847 research outputs found
Linearly Coupled Bose-Einstein Condensates: From Rabi Oscillations and Quasi-Periodic Solutions to Oscillating Domain Walls and Spiral Waves
In this paper, an exact unitary transformation is examined that allows for
the construction of solutions of coupled nonlinear Schr{\"o}dinger equations
with additional linear field coupling, from solutions of the problem where this
linear coupling is absent. The most general case where the transformation is
applicable is identified. We then focus on the most important special case,
namely the well-known Manakov system, which is known to be relevant for
applications in Bose-Einstein condensates consisting of different hyperfine
states of Rb. In essence, the transformation constitutes a distributed,
nonlinear as well as multi-component generalization of the Rabi oscillations
between two-level atomic systems. It is used here to derive a host of periodic
and quasi-periodic solutions including temporally oscillating domain walls and
spiral waves.Comment: 6 pages, 4 figures, Phys. Rev. A (in press
Instabilities of one-dimensional stationary solutions of the cubic nonlinear Schrodinger equation
The two-dimensional cubic nonlinear Schrodinger equation admits a large
family of one-dimensional bounded traveling-wave solutions. All such solutions
may be written in terms of an amplitude and a phase. Solutions with piecewise
constant phase have been well studied previously. Some of these solutions were
found to be stable with respect to one-dimensional perturbations. No such
solutions are stable with respect to two-dimensional perturbations. Here we
consider stability of the larger class of solutions whose phase is dependent on
the spatial dimension of the one-dimensional wave form. We study the spectral
stability of such nontrivial-phase solutions numerically, using Hill's method.
We present evidence which suggests that all such nontrivial-phase solutions are
unstable with respect to both one- and two-dimensional perturbations.
Instability occurs in all cases: for both the elliptic and hyperbolic nonlinear
Schrodinger equations, and in the focusing and defocusing case.Comment: Submitted: 13 pages, 3 figure
Generation Expansion Models including Technical Constraints and Demand Uncertainty
This article presents a Generation Expansion Model of the power system taking into account the operational constraints and the uncertainty of long-term electricity demand projections. The model is based on a discretization of the load duration curve and explicitly considers that power plant ramping capabilities must meet demand variations. A model predictive control method is used to improve the long-term planning decisions while considering the uncertainty of demand projections. The model presented in this paper allows integrating technical constraints and uncertainty in the simulations, improving the accuracy of the results, while maintaining feasible computational time. Results are tested over three scenarios based on load data of an energy retailer in Colombia
Multi-dimensional schemes for scalar advection
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77204/1/AIAA-1991-1532-834.pd
Progress on multidimensional upwind Euler solvers for unstructured grids
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76503/1/AIAA-1991-1550-511.pd
Vortices in Bose-Einstein Condensates: Some Recent Developments
In this brief review we summarize a number of recent developments in the
study of vortices in Bose-Einstein condensates, a topic of considerable
theoretical and experimental interest in the past few years. We examine the
generation of vortices by means of phase imprinting, as well as via dynamical
instabilities. Their stability is subsequently examined in the presence of
purely magnetic trapping, and in the combined presence of magnetic and optical
trapping. We then study pairs of vortices and their interactions, illustrating
a reduced description in terms of ordinary differential equations for the
vortex centers. In the realm of two vortices we also consider the existence of
stable dipole clusters for two-component condensates. Last but not least, we
discuss mesoscopic patterns formed by vortices, the so-called vortex lattices
and analyze some of their intriguing dynamical features. A number of
interesting future directions are highlighted.Comment: 24 pages, 8 figs, ws-mplb.cls, to appear in Modern Physics Letters B
(2005
Cerenkov-like radiation in a binary Schr{\"o}dinger flow past an obstacle
We consider the dynamics of two coupled miscible Bose-Einstein condensates,
when an obstacle is dragged through them. The existence of two different speeds
of sound provides the possibility for three dynamical regimes: when both
components are subcritical, we do not observe nucleation of coherent
structures; when both components are supercritical they both form dark solitons
in one dimension (1D) and vortices or rotating vortex dipoles in two dimensions
(2D); in the intermediate regime, we observe the nucleation of a structure in
the form of a dark-antidark soliton in 1D; subcritical component; the 2D analog
of such a structure, a vortex-lump, is also observed.Comment: 4 pages, 4 figures, submitted to Phys Rev
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