arXiv subjects

Michael A. Morgan

Publications and source records attributed to Michael A. Morgan.

3 recordsLinked to original sources

arXiv2025

Hyperbolic free-surface jets

If a body of inviscid fluid is disturbed, it will typically eject a jet of fluid. If the effects of gravity and surface tension are negligible, these jets travel in straight lines, with the tips approaching a constant velocity. It has been observed that these jets can have a broad base, tapering progressively toward the tip, but the mathematical form of their profile has not been successfully analysed in earlier works. In this paper, we describe the simplest case, in two dimensions: an infinitely deep body of inviscid fluid, with no surface tension or gravitational forces acting, responds to an impulsive disturbance. We find that, contrary to some earlier suggestions, the jet has a hyperbolic profile (away from its tip and its base).

physics.flu-dyn↗

arXiv2022

Velocity Gauge Potentials in Electrodynamics

Vector and scalar potentials are used for convenience in solving boundary value problems involving electromagnetic (EM) fields. The potentials are made unique by choosing a non-unique gauge relationship. The most commonly used gauges are those named for Lorenz and Coulomb, both of which may be defined as special cases of what is termed the velocity gauge, or v-gauge. This generalized gauge is not usually taught to students of electrodynamics. In this paper, we review properties of the velocity gauge, including EM field invariance, and demonstrate its application via an example.

physics.class-ph↗

arXiv1999

Non-adiabatic transitions in multi-level systems

In a quantum system with a smoothly and slowly varying Hamiltonian, which approaches a constant operator at times $t\to \pm \infty$, the transition probabilities between adiabatic states are exponentially small. They are characterized by an exponent that depends on a phase integral along a path around a set of branch points connecting the energy level surfaces in complex time. Only certain sequences of branch points contribute. We propose that these sequences are determined by a topological rule involving the Stokes lines attached to the branch points. Our hypothesis is supported by theoretical arguments and results of numerical experiments.

quant-ph↗