Commencing with a brief survey of Lie-group theory and diierential equations evolving on Lie groups, we describe a number of numerical algorithms designed to respect Lie-group structure: Runge{Kutta{Munthe-Kaas schemes, Fer and Magnus expansions. This is followed by complexity analysis of Fer and Magnus expansions, whose conclusion is that for order four, six and eight an appropriately discreti...

We present a new derivation of the Berry phase picked up during exchange of parallel vortices. This derivation is based on the Bogolubov de Gennes formalism. The origin of the Magnus force is also critically reanalised. The Magnus force can be interpreted as interaction with effective magnetic field. The efective magnetic field may be even of the order 10T/Å. We discuss a possibility of the FQH...

We use Magnus methods to compute the Evans function for spectral problems as arise when determining the linear stability of travelling wave solutions to reactiondiffusion and related partial differential equations. In a typical application scenario, we need to repeatedly sample the solution to a system of linear non-autonomous ordinary differential equations for different values of one or more ...

We present new identities for determinants of matrices (A i,j) with entries A i,j equal to a i,j or a i,0 a 0,j − a i,j , where the a i,j 's are indeterminates. We show that these identities are behind trace identities for SL(2, C) matrices found earlier by Magnus in his study of trace algebras. 1. Introduction. In this paper we derive an infinite family of new trace identities for 2 × 2 matric...

As part of a general study of the interaction between gases and solids in the laboratory of Alfred Magnus (Fig. 1) at the University of Frankfurt, Magnus and Grähling (2) reported the adsorption of ozone on silica gel in 1929. These measurements were complicated by the thermal instability of ozone, which, as shown by Magnus and Grähling, was further catalyzed by silica gel. A second problem was...

The mapping class group of a surface with one boundary component admits numerous interesting representations including as a group of automorphisms of a free group and as a group of symplectic transformations. Insofar as the mapping class group can be identified with the fundamental group of Riemann’s moduli space, it is furthermore identified with a subgroup of the fundamental path groupoid upo...

Momentum production during the phase slip process in SNS Joseph-son junction is discussed. It is caused by the spectral flow of bound states of fermions localized within the junction. This effectively reduces the Magnus force acting on vortices which provides an explanation for the experimental observation of the negligible Magnus force in 2D Josephson junction arrays. The flow of the fermionic...