Browsing by Author "Nigam, Nilima"
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Item Connections for general group actions(2003-09) Lewis, Debra; Nigam, Nilima; Olver, Peter J.Partial connections are (singular) differential systems generalizing classical connections on principal bundles, yielding analogous decompositions for manifolds with nonfree group actions. Connection forms are interpreted as maps determining projections of the tangent bundle onto the partial connection; this approach eliminates many of the complications arising from the presence of isotropy. A connection form taking values in the dual of the Lie algebra is smooth even at singular points of the action, while analogs of the classical algebra-valued connection form are necessarily discontinuous at such points. The curvature of a partial connection form can be defined under mild technical hypotheses; the interpretation of curvature as a measure of the lack of involutivity of the (partial) connection carries over to this general setting.Item A geometric integration algorithm with applications to micromagnetics(2000-08) Lewis, Debra; Nigam, NilimaItem Invariant manifolds in a dynamical model for gene transcription(2002-09) Caberlin, Martin; Mackey, Michael; Nigam, NilimaWe present some recent results concerning stiffness in the Satillán-Mackey model of the tryptophan operon. In particular, we describe the existence of invariant manifolds in this system, and describe their biological significance.Item Problems in ultra-high precision GPS position estimation(1998-10) Beltukov, Aleksei; Choi, Jongho; Hoffnung, Leonard; Nigam, Nilima; Sterling, David; Tupper, PaulItem Problems in Ultra-High Precision GPS Position Estimation(1998-10) Beltukov, Aleksei; Choi, Jongho; Hoffnung, Leonard; Nigam, Nilima; Sterling, David; Tupper, PaulItem Recent progress in the use of geometric integration methods in micromagnetics and rigid body dynamics(2001-06) Lewis, Debra; Nigam, NilimaIn this paper, we report further progress on our work on the use of Lie methods for integrating ordinary differential equations which evolve on manifolds. These algorithms better capture the qualitative behaviour of the trajectories since the numerical updates stay on the correct manifold. We study the effectiveness of higher order Lie methods in the context of rigid body dynamics, and for a problem in micromagnetics. This is work in progress.Item A transmission problem for fluid-structure interaction in the exterior of a thin domain(2002-05) Hsiao, G.C.; Nigam, NilimaItem A variational method for acoustic scattering from a thin penetrable shell(2000-08) Nigam, Nilima