Measurements of the $L$-shell emission of highly charged gold ions were made under controlled laboratory conditions using the SuperEBIT electron beam ion trap, allowing detailed spectral observations of lines from Fe-like ${\mathrm{Au}}^{53+}$ through Ne-like ${\mathrm{Au}}^{69+}$. Using atomic data from the Flexible Atomic Code, we have identified strong $3d_{5∕2}\to 2p_{3∕2}$ emission features that can be used to diagnose the charge state distribution in high energy density plasmas, such as those found in the laser entrance hole of hot hohlraum radiation sources. We provide collisional-radiative calculations of the average ion charge $⟨Z⟩$ as a function of temperature and density, which can be used to relate charge state distributions inferred from $3d_{5∕2}\to 2p_{3∕2}$ emission features to plasma conditions, and investigate the effects of plasma density on calculated $L$-shell Au emission spectra.

Some of the problems with the theory of moving charge radiation in media with frequency dispersion are analyzed. First, some general properties of the integrals for field components are described. The results are applied to the cases of passive and active media. In one instance, the field of a charge moving in passive media with an arbitrary number of resonances is considered. Components of the field have been presented as a sum of the “quasi-Coulomb” field, the wave field, and the “plasma trace.” In another example, the case of an active medium with two resonant frequencies is considered. It has been demonstrated that radiation is amplified even with a purely real refractive index if the following conditions are fulfilled: the “lower” resonance is active, the “upper” one is passive, and the charge movement velocity lies within a certain range. Efficient algorithms for the computation of fields in the cases of passive and active media have been developed.

We present an extension of the coupled dipole approximation technique to model optical properties of large-scale slabs of homogeneous and inhomogeneous materials. This method is based on a modification of the Green’s function to take into account the interaction between dipoles located at arbitrary distances within the slab. This method allows modeling of various aspects of the structural morphology of composite materials, including component size and spatial distribution as well as surface roughness effects. Our procedure provides an adequate description of far-field optical properties such as the specular and diffuse reflection of light.

Based on the phonon Boltzmann equation, a lattice-Boltzmann model for phonon hydrodynamics is developed. Both transverse and longitudinal polarized phonons that interact through normal and umklapp processes are considered in the model. The collision term is approximated by the relaxation time model where normal and umklapp processes tend to relax distributions of phonons to their corresponding equilibrium distribution functions—the displaced Planck distribution and the Planck distribution, respectively. A macroscopic phonon thermal wave equation (PTWE), valid for the second-sound mode, is derived through the technique of Chapman-Enskog expansion. Compared to the dual-phase-lag (DPL) -based thermal wave equation, the PTWE has an additional fourth-ordered spatial derivative term. The fundamental difference between the two models is discussed through examining a propagating thermal pulse in a single-phased medium and the transient and steady-state transport phenomena on a two-layered structure subjected to different temperatures at boundaries. Results show that transport phenomena are significantly different between the two models. The behavior exhibited by the DPL model, as thermal wave behavior goes over to diffusive behavior, ${\tau }_T\to {\tau }_q$ is incompatible with any microscopic phonon propagating mode. Unlike the DPL model, in which ${\tau }_T$ only has an effect on the transient phenomena, in the PTWE model ${\tau }_T$ shows effects on phenomena at both transient and steady state. With the intrinsic compatibility to the microscopic state, discontinuous quantities, such as a jump of temperature at a boundary or at an interface, can be calculated naturally and straightforwardly with the present lattice-Boltzmann method.

Control of the living cell functions with remarkable reliability despite the stochastic nature of the underlying molecular networks—a property presumably optimized by biological evolution. We ask here to what extent the ability of a stochastic dynamical network to produce reliable dynamics is an evolvable trait. Using an evolutionary algorithm based on a deterministic selection criterion for the reliability of dynamical attractors, we evolve networks of noisy discrete threshold nodes. We find that, starting from any random network, reliability of the attractor landscape can often be achieved with only a few small changes to the network structure. Further, the evolvability of networks toward reliable dynamics while retaining their function is investigated and a high success rate is found.

We use a biophysical model of a local neuronal circuit to study the implications of synaptic plasticity for the detection of weak sensory stimuli. Networks with fast plastic coupling show behavior consistent with stochastic resonance. The addition of an additional slow coupling that accounts for the asynchronous release of neurotransmitter results in qualitatively different properties of signal detection, and also leads to the appearance of transient post-stimulus bistability. Our results suggest testable hypothesis with regard to the self-organization and dynamics of local neuronal circuits.

Entangled networks of stiff biopolymers exhibit complex dynamic response, emerging from the topological constraints that neighboring filaments impose upon each other. We propose a class of reference models for entanglement dynamics of stiff polymers and provide a quantitative foundation of the tube concept for stiff polymers. For an infinitely thin needle exploring a planar course of point obstacles, we have performed large-scale computer simulations proving the conjectured scaling relations from the fast transverse equilibration to the slowest process of orientational relaxation. We determine the rotational diffusion coefficient of the tracer, its angular confinement, the tube diameter, and the orientational correlation functions.

We present the application of a method [C. A. Haselwandter and D. D. Vvedensky, Phys. Rev. E 76, 041115 (2007)] for deriving stochastic partial differential equations from atomistic processes to the morphological evolution of epitaxial surfaces driven by the deposition of new material. Although formally identical to the one-dimensional (1D) systems considered previously, our methodology presents substantial additional technical issues when applied to two-dimensional (2D) surfaces. Once these are addressed, subsequent coarse-graining is accomplished as before by calculating renormalization-group (RG) trajectories from initial conditions determined by the regularized atomistic models. Our applications are to the Edwards-Wilkinson (EW) model [S. F. Edwards and D. R. Wilkinson, Proc. R. Soc. London, Ser. A 381, 17 (1982)], the Wolf-Villain (WV) model [D. E. Wolf and J. Villain, Europhys. Lett. 13, 389 (1990)], and a model with concurrent random deposition and surface diffusion. With our rules for the EW model no appreciable crossover is obtained for either 1D or 2D substrates. For the 1D WV model, discussed previously, our analysis reproduces the crossover sequence known from kinetic Monte Carlo (KMC) simulations, but for the 2D WV model, we find a transition from smooth to unstable growth under repeated coarse-graining. Concurrent surface diffusion does not change this behavior, but can lead to extended transient regimes with kinetic roughening. This provides an explanation of recent experiments on Ge(001) with the intriguing conclusion that the same relaxation mechanism responsible for ordered structures during the early stages of growth also produces an instability at longer times that leads to epitaxial breakdown. The RG trajectories calculated for concurrent random deposition and surface diffusion reproduce the crossover sequences observed with KMC simulations for all values of the model parameters, and asymptotically always approach the fixed point corresponding to the equation proposed by Villain [J. Phys. I 1, 19 (1991)] and by Lai and Das Sarma [Phys. Rev. Lett. 66, 2899 (1991)]. We conclude with a discussion of the application of our methodology to other growth settings.

In this paper we reconsider the mass action law (MAL) for the anomalous reversible reaction $A\rightleftarrows B$ with diffusion. We provide a mesoscopic description of this reaction when the transitions between two states $A$ and $B$ are governed by anomalous (heavy-tailed) waiting-time distributions. We derive the set of mesoscopic integro-differential equations for the mean densities of reacting and diffusing particles in both states. We show that the effective reaction rate memory kernels in these equations and the uniform asymptotic states depend on transport characteristics such as jumping rates. This is in contradiction with the classical picture of MAL. We find that transport can even induce an extinction of the particles such that the density of particles $A$ or $B$ tends asymptotically to zero. We verify analytical results by Monte Carlo simulations and show that the mesoscopic densities exhibit a transient growth before decay.

We study analytically and by means of an off-lattice bead-spring dynamic Monte Carlo simulation model the adsorption kinetics of a single macromolecule on a structureless flat substrate in the regime of strong physisorption. The underlying notion of a “stem-flower” polymer conformation, and the related mechanism of “zipping” during the adsorption process are shown to lead to a Fokker-Planck equation with reflecting boundary conditions for the time-dependent probability distribution function (PDF) of the number of adsorbed monomers. The theoretical treatment predicts that the mean fraction of adsorbed segments grows with time as a power law with a power of ${\left(1+\nu \right)}^{-1}$, where $\nu \approx 3/5$ is the Flory exponent. The instantaneous distribution of train lengths is predicted to follow an exponential relationship. The corresponding PDFs for loops and tails are also derived. The complete solution for the time-dependent PDF of the number of adsorbed monomers is obtained numerically from the set of discrete coupled differential equations and shown to be in perfect agreement with the Monte Carlo simulation results. In addition to homopolymer adsorption, we also study regular multiblock copolymers and random copolymers, and demonstrate that their adsorption kinetics may be considered within the same theoretical model.

We propose a theoretical model for the nonlinear mechanical response of Langmuir lipid monolayers subjected to a dilational in-plane deformation. Lateral diffusion in conjunction with free convection has been considered to drive nonlinear mass transport in Langmuir lipid monolayers. The present model combines the conservative dynamical equations for lipid transport along the monolayer plane together with a material relationship accounting for nonlinear hypoelasticity, as experimentally observed from high-strain rheological measurements [Hilles et al., Adv. Colloid Interface Sci. 122, 67 (2007)]. The dynamical equations have been resolved for oscillatory nonlinear motion, the theoretical spectral amplitudes being found in quantitative agreement with the experimental values obtained from surface rheology experiments performed in Langmuir monolayers of two different lipid systems, namely DPPC and native E. Coli lipids. The presence of micrometer-sized phase coexistence domains in these lipid systems has been claimed to pump diffusive transport along the monolayer plane. This dynamical scenario defines a relaxation regime compatible with the observed nonlinear mechanical behavior.

We find by Monte Carlo simulations that the distribution of Voronoï cell sizes for the parking lot model follows a gamma distribution with shape parameter $k\approx 2$ for high enough packing fractions $\varphi$. A gamma distribution of Voronoï cells sizes was found recently by Aste et al. [Europhys. Lett. 79, 24003 (2007)] in experiments of static packings of monodisperse spheres. This statistic implies that, for high $\varphi$, Edwards’ compactivity of the parking lot model depends linearly on the average volume per cell, as predicted by the statistical mechanics calculation of Tarjus and Viot, which explicitly counted the blocked configurations of this model [Phys. Rev. E 69, 011307 (2004)].

Uncorrelated scale-free networks are necessarily small world (and, in fact, smaller than small world). Nonetheless, for scale-free networks with correlated degree distribution this may not be the case. We describe a mechanism to generate highly assortative scale-free networks which are not small world. We show that it is possible to generate scale-free networks, with arbitrary degree exponent $\gamma >1$, such that the average distance between nodes in the network is large. To achieve this, nodes are not added to the network with preferential attachment. Instead, we greedily optimize the assortativity of the network. The network generation scheme is physically motivated, and we show that the recently observed global network of Avian Influenza outbreaks arises through a mechanism similar to what we present here. Simulations show that this network exhibits very similar physical characteristics (very high assortativity, clustering, and path length).

The soliton interaction is investigated based on solving the higher-order nonlinear Schrödinger equation with the effects of third-order dispersion, self-steepening, and stimulated Raman scattering. By using Hirota’s bilinear method, the analytic one-, two-, and three-soliton solutions of this model are obtained. According to those solutions, the relevant properties and features of physical and optical interest are illustrated. The results of this paper will be valuable to the study of signal amplification and pulse compression.

The phenomenon of Anderson localization in expanding one-dimensional Bose-Einstein condensates is investigated by numerically solving the Gross-Pitaevskii equation with a random speckle potential. To this purpose, a quantum lattice Boltzmann (QLB) method is used, and compared with a standard Crank-Nicolson scheme. The QLB simulations show evidence of Anderson localization even for relatively low-energy condensates, with a healing length as large as one-tenth of the Thomas-Fermi length. Moreover, very long-time simulations, lasting up to 15 000 optical confinement periods, indicate that the Anderson localization degrades in time, although at a very slow pace. In particular, the inverse localization length is found to decay according to a $t^{-1/3}$ law. This lends support to the idea that localized wave functions, although not strictly ground states, represent extremely long-lived metastable states of the expanding condensate.

The correlation functions of an arbitrary number of boundary monomers in a system of close-packed dimers on a square lattice are computed exactly in the scaling limit. The equivalence of the $2n$-point correlation functions with those of a complex free fermion is proved, thereby reinforcing the description of the monomer-dimer model by a conformal free-field theory with central charge $c=1$.

In this paper, we consider continuous-time quantum walks (CTQWs) on a one-dimensional ring lattice of $N$ nodes in which every node is connected to its $2m$ nearest neighbors ($m$ on either side). In the framework of the Bloch function ansatz, we calculate the space-time transition probabilities between two nodes of the lattice. We find that the transport of CTQWs between two different nodes is faster than that of the classical continuous-time random walks (CTRWs). The transport speed, which is defined by the ratio of the shortest path length and propagating time, increases with the connectivity parameter $m$ for both CTQWs and CTRWs. For fixed parameter $m$, the transport of CTRWs gets slower with the increase of the shortest distance while the transport (speed) of CTQWs turns out to be a constant value. In the long-time limit, depending on the network size $N$ and connectivity parameter $m$, the limiting probability distributions of CTQWs show various patterns. When the network size $N$ is an even number, the probability of being at the original node differs from that of being at the opposite node, which also depends on the precise value of parameter $m$.

We study spatial anisotropy effects on the bulk and finite-size critical behavior of the $\mathrm{O}\left(n\right)$ symmetric anisotropic ${\phi }^4$ lattice model with periodic boundary conditions in a $d$-dimensional hypercubic geometry above, at, and below $T_c$. The absence of two-scale factor universality is discussed for the bulk order-parameter correlation function, the bulk scattering intensity, and for several universal bulk amplitude relations. The anisotropy parameters are observable by scattering experiments at $T_c$. For the confined system, renormalization-group theory within the minimal subtraction scheme at fixed dimension $d$ for $2<d<4$ is employed. In contrast to the $\epsilon =4-d$ expansion, the fixed-$d$ finite-size approach keeps the exponential form of the order-parameter distribution function unexpanded. For the case of cubic symmetry and for $n=1$, our perturbation approach yields excellent agreement with the Monte Carlo (MC) data for the finite-size amplitude of the free energy of the three-dimensional Ising model at $T_c$ by Mon [Phys. Rev. Lett. 54, 2671 (1985)]. The $\epsilon$ expansion result is in less good agreement. Below $T_c$, a minimum of the scaling function of the excess free energy is found. We predict a measurable dependence of this minimum on the anisotropy parameters. The relative anisotropy effect on the free energy is predicted to be significantly larger than that on the Binder cumulant. Our theory agrees quantitatively with the nonmonotonic dependence of the Binder cumulant on the ferromagnetic next-nearest-neighbor (NNN) coupling of the two-dimensional Ising model found by MC simulations of Selke and Shchur [J. Phys. A 38, L739 (2005)]. Our theory also predicts a nonmonotonic dependence for small values of the antiferromagnetic NNN coupling and the existence of a Lifshitz point at a larger value of this coupling. The nonuniversal anisotropy effects in the finite-size scaling regime are predicted to satisfy a kind of restricted universality. The tails of the large-$L$ behavior at $T\ne T_c$ violate both finite-size scaling and universality even for isotropic systems as they depend on the bare four-point coupling of the ${\phi }^4$ theory, on the cutoff procedure, and on subleading long-range interactions.

The dynamics of homogeneously heated granular gases which fragment due to particle collisions is analyzed. We introduce a kinetic model which accounts for correlations induced at the grain collisions and analyze both the kinetics and relevant distribution functions these systems develop. The work combines analytical and numerical studies based on direct simulation Monte Carlo calculations. A broad family of fragmentation probabilities is considered, and its implications for the system kinetics are discussed. We show that generically these driven materials evolve asymptotically into a dynamical scaling regime. If the fragmentation probability tends to a constant, the grain number diverges at a finite time, leading to a shattering singularity. If the fragmentation probability vanishes, then the number of grains grows monotonously as a power law. We consider different homogeneous thermostats and show that the kinetics of these systems depends weakly on both the grain inelasticity and driving. We observe that fragmentation plays a relevant role in the shape of the velocity distribution of the particles. When the fragmentation is driven by local stochastic events, the long velocity tail is essentially exponential independently of the heating frequency and the breaking rule. However, for a Lowe-Andersen thermostat, numerical evidence strongly supports the conjecture that the scaled velocity distribution follows a generalized exponential behavior $f\left(c\right)\sim \text{exp}\left(-c^n\right)$, with $n\approx 1.2$, regarding less the fragmentation mechanisms.

We propose that there exists a generic class of glass-forming systems that have competing states (of crystalline order or not) which are locally close in energy to the ground state (which is typically unique). Upon cooling, such systems exhibit patches (or clusters) of these competing states which become locally stable in the sense of having a relatively high local shear modulus. It is in between these clusters where aging, relaxation, and plasticity under strain can take place. We demonstrate explicitly that relaxation events that lead to aging occur where the local shear modulus is low (even negative) and result in an increase in the size of local patches of relative order. We examine the aging events closely from two points of view. On the one hand we show that they are very localized in real space, taking place outside the patches of relative order, and from the other point of view we show that they represent transitions from one local minimum in the potential surface to another. This picture offers a direct relation between structure and dynamics, ascribing the slowing down in glass-forming systems to the reduction in relative volume of the amorphous material which is liquidlike. While we agree with the well-known Adam-Gibbs proposition that the slowing down is due to an entropic squeeze (a dramatic decrease in the number of available configurations), we do not agree with the Adam-Gibbs (or the Volger-Fulcher) formulas that predict an infinite relaxation time at a finite temperature. Rather, we propose that generically there should be no singular crisis at any finite temperature: the relaxation time and the associated correlation length (average cluster size) increase at most superexponentially when the temperature is lowered.