Mathematics Colloquia and Seminars

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We will present highlights in ICF research involving wavelet methods. From numerical simulation techniques to experimental data analysis, wavelets are making an impact in ICF research. Whether it is (i) the characterization of the 3D surface roughness of ICF targets or the roughness of inner surfaces, or (ii) the implosion characteristics of highly nonlinear Rayleigh-Taylor instability degraded performance in 2D simulations, or those of smooth ripple free targets which ignite, (iii) whether it is double Z pinch Hohraums and their radiation symmetry from X ray backlit images, or (iv) the single wire or collective wire array behavior of nested wire array Z pinch shots, all the way to (v) denoising particle-in-cell (PIC) simulations using wavelet techniques, the unifying theme is multiresolution analysis, wavelets and curvelets in 1, 2 or 3 dimensional settings.

Multiscale or disparate scale phenomena which require simultaneous analysis, and not the averaging over of one (the fast scales) to have one way communication between scales (to the slow), is the mathematical setting of this work. The techniques include variational minimization over redundant libraries of functions including spherical harmonics and Legendre polynomials. Separation of features with different smoothness properties on different scales or different degrees of symmetry is our goal in many of these applications.

Many of these results should have applications in biological data analysis or molecular dynamics simulations or anywhere where adaptivity to disparate scales is advantageous.

Work supported by Sandia National Laboratories, General Atomics and DOE.