Topic

# Axial symmetry

About: Axial symmetry is a research topic. Over the lifetime, 6496 publications have been published within this topic receiving 100626 citations. The topic is also known as: line symmetry & axisymmetry.

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TL;DR: An overview of the recent developments in the field of cylindrical vector beams is provided in this paper, where the authors also discuss the potential of using these beams in other fields.

Abstract: An overview of the recent developments in the field of cylindrical vector beams is
provided. As one class of spatially variant polarization, cylindrical vector beams
are the axially symmetric beam solution to the full vector electromagnetic wave
equation. These beams can be generated via different active and passive methods.
Techniques for manipulating these beams while maintaining the polarization symmetry
have also been developed. Their special polarization symmetry gives rise to unique
high-numerical-aperture focusing properties that find important applications in
nanoscale optical imaging and manipulation. The prospects for cylindrical vector
beams and their applications in other fields are also briefly discussed.

2,361 citations

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TL;DR: In this paper, a large number of investigations have been devoted to the problem of the formation and the development of a crack during brittle fracture of solids, and the first of these was the well-known work of Griffith [l] devoted to determination of the critical length of the crack at a given load, i.e. the length at which it begins to widen catastrophically.

Abstract: A large number of investigations has been devoted to the problem of the formation and the development of a crack during brittle fracture of solids. The first of these was the well-known work of Griffith [l] devoted to the determination of the critical length of a crack at a given load, i.e. the length of a crack at which it begins to widen catastrophically. Assuming an elliptical form of a crack forming in an infinite body subjected to an infinitely homogeneous tension, Griffith obtained an expression for the critical length of a crack as that corresponding to the total.of the full increase in energy (equal to the sum of the surface energy plus the elastic energy released due to the formation of the crack).

1,154 citations

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TL;DR: In this article, a simple approximate theory is developed for the case in which the fluid is sufficiently inviscid that the poleward flow in the Hadley cell is nearly angular momentum conserving.

Abstract: The structure of certain axially symmetric circulations in a stably stratified, differentially heated, rotating Boussinesq fluid on a sphere is analyzed. A simple approximate theory [similar to that introduced by Schneider (1977)] is developed for the case in which the fluid is sufficiently inviscid that the poleward flow in the Hadley cell is nearly angular momentum conserving. The theory predicts the width of the Hadley cell, the total poleward heat flux, the latitude of the upper level jet in the zonal wind, and the distribution of surface easterlies and westerlies. Fundamental differences between such nearly inviscid circulations and the more commonly studied viscous axisymmetric flows are emphasized. The theory is checked against numerical solutions to the model equations.

867 citations

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TL;DR: In this paper, a new general class of solutions of the Einstein-Maxwell equations is presented, which is based on seven arbitrary parameters that group in a natural way into three complex parameters m + in, a + ib, e + ig, and the cosmological constant λ.

Abstract: A new general class of solutions of the Einstein-Maxwell equations is presented. It depends on seven arbitrary parameters that group in a natural way into three complex parameters m + in , a + ib , e + ig , and the cosmological constant λ. They correspond to mass, NUT parameter, angular momentum per unit mass, acceleration, and electric and magnetic charge. The metric is in general stationary and axially symmetric. These solutions are of type D and contain as special cases all known solutions of type D belonging to this class. The known solutions are recovered by performing limiting transitions. An appropriate limit of our solutions describes an electromagnetic field in flat spacetime. We investigate the properties of that field. Its singular region corresponds in general to two circles moving with uniform acceleration in the positive and negative directions along the axis of symmetry. One can easily extend our solutions to the complex domain. Then it turns out that the metric can be written in a double Kerr-Schild form.

746 citations

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TL;DR: In this paper, a theory of the energy states and the electromagnetic transitions between them for nuclei which do not possess axial symmetry was developed and the reduced probabilities for E2 and M1 transitions between various rotational states were computed.

Abstract: A theory of the energy states and the electromagnetic transitions between them is developed for nuclei which do not possess axial symmetry. It is shown that violation of axial symmetry does not significantly change the rotational states of axial nuclei and leads to the appearance of new energy states. The reduced probabilities for E2 and M1 transitions between various rotational states are computed.

735 citations