On Randers Conformal Transformation of m-th Root Metric

A new algorithm for constructing orthogonal curvilinear grids on a sphere for a fairly general geometric shape of the modeling region is implemented as a “compile-once - use forever” software package. It is based on the numerical solution of the inverse problem by an iterative procedure -- finding such distribution of grid points along its perimeter, so that the conformal transformation of the perimeter into a rectangle turns this distribution into uniform one. The iterative procedure itself turns out to be multilevel - i.e. an iterative loop built around another, internal iterative procedure. Thereafter, knowing this distribution, the grid nodes inside the region are obtained solving an elliptic problem. It is shown that it was possible to obtain the exact orthogonality of the perimeter at the corners of the grid, to achieve very small, previously unattainable level of orthogonality errors, as well as make it isotropic -- local distances between grid nodes about both directions are equal to each other.

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Conformal transformation in an almost Hermitian manifold

Novi Sad Journal of Mathematics ◽

10.30755/nsjom.03301 ◽

2016 ◽

Vol 46 (1) ◽

pp. 217-226

Author(s):

B. B. Chaturvedi ◽

Pankaj Pandey

Keyword(s):

Conformal Transformation ◽

Hermitian Manifold ◽

Almost Hermitian Manifold

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Rectifying curves under conformal transformation

Journal of Geometry and Physics ◽

10.1016/j.geomphys.2021.104117 ◽

2021 ◽

Vol 163 ◽

pp. 104117

Author(s):

Absos Ali Shaikh ◽

Mohamd Saleem Lone ◽

Pinaki Ranjan Ghosh

Keyword(s):

Conformal Transformation

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H-plane horn antenna with enhanced directivity using conformal transformation optics

Scientific Reports ◽

10.1038/s41598-021-93812-6 ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Hossein Eskandari ◽

Juan Luis Albadalejo-Lijarcio ◽

Oskar Zetterstrom ◽

Tomáš Tyc ◽

Oscar Quevedo-Teruel

Keyword(s):

Conformal Transformation ◽

Phase Error ◽

Three Dimensional ◽

Physical Space ◽

Horn Antenna ◽

High Gain ◽

Transformation Optics ◽

Graded Index ◽

Low Profile ◽

Dielectric Lens

AbstractConformal transformation optics is employed to enhance an H-plane horn’s directivity by designing a graded-index all-dielectric lens. The transformation is applied so that the phase error at the aperture is gradually eliminated inside the lens, leading to a low-profile high-gain lens antenna. The physical space shape is modified such that singular index values are avoided, and the optical path inside the lens is rescaled to eliminate superluminal regions. A prototype of the lens is fabricated using three-dimensional printing. The measurement results show that the realized gain of an H-plane horn antenna can be improved by 1.5–2.4 dB compared to a reference H-plane horn.

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The geometry of null-like disformal transformations

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887819501809 ◽

2019 ◽

Vol 16 (11) ◽

pp. 1950180 ◽

Cited By ~ 2

Author(s):

I. P. Lobo ◽

G. G. Carvalho

Keyword(s):

Vector Field ◽

Conformal Transformation ◽

Vector Fields ◽

Killing Vector ◽

Killing Vector Fields ◽

Spinor Structure ◽

Schwarzschild Metric ◽

Killing Vectors ◽

Symmetry Properties ◽

Geometric Objects

Motivated by the hindrance of defining metric tensors compatible with the underlying spinor structure, other than the ones obtained via a conformal transformation, we study how some geometric objects are affected by the action of a disformal transformation in the closest scenario possible: the disformal transformation in the direction of a null-like vector field. Subsequently, we analyze symmetry properties such as mutual geodesics and mutual Killing vectors, generalized Weyl transformations that leave the disformal relation invariant, and introduce the concept of disformal Killing vector fields. In most cases, we use the Schwarzschild metric, in the Kerr–Schild formulation, to verify our calculations and results. We also revisit the disformal operator using a Newman–Penrose basis to show that, in the null-like case, this operator is not diagonalizable.

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Conformal mapping of the Misner–Sharp mass from gravitational collapse

International Journal of Modern Physics D ◽

10.1142/s0218271816500814 ◽

2016 ◽

Vol 25 (07) ◽

pp. 1650081 ◽

Cited By ~ 9

Author(s):

Fayçal Hammad

Keyword(s):

Conformal Mapping ◽

Gravitational Collapse ◽

Conformal Transformation ◽

Conformal Mappings ◽

Conformal Transformations ◽

Theories Of Gravity ◽

Definition Of ◽

Geometric Definition

The conformal transformation of the Misner–Sharp mass is reexamined. It has recently been found that this mass does not transform like usual masses do under conformal mappings of spacetime. We show that when it comes to conformal transformations, the widely used geometric definition of the Misner–Sharp mass is fundamentally different from the original conception of the latter. Indeed, when working within the full hydrodynamic setup that gave rise to that mass, i.e. the physics of gravitational collapse, the familiar conformal transformation of a usual mass is recovered. The case of scalar–tensor theories of gravity is also examined.

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