Time-resolved characterization of a pulsed discharge in a stationary bubble

In recent years, plasma generation in water has been proposed for the application of water treatment. The process efficiency is believed to be improved by the introduction of bubbles in the plasma active region. For further optimization, the initiating and developmental mechanisms of plasma inside bubbles need to be understood to a greater extent. In order to meet this necessity, we investigated pulsed electrical discharge inside a stationary bubble in water. This paper deals with the evolution of the discharge and of the bubble shape during discharge, investigated by electrical characterization and fast imaging. Only several microseconds after the application of the voltage pulse, plasma light is observed. Different phases are observed during plasma formation. The plasma is strongest at the bubble surface, causing the surrounding water to evaporate. This leads to both the formation of propagating streamers into the water and the expansion and collapse of the bubble. These observations show that plasma inside a bubble has the strongest activity at the bubble surface, making it attractive for water treatment

Landau (\Gamma,\chi)-automorphic functions on \mathbb{C}^n of magnitude \nu

We investigate the spectral theory of the invariant Landau Hamiltonian \La^\nu acting on the space ${\mathcal{F}}^\nu_{\Gamma,\chi}$ of $(\Gamma,\chi)$-automotphic functions on \C^n, for given real number $\nu>0$, lattice $\Gamma$ of \C^n and a map $\chi:\Gamma\to U(1)$ such that the triplet $(\nu,\Gamma,\chi)$ satisfies a Riemann-Dirac quantization type condition. More precisely, we show that the eigenspace {\mathcal{E}}^\nu_{\Gamma,\chi}(\lambda)=\set{f\in {\mathcal{F}}^\nu_{\Gamma,\chi}; \La^\nu f = \nu(2\lambda+n) f}; \lambda\in\C, is non trivial if and only if $\lambda=l=0,1,2, ...$. In such case, ${\mathcal{E}}^\nu_{\Gamma,\chi}(l)$ is a finite dimensional vector space whose the dimension is given explicitly. We show also that the eigenspace ${\mathcal{E}}^\nu_{\Gamma,\chi}(0)$ associated to the lowest Landau level of \La^\nu is isomorphic to the space, {\mathcal{O}}^\nu_{\Gamma,\chi}(\C^n), of holomorphic functions on \C^n satisfying g(z+\gamma) = \chi(\gamma) e^{\frac \nu 2 |\gamma|^2+\nu\scal{z,\gamma}}g(z), \eqno{(*)} that we can realize also as the null space of the differential operator $\sum\limits_{j=1}\limits^n(\frac{-\partial^2}{\partial z_j\partial \bar z_j} + \nu \bar z_j \frac{\partial}{\partial \bar z_j})$ acting on $\mathcal C^\infty$ functions on \C^n satisfying $(*)$.Comment: 20 pages. Minor corrections. Scheduled to appear in issue 8 (2008) of "Journal of Mathematical Physics

Generalized modularity matrices

Various modularity matrices appeared in the recent literature on network analysis and algebraic graph theory. Their purpose is to allow writing as quadratic forms certain combinatorial functions appearing in the framework of graph clustering problems. In this paper we put in evidence certain common traits of various modularity matrices and shed light on their spectral properties that are at the basis of various theoretical results and practical spectral-type algorithms for community detection

Detecting and diagnosing faults in dynamic stochastic distributions using a rational b-splines approximation to output PDFs

Describes the process of detecting and diagnosing faults in dynamic stochastic distributions using a rational b-splines approximation to output PDFs

Polynomial Solutions of Shcrodinger Equation with the Generalized Woods Saxon Potential

The bound state energy eigenvalues and the corresponding eigenfunctions of the generalized Woods Saxon potential are obtained in terms of the Jacobi polynomials. Nikiforov Uvarov method is used in the calculations. It is shown that the results are in a good agreement with the ones obtained before.Comment: 14 pages, 2 figures, submitted to Physical Review

Crystal structure of mixed fluorites Ca(1-x)Sr(x)F(2) and Sr(1-x)Ba(x)F(2) and luminescence of Eu(2+) in the crystals

Within the framework of the virtual crystal method implemented in the shell model and pair potential approximation the crystal structure of mixed fluorites Ca(1-x)Sr(x)F(2) and Sr(1-x)Ba(x)F(2) has been calculated. The impurity center Eu(2+) and the distance Eu(2+)-F in this crystals have been also calculated. The low level position of excited 4f65d configuration of the Eu(2+) ion has been expressed using phenomenological dependence on distance E(2+)-F. The dependences of Stokes shift and Huang-Rhys factor on concentration x have been received for yellow luminescence in Sr(1-x)Ba(x)F(2):Eu(2+). The value x, for which the eg -level of Eu(2+) ion will be in conduction band in Sr(1-x)Ba(x)F(2):Eu(2+) has been calculated.Comment: 8 pages, 3 figures. The manuscript is sent to journal 'Physics of the solid state'. The results will be submitted on inernational conference SCINTMAT'2002 in oral session (june,20-22,2002,Ekaterinburg,Russia). Corresponding author e-mail: [email protected]