Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 2 of 2
Full-Text Articles in Physics
Disk-Shaped Bose-Einstein Condensates In The Presence Of An Harmonic Trap And An Optical Lattice, Todd Kapitula, Panayotis G. Kevrekidis, D. J. Frantzeskakis
Disk-Shaped Bose-Einstein Condensates In The Presence Of An Harmonic Trap And An Optical Lattice, Todd Kapitula, Panayotis G. Kevrekidis, D. J. Frantzeskakis
University Faculty Publications and Creative Works
We study the existence and stability of solutions of the two-dimensional nonlinear Schrödinger equation in the combined presence of a parabolic and a periodic potential. The motivating physical example consists of Bose-Einstein condensates confined in an harmonic (e.g., magnetic) trap and an optical lattice. By connecting the nonlinear problem with the underlying linear spectrum, we examine the bifurcation of nonlinear modes out of the linear ones for both focusing and defocusing nonlinearities. In particular, we find real-valued solutions (such as multipoles) and complex-valued ones (such as vortices). A primary motivation of the present work is to develop "rules of thumb" …
Mcplib: A Collection Of Nonlinear Mixed Complementarity Problems, Steven P. Dirkse, Michael C. Ferris
Mcplib: A Collection Of Nonlinear Mixed Complementarity Problems, Steven P. Dirkse, Michael C. Ferris
University Faculty Publications and Creative Works
The origins and some motivational details of a collection of nonlinear mixed complementarity problems are given. This collection serves two purposes. Firstly, it gives a uniform basis for testing currently available and new algorithms for mixed complementarity problems. Function and Jacobian evaluations for the resulting problems are provided via a GAMS interface, making thorough testing of algorithms on practical complementarity problems possible. Secondly, it gives examples of how to formulate many popular problem formats as mixed complementarity problems and how to describe the resulting problems in GAMS format. We demonstrate the ease and power of formulating practical models in the …