The epidemic threshold of the susceptible-infected-susceptible (SIS) dynamics on random networks having a power law degree distribution with exponent $\gamma >3$ has been investigated using different mean-field approaches, which predict different outcomes. We performed extensive simulations in the quasistationary state for a comparison with these mean-field theories. We observed concomitant multiple transitions in individual networks presenting large gaps in the degree distribution and the obtained multiple epidemic thresholds are well described by different mean-field theories. We observed that the transitions involving thresholds which vanish at the thermodynamic limit involve localized states, in which a vanishing fraction of the network effectively contributes to epidemic activity, whereas an endemic state, with a finite density of infected vertices, occurs at a finite threshold. The multiple transitions are related to the activations of distinct subdomains of the network, which are not directly connected.

A clear signature of classical chaoticity in the quantum regime is the fractal Weyl law, which connects the density of eigenstates to the dimension $D_0$ of the classical invariant set of open systems. Quantum systems of interest are often partially open (e.g., cavities in which trajectories are partially reflected or absorbed). In the corresponding classical systems $D_0$ is trivial (equal to the phase-space dimension), and the fractality is manifested in the (multifractal) spectrum of Rényi dimensions $D_q$. In this paper we investigate the effect of such multifractality on the Weyl law. Our numerical simulations in area-preserving maps show for a wide range of configurations and system sizes $M$ that (i) the Weyl law is governed by a dimension different from $D_0=2$, and (ii) the observed dimension oscillates as a function of $M$ and other relevant parameters. We propose a classical model that considers an undersampled measure of the chaotic invariant set, explains our two observations, and predicts that the Weyl law is governed by a nontrivial dimension $D_{\mathrm{asymptotic}}<D_0$ in the semiclassical limit $M\to \infty$.

We discuss a long-standing discrepancy in the equation of state of charge-neutral plasmas, the occurrence of an $e^2$ direct term. This $e^2$ term may appear in dependence of the way to determine the mean value of the potential energy. We show that such a contribution should not appear for pure Coulomb interaction.

We conduct a study on heat conduction through coupled Fermi-Pasta-Ulam (FPU) chains by using classical molecular dynamics simulations. Our attention is dedicated to showing how the phonon transport is affected by the interchain coupling. It has been well accepted that the heat conduction could be impeded by the interchain interaction due to the interface phonon scattering. However, recent theoretical and experimental studies suggest that the thermal conductivity of nanoscale materials can be counterintuitively enhanced by the interaction with the substrate. In the present paper, by consecutively varying the interchain coupling intensity, we observed both enhancement and suppression of thermal transport through the coupled FPU chains. For weak interchain couplings, it is found that the heat flux increases with the coupling intensity, whereas in the case of strong interchain couplings, the energy transport is found to be suppressed by the interchain interaction. Based on the phonon spectral energy density method, we attribute the enhancement of the energy transport to the excited phonon modes (in addition to the intrinsic phonon modes), while the upward shift of the high-frequency phonon branch and the interface phonon-phonon scattering account for the suppressed heat conduction.

Nowadays, massive amounts of data are available for analysis in natural and social systems and the tasks to depict system structures from the data, i.e., the inverse problems, become one of the central issues in wide interdisciplinary fields. In this paper, we study the inverse problem of dynamic complex networks driven by white noise. A simple and universal inference formula of double correlation matrices and noise-decorrelation (DCMND) method is derived analytically, and numerical simulations confirm that the DCMND method can accurately depict both network structures and noise correlations by using available output data only. This inference performance has never been regarded possible by theoretical derivation, numerical computation, and experimental design.

We consider an infinite-sized population where an infinite number of traits compete simultaneously. The replicator equation with a diffusive term describes time evolution of the probability distribution over the traits due to selection and mutation on a mean-field level. We argue that this dynamics can be expressed as a variant of the Fisher equation with high-order correction terms. The equation has a traveling-wave solution, and the phase-space method shows how the wave shape depends on the correction. We compare this solution with empirical time-series data of given names in Quebec, treating it as a descriptive model for the observed patterns. Our model explains the reason that many names exhibit a similar pattern of the rise and fall as time goes by. At the same time, we have found that their dissimilarities are also statistically significant.

We introduce a system of pulse-coupled oscillators that can change both their phases and frequencies and prove that when there is a separation of time scales between phase and frequency adjustment the system converges to exact synchrony on strongly connected graphs with time delays. The analysis involves decomposing the network into a forest of tree-like structures that capture causality. These results provide a robust method of sensor net synchronization as well as demonstrate a new avenue of possible pulse-coupled oscillator research.

Constantly acting centrifugal forces on Turing pattern forming systems have been observed to induce orientation and wavelength changes on Turing structures. Here, we will consider a periodic modulation of such centrifugal forces and their effects on pattern formation. Depending on the oscillation period the system exhibits a wide variety of stationary (stripes, ${\mathrm{H}}_0$, etc.) or nonstationary patterns (black eyes, etc.), as well as transitions and instabilities such as Eckhaus, zigzag, etc. In this paper, a detailed description of the different patterns and patterning mechanisms will be described and understood within the previous context. The system considered is the Belousov-Zhabotinsky reaction encapsulated in AOT micelles modeled by the adapted version of the Oregonator model.

We study a one-dimensional chain of harmonically coupled units in an asymmetric anharmonic soft potential. Due to nonlinear localization of energy, this system exhibits extreme events in the sense that individual elements of the chain show very large excitations. A detailed statistical analysis of extremes in this system reveals some unexpected properties, e.g., a pronounced pattern in the interevent interval statistics. We relate these statistical properties to underlying system dynamics and notice that often when extreme events occur the system dynamics adopts (at least locally) an oscillatory behavior, resulting in, for example, a quick succession of such events. The model therefore might serve as a paradigmatic model for the study of the interplay of nonlinearity, energy transport, and extreme events.

Electrical resistivity is shown to saturate in solid-density aluminum in the warm dense matter regime. Calculations are done using the average-atom model SCAALP and the finite-temperature Ziman-Evans formula for electrical resistivity. The mean free path is estimated using the Drude law. This mean free path is shown to present a minimum of the order of the interatomic spacing.

The acceleration of dense targets driven by the radiation pressure of high-intensity lasers leads to a Rayleigh-Taylor instability (RTI) with rippling of the interaction surface. Using a simple model it is shown that the self-consistent modulation of the radiation pressure caused by a sinusoidal rippling affects substantially the wave vector spectrum of the RTI, depending on the laser polarization. The plasmonic enhancement of the local field when the rippling period is close to a laser wavelength sets the dominant RTI scale. The nonlinear evolution is investigated by three-dimensional simulations, which show the formation of stable structures with “wallpaper” symmetry.

The ion cooling in collisionless plasma expansion is revisited. It is shown that, in the case of an initial Maxwellian ion distribution, the ion cooling is much slower than predicted by an adiabatic law linking the ion temperature to the ion density. The origin of this behavior is a strong distortion of the ion distribution function resulting in a large ion heat flow (not predicted by a simple water-bag model). Also noticeable is the increase of the electron heat flux in the unperturbed plasma compared to the zero ion temperature case.

A recent and unexpected discrepancy between ab initio simulations and the interpretation of a laser shock experiment on aluminum, probed by x-ray Thomson scattering (XRTS), is addressed. The ion-ion structure factor deduced from the XRTS elastic peak (ion feature) is only compatible with a strongly coupled out-of-equilibrium state. Orbital free molecular dynamics simulations with ions colder than the electrons are employed to interpret the experiment. The relevance of decoupled temperatures for ions and electrons is discussed. The possibility that it mimics a transient, or metastable, out-of-equilibrium state after melting is also suggested.

We propose to put the well-known nonthermal and suprathermal empirical distributions, used in plasma physics, onto a more rigorous foundation. Their use is frequently criticized because of a lack of formal derivation and physical explanation. A connection between these non-Maxwellian distributions and the Beck-Cohen superstatistics is suggested. They are perceived as a consequence of typical temperature fluctuations. We show that the suprathermal distribution is generated by the $\Gamma$ distribution of the inverse temperature, in the same way as the Tsallis $q$ statistics. The nonthermal distribution also follows from the ${\chi }^2$ distribution, with a small variance. Our contribution provides a possible physical meaning for these ad hoc distributions.

We investigate the collective dynamics of self-propelled particles able to probe and anticipate the orientation of their neighbors. We show that a simple anticipation strategy hinders the emergence of homogeneous flocking patterns. Yet anticipation promotes two other forms of self-organization: collective spinning and swarming. In the spinning phase, all particles follow synchronous circular orbits, while in the swarming phase, the population condensates into a single compact swarm that cruises coherently without requiring any cohesive interactions. We quantitatively characterize and rationalize these phases of polar active matter and discuss potential applications to the design of swarming robots.

We study the transport process of interacting Brownian particles in a tube of varying cross section. To describe this process we introduce a modified Fick-Jacobs equation, considering particles that interact through a hard-core potential. We were able to solve the equation with numerical methods for the case of symmetric and asymmetric cavities. We focused in the concentration of particles along the direction of the tube. We also preformed Monte Carlo simulations to evaluate the accuracy of the results, obtaining good agreement between theory and simulations.

The adhesion of a stiff film onto a curved substrate often generates elastic stresses in the film that eventually give rise to its delamination. Here we predict that delamination of very thin films can be dramatically suppressed through tiny, smooth deformations of the substrate, dubbed here “wrinklogami,” that barely affect the macro-scale topography. This “prolamination” effect reflects a surprising capability of smooth wrinkles to suppress compression in elastic films even when spherical or other doubly curved topography is imposed, in a similar fashion to origami folds that enable construction of curved structures from an unstretchable paper. We show that the emergence of a wrinklogami pattern signals a nontrivial isometry of the sheet to its planar, undeformed state, in the doubly asymptotic limit of small thickness and weak tensile load exerted by the adhesive substrate. We explain how such an “asymptotic isometry” concept broadens the standard usage of isometries for describing the response of elastic sheets to geometric constraints and mechanical loads.

We isolate single Schallamach waves—detachment fronts that mediate inhomogeneous sliding between an elastomer and a hard surface—to study their creation and dynamics. Based on measurements of surface displacement using high-speed in situ imaging, we establish a Burgers vector for the waves. The crystal dislocation analogs of nucleation stress, defect pinning, and configurational force are demonstrated. It is shown that many experimentally observed features can be quantitatively described using a conventional model of a dislocation line in an elastic medium. We also highlight the evolution of nucleation features, such as surface wrinkles, with consequences for interface delamination.

Pattern formation of a step on a growing crystal surface induced by a straight line source of atoms, which is escaping from the step at a velocity $V_{\mathrm{p}}$, is studied with the use of a phase field model. From a straight step, fluctuations of the most unstable wavelength ${\lambda }_{\max }$ grow. Competition of intrusions leads to coarsening of the pattern, and survived intrusions grow exponentially. With sufficient strength of the crystal anisotropy, a regular comblike pattern appears. This peculiar step pattern is similar to that observed on a Ga-deposited Si(111) surface. The final period of the intrusions, $\Lambda$, is determined when the exponential growth ends. The period depends on the strength $F_u$ of a current noise in diffusion as $\Lambda \sim {\lambda }_{\max }|ln{F}_u|$: such a logarithmic dependence is confirmed for the first time. A nonmonotonic $V_{\mathrm{p}}$ dependence of $\Lambda$ indicates that the comblike pattern with a small $V_{\mathrm{p}}$ is related to an unstable growth mode of the free needle growth in a channel. The pattern is stabilized by the guiding linear source.

Confinement has a strong influence on diffusing nano-sized clusters. In particular, biomolecular aggregates within the shell-like confining space of a bacterial cell have been shown to display a variety of localization patterns, from being midcell to the poles. How does the confining space determine where the aggregate will localize? Here, using Monte Carlo simulations we have calculated the equilibrium spatial distribution of fixed-sized clusters diffusing in spherocylindrical shells. We find that localization to the poles depends strongly on shell thickness and the size of the cluster. Compared to being at midcell, polar clusters can be more bent and hence have higher energy, but they also can have a greater number of defects and hence have more entropy. Under certain conditions this can lead to polar clusters having a lower free energy than at midcell, favoring localization to the poles. Our findings suggest possible localization selection mechanisms within shell-like geometries that can arise purely from cluster confinement.