Localization and pattern formation in Wigner representation via multiresolution

We present an application of variational-wavelet analysis to quasiclassical calculations of solutions of Wigner equations related to nonlinear (polynomial) dynamical problems. (Naive) deformation quantization, multiresolution representations and variational approach are the key points. Numerical calculations demonstrates pattern formation from localized eigenmodes and transition from chaotic to localized (waveleton) types of behaviour.Comment: 3 pages, 3 figures, espcrc2.sty, Presented at VIII International Workshop on Advanced Computing and Analysis Techniques in Physics Research, Section III "Simulations and Computations in Theoretical Physics and Phenomenology", ACAT'2002, June 24-28, 2002, Mosco

Fast Calculations in Nonlinear Collective Models of Beam/Plasma Physics

We consider an application of variational-wavelet approach to nonlinear collective models of beam/plasma physics: Vlasov/Boltzmann-like reduction from general BBGKY hierachy. We obtain fast convergent multiresolution representations for solutions which allow to consider polynomial and rational type of nonlinearities. The solutions are represented via the multiscale decomposition in nonlinear high-localized eigenmodes (waveletons).Comment: 3 pages, 2 figures, espcrc2.sty, Presented at VIII International Workshop on Advanced Computing and Analysis Techniques in Physics Research, Section III "Simulations and Computations in Theoretical Physics and Phenomenology", ACAT'2002, June 24-28, 2002, Mosco

Measurement of the Charged Multiplicities in b, c and Light Quark Events from Z0 Decays

Average charged multiplicities have been measured separately in $b$, $c$ and light quark ($u,d,s$) events from $Z^0$ decays measured in the SLD experiment. Impact parameters of charged tracks were used to select enriched samples of $b$ and light quark events, and reconstructed charmed mesons were used to select $c$ quark events. We measured the charged multiplicities: $\bar{n}_{uds} = 20.21 \pm 0.10 (\rm{stat.})\pm 0.22(\rm{syst.})$, $\bar{n}_{c} = 21.28 \pm 0.46(\rm{stat.}) ^{+0.41}_{-0.36}(\rm{syst.})$ $\bar{n}_{b} = 23.14 \pm 0.10(\rm{stat.}) ^{+0.38}_{-0.37}(\rm{syst.})$, from which we derived the differences between the total average charged multiplicities of $c$ or $b$ quark events and light quark events: $\Delta \bar{n}_c = 1.07 \pm 0.47(\rm{stat.})^{+0.36}_{-0.30}(\rm{syst.})$ and $\Delta \bar{n}_b = 2.93 \pm 0.14(\rm{stat.})^{+0.30}_{-0.29}(\rm{syst.})$. We compared these measurements with those at lower center-of-mass energies and with perturbative QCD predictions. These combined results are in agreement with the QCD expectations and disfavor the hypothesis of flavor-independent fragmentation.Comment: 19 pages LaTex, 4 EPS figures, to appear in Physics Letters

Energy Minimization Problem And Routes To Chaos In Wavelet Approach

: The explicit time description of optimal dynamics for nonlinear differential systems of equations (energy minimization in high power electromechanical system) and computation of Melnikov functions for perturbed Hamiltonian systems are considered. The solution is presented as a multiresolution expansion from wavelet analysis and it is parametrized by solutions of two reduced algebraic problems. Keywords: Nonlinear control, Optimal control, Nonlinear dynamics. 1. INTRODUCTION The problem of energy minimization in electromechanical power systems is a long standing problem. The paper considers a synchronous electrical machine and a mill as load (in this approach one can consider any mechanical load with polynomial approximation for the mechanical moment instead of the mill). The problem of "electrical economizer" is presented as an optimal control problem. The result of the first stage is the explicit time description of the optimal dynamics for that electromechanical system, the result ..

Wavelet Approach to Nonlinear Problems, I. Polynomial Dynamics

this paper we consider the application of powerful methods of wavelet analysis to polynomial approximations of mechanical and physical problems such that accelerator physics problems, dynamics and optimal control problems, Galerkin approximations, routes to chaos in Hamiltonian systems [1]-[7]. The key point in the solution of these problems is the use of the methods of wavelet analysis, relatively novel set of mathematical methods, which gives us a possibility to work with well-localized bases in functional spaces and with the general type of operators (including pseudodifferential) in such bases. Our problem as many related problems in the framework of our type of approximations of complicated nonlinearities is reduced to the problem of the solving of the systems of differential equations with polynomial nonlinearities with or without some constraints. The first main part of our construction is some variational approach to this problem, which reduces initial problem to the problem of solution of functional equations at the first stage and some algebraical problems at the second stage. We consider also two cases of our general construction. In the first case (particular) we have for Riccati equations (particular quadratic approximations) the solution as a series on shifted Legendre polynomials, which is parameterized by the solution of reduced algebraical (also Riccati) system of equations [6]. In the second case (general polynomialsystem) we have the solution in a compactly supported wavelet basis. Multiresolution expansion is the second main part of our construction. The solution is parameterized by solutions of two reduced algebraical problems, one as in the first case and the second is some linear problem, which is obtained from one of the next wavelet construction..