New Horizons

Any people interested by sparse matrix algorithms should know the University of Florida sparse matrix collection and, by the way, Tim Davis . If you don't, please spend some time using the above links, it really worth it ! It collects many different kind of matrices, real, hermitian, symmetric, unsymmetric, rectangular, etc, etc. Moreover you have a nice colored view of each matrices obtained by spectral mapping and colouring. Could you guess for which kind of problem each of the matrices below arised ?

Beautiful movie of Venus passing in front of the Sun at various optical wavelengths. May be you know that observing at a given wavelength is like watching the Sun at a given depth. Not just optical depth, but it's really like seeing inside the Sun peeled.  A must watch ! I love gamma rays, uhhh. Source APOD

For our greatest delight (at least mine), Andrew Lipson is a crazy guy. He's building many funny things in Lego. Like topological surfaces, Klein bottle, from the in/out-side ! Escher pictures, waterfall Or scultpures, like Rodin's thinker However, lego construction may be a way to counter-act the financial crisis which has the inconvenient to cut funding in research laboratory. For instance, Daniel strange (I don't invent anything !) built and programmed a crane that moves in a set path, raising and lowering the sample between beakers containing solutions using a Lego Mindstorms NXT kit. Neat.

You can get very interesting result when plotting different linear combination of eigenfunctions of the Laplacian on a given (convex) shape. Here I use a square plate [0,1] by [0,1] and show the zero iso-value of the some of such linear combination. As time evolves, the linear combination changes. Since the Eigenfunctions are symmetric, I only plot them on the [0, 0.5] interval.  In that case, the eigenfunction are of the form With (n1,n2) such that The associated eigenvalue l= 340*pi^2 is of multiplicity 4 (12,14) (18,4) (14,12) (4,18). Below, same thing with l = 5525 which is of multiplicity 12. Those isocontours are called nodal lines. By the unique continuation property, those nodal lives consist of curves in the interior of the domain (her a square, but the result is valid for any convex shape) which are infinetly differentiable. You may also note, but that is a well known theorem, that when nodal lines interesect a boundary (except may be at corner points...

Yesterday evening, too bored by what TV was proposing to me, I decided to watch a conference of Mathias Fink , a french researcher working on multidisciplinary application of waves. Specially shear waves.  Here is a brief summary of his talk. In solids, waves have two principal components:  compression waves (P-waves for primary) moving in the direction of propagation, and shear waves (S-waves, for secondary) that make ripples in the plane orthogonal to that direction. Since compression waves propagate in the direction of propagation, they move faster than shear waves. Usually ultrasound equipment in medicine only use compressional waves. But since human tissues have a high bulk modulus, the P-wave speed is relatively constant (around 1580 m/s). Human tissues are very stiff if you apply isotropic constraints on them (like pressure of water). However M. Fink and his colleagues proposed a new way to investigate human tissues by first sending a strong compressional wave in ...

As usual, I started this morning by browsing arxiv, watching for article that would potentially have the ability to wake me up from my sleepiness. And I found 'Asymptotic rate of quantum ergodicity inchaotic Euclidean billiards'   with the following picture that shocked me. This image results from tracing cumulative plane wave with random orientation, but same wave-number on a square domain and I found strinking how similar to simulation s in cosmology it was. The second image result from simualtion and we see density fluctuation of a simulated universe. The filaments represent families of galaxies, and black zone, the emptiness of space.