Publication Date
2003
Journal or Book Title
Physics Review E
Abstract
We demonstrate a systematic implementation of coupling between a scalar field and the geometry of the space which carries the field. This naturally gives rise to a feedback mechanism between the field and the geometry. We develop a systematic model for the feedback in a general form, inspired by a specific implementation in the context of molecular dynamics (the so-called Rahman-Parrinello molecular dynamics, or RP-MD). We use a generalized Lagrangian that allows for the coupling of the space’s metric tensor to the scalar field, and add terms motivated by RP-MD. We present two implementations of the scheme: one in which the metric is only time-dependent (which gives rise to an ordinary differential equation for its temporal evolution), and the other with spatiotemporal dependence (wherein the metric’s evolution is governed by a partial differential equation). Numerical results are reported for the (1+1)-dimensional model with a nonlinearity of the sine-Gordon type.
Volume
67
Issue
4
Recommended Citation
Kevrekidis, PG and Williams, F L., "Coupling fields and underlying space curvature: An augmented Lagrangian approach" (2003). Physics Review E. 1109.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/1109
Comments
This is the pre-published version harvested from arXiv. The published version is located at http://pre.aps.org/abstract/PRE/v67/i4/e047602