The dynamical response of metallic clusters up to ${10}^3$ atoms is investigated using the restricted molecular dynamics simulations scheme. Exemplarily, a sodium like material is considered. Correlation functions are evaluated to investigate the spatial structure of collective electron excitations and the optical response of laser-excited clusters. In particular, the spectrum of bilocal correlation functions shows resonances representing different modes of collective excitations inside the nano plasma. The spatial structure, the resonance energy, and the width of the eigenmodes have been investigated for various values of electron density, temperature, cluster size, and ionization degree. Comparison with bulk properties is performed and the dispersion relation of collective excitations is discussed.

We analyze the 1D focusing nonlinear Schrödinger equation in a finite interval with homogeneous Dirichlet or Neumann boundary conditions. There are two main dynamics, the collapse which is very fast and a slow cascade of Fourier modes. For the cubic nonlinearity the calculations show no long-term energy exchange between Fourier modes as opposed to higher nonlinearities. This slow dynamics is explained by fairly simple amplitude equations for the resonant Fourier modes. Their solutions are well behaved so filtering high frequencies prevents collapse. Finally, these equations elucidate the unique role of the zero mode for the Neumann boundary conditions.

We outline a systematic procedure on how to construct and derive interactions for nonideal lattice fluids. Using a mesoscopic approach based on exact lattice theories, we prove the consistency of the resulting diffuse interface theory with continuum thermodynamics. Translated in the framework of the so called “Shan-Chen” model for nonideal lattice fluids, this paper shows how to adjust the associated pseudopotentials to reproduce a free energy model based on a square gradient theory of equilibrium interfaces.

The dynamic rheology of a polymer melt composed of short chains with ten beads between rapidly oscillating plates is investigated for various oscillation frequencies by using the hybrid simulation of the molecular dynamics and computational fluid dynamics. In the quiescent state, the melt is in a supercooled state, and the stress relaxation function $G\left(t\right)$ exhibits a stretched exponential relaxation on the time scale of the $\alpha$ relaxation time ${\tau }_{\alpha }$ (the structural relaxation of beads) and then follows the Rouse relaxation function characterized by the Rouse relaxation time ${\tau }_R$ (the conformational relaxation of polymer chains). In the rapidly oscillating plates, nonuniform boundary layer flows are generated over the plate due to inertia of the fluid, and the local rheological properties of the melt are spatially varied according to the local flow fields. The local strain and local strain rate of the melt monotonically decrease with the distance from the plate at each oscillation frequency of the plate, but their dependencies on the oscillation frequency at a fixed distance from the plate vary with the distance. Far from the plate, the local strain decreases as the oscillation frequency increases such that the dynamic rheology deviates from the linear moduli at the low oscillation frequencies rather than high oscillation frequencies. On the contrary, near the plate, the local strain rate increases with the oscillation frequency such that the shear thinning is enhanced at high oscillation frequencies. In close vicinity to the plate, the dynamic viscosity is mostly independent of the oscillation frequency, and the shear thinning behavior becomes similar to that observed in steady shear flows. We show the diagram of the loss tangent of the melt for different oscillation frequencies and local strain rates. It is seen that the melt generates three different rheological regimes, i.e., the viscous fluid regime, liquidlike viscoelastic regime, and solidlike viscoelastic regime, according to the oscillation frequency and local strain rate. Nonlinear rheological properties are also investigated by the spectrum analysis and the Lissajous-Bowditch curve. It is found that the fractional amplitude of the higher harmonics to the linear harmonics is suppressed within the boundary layer due to the nonslip boundary on the oscillating plate. We also find that the melt exhibits intercycle shear thinning between different positions but exhibits intracycle shear thickening at a fixed position in the vicinity of the plate.

Various researchers have predicted situations where the acoustical or optical radiation force on a sphere centered on a Bessel beam is opposite the direction of beam propagation. We develop the analogy between acoustical and optical radiation forces of arbitrary-order helicoidal and ordinary Bessel beams to gain insight into negative radiation forces. The radiation force is expressed in terms of the asymmetry of the scattered field, the scattered power, the absorbed power, and the conic angle of the Bessel beam and is related to the partial-wave coefficients for the scattering. Negative forces only occur when the scattering into the backward hemisphere is suppressed relative to the scattering into the forward hemisphere. Absorbed power degrades negative radiation forces.

We study the average velocity of crack fronts during stable interfacial fracture experiments in a heterogeneous quasibrittle material under constant loading rates and during long relaxation tests. The transparency of the material (polymethylmethacrylate) allows continuous tracking of the front position and relation of its evolution to the energy release rate. Despite significant velocity fluctuations at local scales, we show that a model of independent thermally activated sites successfully reproduces the large-scale behavior of the crack front for several loading conditions.

Since roughly a decade ago, network science has focused among others on the problem of how the spreading of diseases depends on structural patterns. Here, we contribute to further advance our understanding of epidemic spreading processes by proposing a nonperturbative formulation of the heterogeneous mean-field approach that has been commonly used in the physics literature to deal with this kind of spreading phenomena. The nonperturbative equations we propose have no assumption about the proximity of the system to the epidemic threshold, nor any linear approximation of the dynamics. In particular, we first develop a probabilistic description at the node level of the epidemic propagation for the so-called susceptible-infected-susceptible family of models, and after we derive the corresponding heterogeneous mean-field approach. We propose to use the full extension of the approach instead of pruning the expansion to first order, which leads to a nonperturbative formulation that can be solved by fixed-point iteration, and used with reliability far away from the epidemic threshold to assess the prevalence of the epidemics. Our results are in close agreement with Monte Carlo simulations, thus enhancing the predictive power of the classical heterogeneous mean-field approach, while providing a more effective framework in terms of computational time.

Human diseases spread over networks of contacts between individuals and a substantial body of recent research has focused on the dynamics of the spreading process. Here we examine a model of two competing diseases spreading over the same network at the same time, where infection with either disease gives an individual subsequent immunity to both. Using a combination of analytic and numerical methods, we derive the phase diagram of the system and estimates of the expected final numbers of individuals infected with each disease. The system shows an unusual dynamical transition between dominance of one disease and dominance of the other as a function of their relative rates of growth. Close to this transition the final outcomes show strong dependence on stochastic fluctuations in the early stages of growth, dependence that decreases with increasing network size, but does so sufficiently slowly as still to be easily visible in systems with millions or billions of individuals. In most regions of the phase diagram we find that one disease eventually dominates while the other reaches only a vanishing fraction of the network, but the system also displays a significant coexistence regime in which both diseases reach epidemic proportions and infect an extensive fraction of the network.

Consider the spreading dynamics of a two-dimensional droplet over chemically heterogeneous substrates. Assuming small slopes and strong surface tension effects, a long-wave expansion of the Stokes equations yields a single evolution equation for the droplet thickness. The contact line singularity is removed by assuming slip at the liquid-solid interface. The chemical nature of the substrate is incorporated by local variations in the microscopic contact angle, which appear as boundary conditions in the governing equation. By asymptotically matching the flow in the bulk of the droplet with the flow in the vicinity of the contact lines, we obtain a set of coupled ordinary differential equations for the locations of the two droplet fronts. We verify the validity of our matching procedure by comparing the solutions of the ordinary differential equations with solutions of the full governing equation. The droplet dynamics is examined in detail via a phase-plane analysis. A number of interesting features that are not present in chemically homogeneous substrates are found, such as the existence of multiple equilibria, the pinning of the droplet fronts at localized chemical features, and the possibility for the droplet fronts to exhibit a stick-slip behavior.

The downstream development of the concentration probability distribution along the mean-plume centerline of a dispersing plume in the wake of a ground-level continuous point source in a neutrally stratified wall-shear layer is studied. It is shown that the concentration distribution is well described by a family of one-parameter gamma distributions, as first suggested by Villermaux and Duplat [Phys. Rev. Lett. 91, 184501 (2003)] in the context of confined mixing. A prediction of the downstream evolution of the parameter $k$ (which specifies the gamma distribution) is obtained. This prediction includes explicitly the effects of mean shear on the mean-square concentration.

The asymptotic behaviors of the permeability of isotropic fracture networks at small and large densities are characterized, and a general heuristic formula is obtained which complies with the limiting behaviors and accurately predicts the permeability of these networks over the whole density range. Theses developments are based on extensive numerical calculations and on theoretical arguments inspired by the examination of the flow distribution in the fractures at large densities. Then, the results are extended to anisotropic networks with a Fisher distribution of the fracture orientations, to polydisperse networks, and to fractured porous media. Finally, guidelines are provided for the practical evaluation of the required parameters from typical field data. A summary of the results is given in Table III.

The transient behavior of a leaky dielectric liquid drop under a uniform electric field of small strength is investigated. It is shown that for small distortion from a spherical shape, the drop deforms to an ellipsoid, and the deformation time history is represented by $\mathcal{D}={\mathcal{D}}_{\infty }[1-\exp (-t/\tau )]$, where ${\mathcal{D}}_{\infty }$ is the steady-state deformation and $\tau =(a{\mu }_o/\gamma )(19\tilde{\mu }+16)(2\tilde{\mu }+3)/(40\tilde{\mu }+40)$ is the characteristic time, $a$, $\gamma$, ${\mu }_o$ and $\tilde{\mu }$ being the drop radius, the surface tension, the viscosity of ambient fluid, and ratio of the drop viscosity to that of the ambient fluid, respectively. The contributions of the net normal and tangential electrical stresses in the degree of deformation and fluid flow strength are also determined.

The properties of two-dimensional linearly $s$-polarized solitary waves are investigated by fluid-Maxwell equations and particle-in-cell (PIC) simulations. These self-trapped electromagnetic waves appear during laser-plasma interactions, and they have a dominant electric field component $E_z$, normal to the plane of the wave, that oscillates at a frequency below the electron plasma frequency ${\omega }_{pe}$. A set of equations that describe the waves are derived from the plasma fluid model in the case of cold or warm plasma and then solved numerically. The main features, including the maximum value of the vector potential amplitude, the total energy, the width, and the cavitation radius are presented as a function of the frequency. The amplitude of the vector potential increases monotonically as the frequency of the wave decreases, whereas the width reaches a minimum value at a frequency of the order of $0.82{\omega }_{pe}$. The results are compared with a set of PIC simulations where the solitary waves are excited by a high-intensity laser pulse.

The dynamics of two-dimensional $s$-polarized solitary waves is investigated with the aid of particle-in-cell (PIC) simulations. Instead of the usual excitation of the waves with a laser pulse, the PIC code was directly initialized with the numerical solutions from the fluid plasma model. This technique allows the analysis of different scenarios including the theoretical problems of the solitary wave stability and their collision as well as features already measured during laser-plasma experiments such as the emission of electromagnetic bursts when the waves reach the plasma-vacuum interface, or their expansion on the ion time scale, usually named post-soliton evolution. Waves with a single density depression are stable whereas multihump solutions decay to several waves. Contrary to solitons, two waves always interact through a force that depends on their relative phases, their amplitudes, and the distance between them. On the other hand, the radiation pattern at the plasma-vacuum interface was characterized, and the evolution of the diameter of different waves was computed and compared with the “snow plow” model.

Interactions of 100-fs laser pulses with solid targets at intensities of 10${}^{18}$ W/cm${}^2$ and resultant terahertz (THz) radiation are studied under different laser contrast ratio conditions. THz emission is measured in the specular reflection direction, which appears to decrease as the laser contrast ratio varies from 10${}^{-8}$ to 10${}^{-6}$. Correspondingly, the frequency spectra of the reflected light are observed changing from second harmonic dominant, three-halves harmonic dominant, to vanishing of both harmonics. Two-dimensional particle-in-cell simulation also suggests that this observation is correlated with the plasma density scale length change. The results demonstrate that the THz emission is closely related to the laser-plasma interaction processes. The emission is strong when resonance absorption is a key feature of the interaction, and becomes much weaker when parametric instabilities dominate.

Established already in Biblical times, the Matthew effect refers to the fact that in societies the rich tend to get richer and the potent even more powerful. Here we investigate a game theoretical model describing the evolution of cooperation on structured populations where the distribution of public goods is driven by the reproductive success of individuals. Phase diagrams reveal that cooperation is promoted irrespective of the uncertainty by strategy adoptions and the type of interaction graph, yet the complete dominance of cooperators is elusive due to the spontaneous emergence of superpersistent defectors that owe their survival to extremely rare microscopic patterns. This indicates that success-driven mechanisms are crucial for effectively harvesting benefits from collective actions but that they may also account for the observed persistence of maladaptive behavior.

In this paper we report on the necessity of the refinement of the concept of generalized chaotic synchronization. We show that the state vectors of the interacting chaotic systems being in the generalized synchronization regime are related to each other by the functional, but not the functional relation as it was assumed until now. We propose the phase tube approach explaining the essence of generalized synchronization and allowing the detection and the study of this regime in many relevant physical circumstances. The finding discussed in this Brief Report provides great potential for different applications.

Molecular spiders are synthetic biomolecular walkers that use the asymmetry resulting from cleavage of their tracks to bias the direction of their stepping motion. Using Monte Carlo simulations that implement the Gillespie algorithm, we investigate the dependence of the biased motion of molecular spiders, along with binding time and processivity, on tunable experimental parameters, such as number of legs, span between the legs, and unbinding rate of a leg from a substrate site. We find that an increase in the number of legs increases the spiders’ processivity and binding time but not their mean velocity. However, we can increase the mean velocity of spiders with simultaneous tuning of the span and the unbinding rate of a spider leg from a substrate site. To study the efficiency of molecular spiders, we introduce a time-dependent expression for the thermodynamic efficiency of a molecular motor, allowing us to account for the behavior of spider populations as a function of time. Based on this definition, we find that spiders exhibit transient motor function over time scales of many hours and have a maximum efficiency on the order of 1%, weak compared to other types of molecular motors.

A fundamental problem in the analysis of network data is the detection of network communities, groups of densely interconnected nodes, which may be overlapping or disjoint. Here we describe a method for finding overlapping communities based on a principled statistical approach using generative network models. We show how the method can be implemented using a fast, closed-form expectation-maximization algorithm that allows us to analyze networks of millions of nodes in reasonable running times. We test the method both on real-world networks and on synthetic benchmarks and find that it gives results competitive with previous methods. We also show that the same approach can be used to extract nonoverlapping community divisions via a relaxation method, and demonstrate that the algorithm is competitively fast and accurate for the nonoverlapping problem.