Mathematical and Physical Papers

Kelvin, Lord; Thomson, William

doi:10.1017/cbo9780511996009

Cited by 5 publications

(6 citation statements)

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“…The exploration of 2D point vortex dynamics is a fascinating topic with a rich history for over a century, starting, arguably, with the fundamental contribution of Lord Kelvin [1] and gradually progressing to the consideration of higher numbers of vortices (see e.g. [2,3]) and of not only symmetric but also of asymmetric equilibria thereof (see e.g.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of three noncorotating vortices in Bose-Einstein condensates

Koukouloyannis

Voyatzis

2014

Phys. Rev. E

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In this work we use standard Hamiltonian-system techniques in order to study the dynamics of three vortices with alternating charges in a confined Bose-Einstein condensate. In addition to being motivated by recent experiments, this system offers a natural vehicle for the exploration of the transition of the vortex dynamics from ordered to progressively chaotic behavior. In particular, it possesses two integrals of motion, the energy (which is expressed through the Hamiltonian H) and the angular momentum L of the system. By using the integral of the angular momentum, we reduce the system to a 2-degrees-of-freedom one with L as a parameter and reveal the topology of the phase space through the method of Poincaré surfaces of section. We categorize the various motions that appear in the different regions of the sections and we study the major bifurcations that occur to the families of periodic motions of the system. Finally, we correspond the orbits on the surfaces of section to the real space motion of the vortices in the plane.

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Section: Introductionmentioning

confidence: 99%

Dynamics of three noncorotating vortices in Bose-Einstein condensates

Koukouloyannis

Voyatzis

2014

Phys. Rev. E

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“…The temperature as a function of amplitude is introduced in (18), and the condition of minimum energy leads to equations…”

Section: The Equation Of Adiabatic Processmentioning

confidence: 99%

“…Works in this direction raised long ago [17] [18] [19] [20], but in crystals these effects remained feebly expressed. Modern investigations use high pressures, created also by shock waves, generated in nuclear explosions [21].…”

Section: Introductionmentioning

confidence: 99%

Dynamical Examinations of Vibrator Models, Describing Some Non Elastic Properties of Crystals

Kozlovskiy¹

2017

WJCMP

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On the base of a vibrator atomic model the mechanical and thermal properties of the object are analyzed. The potential energy of the vibrator is represented by means of positive term with coordinate deflection in second power and negative term with deflection in fourth power. With the use of dynamical procedure of calculation, which permits to calculate mean deflection and root mean square amplitude of vibrations, the dependence of applied force from mean amplitude and temperature is calculated. This dependence shows a maximum (or minimum, when the direction of force is reversed), the height of which diminishes with rising temperature. When the force reaches the value of the maximum, the object does not elastic counteract to the force, and gliding begins. It is also considered a vibrator with positive term, containing the deflection in second power and a term, where the deflection treats in third power (Boguslawski vibrator). Exact calculations of the dependence of the force from the temperature in adiabatic process, where the entropy is maintained constant, shows that it is represented by means of a curve with a maximum, so that stretching leads to cooling till the point of maximum is reached.

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“…Proof. Because of Theorem II.1 case (ii), it is sufficient to consider the stability of the steady state x k (t) = R exp (2πik/N ) of the aggregation equation (4). Consider small perturbations of this state, of the form…”

Section: Ring Solutionsmentioning

confidence: 99%

“…Their exploration has been a fascinating topic, garnering considerable attention starting from the fundamental contribution of Lord Kelvin [4], extending to their critical role in turbulent dynamics proposed by Onsager [5] and reaching up to more recent explorations in a diverse range of fields. The latter include (but are not limited to) patterns forming in rotating superfluid 4 He [6], electron columns confined in Malmberg-Penning traps [7] and even magnetized, millimeter sized disks rotating at a liquid-air interface [8]. Numerous theoretical advances have also been made by considering the ordinary differential equations (ODEs) describing the vortex particles.…”

Section: Introductionmentioning

confidence: 99%

A tale of two distributions: from few to many vortices in quasi-two-dimensional Bose–Einstein condensates

Kolokolnikov

Carretero-González

2014

Proc. R. Soc. A.

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Motivated by the recent successes of particle models in capturing the precession and interactions of vortex structures in quasi-two-dimensional BoseEinstein condensates, we revisit the relevant systems of ordinary differential equations. We consider the number of vortices N as a parameter and explore the prototypical configurations ('ground states') that arise in the case of few or many vortices. In the case of few vortices, we modify the classical result illustrating that vortex polygons in the form of a ring are unstable for N ≥ 7. Additionally, we reconcile this modification with the recent identification of symmetry-breaking bifurcations for the cases of N = 2, . . . , 5. We also briefly discuss the case of a ring of vortices surrounding a central vortex (socalled N + 1 configuration). We finally examine the opposite limit of large N and illustrate how a coarsegraining, continuum approach enables the accurate identification of the radial distribution of vortices in that limit.

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Mathematical and Physical Papers

Cited by 5 publications

References 0 publications

Dynamics of three noncorotating vortices in Bose-Einstein condensates

Dynamics of three noncorotating vortices in Bose-Einstein condensates

Dynamical Examinations of Vibrator Models, Describing Some Non Elastic Properties of Crystals

A tale of two distributions: from few to many vortices in quasi-two-dimensional Bose–Einstein condensates

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