We show that the one-loop Euler-Heisenberg QED effective Lagrangian in a constant background field acquires a very different non-perturbative trans-series structure at two-loop and higher-loop order in the fine structure constant. Beyond one-loop, virtual particles interact, causing fluctuations about the instantons, whereby the simple poles of the one-loop Borel transform become branch points. We illustrate this in detail at two-loop order using Ritus's seminal result for the renormalized two-loop effective Lagrangian as an exact double-integral representation, and propose a possible new approach to computations at higher loop order. Our methods yield remarkably accurate extrapolations from weak-field to strong-field, and from magnetic to electric background field, at both one-loop and two-loop order, based on surprisingly little perturbative input.
This paper reports a preliminary study of a method for combined underwater communication and navigation of underwater vehicles (cooperative navigation) equipped with an acoustic modem, attitude, and depth sensors, but lacking a Doppler velocity log (DVL), and a surface vehicle equipped with an acoustic modem and GPS. Few previously reported studies have utilized acoustic range rate in addition to acoustic range for the general navigation of underwater vehicles. This paper reports an observation model for range-rate measurements and preliminary anecdotal simulation studies for cooperative navigation of one underwater vehicle client with one surface vehicle server employing both range and rangerate observations to estimate the vehicle states with a delayedstate extended Kalman filter in the absence of DVL velocity observations. The preliminary studies suggest that the addition of range-rate measurements may offer advantages over the case of range-only observations in a limited set of circumstances, such as poor range-observation accuracy. The present study is preliminary, however, and directions for future study are suggested.
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