Equilibrium configurations of rotating charged or gravitating liquid masses with surface tension. II

Cohen, S.; Plášil, F.; Świa̧tecki, W.J.

doi:10.1016/0003-4916(74)90126-2

Cited by 1,041 publications

(469 citation statements)

References 8 publications

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“…It has been shown that the shapes of rotating liquid droplets held together by capillary forces belong to the same class of solutions and can serve as laboratory scale emulations of astronomical objects [2]. Liquid drop models have also been applied to predict the shapes of rotating atomic nuclei [3].…”

Section: Introductionmentioning

confidence: 99%

“…The stability diagram and corresponding representative shapes for axially symmetric (D ∞ h ) and two-lobed (D 2h ) branches are shown in Fig. 6 [2,[4][5][6][7]. In Fig.…”

Section: Shapes Of Classical Rotating Dropletsmentioning

confidence: 99%

“…Liquid drop models have also been applied to predict the shapes of rotating atomic nuclei [3]. Equilibrium shapes of classical rotating droplets have been extensively studied theoretically [2,[4][5][6][7] and experimentally [7][8]. A droplet that is spherical at rest acquires an oblate axially symmetric shape upon rotation and, with increasing angular momentum, turns into a two-lobed figure that is elongated perpendicular to the rotational axis, as discussed in more detail in Section 4.…”

Section: Introductionmentioning

confidence: 99%

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Shapes of rotating superfluid helium nanodroplets

et al. 2017

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Rotating superfluid He droplets of approximately 1 μm in diameter were obtained in a free nozzle beam expansion of liquid He in vacuum and were studied by single-shot coherent diffractive imaging using an x-ray free electron laser. The formation of strongly deformed droplets is evidenced by large anisotropies and intensity anomalies (streaks) in the obtained diffraction images. The analysis of the images shows that, in addition to previously described axially symmetric oblate shapes, some droplets exhibit prolate shapes. Forward modeling of the diffraction images indicates that the shapes of rotating superfluid droplets are very similar to their classical counterparts, giving direct access to the droplet angular momenta and angular velocities. The analyses of the radial intensity distribution and appearance statistics of the anisotropic images confirm the existence of oblate metastable superfluid droplets with large angular momenta beyond the classical bifurcation threshold.3

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Section: Introductionmentioning

confidence: 99%

“…The stability diagram and corresponding representative shapes for axially symmetric (D ∞ h ) and two-lobed (D 2h ) branches are shown in Fig. 6 [2,[4][5][6][7]. In Fig.…”

Section: Shapes Of Classical Rotating Dropletsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Shapes of rotating superfluid helium nanodroplets

et al. 2017

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“…The physical parameters of the fusion-fission part are relatively well known from the liquid-drop model [103,104]. In contrast, the quasifission process never reaches statistical equilibrium.…”

Section: B Fragment Angular Distributionsmentioning

confidence: 99%

Shape evolution and collective dynamics of quasifission in the time-dependent Hartree-Fock approach

2015

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Background: At energies near the Coulomb barrier, capture reactions in heavy-ion collisions result either in fusion or in quasifission. The former produces a compound nucleus in statistical equilibrium, while the second leads to a reseparation of the fragments after partial mass equilibration without formation of a compound nucleus. Extracting the compound nucleus formation probability is crucial to predict superheavy-element formation crosssections. It requires a good knowledge of the fragment angular distribution which itself depends on quantities such as moments of inertia and excitation energies which have so far been somewhat arbitrary for the quasifission contribution.Purpose: Our main goal is to utlize the time-dependent Hartee-Fock (TDHF) approach to extract ingredients of the formula used in the analysis of experimental angular distributions. These include the moment-of-inertia and temperature.Methods: We investigate the evolution of the nuclear density in TDHF calculations leading to quasifission. We study the dependence of the relevant quantities on various initial conditions of the reaction process.Results: The evolution of the moment of inertia is clearly non-trivial and depends strongly on the characteristics of the collision. The temperature rises quickly when the kinetic energy is transformed into internal excitation. Then, it rises slowly during mass transfer.Conclusions: Fully microscopic theories are useful to predict the complex evolution of quantities required in macroscopic models of quasifission.

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“…Such problem first appeared in the liquid drop model of the atomic nuclei proposed by Gamow in 1928 [13] and then developed by other researchers [3,9], and it is also relevant in some models of diblock copolymer melts [5,17]. In [15,16] (see also [6]) the authors showed that global minimizers of (1) exist if the volume m is small, and do not exist if the volume is large enough.…”

Section: Introductionmentioning

confidence: 99%

Rigidity of critical points for a nonlocal Ohta–Kawasaki energy

2017

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We investigate the shape of critical points for a free energy consisting of a nonlocal perimeter plus a nonlocal repulsive term. In particular, we prove that a volume-constrained critical point is necessarily a ball if its volume is sufficiently small with respect to its isodiametric ratio, thus extending a result previously known only for global minimizers.We also show that, at least in one-dimension, there exist critical points with arbitrarily small volume and large isodiametric ratio. This example shows that a constraint on the diameter is, in general, necessary to establish the radial symmetry of the critical points.

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Equilibrium configurations of rotating charged or gravitating liquid masses with surface tension. II

Cited by 1,041 publications

References 8 publications

Shapes of rotating superfluid helium nanodroplets

Shapes of rotating superfluid helium nanodroplets

Shape evolution and collective dynamics of quasifission in the time-dependent Hartree-Fock approach

Rigidity of critical points for a nonlocal Ohta–Kawasaki energy

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