Density of states of inviscid incompressible two-dimensional fluid unit disk vortex systems

Johnson, Darell J

doi:10.1063/1.866683

Cited by 4 publications

(4 citation statements)

References 27 publications

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“…To determine the temperature of the system, the density of states W (E, I) is obtained from randomly generated 10 7 states for the microcanonical ensemble where E and I are kept constant. Similar work has been done widely [8,9]. In our work, the maximum number of vortices is larger by one order of magnitude, and the number of states is larger by two orders of magnitude than the previous results.…”

Section: Determination Of βsupporting

confidence: 84%

Dynamics of two-sign point vortices in positive and negative temperature states

et al. 2006

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Dynamics of two-sign point vortices in two-dimensional circular boundary is examined by numerical simulations with MDGRAPE-2. The vortex system is characterized by the inverse temperature as determined from the density of states of the microcanonical ensemble of numerically generated 10 7 states. The massive simulation shows that different configurations appear in the time-asymptotic state depending on the sign of. Condensation of the same-sign vortices is observed when < 0, while the both-sign vortices tend to be uniformly neutralized when > 0. During the condensation, a part of the vortices gains energy to form clumps (patches), and the other part of the vortices loses energy to keep the total energy constant and mixes with vortices of the other sign. This observation demonstrates a characteristic feature of negative states that the system energy concentrates into the clumps of the same-sign vortices.

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Section: Determination Of βsupporting

confidence: 84%

Dynamics of two-sign point vortices in positive and negative temperature states

et al. 2006

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“…18 A rigid line represents the values of the parameters at which three point vortices form an equilateral triangle configuration; the center of mass of the equilateral triangle is at the origin. The form of the rigid line is given by…”

Section: Poincaré Sectionmentioning

confidence: 99%

Numerical Simulation of Vortex Crystals and Merging inN-Point Vortex Systems with Circular Boundary

Yoshida

Sano

2005

J. Phys. Soc. Jpn.

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In two-dimensional (2D) inviscid incompressible flow, low background vorticity distribution accelerates intense vortices (clumps) to merge each other and to array in the symmetric pattern which is called "vortex crystals"; they are observed in the experiments on pure electron plasma and the simulations of Euler fluid. Vortex merger is thought to be a result of negative "temperature" introduced by L. Onsager. Slight difference in the initial distribution from this leads to "vortex crystals". We study these phenomena by examining N -point vortex systems governed by the Hamilton equations of motion. First, we study a three-point vortex system without background distribution. It is known that a N -point vortex system with boundary exhibits chaotic behavior for N ≥ 3. In order to investigate the properties of the phase space structure of this three-point vortex system with circular boundary, we examine the Poincaré plot of this system. Then we show that topology of the Poincaré plot of this system drastically changes when the parameters, which are concerned with the sign of "temperature", are varied. Next, we introduce a formula for energy spectrum of a Npoint vortex system with circular boundary. Further, carrying out numerical computation, we reproduce a vortex crystal and a vortex merger in a few hundred point vortices system. We confirm that the energy of vortices is transferred from the clumps to the background in the course of vortex crystallization. In the vortex merging process, we numerically calculate the energy spectrum introduced above and confirm that it behaves as k −α , (α ≈ 2.2 − 2.8) at the region 10 0 < k < 10 1 after the merging.

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“…The density of states WE; I is evaluated as a function of the system energy E and the angular impulse I by employing the large-scale numerical sampling (10 7 times) for a microcanonical ensemble of a system consisting of N=2 positive and N=2 negative point vortices (typically N 6724). Compared to the previous numerical evaluations of the density of states for systems with N 40 [19][20][21], the number of sampling is larger at least by a factor of 10 2 , so that we can discuss the asymptotic form of WE; I over a wider range of E. To obtain time-asymptotic behavior of the vortex distribution, we trace the time evolution of the system from various initial distributions using MDGRAPE-2. The condensation of the same-sign vortices was demonstrated by the numerical simulations under a limited system scale or the mean field approximation [22,23].…”

mentioning

confidence: 99%

Dynamics of Two-Sign Point Vortices in Positive and Negative Temperature States

Yatsuyanagi

Kiwamoto

Tomita

et al. 2006

Prog. Theor. Phys. Suppl.

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Dynamics of two-sign point vortices in two-dimensional circular boundary is examined by numerical simulations with MDGRAPE-2. The vortex system is characterized by the inverse temperature as determined from the density of states of the microcanonical ensemble of numerically generated 10 7 states. The massive simulation shows that different configurations appear in the time-asymptotic state depending on the sign of . Condensation of the same-sign vortices is observed when < 0, while the both-sign vortices tend to be uniformly neutralized when > 0. During the condensation, a part of the vortices gains energy to form clumps (patches), and the other part of the vortices loses energy to keep the total energy constant and mixes with vortices of the other sign. This observation demonstrates a characteristic feature of negative states that the system energy concentrates into the clumps of the same-sign vortices.

show abstract

Density of states of inviscid incompressible two-dimensional fluid unit disk vortex systems

Cited by 4 publications

References 27 publications

Dynamics of two-sign point vortices in positive and negative temperature states

Dynamics of two-sign point vortices in positive and negative temperature states

Numerical Simulation of Vortex Crystals and Merging inN-Point Vortex Systems with Circular Boundary

Dynamics of Two-Sign Point Vortices in Positive and Negative Temperature States

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