14 research outputs found

    The reflection of very cold neutrons from diamond powder nanoparticles

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    We study possibility of efficient reflection of very cold neutrons (VCN) from powders of nanoparticles. In particular, we measured the scattering of VCN at a powder of diamond nanoparticles as a function of powder sample thickness, neutron velocity and scattering angle. We observed extremely intense scattering of VCN even off thin powder samples. This agrees qualitatively with the model of independent nanoparticles at rest. We show that this intense scattering would allow us to use nanoparticle powders very efficiently as the very first reflectors for neutrons with energies within a complete VCN range up to 10−410^{-4} eV

    On the integrability of symplectic Monge-Amp\'ere equations

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    Let u be a function of n independent variables x^1, ..., x^n, and U=(u_{ij}) the Hessian matrix of u. The symplectic Monge-Ampere equation is defined as a linear relation among all possible minors of U. Particular examples include the equation det U=1 governing improper affine spheres and the so-called heavenly equation, u_{13}u_{24}-u_{23}u_{14}=1, describing self-dual Ricci-flat 4-manifolds. In this paper we classify integrable symplectic Monge-Ampere equations in four dimensions (for n=3 the integrability of such equations is known to be equivalent to their linearisability). This problem can be reformulated geometrically as the classification of 'maximally singular' hyperplane sections of the Plucker embedding of the Lagrangian Grassmannian. We formulate a conjecture that any integrable equation of the form F(u_{ij})=0 in more than three dimensions is necessarily of the symplectic Monge-Ampere type.Comment: 20 pages; added more details of proof

    Exotic n-D'Alembert PDEs and stability

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    In the framework of the PDE's algebraic topology, previously introduced by A. Pr\'astaro, {\em exotic nn-d'Alembert PDE's} are considered. These are nn-d'Alembert PDE's, (d′A)n(d'A)_n, admitting Cauchy manifolds N⊂(d′A)nN\subset (d'A)_n identifiable with exotic spheres, or such that ∂N\partial N, can be exotic spheres. For such equations local and global existence theorems and stability theorems are obtained
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