Patterns in Wigner-Weyl approach

We present a family of methods, which can describe behaviour of quantum ensembles and demonstrate the creation of nontrivial (meta) stable states (patterns), localized, chaotic, entangled or decoherent from basic localized modes in collective models arising from the quantum hierarchy of Wigner-von Neumann-Moyal equations.Comment: LaTeX2e, w-art.cls, w-thm.sty, w-pamm.clo, 3 pages, 2 figures, presented at GAMM Meeting, 2006, Berlin, German

Fusion modeling in plasma physics: Vlasov-like systems

The methods developed by authors are applied to some reductions of BBGKY hierarchy, namely, various examples of Vlasov-like systems which are important both for fusion modeling and for particular physical problems related to plasma/beam physics. We mostly concentrate on phenomena of localization and pattern formation.Comment: LaTeX2e, w-art.cls, w-thm.sty, w-pamm.clo, 3 pages, 2 figures, presented at GAMM Meeting, 2006, Berlin, German

Classical and Quantum Ensembles via Multiresolution. I. BBGKY Hierarchy

A fast and efficient numerical-analytical approach is proposed for modeling complex behaviour in the BBGKY hierarchy of kinetic equations. We construct the multiscale representation for hierarchy of reduced distribution functions in the variational approach and multiresolution decomposition in polynomial tensor algebras of high-localized states. 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: 5 pages, 3 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

A Pulsar Time Scale Based on Parkes Observations in 1995--2010

Timing of highly stable millisecond pulsars provides the possibility of independently verifying terrestrial time scales on intervals longer than a year. An ensemble pulsar time scale is constructed based on pulsar timing data obtained on the 64-m Parkes telescope (Australia) in 1995--2010. Optimal Wiener filters were applied to enhance the accuracy of the ensemble time scale. The run of the time--scale difference PT$_{ens}$ $-$ TT(BIPM2011) does not exceed $0.8 {\pm} 0.4$ $\mu s$ over the entire studied time interval. The fractional instability of the difference $_{ens}$ $-$ TT(BIPM2011) over 15 years is ${\sigma_z} = (0.6\pm 1.6){\cdot}10^{-15}$, which corresponds to an upper limit for the energy density of the gravitational--wave background ${\Omega_g}h^2 {\sim} 10^{-10}$ and variations in the gravitational potential ${\sim} 10^{-15}$ Hz at the frequency $2{\cdot}10^{-9}$.Comment: 11 pages, 2 figure

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

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

Quantum points/patterns, Part 1. From geometrical points to quantum points in a sheaf framework

We consider some generalization of the theory of quantum states, which is based on the analysis of long standing problems and unsatisfactory situation with the possible interpretations of quantum mechanics. We demonstrate that the consideration of quantum states as sheaves can provide, in principle, more deep understanding of some phenomena. The key ingredients of the proposed construction are the families of sections of sheaves with values in the category of the functional realizations of infinite-dimensional Hilbert spaces with special (multiscale) filtration. Three different symmetries, kinematical (on space-time), hidden/dynamical (on sections of sheaves), unified (on filtration of the full scale of spaces) are generic objects generating the full zoo of quantum phenomena (e.g., faster than light propagation).Comment: 10 pages, LaTeX, spie.cls, Submitted to Proc. of SPIE Meeting, The Nature of Light: What are Photons? IV, San Diego, CA, August, 201