1,491 research outputs found

    Unidimensional model of the ad-atom diffusion on a substrate submitted to a standing acoustic wave II. Solutions of the ad-atom motion equation

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    The ad-atom dynamic equation, a Langevin type equation is analyzed and solved using some non-linear analytical and numerical tools. We noticeably show that the effect of the surface acoustic wave is to induce an effective potential that governs the diffusion of the ad-atom: the minima of this effective potential correspond to the preferential sites in which the ad-atom spends more time. The strength of this effective potential is compared to the destructuring role of the thermal diffusion and to the crystalline potential induced by the substrate

    On Frobenius structures in symmetric cones

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    We prove that in any strictly convex symmetric cone Ω\Omega there exists a non empty locus where the WDVV equation is satisfied (i.e. there exists a hyperplane being a Frobenius manifold). This result holds over any real division algebra (with a restriction to the rank 3 case if we consider the field O\mathbb{O}) but also on their linear combinations. This theorem holds as well in the case of pseudo-Riemannian geometry, in particular for a Lorentz symmetric cone of Anti-de-Sitter type. Our statement can be considered as a generalisation of a result by Ferapontov--Kruglikov--Novikov and Mokhov. Our construction is achieved by merging two different approaches: an algebraic/geometric one and the analytic approach given by Calabi in his investigations on the Monge--Amp\`ere equation for the case of affine hyperspheres

    Does cost reduction in Health Care ultimately value?

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