14 research outputs found
The reflection of very cold neutrons from diamond powder nanoparticles
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
eV
On the integrability of symplectic Monge-Amp\'ere equations
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
Coherent scattering of slow neutrons at nanoparticles in particle physics experiments
International audienc
New methodical developments for GRANIT. Nouveaux développements méthodologiques pour GRANIT
International audienc
Exotic n-D'Alembert PDEs and stability
In the framework of the PDE's algebraic topology, previously introduced by A. Pr\'astaro, {\em exotic -d'Alembert PDE's} are considered. These are -d'Alembert PDE's, , admitting Cauchy manifolds identifiable with exotic spheres, or such that , can be exotic spheres. For such equations local and global existence theorems and stability theorems are obtained