Quasiperiodic Dynamics in Bose-Einstein Condensates in Periodic Lattices and Superlattices

We employ KAM theory to rigorously investigate quasiperiodic dynamics in cigar-shaped Bose-Einstein condensates (BEC) in periodic lattices and superlattices. Toward this end, we apply a coherent structure ansatz to the Gross-Pitaevskii equation to obtain a parametrically forced Duffing equation describing the spatial dynamics of the condensate. For shallow-well, intermediate-well, and deep-well potentials, we find KAM tori and Aubry-Mather sets to prove that one obtains mostly quasiperiodic dynamics for condensate wave functions of sufficiently large amplitude, where the minimal amplitude depends on the experimentally adjustable BEC parameters. We show that this threshold scales with the square root of the inverse of the two-body scattering length, whereas the rotation number of tori above this threshold is proportional to the amplitude. As a consequence, one obtains the same dynamical picture for lattices of all depths, as an increase in depth essentially only affects scaling in phase space. Our approach is applicable to periodic superlattices with an arbitrary number of rationally dependent wave numbers.Comment: 29 pages, 6 figures (several with multiple parts; higher-quality versions of some of them available at http://www.its.caltech.edu/~mason/papers), to appear very soon in Journal of Nonlinear Scienc

New species of Solanum and Capsicum (Solanaceae) from Bolivia, with clarification of nomenclature in some Bolivian Solanum

Journal ArticleBolivian floristic diversity is high, reflecting its great topographic and habitat diversity. Habitats in Bolivia range from seasonally flooded savannas to arid Chaco and high elevation deserts to hyper-humid montane and lowland rainforests

A Stochastic Dynamic Programming Approach To Balancing Wind Intermittency With Hydropower

Hydropower is a rapid response energy source and thus a perfect complement to the intermittency of wind power. However, the effect wind energy has on conventional hydropower systems can be felt, especially if the system is subject to several other environmental and non-power use constraints. The goal of this paper is to develop a general method for optimizing short-term hydropower operations of a realistic multireservoir hydropower system in a deregulated market setting when there is a stochastic wind input. The approach used is a modification of stochastic dynamic programming (SDP). The methodology is applied to a representation of multiple projects in the Federal Columbia River Power System, which is currently being dispatched by the Bonneville Power Administration. Currently, studies on hydropower operations optimization with wind have involved linear programming orstochastic programming, which are based on linearity of the objective function and constraints. SDP, by contrast, is a stochastic optimization method that does not require assumptions of linearity of the objective function or the constraints. The true adaptive and stochastic nonlinear formulation of the objective function can be applied to multiple timesteps, and is efficient for many timesteps compared to stochastic programming

Photodynamic Oxidation of Iodide Ion by Anthracene Sulphonates

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