a decreasing ${\chi }_4$.

Protein folding and hydrodynamic turbulence are two long-standing challenges, in molecular biophysics and fluid dynamics, respectively. The theories of these phenomena have been developed independently and used different formalisms. Here we show that the protein folding flows can be surprisingly similar to turbulent fluid flows. Studying a benchmark model protein (an SH3 domain), we have found that the flows for the slow folding trajectories of the protein, in which a partly formed N- and C-terminal $\beta$ sheet hinders the RT loop from attaching to the protein core, have many properties of turbulent flows of a fluid. The flows are analyzed in a three-dimensional (3D) space of collective variables, which are the numbers of native contacts between the terminal $\beta$ strands, between the RT loop and the protein core, and the rest of the native contacts. We have found that the flows have fractal nature and are filled with 3D eddies; the latter contain strange attractors, at which the tracer flow paths behave as saddle trajectories. Two regions of the space increment have been observed, in which the flux variations are self-similar with the scaling exponent $h=1/3$, in surprising agreement with the Kolmogorov inertial range theory of turbulence. In one region, the cascade of protein rearrangements is directed from larger to smaller scales (net folding), and in the other, it is oppositely directed (net unfolding). Folding flows for the fast trajectories are essentially “laminar” and do not have the property of self-similarity. Based on the results of our study, we infer, and support this inference by simulations, that the origin of the similarity between the protein folding and turbulent motion of a fluid is in a cascade mechanism of structural transformations in the systems that underlies these phenomena.

It has been observed that the transportability of mucus by cilial mats is dependent on the rheological properties of the mucus. Mucus is a non-Newtonian fluid that exhibits a plethora of phenomena such as stress relaxation, tensile stresses, shear thinning, and yielding behavior. These observations motivate the analysis in this paper that considers the first two attributes in order to construct a transport model. The model developed here assumes that the mucus is transported as a rigid body, the metachronal wave exhibits symplectic behavior, that the mucus is thin compared to the metachronal wavelength, and that the effects of individual cilia can be lumped together to impart an average strain to the mucus during contact. This strain invokes a stress in the mucus, whose non-Newtonian rheology creates tensile forces that persist into unsheared regions and allow the unsupported mucus to move as a rigid body whereas a Newtonian fluid would retrograde. This work focuses primarily on the Doi-Edwards model but results are generalized to the Jeffrey's and Maxwell fluids as well. The model predicts that there exists an optimal mucus rheology that maximizes the shear stress imparted to the mucus by the cilia for a given cilia motion. We propose that this is the rheology that the body strives for in order to minimize energy consumption. Predicted optimal rheologies are consistent with results from previous experimental studies when reasonable model parameters are chosen.

Community structures are found to exist ubiquitously in a number of systems conveniently represented as complex networks. Partitioning networks into communities is thus important and crucial to both capture and simplify these systems’ complexity. The prevalent and standard approach to meet this goal is related to the maximization of a quality function, modularity, which measures the goodness of a partition of a network into communities. However, it has recently been found that modularity maximization suffers from a resolution limit, which prevents its effectiveness and range of applications. Even when neglecting the resolution limit, methods designed for detecting communities in undirected networks cannot always be easily extended, and even less directly applied, to directed networks (for which specifically designed community detection methods are very limited). Furthermore, real-world networks are frequently found to possess hierarchical structure and the problem of revealing such type of structure is far from being addressed. In this paper, we propose a scheme that partitions networks into communities by electing community leaders via message passing between nodes. Using random walk on networks, this scheme derives an effective similarity measure between nodes, which is closely related to community memberships of nodes. Importantly, this approach can be applied to a very broad range of networks types. In fact, the successful validation of the proposed scheme on real and synthetic networks shows that this approach can effectively (i) address the problem of resolution limit and (ii) find communities in both directed and undirected networks within a unified framework, including revealing multiple levels of robust community partitions.

Spanning trees provide crucial insight into the origin of fractality in fractal scale-free networks. In this paper, we present the number of spanning trees in a particular fractal scale-free lattice (network). We first study analytically the topological characteristics of the lattice and show that it is simultaneously scale-free, highly clustered, “large-world,” fractal, and disassortative. Any previous model does not have all the properties as the studied one. Then, by using the renormalization group technique we derive analytically the number of spanning trees in the network under consideration, based on which we also determine the entropy for the spanning trees of the network. These results shed light on understanding the structural characteristics of and dynamical processes on scale-free networks with fractality. Moreover, our method and process for employing the decimation technique to enumerate spanning trees are general and can be easily extended to other deterministic media with self-similarity.

Solid substrates can be endued with self-organized regular stripe patterns of nanoscopic length scale by Langmuir-Blodgett transfer of organic monolayers. Here we consider the effect of periodically prepatterned substrates on this process of pattern formation. It leads to a time periodic forcing of the oscillatory behavior at the meniscus. Utilizing higher-order synchronization with this forcing, complex periodic patterns of predefined wavelength can be created. The dependence of the synchronization on the amplitude and the wavelength of the wetting contrast is investigated in one and two spatial dimensions, and the resulting patterns are discussed. Furthermore, the effect of prepatterned substrates on the pattern selection process is investigated.

In this work we study the possibility of detecting the so-called strong stochasticity threshold (i.e., the transition between weak and strong chaos as the energy density of the system is increased) in anharmonic oscillator chains by means of the 0-1 test for chaos. We compare the result of the aforementioned methodology with the scaling behavior of the largest Lyapunov exponent computed by means of tangent space dynamics, which has, so far, been the most reliable method available to detect the strong stochasticity threshold. We find that indeed the 0-1 test can perform the detection in the range of energy density values studied. Furthermore, we determined that conventional nonlinear time series analysis methods fail to properly compute the largest Lyapounov exponent even for very large data sets, whereas the computational effort of the 0-1 test remains the same in the whole range of values of the energy density considered with moderate size time series. Therefore, our results show that, for a qualitative probing of phase space, the 0-1 test can be an effective tool if its limitations are properly taken into account.

We study fidelity decay in classically chaotic microwave billiards for a local, pistonlike boundary perturbation. We experimentally verify a predicted nonmonotonic crossover from the Fermi golden rule to the escape-rate regime of the Loschmidt echo decay with increasing local boundary perturbation. In particular, we observe pronounced oscillations of the decay rate as a function of the piston position which quantitatively agree with corresponding theoretical results based on a refined semiclassical approach for local boundary perturbations.

We analyze the influence of plasma electron density on frequency-dependent linear field-response behavior of an atomic ion embedded in a dense plasma medium. The frequency-dependent atomic response, characterized by the dynamic dipole polarizability $\alpha$${}_d$(ω) as a function of the angular frequency ω of the time-dependent field, is estimated here up to the first pole of $\alpha$${}_d$(ω) on the ω axis (corresponding to the lowest resonance transition $1s^2\hspace{0.5em}{}^{1}S\to 1s2p\hspace{0.5em}{}^{1}P$) for the ground state $1s^2\hspace{0.5em}{}^{1}S$ of a two-electron atomic ion Ne${}^{8+}$ ($\mathit{Z}$ = 10) at different plasma electron densities, as a typical example, employing the time-dependent coupled Hartree-Fock scheme within the framework of the ion-sphere model. It is observed that, owing to plasma density-induced enhancement of $\alpha$${}_d$(ω) at every ω, the pole position of $\alpha$${}_d$(ω) on the ω axis retracts toward the origin. This indicates a density-induced lowering (redshift) of the corresponding transition energy that conforms to experimentally observed trends. The polarizability calculation suggests a density-induced drop in the $1s^2\hspace{0.5em}{}^{1}S\to 1s2p\hspace{0.5em}{}^{1}P$ absorption oscillator strength in the atomic ion within dense plasmas.

We study the dynamics of two-dimensional (2D) localized modes in the nonlinear lattice described by the discrete nonlinear Schrödinger equation, including a local linear or nonlinear defect. Discrete solitons pinned to the defects are investigated by means of the numerical continuation from the anticontinuum limit and also using the variational approximation, which features a good agreement for strongly localized modes. The models with the time-modulated strengths of the linear or nonlinear defect are considered too. In that case, one can temporarily shift the critical norm, below which localized 2D modes cannot exist, to a level above the norm of the given soliton, which triggers the irreversible delocalization transition.