RMS/Rate Dynamics via Localized Modes

We consider some reduction from nonlinear Vlasov-Maxwell equation to rms/rate equations for second moments related quantities. Our analysis is based on variational wavelet approach to rational (in dynamical variables) approximation. It allows to control contribution from each scale of underlying multiscales and represent solutions via multiscale exact nonlinear eigenmodes (waveletons) expansions. Our approach provides the possibility to work with well-localized bases in phase space and best convergence properties of the corresponding expansions without perturbations or/and linearization procedures.Comment: 4 pages, 2 figures, JAC2001.cls, presented at European Particle Accelerator Conference (EPAC02), Paris, June 3-7, 2002; changed from A4 to US format for correct printin

Classical and Quantum Ensembles via Multiresolution. II. Wigner Ensembles

We present the application of the variational-wavelet analysis to the analysis of quantum ensembles in Wigner framework. (Naive) deformation quantization, the multiresolution representations and the variational approach are the key points. We construct the solutions of Wigner-like equations via the multiscale expansions in the generalized coherent states or high-localized nonlinear eigenmodes in the base of the compactly supported wavelets and the wavelet packets. We demonstrate the appearance of (stable) localized patterns (waveletons) and consider entanglement and decoherence as possible applications.Comment: 5 pages, 2 figures, espcrc2.sty, Presented at IX International Workshop on Advanced Computing and Analysis Techniques in Physics Research, Section III "Simulations and Computations in Theoretical Physics and Phenomenology", ACAT 2003, December, 2003, KEK, Tsukub

BBGKY Dynamics: from Localization to Pattern Formation

A fast and efficient numerical-analytical approach is proposed for modeling complex behaviour in the BBGKY--hierarchy of kinetic equations. Our calculations are based on variational and multiresolution approaches in the basis of polynomial tensor algebras of generalized coherent states/wavelets. We construct the representation for hierarchy of reduced distribution functions via the multiscale decomposition in highly-localized eigenmodes. Numerical modeling shows the creation of various internal structures from localized modes, which are related to localized or chaotic type of behaviour and the corresponding patterns (waveletons) formation. The localized pattern is a model for energy confinement state (fusion) in plasma.Comment: 14 pages, 3 figures, ws-procs9x6.cls, presented at Workshop "Progress in Nonequilibrium Greens Functions", Dresden, Germany, August 19-23, 200

Pattern Formation in Wigner-like Equations via Multiresolution

We present the application of the variational-wavelet analysis to the quasiclassical calculations of the solutions of Wigner/von Neumann/Moyal and related equations corresponding to the nonlinear (polynomial) dynamical problems. (Naive) deformation quantization, the multiresolution representations and the variational approach are the key points. We construct the solutions via the multiscale expansions in the generalized coherent states or high-localized nonlinear eigenmodes in the base of the compactly supported wavelets and the wavelet packets. We demonstrate the appearance of (stable) localized patterns (waveletons) and consider entanglement and decoherence as possible applications.Comment: 15 pages, 6 figures, ws-procs9x6.cls, Presented at Joint 28th ICFA Advanced Beam Dynamics & Advanced & Novel Accelerators Workshop on Quantum Aspects of Beam Physics and Other Critical Issues of Beams in Physics and Astrophysics, January 7-11, 2003, Hiroshima University, Higashi-Hiroshima, Japa

Space-Charge Dominated Beam Transport via Multiresolution

We consider space-charge dominated beam transport systems, where space-charge forces are the same order as external focusing forces and dynamics of the corresponding emittance growth. We consider the coherent modes of oscillations and coherent instabilities both in the different nonlinear envelope models and in initial collective dynamics picture described by Vlasov system. Our calculations are based on variation approach and multiresolution in the base of high-localized generalized coherent states/wavelets. We control contributions to dynamical processes from underlying multiscales via nonlinear high-localized eigenmodes expansions in the base of compactly supported wavelet and wavelet packets bases.Comment: 3 pages, 3 figures, JAC2001.cls, submitted to Proc. Particle Accelerator Conference (PAC 2001), Chicago, June 18-22, 200