scholarly journals Torques and angular momenta of fluid elements in the octonion spaces

2021 ◽  
Author(s):  
Zi-Hua Weng
Keyword(s):  
Angular Momentum ◽  
Continuity Equation ◽  
Field Potential ◽  
Gravitational Theory ◽  
External Torque ◽  
Angular Momenta ◽  
Gravitational Theories ◽  
Vortex Streets ◽  
Karman Vortex ◽  
Lift And Drag

The paper focuses on applying the octonions to explore the influence of the external torque on the angular momentum of fluid elements, revealing the interconnection of the external torque and the vortices of vortex streets. J. C. Maxwell was the first to introduce the quaternions to study the physical properties of electromagnetic fields. The contemporary scholars utilize the quaternions and octonions to investigate the electromagnetic theory, gravitational theory, quantum mechanics, special relativity, general relativity and curved spaces and so forth. The paper adopts the octonions to describe the electromagnetic and gravitational theories, including the octonionic field potential, field strength, linear momentum, angular momentum, torque and force and so on. In case the octonion force is equal to zero, it is able to deduce eight independent equations, including the fluid continuity equation, current continuity equation, and force equilibrium equation and so forth. Especially, one of the eight independent equations will uncover the interrelation of the external torque and angular momentums of fluid elements. One of its inferences is that the direction, magnitude and frequency of the external torque must impact the direction and curl of the angular momentum of fluid elements, altering the frequencies of Karman vortex streets within the fluids. It means that the external torque is interrelated with the velocity circulation, by means of the liquid viscosity. The external torque is able to exert an influence on the direction of downwash flows, improving the lift and drag characteristics generated by the fluids.

scholarly journals Dynamic of astrophysical jets in the complex octonion space

2015 ◽  
Vol 24 (10) ◽  
pp. 1550072 ◽  
Author(s):  
Zi-Hua Weng
Keyword(s):  
Angular Momentum ◽  
Field Strength ◽  
Field Potential ◽  
Electromagnetic Theory ◽  
Gradient Force ◽  
Astrophysical Jets ◽  
Field Source ◽  
Gravitational Theories ◽  
Complex Quaternion ◽  
Strength Gradient

The paper aims to consider the strength gradient force as the dynamic of astrophysical jets, explaining the movement phenomena of astrophysical jets. J. C. Maxwell applied the quaternion analysis to describe the electromagnetic theory. This encourages others to adopt the complex quaternion and octonion to depict the electromagnetic and gravitational theories. In the complex octonion space, it is capable of deducing the field potential, field strength, field source, angular momentum, torque, force and so forth. As one component of the force, the strength gradient force relates to the gradient of the norm of field strength only, and is independent of not only the direction of field strength but also the mass and electric charge for the test particle. When the strength gradient force is considered as the thrust of the astrophysical jets, one can deduce some movement features of astrophysical jets, including the bipolarity, matter ingredient, precession, symmetric distribution, emitting, collimation, stability, continuing acceleration and so forth. The above results reveal that the strength gradient force is able to be applied to explain the main mechanical features of astrophysical jets, and is the competitive candidate of the dynamic of astrophysical jets.

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

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.

scholarly journals Entanglement entropy in cubic gravitational theories

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Elena Cáceres ◽  
Rodrigo Castillo Vásquez ◽  
Alejandro Vilar López
Keyword(s):  
Entanglement Entropy ◽  
Gravitational Theory ◽  
Riemann Tensor ◽  
Holographic Entanglement Entropy ◽  
Gravitational Theories ◽  
Entropy Functional ◽  
Wide Range ◽  
Splitting Problem ◽  
Range Of Values

Abstract We derive the holographic entanglement entropy functional for a generic gravitational theory whose action contains terms up to cubic order in the Riemann tensor, and in any dimension. This is the simplest case for which the so-called splitting problem manifests itself, and we explicitly show that the two common splittings present in the literature — minimal and non-minimal — produce different functionals. We apply our results to the particular examples of a boundary disk and a boundary strip in a state dual to 4- dimensional Poincaré AdS in Einsteinian Cubic Gravity, obtaining the bulk entanglement surface for both functionals and finding that causal wedge inclusion is respected for both splittings and a wide range of values of the cubic coupling.

Description of transient states of von Kármán vortex streets by low‐dimensional differential equations

1990 ◽  
Vol 2 (4) ◽  
pp. 479-481 ◽  
Author(s):  
F. Ohle ◽  
P. Lehmann ◽  
E. Roesch ◽  
H. Eckelmann ◽  
A. Hübler
Keyword(s):  
Differential Equations ◽  
Transient States ◽  
Von Karman ◽  
Vortex Streets ◽  
Karman Vortex ◽  
Low Dimensional ◽  
Von Kármán

scholarly journals The Angular Momentum of Brightest Cluster Galaxies

2012 ◽  
Vol 8 (S295) ◽  
pp. 229-229
Author(s):  
S. Brough ◽  
K.-V. Tran ◽  
A. von der Linden
Keyword(s):  
Angular Momentum ◽  
Cluster Galaxies ◽  
Angular Momenta ◽  
Brightest Cluster Galaxies

AbstractMassive Brightest Cluster Galaxies (BCGs) are observed to have a range of angular momenta, suggesting a variety of merging histories.

The Field Equations of Metric-Affine Gravitational Theories

1978 ◽  
Vol 33 (4) ◽  
pp. 398-401 ◽  
Author(s):  
S. J. Aldersley
Keyword(s):  
Vector Potential ◽  
Gravitational Theory ◽  
Field Equations ◽  
Gravitational Theories ◽  
Special Case ◽  
Potential Conditions

The notions of conservation of charge and dimensional consistency are used to obtain conditions which uniquely characterize the field equations of electromagnetism and gravitation in a metric-affine gravitational framework with a vector potential. Conditions for the uniqueness of the choice of field equations of a metric-affine gravitational theory (in the absence of electromagnetism) follow as a special case. Some consequences are discussed.

Modeling and Control of Karman Vortex Streets

1991 ◽  
pp. 111-119
Author(s):  
E. Roesch ◽  
F. Ohle ◽  
H. Eckelmann ◽  
A. Hübler
Keyword(s):  
Modeling And Control ◽  
Vortex Streets ◽  
Karman Vortex ◽  
And Control

TRANSFORMATION AMPLITUDES FOR VECTOR ADDITION OF ANGULAR MOMENTUM; (j3mm′|j3JM)

1952 ◽  
Vol 30 (3) ◽  
pp. 253-256 ◽  
Author(s):  
G. S. Colladay ◽  
R. E. Sells ◽  
D. L. Falkoff
Keyword(s):  
Angular Momentum ◽  
Quantum Mechanical ◽  
Angular Momenta ◽  
Vector Addition

The transformation amplitudes for the quantum-mechanical vector addition of angular momenta, [Formula: see text] are given.

scholarly journals Partial conservation law in a schematic single j shell model

2017 ◽  
Vol 26 (01n02) ◽  
pp. 1740021 ◽  
Author(s):  
Wesley Pereira ◽  
Ricardo Garcia ◽  
Larry Zamick ◽  
Alberto Escuderos ◽  
Kai Neergård
Keyword(s):  
Angular Momentum ◽  
Matrix Element ◽  
Shell Model ◽  
Linear Function ◽  
Conservation Law ◽  
Interaction Matrix ◽  
Stationary States ◽  
Interaction Matrix Element ◽  
Angular Momenta ◽  
Partial Conservation

We report the discovery of a partial conservation law obeyed by a schematic Hamiltonian of two protons and two neutrons in a [Formula: see text] shell. In our Hamiltonian, the interaction matrix element of two nucleons with combined angular momentum [Formula: see text] is linear in [Formula: see text] for even [Formula: see text] and constant for odd [Formula: see text]. It turns out that in some stationary states, the sum of the angular momenta [Formula: see text] and [Formula: see text] of the proton and neutron pairs is conserved. The energies of these states are given by a linear function of [Formula: see text]. The systematics of their occurrence is described and explained.

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