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

Microlensing effects and structure of gravitational lens systems

A study of gravitational microlensing of distant objects is presented. We performed simulations of light curves and trajectories of the image centroid of an extended source in the Chang–Refsdal lens with shear and continual dark matter. Various brightness distributions over the source (Gaussian, power-law, Shakura–Synyaev accretion disc) have been studied. We considered in detail approximate relations and corresponding algorithms used to fit observational data on high amplification events (HAE). The results are applied to interpretation of HAE observed by OGLE and GLITP groups. The source size and caustic crossing moment are estimated from these data, however, the determination of the brightness profile is statistically not reliable

Observation Of Very High Energy Cosmic-ray Families In Emulsion Chambers At High Mountain Altitudes (i)

Characteristics of cosmic-ray hadronic interactions in the 1015 - 1017 eV range are studied by observing a total of 429 cosmic-ray families of visible energy greater than 100 TeV found in emulsion chamber experiments at high mountain altitudes, Chacaltaya (5200 m above sea level) and the Pamirs (4300 m above sea level). Extensive comparisons were made with simulated families based on models so far proposed, concentrating on the relation between the observed family flux and the behaviour of high-energy showers in the families, hadronic and electromagnetic components. It is concluded that there must be global change in characteristics of hadronic interactions at around 1016 eV deviating from thise known in the accelerator energy range, specially in the forwardmost angular region of the collision. A detailed study of a new shower phenomenon of small-pT particle emissions, pT being of the order of 10 MeV/c, is carried out and its relation to the origin of huge "halo" phenomena associated with extremely high energy families is discussed as one of the possibilities. General characteristics of such super-families are surveyed. © 1992.3702365431Borisov, (1981) Nucl. Phys., 191 BBaybrina, (1984) Trudy FIAN 154, p. 1. , [in Russian], Nauka, MoscowLattes, Hadronic interactions of high energy cosmic-ray observed by emulsion chambers (1980) Physics Reports, 65, p. 151Hasegawa, ICR-Report-151-87-5 (1987) presented at FNAL CDF Seminar, , Inst. for Cosmic Ray Research, Univ. of TokyoCHACALTAYA Emulsion Chamber Experiment (1971) Progress of Theoretical Physics Supplement, 47, p. 1Yamashita, Ohsawa, Chinellato, (1984) Proc. 3rd Int. Symp. on Cosmic Rays and Particle Physics, p. 30. , Tokyo, 1984, Inst. for Cosmic Ray Research, Univ. of Tokyo(1984) Proc. 3rd Int. Symp. on Cosmic Rays and Particle Physics, p. 1. , Tokyo, 1984Baradzei, (1984) Proc. 3rd Int. Symp. on Cosmic Rays and Particle Physics, p. 136. , Tokyo, 1984Yamashita, (1985) J. Phys. Soc. Jpn., 54, p. 529Bolisov, (1984) Proc. 3rd Int. Symp. on Cosmic rays and Particle Physics, p. 248. , Tokyo, 1984, Inst. for Cosmic Ray Research, Univ. of TokyoTamada, Tomaszewski, (1988) Proc. 5th Int. Symp. on Very High Energy Cosmic-Ray Interactions, p. 324. , Lodz, 1988, Inst. for Cosmic Ray Research, Univ. of Tokyo, PolandHasegawa, (1989) ICR-Report-197-89-14, , Inst. for Cosmic Ray Research, Univ. of TokyoCHACALTAYA Emulsion Chamber Experiment (1971) Progress of Theoretical Physics Supplement, 47, p. 1Okamoto, Shibata, (1987) Nucl. Instrum. Methods, 257 A, p. 155Zhdanov, (1980) FIAN preprint no. 45, , Lebedev Physical Institute, MoscowSemba, Gross Features of Nuclear Interactions around 1015eV through Observation of Gamma Ray Families (1983) Progress of Theoretical Physics Supplement, 76, p. 111Nikolsky, (1975) Izv. Akad. Nauk. USSR Ser. Fis., 39, p. 1160Burner, Energy spectra of cosmic rays above 1 TeV per nucleon (1990) The Astrophysical Journal, 349, p. 25Takahashi, (1990) 6th Int. Symp. on Very High Energy Cosmic-ray Interactions, , Tarbes, FranceRen, (1988) Phys. Rev., 38 D, p. 1404Alner, The UA5 high energy simulation program (1987) Nuclear Physics B, 291 B, p. 445Bozzo, Measurement of the proton-antiproton total and elastic cross sections at the CERN SPS collider (1984) Physics Letters B, 147 B, p. 392Wrotniak, (1985) Proc. 19th Cosmic-Ray Conf. La Jolla, 1985, 6, p. 56. , NASA Conference Publication, Washington, D.CWrotniak, (1985) Proc. 19th Cosmic-Ray Conf. La Jolla, 1985, 6, p. 328. , NASA Conference Publication, Washington, D.CMukhamedshin, (1984) Trudy FIAN, 154, p. 142. , Nauka, Moscow, [in Russian]Dunaevsky, Pluta, Slavatinsky, (1988) Proc. 5th Int. Symp. on Very High Energy Cosmic-Ray Interactions, p. 143. , Lodz, 1988, Inst. of Physics, Univ. of Lodz, PolandKaidalov, Ter-Martirosyan, (1987) Proc. 20th Int. Cosmic-Ray Conf., Moscow, 1987, 5, p. 141. , Nauka, MoscowShabelsky, (1985) preprints LNPI-1113Shabelsky, (1986) preprints LNPI-1224, , Leningrad [in Russian]Hillas, (1979) Proc. 16th Int. Cosmic-Ray Conf., Kyoto, 6, p. 13. , Inst. for Cosmic Ray Research, Univ. of TokyoBorisov, (1987) Phys. Lett., 190 B, p. 226Hasegawa, Tamada, (1990) 6th Int. Symp. on Very High Energy Cosmic-Ray Interactions, , Tarbes, FranceSemba, Gross Features of Nuclear Interactions around 1015eV through Observation of Gamma Ray Families (1983) Progress of Theoretical Physics Supplement, p. 111Ren, (1988) Phys. Rev., 38 D, p. 1404Dynaevsky, Zimin, (1988) Proc. 5th Int. Symp. on Very High Energy Cosmic-Ray Interaction, p. 93. , Lodz, 1988, Inst. of Physics, Univ. of Lodz, PolandDynaevsky, (1990) Proc. 6th Int. Symp. on Very High Energy Cosmic-Ray Interactions, , Tarbes, France(1989) FIAN preprint no. 208, , Lebedev Physical Institute, Moscow(1990) Proc. 21st Int. Cosmic-Ray Conf., Adelaide, 8, p. 259. , Dept. Physics and Mathematical Physics, Univ. of Adelaide, AustraliaHasegawa, (1990) ICR-Report-216-90-9, , Inst. for Cosmic-Ray Research, Univ. of TokyoTamada, (1990) Proc. 21st Int. Cosmic-Ray Conf., Adelaide, 1990, 8. , Dept. Physics and Mathematical Physics, Univ. of Adelaide, AustraliaTamada, (1990) ICR-Report-216-90-9(1981) Proc. 17th Int. Cosmic-Ray Conf., Paris, 5, p. 291(1990) Proc. Int. Cosmic-Ray Conf., Adelaide, 1990, 8, p. 267. , Dept. Physics and Mathematical Physics, Univ. of Adelaide, Australia(1989) Inst. Nucl. Phys. 89-67/144, , preprint, Inst. Nucl. Phys., Moscow State UnivSmilnova, (1988) Proc. 5th Int. Sym. on Very High Energy Cosmic-Ray Interactions, p. 42. , Lodz, 1988, Inst. of Physics, Univ. of Lodz, PolandGoulianos, (1986) Proc. Workshop of Particle Simulation at High Energies, , University of Wisconsin, Madison, USAIvanenko, (1983) Proc. 18th Int. Cosmic-Ray Conf., Bangalore, 1983, 5, p. 274. , Tata Inst. Fundamental Research, Bombay, IndiaIvanenko, (1984) Proc. Int. Symp. on Cosmic-Rays and Particle Physics, p. 101. , Tokyo, 1984, Inst. for Cosmic Ray Research, Univ. of Tokyo(1988) 5th Int. Symp. on Very High Energy Cosmic-Ray Interactions, p. 180. , Lodz, 1988, Inst. of Physics, Univ. of Lodz, Poland(1990) Proc. 21st Int. Cosmic-Ray Conf., Adelaide, 1990, 8, p. 251. , Dept. Physics and Mathematical Physics, Univ. of Adelaide, Australia(1991) Izv. AN USSR No. 4, , to be publishedNikolsky, Shaulov, Cherdyntseva, (1990) FIAN preprint no. 140, , Lebedev Physical Institute, Moscow, [in Russian](1987) Proc. 20th Int. Cosmic-Ray Conf., Moscow, 1987, 5, p. 326. , Nauka, Mosco

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..

Wavelet Approach to Nonlinear Problems, IV. Routes to Chaos and Constrained Problems

'(x 5 ) x 4 = ex 3 \Gamma f[cos(rx 5 ) + cos(sx 6 )]x 3 \Gamma gx 3 3 \Gamma kx 2 1 x 3 \Gamma gx 4 \Gamma /(x 5 ) or in Hamiltonian form x = J \Delta rH(x)+ "g(x; \Theta); \Theta = !; (x; \Theta) 2 R 4 \Theta T 2 ; T 2 = S 1 \Theta S 1 . For " = 0 we have: x = J \Delta rH(x); \Theta = ! (1) 2. For pictures and details one

Wavelet Approach to Nonlinear Problems

We give via variational approach and multiresolution expansion in the base of compactly supported wavelets the explicit time description of four following problems: dynamics and optimal dynamics for some important electromechanical system, Galerkin approximation for beam equation, computations of Melnikov functions for perturbed Hamiltonian systems. We also consider wavelet parametrization in Floer variational approach for periodic loop solutions. We give the explicit time description of the following problems: dynamics and optimal dynamics for nonlinear dynamical systems, Galerkin approximations for some class of partial differential equations, computations of Melnikov functions for perturbed Hamiltonian systems. All these problems are 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 p..

Nonlinear Optimal Control Problem Via Wavelet Approach

We give wavelet description for nonlinear optimal dynamics (energy minimization in high power electromechanical system). We consider two cases of our general construction. In a particular case we have the solution as a series on shifted Legendre polynomials, which is parametrized by the solution of reduced algebraical system of equations. In the general case we have the solution as a multiresolution expansion from wavelet analysis. In this case the solution is parametrized by solutions of two reduced algebraic problems, one as in the first case 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. 1 Introduction The problem of energy minimization in electromechanical power systems is long standing problem [24]. In this paper we consider synchronous electrical machine and a mill as load (in this approach we can consider instead of a mill any mech..