scholarly journals Polar angle tangent vectors follow Cauchy distributions under spherical symmetry

2014 ◽  
Vol 128 ◽  
pp. 147-153 ◽  
Author(s):  
T. Cacoullos
Keyword(s):  
Spherical Symmetry ◽  
Polar Angle ◽  
Tangent Vectors

scholarly journals Spherical symmetry breaking in electric, magnetic and toroidal multipole moment radiations in spherical toroidal resonant cavities and optimum-efficiency antennas

2021 ◽  
Vol 67 (2 Mar-Apr) ◽  
pp. 174
Author(s):  
E. Ley Koo ◽  
H. Torres-Bustamante ◽  
A. Góngora T.
Keyword(s):  
Spherical Symmetry ◽  
Spherical Surface ◽  
Polar Angle ◽  
Multipole Expansion ◽  
Multipole Moment ◽  
Outgoing Wave ◽  
Legendre Functions ◽  
Resonant Cavities ◽  
The Green Function ◽  
Physical Changes

This Letter reports the breaking of the spherical symmetry in the complete electromagnetic multipole expansion when its sources are distributed on spherical toroidal surfaces, identifying the specic geometrical and physical changes fromthe familiar case of sources on a spherical surface. In fact, for spherical toroids dened by concentric spherical rings and symmetric conical rings, the boundary conditions at the latter are not compatible in general with integer values for the orbital angular momentum label of the multipole moments: the polar angle eigenfunctions become Legendre functions of order λ and associativity m represented as innite series with a denite parity, and their complementary associated radial functions are spherical Bessel functions of the same order λ. Consequently, the corresponding multipole sources for the electric, magnetic and toroidal moments and their connections are identied within the Debye formalism, and theappropriate outgoing wave Green functions are constructed in the new basis of eigenfunctions of the Helmholtz equation. Our familiarity with the exact solutions, for the cases of the complete sphere and of cylindrical toroids, allow us to give a preliminary account of the electromagnetic elds for the spherical toroids via the integration of their sources and the Green function for resonant cavities and optimum effciency antennas.

Nearly spherical constant-power detonation waves as driven by focused radiation

1973 ◽  
Vol 61 (3) ◽  
pp. 481-498 ◽  
Author(s):  
Y. H. George ◽  
F. K. Moore
Keyword(s):  
Spherical Symmetry ◽  
Three Dimensional ◽  
Tangential Velocity ◽  
Polar Angle ◽  
Strong Shock ◽  
Order System ◽  
Detonation Waves ◽  
Self Similarity ◽  
Self Similar ◽  
Pressure Perturbations

An analysis is made of the flow within a three-dimensional explosion, or spark, created in a gas absorbing energy from a steady conical beam of radiation with nearly spherical symmetry. The radiation, typically from an array of lasers with a common focus, is assumed to be very intense, and absorbed immediately behind an outwardly advancing strong shock. The resulting self-similar flow has previously been studied for spherical symmetry; somewhat improved calculations for that case are presented here.Departures of the laser power from spherical uniformity, which would result from practical problems of arrangement, are conveniently represented by an ascending series of Legendre polynomials in the polar angle. For non-uniformities of small amplitude, first-order perturbations of the flow field are analysed in detail. Self-similarity is shown to be retained, for zero counter-pressure and power constant with time.For the first five harmonics in power distortion, the resulting fourth-order system of equations is solved numerically for profiles of velocity components, density and pressure, and for shock shape. Results are presented graphically. These solutions are singular near the focus, but are nevertheless fully determined. In the limit of large wavenumber, the core of the flow has vanishing tangential velocity and pressure perturbations, and hence the governing equations are only of second order, except presumably in a boundary layer appearing near the shock.Study of the nonlinear case of large wavenumber along the axis of symmetry shows that the singularity at the focus reflects the existence of a ‘forbidden zone’ whose extent depends on the degree of asymmetry. It is argued that this zone is one within which diffusional processes must dominate.

Polar Angle in Terms of Jacobi Hyperbolic Functions

2012 ◽  
Vol 3 (5) ◽  
pp. 105-106
Author(s):  
Parveen Bawa ◽  
Keyword(s):  
Polar Angle ◽  
Hyperbolic Functions

scholarly journals Horizons as boundary conditions in spherical symmetry

2019 ◽  
Vol 100 (6) ◽  
Author(s):  
Sharmila Gunasekaran ◽  
Ivan Booth
Keyword(s):  
Boundary Conditions ◽  
Spherical Symmetry

scholarly journals Tunable multichannel Photonic spin Hall effect in metal-dielectric-metal waveguide

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Li-Ming Zhao ◽  
Yun-Song Zhou
Keyword(s):  
Hall Effect ◽  
Polar Angle ◽  
Spin Hall Effect ◽  
Dipole Source ◽  
Interference Theory ◽  
Wave Interference ◽  
Metal Waveguide ◽  
Component Wave ◽  
Plasmon Polaritons ◽  
Important Progress

AbstractThe discovery of Photonic spin Hall effect (PSHE) on surface plasmon polaritons (SPPs) is an important progress in photonics. In this paper, a method of realizing multi-channel PSHE in two-dimensional metal-air-metal waveguide is proposed. By modulating the phase difference $$\phi$$ ϕ and polar angle $$\theta$$ θ of the dipole source, the SPP can propagate along a specific channel. We further prove that PSHE results from the component wave interference theory. We believe that our findings will rich the application of SPPs in optical devices.

Problems with Spherical Symmetry

2021 ◽  
pp. 102-111
Keyword(s):  
Spherical Symmetry

scholarly journals Study of relativistic magnetized outflows with relativistic equation of state

2019 ◽  
Vol 488 (4) ◽  
pp. 5713-5727
Author(s):  
Kuldeep Singh ◽  
Indranil Chattopadhyay
Keyword(s):  
Magnetic Field ◽  
Angular Momentum ◽  
Equation Of State ◽  
Polar Angle ◽  
Relativistic Equation ◽  
Azimuthal Velocity ◽  
Astrophysical Jets ◽  
Composition Parameter ◽  
Field Lines ◽  
Flow Experiences

ABSTRACT We study relativistic magnetized outflows using relativistic equation of state having variable adiabatic index (Γ) and composition parameter (ξ). We study the outflow in special relativistic magnetohydrodynamic regime, from sub-Alfvénic to super-fast domain. We showed that, after the solution crosses the fast point, magnetic field collimates the flow and may form a collimation-shock due to magnetic field pinching/squeezing. Such fast, collimated outflows may be considered as astrophysical jets. Depending on parameters, the terminal Lorentz factors of an electron–proton outflow can comfortably exceed few tens. We showed that due to the transfer of angular momentum from the field to the matter, the azimuthal velocity of the outflow may flip sign. We also study the effect of composition (ξ) on such magnetized outflows. We showed that relativistic outflows are affected by the location of the Alfvén point, the polar angle at the Alfvén point and also the angle subtended by the field lines with the equatorial plane, but also on the composition of the flow. The pair dominated flow experiences impressive acceleration and is hotter than electron–proton flow.

scholarly journals 3-D flow of a compressible viscous micropolar fluid with spherical symmetry: Regularity of the solution

2016 ◽  
Vol 438 (1) ◽  
pp. 162-183 ◽  
Author(s):  
Ivan Dražić ◽  
Loredana Simčić ◽  
Nermina Mujaković
Keyword(s):  
Spherical Symmetry ◽  
Micropolar Fluid

scholarly journals Rotor Interaction Noise in Counter-Rotating Propfan Propulsion Systems

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
Andreas Peters ◽  
Zoltán S. Spakovszky
Keyword(s):  
Polar Angle ◽  
Secondary Flows ◽  
Tip Vortex ◽  
System Level ◽  
Analysis Tool ◽  
Acoustic Analogy ◽  
Wake Interaction ◽  
Open Rotor ◽  
And Performance ◽  
The Individual

Due to their inherent noise challenge and potential for significant reductions in fuel burn, counter-rotating propfans (CRPs) are currently being investigated as potential alternatives to high-bypass turbofan engines. This paper introduces an integrated noise and performance assessment methodology for advanced propfan powered aircraft configurations. The approach is based on first principles and combines a coupled aircraft and propulsion system mission and performance analysis tool with 3D unsteady, full-wheel CRP computational fluid dynamics computations and aeroacoustic simulations. Special emphasis is put on computing CRP noise due to interaction tones. The method is capable of dealing with parametric studies and exploring noise reduction technologies. An aircraft performance, weight and balance, and mission analysis was first conducted on a candidate CRP powered aircraft configuration. Guided by data available in the literature, a detailed aerodynamic design of a pusher CRP was carried out. Full-wheel unsteady 3D Reynolds-averaged Navier-Stokes (RANS) simulations were then used to determine the time varying blade surface pressures and unsteady flow features necessary to define the acoustic source terms. A frequency domain approach based on Goldstein’s formulation of the acoustic analogy for moving media and Hanson’s single rotor noise method was extended to counter-rotating configurations. The far field noise predictions were compared to measured data of a similar CRP configuration and demonstrated good agreement between the computed and measured interaction tones. The underlying noise mechanisms have previously been described in literature but, to the authors’ knowledge, this is the first time that the individual contributions of front-rotor wake interaction, aft-rotor upstream influence, hub-endwall secondary flows, and front-rotor tip-vortices to interaction tone noise are dissected and quantified. Based on this investigation, the CRP was redesigned for reduced noise incorporating a clipped rear-rotor and increased rotor-rotor spacing to reduce upstream influence, tip-vortex, and wake interaction effects. Maintaining the thrust and propulsive efficiency at takeoff conditions, the noise was calculated for both designs. At the interaction tone frequencies, the redesigned CRP demonstrated an average reduction of 7.25 dB in mean sound pressure level computed over the forward and aft polar angle arcs. On the engine/aircraft system level, the redesigned CRP demonstrated a reduction of 9.2 dB in effective perceived noise (EPNdB) and 8.6 EPNdB at the Federal Aviation Regulations (FAR) 36 flyover and sideline observer locations, respectively. The results suggest that advanced open rotor designs can possibly meet Stage 4 noise requirements.

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