48 research outputs found
Localization and Pattern Formation in Quantum Physics. II. Waveletons in Quantum Ensembles
In this second part we present a set of methods, analytical and numerical,
which can describe behaviour in (non) equilibrium ensembles, both classical and
quantum, especially in the complex systems, where the standard approaches
cannot be applied. The key points demonstrating advantages of this approach
are: (i) effects of localization of possible quantum states; (ii) effects of
non-perturbative multiscales which cannot be calculated by means of
perturbation approaches; (iii) effects of formation of complex/collective
quantum patterns from localized modes and classification and possible control
of the full zoo of quantum states, including (meta) stable localized patterns
(waveletons). We demonstrate the appearance of nontrivial localized (meta)
stable states/patterns in a number of collective models covered by the
(quantum)/(master) hierarchy of Wigner-von Neumann-Moyal-Lindblad equations,
which are the result of ``wignerization'' procedure (Weyl-Wigner-Moyal
quantization) of classical BBGKY kinetic hierarchy, and present the explicit
constructions for exact analytical/numerical computations (fast convergent
variational-wavelet representation). Numerical modeling shows the creation of
different internal structures from localized modes, which are related to the
localized (meta) stable patterns (waveletons), entangled ensembles (with
subsequent decoherence) and/or chaotic-like type of behaviour.Comment: LaTeX2e, spie.cls, 13 pages, 6 figures, submitted to Proc. of SPIE
Meeting, The Nature of Light: What is a Photon? Optics & Photonics, SP200,
San Diego, CA, July-August, 200
Nonlinear Dynamics of High-Brightness Beams
The consideration of transverse dynamics of relativistic space-charge
dominated beams and halo growth due to bunch oscillations is based on
variational approach to rational (in dynamical variables) approximation for rms
envelope equations. It allows to control contribution from each scale of
underlying multiscales and represent solutions via exact nonlinear eigenmodes
expansions. Our approach is based on methods provided possibility to work with
well-localized bases in phase space and good convergence properties of the
corresponding expansions.Comment: 3 pages, 2 figures, JAC2001.cls, submitted to Proc. Particle
Accelerator Conference (PAC 2001), Chicago, June 18-22, 200
Variational-Wavelet Approach to RMS Envelope Equations
We present applications of variational-wavelet approach to nonlinear
(rational) rms envelope equations. We have the solution as a multiresolution
(multiscales) expansion in the base of compactly supported wavelet basis. We
give extension of our results to the cases of periodic beam motion and
arbitrary variable coefficients. Also we consider more flexible variational
method which is based on biorthogonal wavelet approach.Comment: 21 pages, 8 figures, LaTeX2e, presented at Second ICFA Advanced
Accelerator Workshop, UCLA, November, 199
Variational Approach in Wavelet Framework to Polynomial Approximations of Nonlinear Accelerator Problems
In this paper we present applications of methods from wavelet analysis to
polynomial approximations for a number of accelerator physics problems.
According to variational approach in the general case we have the solution as a
multiresolution (multiscales) expansion in the base of compactly supported
wavelet basis. We give extension of our results to the cases of periodic
orbital particle motion and arbitrary variable coefficients. Then we consider
more flexible variational method which is based on biorthogonal wavelet
approach. Also we consider different variational approach, which is applied to
each scale.Comment: LaTeX2e, aipproc.sty, 21 Page
Multiscale approaches for the failure analysis of fiber-reinforced composite structures using the 1D CUF
Composites provide significant advantages in performance, efficiency and costs; thanks to
these features, their application is increasing in many engineering fields, such as aerospace,
naval and mechanical engineering. Although the adoption of composites is rising, there
are still open issues to be investigated, in particular, understanding their failure mechanism has a prominent role in enhancing component designs. Numerous methodologies are available to compute
accurate stress/strain fields for laminated structures, multi-scale approaches are required
when micro- and macro-scales are accounted for. Despite the increasing development in
computer hardware, the computational effort of these methods is still prohibitive for extensive applications, especially when a high number of layers is considered. Then, the
reduction of the computational time and cost required to perform failure analysis is still
a challenging task.
This work proposes two multiscale approaches for the failure analysis of fiber-reinforced composites.
A concurrent multiscale approach ("Component-Wise") and a hierarchical method are developed based on the
1D Carrera Unified Formulation (CUF). 1D higher order elements are very powerful tools for multiscale analysis
since they provide accurate stress and strain fields with very low computational costs
A Review of Computational Methods in Materials Science: Examples from Shock-Wave and Polymer Physics
This review discusses several computational methods used on different length and time scales for the simulation of material behavior. First, the importance of physical modeling and its relation to computer simulation on multiscales is discussed. Then, computational methods used on different scales are shortly reviewed, before we focus on the molecular dynamics (MD) method. Here we survey in a tutorial-like fashion some key issues including several MD optimization techniques. Thereafter, computational examples for the capabilities of numerical simulations in materials research are discussed. We focus on recent results of shock wave simulations of a solid which are based on two different modeling approaches and we discuss their respective assets and drawbacks with a view to their application on multiscales. Then, the prospects of computer simulations on the molecular length scale using coarse-grained MD methods are covered by means of examples pertaining to complex topological polymer structures including star-polymers, biomacromolecules such as polyelectrolytes and polymers with intrinsic stiffness. This review ends by highlighting new emerging interdisciplinary applications of computational methods in the field of medical engineering where the application of concepts of polymer physics and of shock waves to biological systems holds a lot of promise for improving medical applications such as extracorporeal shock wave lithotripsy or tumor treatment