Experimental Investigation and Method of Mathematical Modeling of Electrostatic Discharges

The danger of discharges on dielectric materials in a space environment is usually estimated by testing samples in vacuum installations. It has been deduced from experiments that a correspondence of order is between the topology of the discharges and the group of pulse invariants in the grounded circuit of the sample substrate. These mathematical properties determine a model of discharge by the symplectic product of a logical tensor of an embedded topomorphic discharge structure by the algebraic tensor of a pulse group from the parametric series. The general group of numbers with a transfinite extension of tensor indexes in the discharge model connects three classes of mathematical objects: topology of connections, algebra of properties, and numbers of their common order. This extension of property variety in general mathematics was forecast by Poincare. The model of discharge is defined on a hyperplane embedded into a space of complex variables with an extension of polysheet Riemann's surface over the group of sliding that is determined by the Clifford virtual quantifier delta = root 0 with the argument of the circumferential group. The analytical function of the model on the hyperplane extends over basis parameters of symplectic generalized functions into a series of wavelet pulses and harmonics. Therefore, the complicated pulse is identified by parametric groups of the previous expansions. This is a clef to the identification of discharges and creating the generalized database of tests for materials.