Microscopic analysis of homogeneous electron gas by considering dipole–dipole interaction

Implying perturbation theory, the impact of the dipole–dipole interaction (DDI) on the thermodynamic properties of a homogeneous electron gas at zero temperature is investigated. Through the second quantization formalism, the analytic expressions for the ground state energy and the DDI energy are obtained. In this paper, the DDI energy has similarities with the previous works done by others. We show that its general behavior depends on density and the total angular momentum. Especially, it is found that the DDI energy has a highly state-dependent behavior. With the growth of density, the magnitude of DDI energy, which is found to be the summation of all energy contributions of the states with even and odd total angular momenta, grows linearly. It is also found that for the states with even and odd total angular momenta, the DDI energy contributions are corresponding to the positive and negative values, respectively. In particular, an increase of total angular momentum leads to decline in the magnitude of energy contribution. Therefore, the dipole–dipole interaction reveals distinct characteristics in comparison with central-like interactions.

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Calibration of the angular momenta of the minor planets in the solar system

Astronomy and Astrophysics ◽

10.1051/0004-6361/201834196 ◽

2019 ◽

Vol 630 ◽

pp. A68 ◽

Cited By ~ 1

Author(s):

Jian Li ◽

Zhihong Jeff Xia ◽

Liyong Zhou

Keyword(s):

Angular Momentum ◽

Solar System ◽

Total Angular Momentum ◽

Physical Parameters ◽

Minor Planets ◽

The Sun ◽

Relative Angle ◽

Angular Momenta ◽

Dwarf Planets ◽

Invariable Plane

Aims. We aim to determine the relative angle between the total angular momentum of the minor planets and that of the Sun-planets system, and to improve the orientation of the invariable plane of the solar system. Methods. By utilizing physical parameters available in public domain archives, we assigned reasonable masses to 718 041 minor planets throughout the solar system, including near-Earth objects, main belt asteroids, Jupiter trojans, trans-Neptunian objects, scattered-disk objects, and centaurs. Then we combined the orbital data to calibrate the angular momenta of these small bodies, and evaluated the specific contribution of the massive dwarf planets. The effects of uncertainties on the mass determination and the observational incompleteness were also estimated. Results. We determine the total angular momentum of the known minor planets to be 1.7817 × 1046 g cm2 s−1. The relative angle α between this vector and the total angular momentum of the Sun-planets system is calculated to be about 14.74°. By excluding the dwarf planets Eris, Pluto, and Haumea, which have peculiar angular momentum directions, the angle α drops sharply to 1.76°; a similar result applies to each individual minor planet group (e.g., trans-Neptunian objects). This suggests that, without these three most massive bodies, the plane perpendicular to the total angular momentum of the minor planets would be close to the invariable plane of the solar system. On the other hand, the inclusion of Eris, Haumea, and Makemake can produce a difference of 1254 mas in the inclination of the invariable plane, which is much larger than the difference of 9 mas induced by Ceres, Vesta, and Pallas as found previously. By taking into account the angular momentum contributions from all minor planets, including the unseen ones, the orientation improvement of the invariable plane is larger than 1000 mas in inclination with a 1σ error of ∼50−140 mas.

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Boundary conditions for the formation of the Moon

Netherlands Journal of Geosciences – Geologie en Mijnbouw ◽

10.1017/njg.2015.24 ◽

2015 ◽

Vol 95 (2) ◽

pp. 131-139 ◽

Cited By ~ 1

Author(s):

M. Reuver ◽

R.J. de Meijer ◽

I.L. ten Kate ◽

W. van Westrenen

Keyword(s):

Angular Momentum ◽

Boundary Conditions ◽

Total Angular Momentum ◽

Nuclear Explosion ◽

Moment Of Inertia ◽

The Moon ◽

Moon System ◽

Giant Impact ◽

The Earth ◽

The Impact

AbstractRecent measurements of the chemical and isotopic composition of lunar samples indicate that the Moon's bulk composition shows great similarities with the composition of the silicate Earth. Moon formation models that attempt to explain these similarities make a wide variety of assumptions about the properties of the Earth prior to the formation of the Moon (the proto-Earth), and about the necessity and properties of an impactor colliding with the proto-Earth. This paper investigates the effects of the proto-Earth's mass, oblateness and internal core-mantle differentiation on its moment of inertia. The ratio of angular momentum and moment of inertia determines the stability of the proto-Earth and the binding energy, i.e. the energy needed to make the transition from an initial state in which the system is a rotating single body with a certain angular momentum to a final state with two bodies (Earth and Moon) with the same total angular momentum, redistributed between Earth and Moon. For the initial state two scenarios are being investigated: a homogeneous (undifferentiated) proto-Earth and a proto-Earth differentiated in a central metallic and an outer silicate shell; for both scenarios a range of oblateness values is investigated. Calculations indicate that a differentiated proto-Earth would become unstable at an angular momentum L that exceeds the total angular momentum of the present-day Earth–Moon system (L0) by factors of 2.5–2.9, with the precise maximum dependent on the proto-Earth's oblateness. Further limitations are imposed by the Roche limit and the logical condition that the separated Earth–Moon system should be formed outside the proto-Earth. This further limits the L values of the Earth–Moon system to a maximum of about L/L0 = 1.5, at a minimum oblateness (a/c ratio) of 1.2. These calculations provide boundary conditions for the main classes of Moon-forming models. Our results show that at the high values of L used in recent giant impact models (1.8 < L/L0 < 3.1), the proposed proto-Earths are unstable before (Cuk & Stewart, 2012) or immediately after (Canup, 2012) the impact, even at a high oblateness (the most favourable condition for stability). We conclude that the recent attempts to improve the classic giant impact hypothesis by studying systems with very high values of L are not supported by the boundary condition calculations in this work. In contrast, this work indicates that the nuclear explosion model for Moon formation (De Meijer et al., 2013) fulfills the boundary conditions and requires approximately one order of magnitude less energy than originally estimated. Hence in our view the nuclear explosion model is presently the model that best explains the formation of the Moon from predominantly terrestrial silicate material.

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Takeoff Mechanics of the Double Backward Somersault

International Journal of Sport Biomechanics ◽

10.1123/ijsb.6.2.177 ◽

1990 ◽

Vol 6 (2) ◽

pp. 177-186 ◽

Cited By ~ 7

Author(s):

Inseong Hwang ◽

Gukung Seo ◽

Zhi Cheng Liu

Keyword(s):

Angular Momentum ◽

Total Angular Momentum ◽

Dominant Role ◽

Center Of Mass ◽

Velocity Curve ◽

The Other ◽

Transverse Axis ◽

Angular Momenta ◽

Total Body ◽

Direction Opposite

This study examined the biomechanical profiles of the takeoff phase of double backward somersaults in three flight positions: seven layout double backward somersaults (L), seven twisting double backward somersaults (TW), and seven tucked double backward somersaults (TDB). Selected kinematic variables and angular momenta were calculated in order to compare the differences resulting from different aerial maneuvers. The amount of total body angular momentum about the transverse axis through the gymnasts' center of mass progressively increased from TDB to TW to L. The gymnasts performing the skill in the layout position tried to minimize the angle of block in a direction opposite the intended motion by maximizing the angle of touchdown and takeoff. In so doing, the horizontal velocity center-of-mass curve of the L showed a slowly decreasing curve compared with those of the other two somersaults while the vertical velocity curve of the L increased more slowly than the other curves during the takeoff phase. In all cases the legs played the dominant role in contributing to total angular momentum during takeoff.

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Angular Momentum Growth around Local Density Maxima

Symposium - International Astronomical Union ◽

10.1017/s0074180900136812 ◽

1988 ◽

Vol 130 ◽

pp. 552-552

Author(s):

A. F. Heavens ◽

J. A. Peacock

Keyword(s):

Dark Matter ◽

Angular Momentum ◽

Power Spectrum ◽

Total Angular Momentum ◽

Cold Dark Matter ◽

Local Density ◽

Probability Distributions ◽

Power Spectra ◽

Elliptical Galaxies ◽

Angular Momenta

We have calculated the growth of angular momentum about local density maxima at early epochs. We find that high peaks experience higher torques than low peaks, counteracting the short collapse time during which the high peaks can acquire angular momentum. Which effect is dominant depends on the perturbation power spectrum: for power spectra characteristic of both cold dark matter and hot dark matter, the effects nearly cancel, and the total angular momentum acquired by a collapsing object is almost independent of the height of the peak. Furthermore, the distributions of angular momenta acquired by collapsing protosystems are extremely broad, for all power spectra, far exceeding any modest differences between peaks of different height.These results indicate that it is not possible to account for the systematic differences in angular momentum properties of disk and elliptical galaxies simply by postulating that the latter arise from fluctuations of greater overdensity, contrary to some recent suggestions. The figure shows the probability distributions for the final angular momentum acquired by peaks of dimensionless height 1–4, for a power spectrum similar to cold dark matter. A fuller account of this work has been submitted to MNRAS.

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Staggering of angular momentum distribution in fission

EPJ Web of Conferences ◽

10.1051/epjconf/201816900023 ◽

2018 ◽

Vol 169 ◽

pp. 00023

Author(s):

Pierre Tamagno ◽

Olivier Litaize

Keyword(s):

Angular Momentum ◽

Excitation Energy ◽

Momentum Distribution ◽

Ad Hoc ◽

Rayleigh Distribution ◽

Fission Process ◽

Angular Momenta ◽

Model Derivation ◽

The Impact

We review here the role of angular momentum distributions in the fission process. To do so the algorithm implemented in the FIFRELIN code [?] is detailed with special emphasis on the place of fission fragment angular momenta. The usual Rayleigh distribution used for angular momentum distribution is presented and the related model derivation is recalled. Arguments are given to justify why this distribution should not hold for low excitation energy of the fission fragments. An alternative ad hoc expression taking into account low-lying collectiveness is presented as has been implemented in the FIFRELIN code. Yet on observables currently provided by the code, no dramatic impact has been found. To quantify the magnitude of the impact of the low-lying staggering in the angular momentum distribution, a textbook case is considered for the decay of the 144Ba nucleus with low excitation energy.

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Spin-decoupled metasurface for simultaneous detection of spin and orbital angular momenta via momentum transformation

Light Science & Applications ◽

10.1038/s41377-021-00497-7 ◽

2021 ◽

Vol 10 (1) ◽

Author(s):

Yinghui Guo ◽

Shicong Zhang ◽

Mingbo Pu ◽

Qiong He ◽

Jinjin Jin ◽

...

Keyword(s):

Angular Momentum ◽

Simultaneous Detection ◽

Single Element ◽

Single Shot ◽

Single Spin ◽

Dual Functional ◽

Angular Momenta ◽

Quadratic Phase ◽

Mode Space ◽

Optical Configuration

AbstractWith inherent orthogonality, both the spin angular momentum (SAM) and orbital angular momentum (OAM) of photons have been utilized to expand the dimensions of quantum information, optical communications, and information processing, wherein simultaneous detection of SAMs and OAMs with a single element and a single-shot measurement is highly anticipated. Here, a single azimuthal-quadratic phase metasurface-based photonic momentum transformation (PMT) is illustrated and utilized for vortex recognition. Since different vortices are converted into focusing patterns with distinct azimuthal coordinates on a transverse plane through PMT, OAMs within a large mode space can be determined through a single-shot measurement. Moreover, spin-controlled dual-functional PMTs are proposed for simultaneous SAM and OAM sorting, which is implemented by a single spin-decoupled metasurface that merges both the geometric phase and dynamic phase. Interestingly, our proposed method can detect vectorial vortices with both phase and polarization singularities, as well as superimposed vortices with a certain interval step. Experimental results obtained at several wavelengths in the visible band exhibit good agreement with the numerical modeling. With the merits of ultracompact device size, simple optical configuration, and prominent vortex recognition ability, our approach may underpin the development of integrated and high-dimensional optical and quantum systems.

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