Experimental Investigation and Method of Mathematical Modeling of Electrostatic Discharges

摘要

The danger of discharges on dielectric materials in a space environment is usually estimated by testing samples innvacuuminstallations. It has been deduced fromexperiments that a correspondence of order is between the topologynof the discharges and the group of pulse invariants in the grounded circuit of the sample substrate. Thesenmathematical properties determine amodel of discharge by the symplectic product of a logical tensor of an embeddedntopomorphic discharge structure by the algebraic tensor of a pulse group from the parametric series. The generalngroup of numbers with a transfinite extension of tensor indexes in the discharge model connects three classes ofnmathematical objects: topology of connections, algebra of properties, and numbers of their common order. Thisnextension of property variety in generalmathematicswas forecast by Poincaré.Themodel of discharge is defined on anhyperplane embedded into a space of complex variables with an extension of polysheet Riemann’s surface over thengroup of sliding that is determined by theClifford virtual quantifier u0001 u0001p0with the argument of the circumferentialngroup. The analytical function of the model on the hyperplane extends over basis parameters of symplecticngeneralized functions into a series of wavelet pulses and harmonics. Therefore, the complicated pulse is identified bynparametric groups of the previous expansions. This is a clef to the identification of discharges and creating thengeneralized database of tests for materials.