Triple-coalescence singularity in a dynamical atomic process

Design of a Triple Singularity Drive for Mobile Wheeled

This thesis encompasses the development of a mobile robotic platform using three singularity drive modules. The process begins with a review of other omnidirectional platforms, comparing and contrasting their strengths and weaknesses. It continues with a discussion of the mechanical and electrical design of a robot prototype, then into kinematic modeling of the system. Both the inverse and forw...

2+1 Black Hole with a Dynamical Conical Singularity

We find black hole solutions to Euclidean 2+1 gravity coupled to a relativistic particle which have a dynamical conical singularity at the horizon. These solutions violate the standard area law for black hole entropy, their entropy being proportional to the total opening angle. Since each solution depends on the number of windings of the particle path around the horizon, the significance of the...

Close encounters: The influence of electron coalescence on atomic wavefunctions

Expected Coalescence Time for a Nonuniform Allocation Process

We study a process where balls are repeatedly thrown into n boxes independently according to some probability distribution p. We start with n balls, and at each step all balls landing in the same box are fused into a single ball; the process terminates when there is only one ball left (coalescence). Let c := P j p 2 j , the collision probability of two fixed balls. We show that the expected coa...

On a coalescence process and its branching genealogy

We define and analyze a coalescent process as a recursive boxfilling process whose genealogy is given by an ancestral time-reversed, timeinhomogeneous Bienyamé-Galton-Watson process. Special interest is on the expected size of a typical box and its probability of being empty. Special cases leading to exact asymptotic computations are investigated when the coalescing mechanisms are either linear...