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.

A Numerical Solution of Two-Dimensional Deep Water Wave-Body Problems

1984 ◽  
Vol 28 (01) ◽  
pp. 48-54 ◽  
Author(s):  
A. Nestegard ◽  
P. D. Sclavounos
Keyword(s):  
Deep Water ◽  
Numerical Technique ◽  
Logarithmic Singularity ◽  
Harmonic Wave ◽  
Outer Region ◽  
Multipole Expansion ◽  
Two Dimensions ◽  
The Body ◽  
Forced Oscillations ◽  
The Green Function

A numerical technique is presented for the solution of deep water linear and time-harmonic wave-body-interaction problems in two dimensions. A mathematical boundary of circular shape surrounding the body is introduced in the fluid domain, thus defining two flow regions. A multipole expansion valid in the outer region is then matched to an integral representation of the solution in the inner region which is obtained by applying Green's theorem and by using the fundamental logarithmic singularity as the Green function. The method applies both to surface-piercing and submerged bodies. Numerical results are presented for the forced oscillations of three surface-piercing ship-like sections of regular shape. No irregular frequencies are encountered. Comparisons with existing numerical methods are made to test the accuracy and emphasize the computational efficiency of the present approach.

scholarly journals Wave radiation and diffraction by a circular cylinder submerged below an ice sheet with a crack

2018 ◽  
Vol 845 ◽  
pp. 682-712 ◽  
Author(s):  
Zhi Fu Li ◽  
Guo Xiong Wu ◽  
Chun Yan Ji
Keyword(s):  
Green Function ◽  
Circular Cylinder ◽  
Body Surface ◽  
Ice Sheet ◽  
Integral Form ◽  
Multipole Expansion ◽  
The Body ◽  
Wave Radiation ◽  
Surface Boundary ◽  
The Green Function

Wave radiation and diffraction by a circular cylinder submerged below an ice sheet with a crack are considered based on the linearized velocity potential theory together with multipole expansion. The solution starts from the potential due to a single source, or the Green function satisfying both the ice sheet condition and the crack condition, as well as all other conditions apart from that on the body surface. This is obtained in an integral form through Fourier transform, in contrast to what has been obtained previously in which the Green function is in the series form based on the method of matched eigenfunction expansion in each domain on both sides of the crack. The multipole expansion is then constructed through direct differentiation of the Green function with respect to the source position, rather than treating each multipole as a separate problem. The use of the Green function enables the problem of wave diffraction by the crack in the absence of the body to be solved directly. For the circular cylinder, wave radiation and diffraction problems are solved by applying the body surface boundary condition to the multipole expansion, through which the unknown coefficients are obtained. Extensive results are provided for the added mass and damping coefficient as well as the exciting force. When the cylinder is away from the crack, a wide spacing approximation method is used, which is found to provide accurate results apart from when the cylinder is quite close to the crack.

A Simple, Accurate Model for Porphyrin Ring-Current Shifts

1992 ◽  
Vol 45 (6) ◽  
pp. 991 ◽  
Author(s):  
KJ Cross ◽  
MJ Crossley
Keyword(s):  
Excellent Agreement ◽  
Ring Current ◽  
Cytochrome B5 ◽  
Polar Angle ◽  
Multipole Expansion ◽  
Porphyrin Ring ◽  
Simple Analytical Expression ◽  
X Ray ◽  
Accurate Model ◽  
Current Shift

A computationally simple, but accurate, model for porphyrin ring-current shifts is presented and calibrated by using X-ray and n.m.r. data from cytochrome c, cytochrome C551, cytochrome b5, and pyridine and picoline complexes of zinc porphyrin . The model involves a multipole expansion in terms of Legendre polynomials of the cosine of the polar angle and reciprocal powers of the distance between the centre of the porphyrin ring and the atom of interest. The multipole model offers a simple analytical expression for the ring-current shift in contrast to the complex expressions derived from the Johnson-Bovey and Haigh-Mallion models. The model was tested with a series of capped porphyrins and gave capto-porphyrin separations in excellent agreement with the X-ray structures at low temperature. Excellent agreement is also observed between calculated and observed ring-current shifts, even for protons in close proximity to the porphyrin ring.

scholarly journals Interação quadrupolar e sua correlação com o efeito Mössbauer

1982 ◽  
Vol 4 (4) ◽  
pp. 01
Author(s):  
Sylvestre Schneider
Keyword(s):  
Moment Tensor ◽  
Energy Levels ◽  
Multipole Expansion ◽  
Multipole Moment ◽  
Quadrupolar Interaction ◽  
Matrix Elements ◽  
Multipole Moments ◽  
Classical Charge ◽  
The Matrix ◽  
Mechanical Expression

By means multipole expansion, we guess the concept of "multipole moment". They are given examples of multipole moments. We start of them to define the "quadruploe moment tensor". By starting from the classical chargedents distribution of loads ρ (r-> ') and from the potencial expanded in a Taylor series, in which one one of the terms allows us to see the quadrupole moment, we construct a classical Hamiltonian in terms of quadrupole. The quantum-mechanical expression ĤQ por HQ is given, by substitution of the classical charge density ρ (r->) by an operator ρ (op), which describes adequately the real configuration in a non-continuous charge distribution. By use of the Clebsh-Gordan tecnology-coefficients with the irredutible tensors, the matrix-elements of ĤQ was calculated. The relation develloped, which allows the calcule of the matrix-elements of ĤQ, this is used for an application to a specific case, of a strong mafnetic field exerted on an atom. It is obtained a particular relation, for calculating the energy levels of quadrupolar interaction. The sequente purpose was to work out an application for an atom or ion in the fundamental staton 2S1/2, and nuclear spin 3/2 in a strong magnetic field.The results was a splitting in energy levels for the quadrupolar interaction. The quadrupolar interaction was examined in correlation of the Mössbauer-Effect in different examples.

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.

scholarly journals From discrete to continuous description of spherical surface charge distributions

Soft Matter ◽  
2018 ◽  
Vol 14 (7) ◽  
pp. 1149-1161 ◽  
Author(s):  
Anže Lošdorfer Božič
Keyword(s):  
Particle Size ◽  
Surface Charge ◽  
Spherical Surface ◽  
Multipole Expansion ◽  
Spatial Extent ◽  
Charge Distributions ◽  
Continuous Description

Multipole expansion of spherical surface charge distributions which takes into account the finite spatial extent of charges relative to particle size.

“Where is Dementia?” A Systematic Literature Review Exploring Neuroanatomical Aspects of Dementia

2017 ◽  
Vol 2 (15) ◽  
pp. 9-23 ◽  
Author(s):  
Chorong Oh ◽  
Leonard LaPointe
Keyword(s):  
English Language ◽  
Signs And Symptoms ◽  
Behavioral Symptoms ◽  
Journal Articles ◽  
People With Dementia ◽  
Different Types ◽  
Precise Diagnosis ◽  
Physical Changes ◽  
The Brain ◽  
Language Literature

Dementia is a condition caused by and associated with separate physical changes in the brain. The signs and symptoms of dementia are very similar across the diverse types, and it is difficult to diagnose the category by behavioral symptoms alone. Diagnostic criteria have relied on a constellation of signs and symptoms, but it is critical to understand the neuroanatomical differences among the dementias for a more precise diagnosis and subsequent management. With this regard, this review aims to explore the neuroanatomical aspects of dementia to better understand the nature of distinctive subtypes, signs, and symptoms. This is a review of English language literature published from 1996 to the present day of peer-reviewed academic and medical journal articles that report on older people with dementia. This review examines typical neuroanatomical aspects of dementia and reinforces the importance of a thorough understanding of the neuroanatomical characteristics of the different types of dementia and the differential diagnosis of them.

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