The effect of a magnetic field at right angles to an electric field on spatial relaxation of a swarm of charged particles emitted by a plane source into a gas—the idealized steady-state Townsend experiment—is examined. The Boltzmann equation is solved using an adaptation of the “two-temperature” moment method, involving a Burnett function representation of the velocity distribution function, a technique which is valid for charged particles of arbitrary mass and is intrinsically of a “multiterm” nature. Results are presented for electrons in model and real gases, and are benchmarked against an exact analytical solution of the Boltzmann equation for a particular collision model. The application of a magnetic field significantly alters the relaxation profiles: in general, it can both enhance or retard spatial relaxation of transport properties. For methane gas, a multiterm analysis is essential to correctly account for the relaxation near the source, even though a two-term approximation may be sufficient when the magnetic field is sufficiently strong and hydrodynamic conditions dominate.

Ti $K\alpha$ emission yields from foils irradiated with $\sim 45\mathrm{fs}$, $p$-polarized pulses of a frequency-doubled Ti:sapphire laser are presented. A simple model invoking vacuum heating to predict absorption and hot electron temperature was coupled with the cross section for $K$-shell ionization of Ti and the Bethe-Bloch stopping power equation for electrons. The peak predicted $K\alpha$ emission was in generally good agreement with experiment. This contrasts strongly with previous work at the fundamental frequency. Similar predictions using particle-in-cell (PIC) code simulation to estimate the number and temperature of hot electrons also gave good agreement for yield.

Recent work has demonstrated that undriven and overdamped bistable systems, which are normally quiescent, can oscillate if unidirectionally coupled into arrays with cyclic boundary conditions. Here, we understand such oscillations as corresponding to the propagation of solitonlike waves. Further, in large arrays, we demonstrate how noise and coupling, together, mediate the resulting complex spatiotemporal dynamics.

We extended a previous analysis of the classical Rayleigh instability of spherical charged droplets in the presence of neutralizing monovalent counterions [M. Deserno, Eur. Phys. J. E 6, 163 (2001)], by generalizing the problem for suspensions of aggregates with $D$-dimensional symmetry, corresponding for $D=2$ to infinite (rodlike) cylindrical charged bundles and for $D=3$ to spherical charged droplets. In addition, we include the effects of added monovalent salt and of dielectric contrast between the charged aggregate and the surrounding solvent. The electrostatic energy taking the microion screening into account is estimated using uniform profiles within the framework of the cell model. We verify the robustness of these results by also considering Debye-Hückel-type microion profiles that are obtained by the minimization of a linearized Poisson-Boltzmann free-energy functional. In the case when the microions can enter inside the charged aggregates, we confirm the occurrence of a discontinuous phase change between aggregates of finite size and an infinite aggregate, which takes place at a collapse temperature that depends on their volume fraction $\varphi$ and on the salt content. Decrease of $\varphi$ shifts the phase-change temperature toward higher values, while salt addition has an opposite effect. We obtain analytical expressions for the phase-separation line in the asymptotic limit of infinite dilution $(\varphi \to 0)$, showing that the collapse temperature depends logarithmically on $\varphi$. As an application for $D=3$ we discuss the stability of the pearl-necklace structures of flexible polyelectrolytes in poor solvents. The case $D=2$ is applied to the problem of finite bundle sizes of stiff polyelectrolytes that attract each other—via, e.g., multivalent counterions—leading to an effective surface tension.

We study the out-of-equilibrium large-time dynamics of a Gaussian polymer chain in a quenched random potential. The dynamics studied is a simple Langevin dynamics commonly referred to as the Rouse model. The equations for the two-time correlation and response functions are derived within the Gaussian variational approximation. In order to implement this approximation faithfully, we employ the supersymmetric representation of the Martin-Siggia-Rose dynamical action. For a short-ranged correlated random potential the equations are solved analytically in the limit of large times using certain assumptions concerning the asymptotic behavior. Two possible dynamical behaviors are identified depending upon the time separation: a stationary regime and an aging regime. In the stationary regime time translation invariance holds and so does the fluctuation dissipation theorem. The aging regime which occurs for large time separations of the two-time correlation functions is characterized by a history dependence and the breakdown of certain equilibrium relations. The large-time limit of the equations yields equations among the order parameters that are similar to the equations obtained in statics using replicas. In particular the aging solution corresponds to the broken replica solution. But there is a difference in one equation that leads to important consequences for the solution. The stationary regime corresponds to the motion of the polymer inside a local minimum of the random potential, whereas in the aging regime the polymer hops between different minima. As a by-product we also solve exactly the dynamics of a chain in a random potential with quadratic correlations.

We characterize the capability of time-resolved reflectance measurements at small source-detector separation (less than $5\mathrm{mm}$) to localize small inhomogeneities embedded in an otherwise homogeneous or layered diffusive medium. By considering both absorption and scattering inhomogeneities, we demonstrate the improvement of this approach in terms of contrast and spatial resolution, as compared to more typical set-ups involving larger source-detection separations (few centimeters). Simulations are performed exploiting an analytical perturbation approach to diffusion theory and a four-layer heterogeneous time-resolved Monte Carlo code, considering realistic tissue geometries. Exhaustive investigation in the parameters space is reported.

The Davydov-Scott model describes the transfer of energy along hydrogen-bonded chains, like those that stabilize the structure of $\alpha$ helices. It is based on the hypothesis that amide I excitations are created (by the hydrolysis of ATP, for instance) and kept in the system. Recent experimental results confirm that the energy associated with amide I excitations does indeed last for tens of picoseconds in proteins and model systems. However, the Davydov-Scott model cannot describe the conversion of that energy into work, because it conserves the number of excitations. With the aim of describing conformational changes, we consider, in this paper, a nonconserving generalization of the model, which is found to describe essentially a contraction of the hydrogen bond adjacent to the site where an excitation is present. Unlike the one-site Davydov-Scott model, that contraction is time dependent because the number of excitations is not conserved. However, considering the time average of the dynamical variables, the results reported here tend to the known results of the Davydov-Scott model.

A threshold system with feedback is studied from the viewpoint of an ergodic-nonergodic transition, a kind of nonequilibrium phase transition, as the rate of input signal variation is changed. By discussing the time evolution of the distribution function, instead of its lowest moment (an order parameter), we can determine the transition point and make clear the role and limitation of the self-consistent equation for the order parameter. Finally the feedback strength is related to an activation energy from a statistical mechanical viewpoint.

To investigate an effect of social interaction on the bystanders’ intervention in emergency situations a rescue model was introduced which includes the effects of the victim’s acquaintance with bystanders and those among bystanders from a network perspective. This model reproduces the experimental result that the helping rate (success rate in our model) tends to decrease although the number of bystanders $k$ increases. And the interaction among homogeneous bystanders results in the emergence of hubs in a helping network. For more realistic consideration it is assumed that the agents are located on a one-dimensional lattice (ring), then the randomness $p∊[0,1]$ is introduced: the $kp$ random bystanders are randomly chosen from a whole population and the $k-kp$ near bystanders are chosen in the nearest order to the victim. We find that there appears another peak of the network density in the vicinity of $k=9$ and $p=0.3$ due to the cooperative and competitive interaction between the near and random bystanders.

The finite-sample effect on the growth of moments of the perturbation observed in numerical simulations of chaotic dynamical systems is studied. To numerically estimate the moments, only a limited number of sample trajectories can be utilized, and therefore the moments exhibit pure exponential growth only initially, and give way to relaxed growth thereafter. Such transition is a consequence of the unobservability of rare events in finite sample sets. Using the large-deviation formalism for chaotic time series, we estimate the relaxation time and derive the post-relaxation growth law. We demonstrate that even after the relaxation, each moment still obeys a universal growth law of different type, which reflects physical information on the statistics of chaotic expansion rates.

Vorticity banding under steady shear flow is observed in a suspension of semiflexible colloidal rods (fd virus particles) within a part of the paranematic-nematic biphasic region. Banding occurs uniformly throughout the cell gap within a shear-rate interval $({\dot{\gamma }}_{-},{\dot{\gamma }}_{+})$, which depends on the fd concentration. For shear rates below the lower-border shear rate ${\dot{\gamma }}_{-}$ only shear elongation of inhomogeneities, which are formed due to paranematic-nematic phase separation, is observed. Within a small region just above the upper-border shear rate ${\dot{\gamma }}_{+}$, banding occurs heterogeneously. An essential difference in the kinetics of vorticity banding is observed, depending on the morphology of inhomogeneities formed during the initial stages of the paranematic-nematic phase separation. Particle tracking and polarization experiments indicate that the vorticity bands are in a weak rolling flow, superimposed on the applied shear flow. We propose a mechanism for the origin of the banding instability and the transient stability of the banded states. This mechanism is related to the normal stresses generated by inhomogeneities formed due to the underlying paranematic-nematic phase transition.

Accurate molecular dynamics simulations are reported which quantify the contributions of two- and three-body interactions in the gas, liquid, and solid phases of argon at both subcritical and supercritical conditions. The calculations use an accurate two-body potential in addition to contributions from three-body dispersion interactions from third-order triple-dipole interactions. The number dependence of three-body interactions is quantified, indicating that a system size of at least five hundred atoms is required for reliable calculations. The results indicate that, although the contribution of three-body interaction to the overall energy is small, three-body interactions significantly affect the pressure at which vapor-liquid and solid-liquid transitions are observed. In particular, three-body interactions substantially increase the pressure of the freezing point. Unlike two-body interactions, which vary with both density and temperature, for a given density, three-body interactions have a near-constant ‘background’ value irrespective of the temperature. Both two-body interactions and kinetic energy have an important role in vapor-liquid equilibria whereas solid-liquid equilibria are dominated by two-body interactions.

The motion of particles, dispersed in a medium, between collisions with each other can, in limiting situations, be either ballistic (straight line) or diffusive (random walker). The diffusive regime can be divided into two distinct subregimes. The “continuum regime” exhibits Stokes-Einstein-type diffusion (no-slip surface boundary condition) with a frictional coefficient proportional to the particle size (linear dimension). The “Epstein regime,” as we shall refer to it, is characterized by a frictional coefficient proportional to the particle cross-sectional area, hence an Epstein-type diffusion (slip surface). The purpose of the current study is to illuminate the dynamics of dilute-limit aggregation in the Epstein regime. We present results from low volume fraction Monte Carlo simulations of cluster-cluster aggregation in the Epstein regime with the particle motion based on each particle’s cross-sectional area. Our findings indicate that aggregates grown under Epstein conditions have a fractal dimension of $\sim 1.8$, similar to that of diffusion-limited cluster-cluster aggregates (DLCA) in the continuum regime. The kinetic exponent $z$ in the Epstein regime is found to be $z\approx 0.8$, lower than its value for both the continuum regime DLCA $(z=1)$ and for the ballistic cluster aggregation regime $(z\approx 2)$. Cluster size distribution data for Epstein systems are found to scale at large cluster sizes with exponents consistent with the kinetic data. A scaling argument for predicting the kinetic exponent and kernel homogeneity based on the mass or size dependence of the particle velocity and collision cross section is presented and is seen to give accurate results for dilute and intermediate values of particle volume fractions not only for the current study, but also for work done by other researchers with various choices for the aggregation kernel.

The nucleation of liquid droplets at a liquid-gas interface from a saturated vapor in the gas phase, as well as the droplet growth after the nucleation are studied. These two processes determine the formation of a regular hexagonal array of drops on the surface of an evaporating film of polymer solution that is used for the fabrication of polymer membranes with a regular microporous structure. The free-energy barrier for the nucleation of a droplet at a liquid-gas interface is found as a function of the droplet radius and the contact angles, and the critical nucleation radius is computed. It is shown that the heterogeneous nucleation is thermodynamically more preferable than the homogeneous one. The role of the line tension between the phases is also estimated. Further growth of a droplet nucleated at the liquid-gas interface is studied. Two growth mechanisms are considered: by the vapor diffusion flux from the gas phase and by the surface diffusion of the vapor molecules adsorbed at the liquid-gas interface outside the droplet. Two cases, corresponding to unsaturated and saturated condensation, are considered. The droplet growth is described by a free-boundary problem which is solved analytically and numerically. The droplet growth exponents at different stages of growth are found.

Modeling the intermittent behavior of turbulent energy dissipation processes in both space and time is often a relevant problem when dealing with phenomena occurring in high-Reynolds-number flows, especially in astrophysical and space fluids. In this paper, a dynamical model is proposed to describe the intermittency of the energy dissipation rate in a turbulent system. This is done by using a shell model to simulate the time evolution of the turbulent cascade and introducing some heuristic rules, partly inspired by the well-known $p$ model, to construct a spatial structure of the energy dissipation rate. In order to validate the model and to study its spatial intermittency properties, a series of numerical simulations have been performed. These show that the level of spatial intermittency of the system can be simply tuned by varying a single parameter of the model and that scaling laws in agreement with those obtained from experiments on fully turbulent hydrodynamic flows can be recovered. It is finally suggested that the model could represent a useful tool to simulate the intermittent structure of turbulent energy dissipation in those high-Reynolds-number astrophysical fluids where impulsive energy release processes can be associated with the dynamics of the turbulent cascade.

Time and space resolved measurements of Thomson scattering of $532\mathrm{nm}$, $6\mathrm{ns}$ laser pulses were performed on argon thermal discharge plasma with electron temperature $T_e>10000\mathrm{K}$ and electron density $8\times {10}^{22}{\mathrm{m}}^{-3}<n_e<2\times {10}^{23}{\mathrm{m}}^{-3}$. From these measurements, variations of the electron density and temperature across the laser beam and their evolution during the laser pulse were determined. While the electron density is augmented by no more than a few percent the electron temperature is significantly increased along the axis of the laser beam due to laser heating. It is also shown that the higher initial electron density, the more disturbed is the plasma. The initial “undisturbed” electron density was derived by studying the spatial variations of $n_e$ within the laser beam. On the other hand, the initial electron temperature was determined by studying the temporal evolution of $T_e$ during the laser pulse and then by extrapolating the results to the origin of the pulse. Despite strong and nonlinear plasma heating by the Thomson scattered laser light, our study yields temperatures close to those obtained by modeling and time-resolved spectroscopic measurements.

In the above mentioned paper by E. Moreau and O. Vallée [Phys. Rev. E 73, 016112 (2006)], the one-dimensional Burgers equation with an elastic (attractive) forcing term has been claimed to be connected with the Ornstein-Uhlenbeck process. We point out that this connection is valid only in the case of repulsive forcing.

As pointed out by Garbaczewski in the Comment [Phys. Rev. E 74, 028101 (2006)], the quantity $+{\kappa }^{2}x$ should appear in Eq. (34) of the original paper [E. Moreau and O. Vallée, Phys. Rev. E 73, 016112 (2006)], instead of $-{\kappa }^{2}x$. Nevertheless, the main results are not affected by this fact, and, in particular, our methods of resolution and the conclusions exposed in our paper are unaffected by the error since the phrase “linear forcing term” is employed instead of “elastic forcing term.”

Pebble-bed nuclear reactor technology, which is currently being revived around the world, raises fundamental questions about dense granular flow in silos. A typical reactor core is composed of graphite fuel pebbles, which drain very slowly in a continuous refueling process. Pebble flow is poorly understood and not easily accessible to experiments, and yet it has a major impact on reactor physics. To address this problem, we perform full-scale, discrete-element simulations in realistic geometries, with up to $440000$ frictional, viscoelastic 6-cm-diam spheres draining in a cylindrical vessel of diameter $3.5\mathrm{m}$ and height $10\mathrm{m}$ with bottom funnels angled at 30° or 60°. We also simulate a bidisperse core with a dynamic central column of smaller graphite moderator pebbles and show that little mixing occurs down to a 1:2 diameter ratio. We analyze the mean velocity, diffusion and mixing, local ordering and porosity (from Voronoi volumes), the residence-time distribution, and the effects of wall friction and discuss implications for reactor design and the basic physics of granular flow.

We theoretically study the nematic ordering transition of rods that are able to elastically adjust their mutually excluded volumes. The model rods, which consist of a hard core surrounded by a deformable shell, mimic the structure of polymer-coated, rodlike fd virus particles that have recently been the object of experimental study [K. Purdy et al., Phys. Rev. Lett. 94, 057801 (2005)]. We find that fluids of such soft rods exhibit an isotropic-nematic phase transition at a density higher than that of the corresponding hard-rod system of identical diameter, and that at coexistence the order parameter of the nematic phase depends nonmonotonically on the elastic properties of the polymer coating. For binary mixtures of hard and soft rods, the topology of the phase diagram turns out to depend sensitively on the elasticity of a shell. The lower nematic-nematic critical point, discovered in mixtures of bare and polymer-coated fd virus particles, is not reproduced by the theory.