31,893 research outputs found
Fast and Simple Methods For Computing Control Points
The purpose of this paper is to present simple and fast methods for computing
control points for polynomial curves and polynomial surfaces given explicitly
in terms of polynomials (written as sums of monomials). We give recurrence
formulae w.r.t. arbitrary affine frames. As a corollary, it is amusing that we
can also give closed-form expressions in the case of the frame (r, s) for
curves, and the frame ((1, 0, 0), (0, 1, 0), (0, 0, 1) for surfaces. Our
methods have the same low polynomial (time and space) complexity as the other
best known algorithms, and are very easy to implement.Comment: 15 page
Control of unstable macroscopic oscillations in the dynamics of three coupled Bose condensates
We study the dynamical stability of the macroscopic quantum oscillations
characterizing a system of three coupled Bose-Einstein condensates arranged
into an open-chain geometry. The boson interaction, the hopping amplitude and
the central-well relative depth are regarded as adjustable parameters. After
deriving the stability diagrams of the system, we identify three mechanisms to
realize the transition from an unstable to stable behavior and analyze specific
configurations that, by suitably tuning the model parameters, give rise to
macroscopic effects which are expected to be accessible to experimental
observation. Also, we pinpoint a system regime that realizes a
Josephson-junction-like effect. In this regime the system configuration do not
depend on the model interaction parameters, and the population oscillation
amplitude is related to the condensate-phase difference. This fact makes
possible estimating the latter quantity, since the measure of the oscillating
amplitudes is experimentally accessible.Comment: 25 pages, 12 figure
Algebraic methods for dynamic systems
Algebraic methods for application to dynamic control system
Some Applications of the Extended Bendixson-Dulac Theorem
During the last years the authors have studied the number of limit cycles of
several families of planar vector fields. The common tool has been the use of
an extended version of the celebrated Bendixson-Dulac Theorem. The aim of this
work is to present an unified approach of some of these results, together with
their corresponding proofs. We also provide several applications.Comment: 19 pages, 3 figure
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