Velocity–Space Drag and Diffusion in a Model, Two-Dimensional Plasma

The quasilinear fluctuation integral is calculated for a two-dimensional, unmagnetized plasma ~composed of charged rods!, and is expressed in terms of Fokker–Planck coefficients. It is found that in two dimensions, the enhanced fluctuations generated by fast electrons lead to anomalously large transport coefficients. In particular, the effect of a small population of fast electrons is only weakly dependent on their density. In three dimensions, the effect of fast electrons is masked by the dominant approximation, but higher-order terms describe processes similar to those in two dimensions, and these terms can become significant for weakly stable plasmas. The differences between two and three dimensions arise from the fact that both emission and damping of plasma waves are retained to lowest order in two dimensions, while the three-dimensional dominant approximation effectively includes only wave emission by test particles. An understanding of the differences between two and three dimensions is crucial to the interpretation of two-dimensional particle simulations

Thermodynamics of non-local materials: extra fluxes and internal powers

The most usual formulation of the Laws of Thermodynamics turns out to be suitable for local or simple materials, while for non-local systems there are two different ways: either modify this usual formulation by introducing suitable extra fluxes or express the Laws of Thermodynamics in terms of internal powers directly, as we propose in this paper. The first choice is subject to the criticism that the vector fluxes must be introduced a posteriori in order to obtain the compatibility with the Laws of Thermodynamics. On the contrary, the formulation in terms of internal powers is more general, because it is a priori defined on the basis of the constitutive equations. Besides it allows to highlight, without ambiguity, the contribution of the internal powers in the variation of the thermodynamic potentials. Finally, in this paper, we consider some examples of non-local materials and derive the proper expressions of their internal powers from the power balance laws.Comment: 16 pages, in press on Continuum Mechanics and Thermodynamic

Coupled Bose-Einstein condensate: Collapse for attractive interaction

We study the collapse in a coupled Bose-Einstein condensate of two types of bosons 1 and 2 under the action of a trap using the time-dependent Gross-Pitaevskii equation. The system may undergo collapse when one, two or three of the scattering lengths $a_{ij}$ for scattering of boson $i$ with $j$, $i,j = 1, 2$, are negative representing an attractive interaction. Depending on the parameters of the problem a single or both components of the condensate may experience collapse.Comment: 5 pages and 9 figures, small changes mad

Distributed optimal control of a nonstandard system of phase field equations

We investigate a distributed optimal control problem for a phase field model of Cahn-Hilliard type. The model describes two-species phase segregation on an atomic lattice under the presence of diffusion; it has been recently introduced by the same authors in arXiv:1103.4585v1 [math.AP] and consists of a system of two highly nonlinearly coupled PDEs. For this reason, standard arguments of optimal control theory do not apply directly, although the control constraints and the cost functional are of standard type. We show that the problem admits a solution, and we derive the first-order necessary conditions of optimality.Comment: Key words: distributed optimal control, nonlinear phase field systems, first-order necessary optimality condition

Radiation of electrons in Weibel-generated fields: a general case

Weibel instability turns out to be the a ubiquitous phenomenon in High-Energy Density environments, ranging from astrophysical sources, e.g., gamma-ray bursts, to laboratory experiments involving laser-produced plasmas. Relativistic particles (electrons) radiate in the Weibel-produced magnetic fields in the Jitter regime. Conventionally, in this regime, the particle deflections are considered to be smaller than the relativistic beaming angle of 1/$\gamma$ ($\gamma$ being the Lorentz factor of an emitting particle) and the particle distribution is assumed to be isotropic. This is a relatively idealized situation as far as lab experiments are concerned. We relax the assumption of the isotropy of radiating particle distribution and present the extension of the jitter theory amenable for comparisons with experimental data.Comment: Proceedings of International Conference on HEDP/HEDLA-0

Mean-field analysis of collapsing and exploding Bose-Einstein condensates

The dynamics of collapsing and exploding trapped Bose-Einstein condensat es caused by a sudden switch of interactions from repulsive to attractive a re studied by numerically integrating the Gross-Pitaevskii equation with atomic loss for an axially symmetric trap. We investigate the decay rate of condensates and the phenomena of bursts and jets of atoms, and compare our results with those of the experiments performed by E. A. Donley {\it et al.} [Nature {\bf 412}, 295 (2001)]. Our study suggests that the condensate decay and the burst production is due to local intermittent implosions in the condensate, and that atomic clouds of bursts and jets are coherent. We also predict nonlinear pattern formation caused by the density instability of attractive condensates.Comment: 7 pages, 8 figures, axi-symmetric results are adde

Ground state and elementary excitations of single and binary Bose-Einstein condensates of trapped dipolar gases

We analyze the ground-state properties and the excitation spectrum of Bose-Einstein condensates of trapped dipolar particles. First, we consider the case of a single-component polarized dipolar gas. For this case we discuss the influence of the trapping geometry on the stability of the condensate as well as the effects of the dipole-dipole interaction on the excitation spectrum. We discuss also the ground state and excitations of a gas composed of two antiparallel dipolar components.Comment: 12 pages, 9 eps figures, final versio