168 research outputs found
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
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
Nonlinear Dynamics of Accelerator via Wavelet Approach
In this paper we present the applications of methods from wavelet analysis to
polynomial approximations for a number of accelerator physics problems. In the
general case we have the solution as a multiresolution expansion in the base of
compactly supported wavelet basis. The solution is parametrized by the
solutions of two reduced algebraical problems, one is nonlinear and the second
is some linear problem, which is obtained from one of the next wavelet
constructions: Fast Wavelet Transform, Stationary Subdivision Schemes, the
method of Connection Coefficients. According to the orbit method and by using
construction from the geometric quantization theory we construct the symplectic
and Poisson structures associated with generalized wavelets by using
metaplectic structure. We consider wavelet approach to the calculations of
Melnikov functions in the theory of homoclinic chaos in perturbed Hamiltonian
systems and for parametrization of Arnold-Weinstein curves in Floer variational
approach.Comment: 16 pages, no figures, LaTeX2e, aipproc.sty, aipproc.cl
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
Localization and Coherent Structures in Wave Dynamics via Multiresolution
We apply variational-wavelet approach for constructing multiscale
high-localized eigenmodes expansions in different models of nonlinear waves. We
demonstrate appearance of coherent localized structures and stable pattern
formation in different collective dynamics models.Comment: 3 pages, 2 figures, presented at GAMM Meeting, February, 2001, ETH,
Zurich; changed margins for printin
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