Multiscale Computation with Interpolating Wavelets

Multiresolution analyses based upon interpolets, interpolating scaling functions introduced by Deslauriers and Dubuc, are particularly well-suited to physical applications because they allow exact recovery of the multiresolution representation of a function from its sample values on a finite set of points in space. We present a detailed study of the application of wavelet concepts to physical problems expressed in such bases. The manuscript describes algorithms for the associated transforms which, for properly constructed grids of variable resolution, compute correctly without having to introduce extra grid points. We demonstrate that for the application of local homogeneous operators in such bases, the non-standard multiply of Beylkin, Coifman and Rokhlin also proceeds exactly for inhomogeneous grids of appropriate form. To obtain less stringent conditions on the grids, we generalize the non-standard multiply so that communication may proceed between non-adjacent levels. The manuscript concludes with timing comparisons against naive algorithms and an illustration of the scale-independence of the convergence rate of the conjugate gradient solution of Poisson's equation using a simple preconditioning, suggesting that this approach leads to an O(n) solution of this equation.Comment: 33 pages, figures available at http://laisla.mit.edu/muchomas/Papers/nonstand-figs.ps . Updated: (1) figures file (figs.ps) now appear with the posting on the server; (2) references got lost in the last submissio

An adaptive numerical method for the Vlasov equation based on a multiresolution analysis.

International audienceIn this paper, we present very first results for the adaptive solution on a grid of the phase space of the Vlasov equation arising in particles accelarator and plasma physics. The numerical algorithm is based on a semi-Lagrangian method while adaptivity is obtained using multiresolution analysis

Defect production in silica fibers doped with Tm³⁺

Irradiation of Tm3+ fibers with blue light at 476 nm induces a broad-bandwidth loss in these fibers. We have measured the spectral dependence of the loss for both silica-germania and silica-alumina fibers and show through micro-Raman studies of the core regions of the fibers that this induced loss is correlated with the production of structural defects in the glass host

Multiresolution analysis of electronic structure: semicardinal and wavelet bases

This article reviews recent developments in multiresolution analysis which make it a powerful tool for the systematic treatment of the multiple length-scales inherent in the electronic structure of matter. Although the article focuses on electronic structure, the advances described are useful for non-linear problems in the physical sciences in general. The new language and notations introduced are well- suited for both formal manipulations and the development of computer software using higher-level languages such as C++. The discussion is self-contained, and all needed algorithms are specified explicitly in terms of simple operators and illustrated with straightforward diagrams which show the flow of data. Among the reviewed developments is the construction of_exact_ multiresolution representations from extremely limited samples of physical fields in real space. This new and profound result is the critical advance in finally allowing systematic, all electron calculations to compete in efficiency with state-of-the-art electronic structure calculations which depend for their celerity upon freezing the core electronic degrees of freedom. This review presents the theory of wavelets from a physical perspective, provides a unified and self-contained treatment of non-linear couplings and physical operators and introduces a modern framework for effective single-particle theories of quantum mechanics.Comment: A "how-to from-scratch" book presently in press at Reviews of Modern Physics: 88 pages, 31 figures, 5 tables, 88 references. Significantly IMPROVED version, including (a) new diagrams illustrating algorithms; (b) careful proof-reading of equations and text; (c) expanded bibliography; (d) cosmetic changes including lists of figures and tables and a more reasonable font. Latest changes (Dec. 11, 1998): a more descriptive abstract, and minor lexicographical change

Ordered helium trapping and bonding in compressed arsenolite: Synthesis of As4O6 2He

Compression of arsenolite has been studied from a joint experimental and theoretical point of view. Experiments on this molecular solid at high pressures with different pressure-transmitting media have been interpreted thanks to state-of-the-art ab initio calculations. Our results confirm arsenolite as one of the most compressible minerals and provide evidence for ordered helium trapping above 3 GPa between adamantane-type As4O6 cages. Our calculations indicate that, at relatively small pressures, helium establishes rather localized structural bonds with arsenic forming a compound with stoichiometry As4O6 center dot 2He. All properties of As4O6 center dot 2He are different from those of parent As4O6. In particular, pressure-induced amorphization, which occurs in arsenolite above 15 GPa, is impeded in As4O6 center dot 2He, thus resulting in a mechanical stability of As4O6 center dot 2He beyond 30 GPa. Our work paves the way to explore the formation of alternative compounds by pressure-induced trapping and reaction of gases, small atomic or molecular species, in the voids of molecular solids containing active lone electron pairs.We acknowledge financial support from the Spanish Consolider Ingenio 2010 Program (Project No. MAT2015-71070-REDC). The work was also supported by Spanish MINECO under Projects No. MAT2014-46649-C4-1/2/3-P and from Vicerrectorado de Investigacion de la Universitat Politecnica de Valencia under Projects No. SP20140701 and No. SP20140871. Supercomputer time has been provided by the Red Espanola de Supercomputacion (RES) and the MALTA cluster. J.A.S. acknowledges Juan de la Cierva fellowship program for his financial support. A.M. and P.R.-H. acknowledge S. Munoz Rodriguez for providing them with a data parsing application. A.L.J.P. acknowledges financial support through Brazilian CNPq (Project No. 201050/2012-9).Sans Tresserras, JÁ.; Manjón Herrera, FJ.; Popescu, C.; Cuenca Gotor, VP.; Gomis, O.; Muñoz, A.; Rodríguez Hernández, P.... (2016). Ordered helium trapping and bonding in compressed arsenolite: Synthesis of As4O6 2He. Physical review B: Condensed matter and materials physics. 93(5):054102 - 1-054102 - 5. https://doi.org/10.1103/PhysRevB.93.054102S054102 - 1054102 - 593