Soft-x-ray free-electron lasers have enabled materials studies in which structural information is obtained faster than the relevant probe-induced damage mechanisms. We present a continuum model to describe the damage process based on hot-dense plasma theory, which includes a description of the energy deposition in the samples, the subsequent dynamics of the sample, and the detector signal. We compared the model predictions with experimental data and mostly found reasonable agreement. In view of future free-electron-laser performance, the model was also used to predict damage dynamics of samples and optical elements at shorter wavelengths and larger photon fluences than currently available.

The temporal behavior of electric fields in arbitrary double-negative planar slabs is systematically investigated in this paper, from both analytical and numerical perspectives. Concerning infinite slabs, a set of exact expressions for an exponential current excitation is derived through an efficient complex analysis, and an integrated study of surface polariton frequencies is performed. Subsequently, the significant case of a source with a random spatial profile is explored in order to obtain rigorous relations for the field and transient phenomena damping time with respect to problem parameters. On the other hand, a robust finite-difference time-domain methodology is introduced for the comprehensive examination of finite slabs, whose numerical simulations dictate the adoption of a resonatorlike discipline. This inevitable, yet very instructive, convention is physically justified by the almost perfect surface mode reflections at the edges of the slab. In this manner, the proposed formulation reveals a prominent increase in the excited polariton amplitude, relative to the corresponding infinite arrangements, which leads to larger transient times.

We describe the application of the reduced-basis method in rapid and accurate determination of band energies in band structure calculations. The method is well suited for problems requiring repetitive evaluations of the band energies, especially in the many-query limit. We demonstrate the efficacy of the method in the determination of the spectral properties of crystalline silicon.

Properties of systems driven by white non-Gaussian noises can be very different from these of systems driven by the white Gaussian noise. We investigate stationary probability densities for systems driven by $\alpha$-stable Lévy-type noises, which provide natural extension to the Gaussian noise having, however, a new property, namely a possibility of being asymmetric. Stationary probability densities are examined for a particle moving in parabolic, quartic, and in generic double well potential models subjected to the action of $\alpha$-stable noises. Relevant solutions are constructed by methods of stochastic dynamics. In situations where analytical results are known they are compared with numerical results. Furthermore, the problem of estimation of the parameters of stationary densities is investigated.

In this paper, we report results and analysis on a simulation study of the effects of thermal expansion in granular systems. We show that these effects impact the force distribution inside a two-dimensional system of disks that are subject to thermal heating under two different boundary conditions. A significant increase in the average force is observed for steel particles confined within a box with fixed walls at temperature rises of $50°\text{C}$ and $100°\text{C}$, respectively. As previously noted in the literature, thermal expansion also induces compaction. The results show that a systematic and controllable increase in granular packing can be induced by simply raising and then lowering the temperature, without the input of mechanical energy in agreement with previous experimental observations. We find that the evolution of the packing fraction is well described by a fractional relaxation model, which follows the Mittag-Leffler law.

The spontaneous spreading of small liquid metal (Cu, Ag, Au) and oxide drops on Mo substrates has been studied using a drop transfer setup combined with high-speed video. Under the experimental conditions used in this work, spreading occurs in the absence of interfacial reactions or ridging. The analysis of the spreading data indicates that dissipation at the triple junction (that can be described in terms of a triple-line friction) is playing a dominant role in the movement of the liquid front. This is due, in part, to the much stronger atomic interactions in high-temperature systems when compared to organic liquids. As a result of this analysis, a comprehensive view of spreading emerges in which the strength of the atomic interactions (solid-liquid, liquid-liquid) determines the relative roles of viscous impedance and dissipation at the triple junction in spreading kinetics.

A lattice field theory approach to the statistical mechanics of charged polymers in electrolyte solutions [S. Tsonchev, R. D. Coalson, and A. Duncan, Phys. Rev. E 60, 4257 (1999)] is applied to the study of a polymer chain contained in a spherical cavity but able to diffuse into a surrounding gel. The distribution of the polymer chain between the cavity and the gel is described by its partition coefficient, which is computed as a function of the number of monomers in the chain, the monomer charge, and the ion concentrations in the solution.

Emerging infectious diseases are among the main threats to conservation of biological diversity. A crucial task facing epidemiologists is to predict the vulnerability of populations of endangered animals to disease outbreaks. In this context, the network structure of social interactions within animal populations may affect disease spreading. However, endangered animal populations are often small and to investigate the dynamics of small networks is a difficult task. Using network theory, we show that the social structure of an endangered population of mammal-eating killer whales is vulnerable to disease outbreaks. This feature was found to be a consequence of the combined effects of the topology and strength of social links among individuals. Our results uncover a serious challenge for conservation of the species and its ecosystem. In addition, this study shows that the network approach can be useful to study dynamical processes in very small networks.

We experimentally observe fractal patterns of chaotic light scattering in regular polyhedral mirror ball structures that consist of spherical reflectors located at the vertices of polyhedra as optical scattering devices. We measure the fractal dimension of the basin boundaries of the light scattering patterns in the regular polyhedral mirror ball structures.

In this paper we present results for the wave-vector dependent shear viscosity for a model atomic fluid with short ranged repulsive interactions computed by molecular dynamics simulations. It is shown that the data can be fitted to two different simple functional forms over a large density range, namely, a function composed of two Gaussian terms and a Lorentzian type function with a variable wave-vector exponent. The parameters of both functional forms are found to obey simple density dependencies. While the first functional form has the advantage that the inverse Fourier transform can be found analytically, the Lorentzian type function fits the wave-vector dependence better over the range of wave vectors and densities studied here. The results show that the real space viscosity kernel has a width of 2 to 3 atomic diameters. This means that the generalized hydrodynamic constitutive relation is required if the strain rate varies significantly over this distance, a situation commonly encountered for nanofluidic flows.

We have investigated ion current rectification properties of a recently prepared bipolar nanofluidic diode. This device is based on a single conically shaped nanopore in a polymer film whose pore walls contain a sharp boundary between positively and negatively charged regions. A semiquantitative model that employs Poisson and Nernst-Planck equations predicts current-voltage curves as well as ionic concentrations and electric potential distributions in this system. We show that under certain conditions the rectification degree, defined as a ratio of currents recorded at the same voltage but opposite polarities, can reach values of over 1000 at a voltage range $⟨-2\text{V},+2\text{V}⟩$. The role of thickness and position of the transition zone on the ion current rectification is discussed as well. We also show that the rectification degree scales with the applied voltage.

We have studied the behavior of a colloidal gel under oscillatory shear. The quiescent gel was an arrested structure formed by a 40% volume fraction hard-sphere suspension in which a “depletion” interparticle attraction was induced by adding nonadsorbing polymer. We applied progressively larger amplitude oscillatory shear to the sample, and observed its behavior using conventional and confocal microscopy as well as dynamic light scattering echo spectroscopy. We find that, to within experimental uncertainties, the point at which irreversible particle rearrangements (or yielding) occur coincides with the observation of crystallization. We summarize our findings in a “shear state diagram.” The strain amplitude required for yielding/crystallization increases with decreasing oscillation frequency. We can quantitatively account for our observations by estimating the effect of shear on the probability for a particle to escape from the attractive potential of its neighbor using a Kramers approach.

We study the exact solutions for the problem of adsorption of polymers in a system containing two interfaces within the mean-field ground-state dominance approximation both for penetrable and nonpenetrable interfaces. We discuss the case of saturation of the polymer double layer for the limiting case of zero bulk concentration. Here, the exact solution is controlled by a single scaling variable which describes the coupling between the interfaces due to the polymer chains. For the case of penetrable interfaces we obtain a nonmonotonous behavior of the amount of adsorbed polymers as a function of the distance between the interfaces. This leads to a high- and a low-energy phase for the double layer with respect to the amount of polymers localized. At the saturation point, the force acting between the interfaces is strictly attractive and monotonously decaying toward zero for increasing interface distance for both types of interfaces. The exact solution for the chemical equilibrium state of the polymer double layer with a semidilute bulk state is governed by two scaling variables and explicit concentration dependence can be removed. The scaling variables describe the ratio between the interface distance and the bulk correlation length and the ratio between the localization length of the interfaces and the bulk correlation length, respectively. Using the exact solution on intervals of constant potentials opens the possibility to treat various localization problems for polymer chains using the appropriate boundary conditions.

The evolution of dense aluminum and carbon plasmas produced by laser irradiation of $500\text{−}\mu \mathrm{m}$-diam semicylindrical targets was studied using soft x-ray laser interferometry. Plasmas created heating the cavity walls with $120\text{−}\mathrm{ps}$—duration optical laser pulses of $\sim 1\times {10}^{12}\mathrm{W}{\mathrm{cm}}^{-2}$ peak intensity were observed to expand and converge on axis to form a localized high-density plasma region. Electron density maps were measured using a $46.9\text{−}\mathrm{nm}$-wavelength tabletop capillary discharge soft x-ray laser probe in combination with an amplitude division interferometer based on diffraction gratings. The measurements show that the plasma density on axis exceeds $1\times {10}^{20}{\mathrm{cm}}^{-3}$. The electron density profiles are compared with simulations conducted using the hydrodynamic code HYDRA, which show that the abrupt density increase near the axis is dominantly caused by the convergence of plasma generated at the bottom of the groove during laser irradiation.

A lattice Boltzmann (LB) model for the simulation of realistic multicomponent mixtures is constructed. In the hydrodynamic limit, the LB model recovers the equations of continuum mechanics within the mixture-averaged diffusion approximation. The present implementation can be used to simulate realistic mixtures with arbitrary Schmidt numbers and molecular masses of the species. The model is applied to the mixing of two opposed jets of different concentrations and the results are in excellent agreement with a continuum model. An application to the simulation of mixtures in microflows is also presented. Results compare well with existing kinetic theory predictions of the slip coefficient for mixtures in a Couette flow.

Adaptive-resolution molecular dynamics (MD) schemes allow for changing the number of degrees of freedom on the fly and preserve the free exchange of particles between regions of different resolution. There are two main alternatives on how to design the algorithm to switch resolution using auxiliary “switching” functions: force based and potential energy based approaches. In this work we show that, in the framework of classical MD, the latter presents fundamental conceptual problems which make unlikely, if not impossible, the derivation of a robust algorithm based on the potential energy.

The extreme statistics of time signals is studied when the maximum is measured from the initial value. In the case of independent, identically distributed (iid) variables, we classify the limiting distribution of the maximum according to the properties of the parent distribution from which the variables are drawn. Then we turn to correlated periodic Gaussian signals with a $1∕f^{\alpha }$ power spectrum and study the distribution of the maximum relative height with respect to the initial height $\left({\mathrm{MRH}}_{\mathrm{I}}\right)$. The exact ${\mathrm{MRH}}_{\mathrm{I}}$ distribution is derived for $\alpha =0$ (iid variables), $\alpha =2$ (random walk), $\alpha =4$ (random acceleration), and $\alpha =\infty$ (single sinusoidal mode). For other, intermediate values of $\alpha$, the distribution is determined from simulations. We find that the ${\mathrm{MRH}}_{\mathrm{I}}$ distribution is markedly different from the previously studied distribution of the maximum height relative to the average height for all $\alpha$. The two main distinguishing features of the ${\mathrm{MRH}}_{\mathrm{I}}$ distribution are the much larger weight for small relative heights and the divergence at zero height for $\alpha >3$. We also demonstrate that the boundary conditions affect the shape of the distribution by presenting exact results for some nonperiodic boundary conditions. Finally, we show that, for signals arising from time-translationally invariant distributions, the density of near extreme states is the same as the ${\mathrm{MRH}}_{\mathrm{I}}$ distribution. This is used in developing a scaling theory for the threshold singularities of the two distributions.

We propose a simple model that captures the salient properties of distribution networks, and study the possible occurrence of blackouts, i.e., sudden failings of large portions of such networks. The model is defined on a random graph of finite connectivity. The nodes of the graph represent hubs of the network, while the edges of the graph represent the links of the distribution network. Both, the nodes and the edges carry dynamical two state variables representing the functioning or dysfunctional state of the node or link in question. We describe a dynamical process in which the breakdown of a link or node is triggered when the level of maintenance it receives falls below a given threshold. This form of dynamics can lead to situations of catastrophic breakdown, if levels of maintenance are themselves dependent on the functioning of the net, once maintenance levels locally fall below a critical threshold due to fluctuations. We formulate conditions under which such systems can be analyzed in terms of thermodynamic equilibrium techniques, and under these conditions derive a phase diagram characterizing the collective behavior of the system, given its model parameters. The phase diagram is confirmed qualitatively and quantitatively by simulations on explicit realizations of the graph, thus confirming the validity of our approach.

The classical $XY$ model describes particles in three-dimensional space that carry magnetic moments or spins whose motion is restricted to rotations in a plane. Introduction of an external magnetic field lying in the same plane then generates a system that is anisotropic in the azimuthal angle $\phi$. We use numerical simulations and integral equation techniques to study this system, producing in the latter case a formalism that is identical to that of the simpler isotropic version having no external field. The basis for this simplification is a generalization ${\mathcal{E}}_m\left(\phi \right)$ of the ordinary exponential basis set $e^{im\phi }$ that restores orthogonality in the presence of the external field. We display results of sample calculations obtained with two integral equation closures, reference hypernetted-chain and soft mean-spherical approximation, both coupled to the Lovett-Mou-Buff-Wertheim relation, along with results from the numerical simulations for comparison. Construction of the ${\mathcal{E}}_m\left(\phi \right)$ is described in an Appendix.

Scroll rings are three-dimensional spiral waves of excitation that rotate around circular filaments. In a modified Belousov-Zhabotinsky reaction, these filaments expand, buckle, and build up gradients in rotation phase. The instability is caused by negative filament tension $(-4.3\times {10}^{-4}{\mathrm{cm}}^2∕\mathrm{s})$. Initial deformations are strongest in the direction normal to the filament’s osculating plane, and their growth rates decrease rapidly with increasing wave number.