A discontinuous Galerkin method for the Vlasov-Poisson system

A discontinuous Galerkin method for approximating the Vlasov-Poisson system of equations describing the time evolution of a collisionless plasma is proposed. The method is mass conservative and, in the case that piecewise constant functions are used as a basis, the method preserves the positivity of the electron distribution function and weakly enforces continuity of the electric field through mesh interfaces and boundary conditions. The performance of the method is investigated by computing several examples and error estimates associated system's approximation are stated. In particular, computed results are benchmarked against established theoretical results for linear advection and the phenomenon of linear Landau damping for both the Maxwell and Lorentz distributions. Moreover, two nonlinear problems are considered: nonlinear Landau damping and a version of the two-stream instability are computed. For the latter, fine scale details of the resulting long-time BGK-like state are presented. Conservation laws are examined and various comparisons to theory are made. The results obtained demonstrate that the discontinuous Galerkin method is a viable option for integrating the Vlasov-Poisson system.Comment: To appear in Journal for Computational Physics, 2011. 63 pages, 86 figure

Percolation, Morphogenesis, and Burgers Dynamics in Blood Vessels Formation

Experiments of in vitro formation of blood vessels show that cells randomly spread on a gel matrix autonomously organize to form a connected vascular network. We propose a simple model which reproduces many features of the biological system. We show that both the model and the real system exhibit a fractal behavior at small scales, due to the process of migration and dynamical aggregation, followed at large scale by a random percolation behavior due to the coalescence of aggregates. The results are in good agreement with the analysis performed on the experimental data.Comment: 4 pages, 11 eps figure

The Lyapunov Spectrum of a Continuous Product of Random Matrices

We expose a functional integration method for the averaging of continuous products $\hat{P}_t$ of $N\times N$ random matrices. As an application, we compute exactly the statistics of the Lyapunov spectrum of $\hat{P}_t$. This problem is relevant to the study of the statistical properties of various disordered physical systems, and specifically to the computation of the multipoint correlators of a passive scalar advected by a random velocity field. Apart from these applications, our method provides a general setting for computing statistical properties of linear evolutionary systems subjected to a white noise force field.Comment: Latex, 9 page

The general classical solution of the superparticle

The theory of vectors and spinors in 9+1 dimensional spacetime is introduced in a completely octonionic formalism based on an octonionic representation of the Clifford algebra \Cl(9,1). The general solution of the classical equations of motion of the CBS superparticle is given to all orders of the Grassmann hierarchy. A spinor and a vector are combined into a $3 \times 3$ Grassmann, octonionic, Jordan matrix in order to construct a superspace variable to describe the superparticle. The combined Lorentz and supersymmetry transformations of the fermionic and bosonic variables are expressed in terms of Jordan products.Comment: 11 pages, REVTe

Familial Transmission of a Serious Disease—Producing Group A Streptococcus Clone: Case Reports and Review

Invasive group A streptococcus (GAS) infections are emerging diseases; however, person-to-person transmission of invasive GAS producing life-threatening infection has been observed rarely. We report a small intrafamilial cluster of life-threatening GAS infections. A previously healthy 47-year-old father developed necrotizing fasciitis of the neck. Two days later, his 16-year-old daughter developed streptococcal angina, pneumonia, and pleural empyema. Both patients had signs of streptococcal toxic shock syndrome. Pulsed field gel electrophoresis revealed that the M6 strains of GAS isolated from the father and daughter had identical patterns. Cases of person-to-person transmission of invasive GAS infection reported in the literature are also reviewe

Notes about Passive Scalar in Large-Scale Velocity Field

We consider advection of a passive scalar theta(t,r) by an incompressible large-scale turbulent flow. In the framework of the Kraichnan model the whole PDF's (probability distribution functions) for the single-point statistics of theta and for the passive scalar difference theta(r_1)-theta(r_2) (for separations r_1-r_2 lying in the convective interval) are found.Comment: 19 pages, RevTe