Chemical Principle and PDE of variational electrodynamics

[摘要] The two-body problem of variational electrodynamics possesses differential-delay equations of motion with state-dependent delays of neutral type and solutions that can have velocity discontinuities on countable sets. From a periodic orbit possessing some mild properties at breaking points, we define a synchronization function in R x R-3, which is further used to construct two bounded oscillatory functions vanishing at breaking points and whose first derivatives are continuous and defined everywhere but at breaking points. The oscillatory functions are associated with a natural PDE identity in W-2,W-2 (R-3). We postulate an asymptotic ordering for a generalized PDE identity, which defines a Fredholm-Schroedinger operator in W-2,W-2 (R-3) with a forcing term belonging to {L-2(R-3) boolean AND O( 1/r(2))}. As an application, we introduce the Chemical Principle criterion to select orbits with asymptotically vanishing far-fields and estimate the Bohr radius parameter of the Fredholm-Schroedinger PDE using the boundary-layers of orbits chosen according to the Chemical Principle criterion. Last, working backward, we derive an orbital property of the Chemical Principle type from the ordering conditions. (C) 2019 Elsevier Inc. All rights reserved.

[发布日期] 2019-12-15

[关键词] Variational electrodynamics;Functional analysis;Neutral differential-delay equations;State-dependent delay