338 research outputs found
An analytical study of resonant transport of Bose-Einstein condensates
We study the stationary nonlinear Schr\"odinger equation, or Gross-Pitaevskii
equation, for a one--dimensional finite square well potential. By neglecting
the mean--field interaction outside the potential well it is possible to
discuss the transport properties of the system analytically in terms of ingoing
and outgoing waves. Resonances and bound states are obtained analytically. The
transmitted flux shows a bistable behaviour. Novel crossing scenarios of
eigenstates similar to beak--to--beak structures are observed for a repulsive
mean-field interaction. It is proven that resonances transform to bound states
due to an attractive nonlinearity and vice versa for a repulsive nonlinearity,
and the critical nonlinearity for the transformation is calculated
analytically. The bound state wavefunctions of the system satisfy an
oscillation theorem as in the case of linear quantum mechanics. Furthermore,
the implications of the eigenstates on the dymamics of the system are
discussed.Comment: RevTeX4, 16 pages, 19 figure
Integration of the primer vector in a central force field
This paper examines the primer vector which governs optimal solutions for orbital transfer when the central force field has a more general form than the usual inverse-square-force law. Along a null-thrust are that connects two successive impulses, the two sets of state and adjoint equations are decoupled. This allows the reduction of the problem to the integration of a linear first-order differential equation, and hence the solution of the optimal coasting are in the most general central force field can be obtained by simple quadratures. Immediate applications of the results can be seen in solving problems of escape in the equatorial plane of an oblate planet, satellite swing by, or station keeping around Lagrangian points in the three-body problem.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45248/1/10957_2004_Article_BF00932804.pd
The probability of an encounter of two Brownian particles before escape
We study the probability of two Brownian particles to meet before one of them
exits a finite interval. We obtain an explicit expression for the probability
as a function of the initial distance of the two particles using the
Weierstrass elliptic function. We also find the law of the meeting location.
Brownian simulations show the accuracy of our analysis. Finally, we discuss
some applications to the probability that a double strand DNA break repairs in
confined environments.Comment: To appear J. Phys
On the generalized continuity equation
A generalized continuity equation extending the ordinary continuity equation
has been found using quanternions. It is shown to be compatible with Dirac,
Schrodinger, Klein-Gordon and diffusion equations. This generalized equation is
Lorentz invariant. The transport properties of electrons are found to be
governed by Schrodinger-like equation and not by the diffusion equation.Comment: 9 Latex pages, no figure
The Picard-Fuchs equations for complete hyperelliptic integrals of even order curves, and the actions of the generalized Neumann system
We consider a family of genus 2 hyperelliptic curves of even order and obtain explicitly the systems of 5 linear ordinary differential equations for periods of the corresponding Abelian integrals of first, second, and third kind, as functions of some parameters of the curves. The systems can be regarded as extensions of the well-studied Picard-Fuchs equations for periods of complete integrals of first and second kind on odd hyperelliptic curves. The periods we consider are linear combinations of the action variables of several integrable systems, in particular the generalized Neumann system with polynomial separable potentials. Thus the solutions of the extended Picard-Fuchs equations can be used to study various properties of the actions. (C) 2014 AIP Publishing LLC.Peer ReviewedPostprint (published version
Heating mechanisms in radio frequency driven ultracold plasmas
Several mechanisms by which an external electromagnetic field influences the
temperature of a plasma are studied analytically and specialized to the system
of an ultracold plasma (UCP) driven by a uniform radio frequency (RF) field.
Heating through collisional absorption is reviewed and applied to UCPs.
Furthermore, it is shown that the RF field modifies the three body
recombination process by ionizing electrons from intermediate high-lying
Rydberg states and upshifting the continuum threshold, resulting in a
suppression of three body recombination. Heating through collisionless
absorption associated with the finite plasma size is calculated in detail,
revealing a temperature threshold below which collisionless absorption is
ineffective.Comment: 14 pages, 7 figure
Hamiltonian flows on null curves
The local motion of a null curve in Minkowski 3-space induces an evolution
equation for its Lorentz invariant curvature. Special motions are constructed
whose induced evolution equations are the members of the KdV hierarchy. The
null curves which move under the KdV flow without changing shape are proven to
be the trajectories of a certain particle model on null curves described by a
Lagrangian linear in the curvature. In addition, it is shown that the curvature
of a null curve which evolves by similarities can be computed in terms of the
solutions of the second Painlev\'e equation.Comment: 14 pages, v2: final version; minor changes in the expositio
Stability of non-time-reversible phonobreathers
Non-time reversible phonobreathers are non-linear waves that can transport
energy in coupled oscillator chains by means of a phase-torsion mechanism. In
this paper, the stability properties of these structures have been considered.
It has been performed an analytical study for low-coupling solutions based upon
the so called {\em multibreather stability theorem} previously developed by
some of the authors [Physica D {\bf 180} 235]. A numerical analysis confirms
the analytical predictions and gives a detailed picture of the existence and
stability properties for arbitrary frequency and coupling.Comment: J. Phys. A.:Math. and Theor. In Press (2010
Breathers in the weakly coupled topological discrete sine-Gordon system
Existence of breather (spatially localized, time periodic, oscillatory)
solutions of the topological discrete sine-Gordon (TDSG) system, in the regime
of weak coupling, is proved. The novelty of this result is that, unlike the
systems previously considered in studies of discrete breathers, the TDSG system
does not decouple into independent oscillator units in the weak coupling limit.
The results of a systematic numerical study of these breathers are presented,
including breather initial profiles and a portrait of their domain of existence
in the frequency-coupling parameter space. It is found that the breathers are
uniformly qualitatively different from those found in conventional spatially
discrete systems.Comment: 19 pages, 4 figures. Section 4 (numerical analysis) completely
rewritte
Reduction of Low-Thrust Continuous Controls for Trajectory Dynamics
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76670/1/AIAA-40619-128.pd
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