An Example of Physical Interest

2016 ◽  
pp. 199-219
Author(s):  
Debashish Goswami ◽  
Jyotishman Bhowmick
Keyword(s):  
Physical Interest

scholarly journals An Application of Hankel Transforms in Axially Symmetric Potential Flow

1956 ◽  
Vol 9 (3) ◽  
pp. 128-131
Author(s):  
A. G. Mackie
Keyword(s):  
New York ◽  
Incompressible Fluid ◽  
Circular Hole ◽  
Potential Flow ◽  
Fourier Transforms ◽  
The Other ◽  
Axially Symmetric ◽  
Symmetric Potential ◽  
Physical Interest ◽  
Hankel Transforms

In his book on Hydrodynamics, Lamb obtained a solution for the potential flow of an incompressible fluid through a circular hole in a plane wall. More recently Sneddon (Fourier Transforms, New York, 1951) obtained Lamb's solution by an elegant application of Hankel transforms.Since the streamlines in this solution are symmetric about the wall, it is not of particular physical interest. In this note, Sneddon's method is used to give a solution in which the fluid is infinite in extent on one side of the aperture but issues as a jet of finite diameter on the other side.

scholarly journals Generalized function treatment of the Alfvén-gravity wave problem

1983 ◽  
Vol 6 (2) ◽  
pp. 395-402
Author(s):  
L. Debnath ◽  
K. Vajravelu
Keyword(s):  
Steady State ◽  
Gravity Waves ◽  
Function Method ◽  
Radiation Condition ◽  
Physical Significance ◽  
Generalized Function ◽  
Wave Problem ◽  
Physical Interest ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid

A study is made of the steady-state Alfvén-gravity waves in an inviscid incompressible electrically conducting fluid with an interface due to a harmonically oscillating pressure distribution acting on the interface. The generalized function method is employed to solve the problem in the fluid of infinite, finite and shallow depth. A unique solution of physical interest is derived by imposing the Sommerfeld radiation condition at infinity. Several limiting cases of physical interest are obtained from the present analysis. The physical significance of the solutions and their limiting cases are discussed.

scholarly journals Generating solutions to the Einstein field equations

2016 ◽  
Vol 25 (02) ◽  
pp. 1650022 ◽  
Author(s):  
I. G. Contopoulos ◽  
F. P. Esposito ◽  
K. Kleidis ◽  
D. B. Papadopoulos ◽  
L. Witten
Keyword(s):  
Exact Solutions ◽  
Killing Vector ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Physical Interest ◽  
Axisymmetric Solutions

Exact solutions to the Einstein field equations may be generated from already existing ones (seed solutions), that admit at least one Killing vector. In this framework, a space of potentials is introduced. By the use of symmetries in this space, the set of potentials associated to a known solution is transformed into a new set, either by continuous transformations or by discrete transformations. In view of this method, and upon consideration of continuous transformations, we arrive at some exact, stationary axisymmetric solutions to the Einstein field equations in vacuum, that may be of geometrical or/and physical interest.

The shot effect with space charge

1938 ◽  
Vol 34 (2) ◽  
pp. 158-166 ◽  
Author(s):  
J. M. Whittaker
Keyword(s):  
Space Charge ◽  
Background Noise ◽  
Physical Interest ◽  
Secondary Ions

The technical importance of constructing valve amplifiers disturbed by as little background noise as possible has led to a very searching investigation of the causes of this defect. Some causes—bad contacts, changes in the surface of the filament, secondary ions from the grid, and so forth—though technically speaking not trivial, are of minor physical interest; but it has long been recognized that there are two which cannot be dismissed so easily.

The momentum of light in a refracting medium

1976 ◽  
Vol 347 (1651) ◽  
pp. 475-491 ◽  
Keyword(s):  
Refractive Index ◽  
Electromagnetic Field ◽  
Light Pulse ◽  
Correct Answer ◽  
Light Wave ◽  
Physical Interest ◽  
Momentum Change ◽  
Uniform Medium ◽  
Acoustic Transients ◽  
Mechanical Momentum

It is shown that neither Minkowski’s result, according to which the ratio of momentum to energy for a light wave in a medium of refractive index n is n / c , nor that of Abraham, who found 1/ nc , is correct. For a broad wave in a uniform medium, the correct answer is given by (2.12) with σ = 1/5. For weak refraction it is approximately equal to the average of the Abraham and Minkowski results. Abraham’s formula gives correctly the part of the momentum which resides in the electromagnetic field, but not the mechanical momentum of the medium which travels with the light pulse. Minkowski’s formula gives the pseudo-momentum, a quantity of physical interest. The momentum change upon reflexion or transmission usually involves also acoustic transients, these are discussed for some simple cases.

scholarly journals Division algebra representations of SO(4, 2)

2014 ◽  
Vol 29 (25) ◽  
pp. 1450128 ◽  
Author(s):  
Joshua Kincaid ◽  
Tevian Dray
Keyword(s):  
Clifford Algebra ◽  
Division Algebra ◽  
Conformal Group ◽  
Algebra Structure ◽  
Physical Interest

Representations of SO (4, 2) are constructed using 4×4 and 2×2 matrices with elements in ℍ' ⊗ ℂ and the known isomorphism between the conformal group and SO (4, 2) is written explicitly in terms of the 4×4 representation. The Clifford algebra structure of SO (4, 2) is briefly discussed in this language, as is its relationship to other groups of physical interest.

The physics of meron pairs. II. The bare activity

1980 ◽  
Vol 58 (6) ◽  
pp. 859-880 ◽  
Author(s):  
David G. Laughton
Keyword(s):  
Detailed Analysis ◽  
Numerical Work ◽  
Detailed Consideration ◽  
Physical Interest ◽  
The Third ◽  
Constraint Systems

In this second paper of the series, the details are given of the calculation of the bare activity of the meron pairs described in the first paper. The instanton limit is computed and found to be consistent with the discussion presented in the first paper. The bulk of the calculation for the regime of physical interest is performed using one set of constraints. An outline is given of one possible treatment of an instability in the calculation in part of this regime. A detailed analysis of this instability, a more detailed consideration of other constraint systems, and some further numerical work are left for the third paper.

scholarly journals SUPER TENSOR MODELS, SUPER FUZZY SPACES AND SUPER n-ARY TRANSFORMATIONS

2011 ◽  
Vol 26 (24) ◽  
pp. 4203-4216 ◽  
Author(s):  
NAOKI SASAKURA
Keyword(s):  
Lie Algebra ◽  
General Framework ◽  
Space Form ◽  
Quantum Corrections ◽  
Physical Interest ◽  
Dynamical Generation ◽  
Fuzzy Space ◽  
Tensor Models ◽  
Algebraic Description ◽  
Super Lie Algebra

By extending the algebraic description of the bosonic rank-three tensor models, a general framework for super rank-three tensor models and correspondence to super fuzzy spaces is proposed. The corresponding super fuzzy spaces must satisfy a certain cyclicity condition on the algebras of functions on them. Due to the cyclicity condition, the symmetry of the super rank-three tensor models are represented by super n-ary transformations. The Leibnitz rules and the fundamental identities for the super n-ary transformations are discussed from the perspective of the symmetry of the algebra of a fuzzy space. It is shown that the super n-ary transformations of finite orders which conserve the algebra of a fuzzy space form a finite closed n-ary super Lie algebra. Super rank-three tensor models would be of physical interest as background independent models for dynamical generation of supersymmetric fuzzy spaces, in which quantum corrections are under control.

scholarly journals A way of decoupling gravitational sources in pure Lovelock gravity

2019 ◽  
Vol 79 (11) ◽  
Author(s):  
Milko Estrada
Keyword(s):  
Black Hole ◽  
Extra Dimensions ◽  
De Sitter Space ◽  
Analytic Solutions ◽  
De Sitter ◽  
Lovelock Gravity ◽  
Regular Black Hole ◽  
Physical Interest ◽  
Geometric Deformation ◽  
Black Hole Solutions

Abstract We provide an algorithm that shows how to decouple gravitational sources in pure Lovelock gravity. This method allows to obtain several new and known analytic solutions of physical interest in scenarios with extra dimensions and with presence of higher curvature terms. Furthermore, using our method, it is shown that applying the minimal geometric deformation to the Anti de Sitter space time it is possible to obtain regular black hole solutions.

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