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Journal articles on the topic 'Transformations (Mathematics) Conformal mapping'

Author: Grafiati

Published: 4 June 2021

Last updated: 16 February 2022

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1

Hammad, Fayçal. "Conformal mapping of the Misner–Sharp mass from gravitational collapse." International Journal of Modern Physics D 25, no. 07 (June 2016): 1650081. http://dx.doi.org/10.1142/s0218271816500814.

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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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2

Mughal, Adil, and Denis Weaire. "Curvature in conformal mappings of two-dimensional lattices and foam structure." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465, no. 2101 (October 7, 2008): 219–38. http://dx.doi.org/10.1098/rspa.2008.0260.

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The elegant properties of conformal mappings, when applied to two-dimensional lattices, find interesting applications in two-dimensional foams and other cellular or close-packed structures. In particular, the two-dimensional honeycomb (whose dual is the triangular lattice) may be transformed into various conformal patterns, which compare approximately to experimentally realizable two-dimensional foams. We review and extend the mathematical analysis of such transformations, with several illustrative examples. New results are adduced for the local curvature generated by the transformation.

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3

Haruki, H., and T. M. Rassias. "A New Invariant Characteristic Property of Möbius Transformations from the Standpoint of Conformal Mapping." Journal of Mathematical Analysis and Applications 181, no. 2 (January 1994): 320–27. http://dx.doi.org/10.1006/jmaa.1994.1024.

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4

Lo, Wei-Lin, Nan-Jing Wu, Chuin-Shan Chen, and Ting-Kuei Tsay. "Exact Boundary Derivative Formulation for Numerical Conformal Mapping Method." Mathematical Problems in Engineering 2016 (2016): 1–18. http://dx.doi.org/10.1155/2016/5072309.

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Conformal mapping is a useful technique for handling irregular geometries when applying the finite difference method to solve partial differential equations. When the mapping is from a hyperrectangular region onto a rectangular region, a specific length-to-width ratio of the rectangular region that fitted the Cauchy-Riemann equations must be satisfied. In this research, a numerical integral method is proposed to find the specific length-to-width ratio. It is conventional to employ the boundary integral method (BIEM) to perform the conformal mapping. However, due to the singularity produced by the BIEM in seeking the derivatives on the boundaries, the transformation Jacobian determinants on the boundaries have to be evaluated at inner points instead of directly on the boundaries. This approximation is a source of numerical error. In this study, the transformed rectangular property and the Cauchy-Riemann equations are successfully applied to derive reduced formulations of the derivatives on the boundaries for the BIEM. With these boundary derivative formulations, the Jacobian determinants can be evaluated directly on the boundaries. Furthermore, the results obtained are more accurate than those of the earlier mapping method.

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5

Cazacu, Cabiria Andreian, and Dorin Ghisa. "Fundamental Domains of Gamma and Zeta Functions." International Journal of Mathematics and Mathematical Sciences 2011 (2011): 1–21. http://dx.doi.org/10.1155/2011/985323.

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Branched covering Riemann surfaces(ℂ,f)are studied, wherefis the Euler Gamma function and the Riemann Zeta function. For both of them fundamental domains are found and the group of cover transformations is revealed. In order to find fundamental domains, preimages of the real axis are taken and a thorough study of their geometry is performed. The technique of simultaneous continuation, introduced by the authors in previous papers, is used for this purpose. Color visualization of the conformal mapping of the complex plane by these functions is used for a better understanding of the theory. A version of this paper containing colored images can be found in arXiv at Andrian Cazacu and Ghisa.

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6

Najarbashi, G., S. Ahadpour, M. A. Fasihi, and Y. Tavakoli. "Geometry of a two-qubit state and intertwining quaternionic conformal mapping under local unitary transformations." Journal of Physics A: Mathematical and Theoretical 40, no. 24 (May 30, 2007): 6481–89. http://dx.doi.org/10.1088/1751-8113/40/24/014.

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7

Prokert, G. "On the existence of solutions in plane quasistationary Stokes flow driven by surface tension." European Journal of Applied Mathematics 6, no. 5 (October 1995): 539–58. http://dx.doi.org/10.1017/s0956792500002035.

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Recently, the free boundary problem of quasistationary Stokes flow of a mass of viscous liquid under the action of surface tension forces has been considered by R. W. Hopper, L. K. Antanovskii, and others. The solution of the Stokes equations is represented by analytic functions, and a time dependent conformal mapping onto the flow domain is applied for the transformation of the problem to the unit disk. Two coupled Hilbert problems have to be solved there, which leads to a Fredholm boundary integral equation. The solution of this equation determines the time evolution of the conformal mapping. The question of the existence of a solution to this evolution problem for arbitrary (smooth) initial data has not yet been answered completely. In this paper, local existence in time is proved using a theorem of Ovsiannikov on Cauchy problems in an appropriate scale of Banach spaces. The necessary estimates are obtained in a way that is oriented at the a priori estimates for the solution given by Antanovskii. In the case of small deviations from the stationary solution represented by a circle, these a priori estimates, together with the local results, are used to prove even global existence of the solution in time.

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8

Renedo Anglada, Jaime, Suleiman Sharkh, and Arfakhshand Qazalbash. "Influence of curvature on air-gap magnetic field distribution and rotor losses in PM electric machines." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 36, no. 4 (July 3, 2017): 871–91. http://dx.doi.org/10.1108/compel-05-2016-0200.

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Purpose The purpose of this paper is to study the effect of curvature on the magnetic field distribution and no-load rotor eddy current losses in electric machines, particularly in high-speed permanent magnet (PM) machines. Design/methodology/approach The magnetic field distribution is obtained using conformal mapping, and the eddy current losses are obtained using a cylindrical multilayer model. The analytical results are validated using a two-dimensional finite element analysis. The analytical method is based on a proportional-logarithmic conformal transformation that maps the cylindrical geometry of a rotating electric machine into a rectangular configuration without modifying the length scale. In addition, the appropriate transformation of PM cylindrical domains into the rectangular domain is deduced. Based on this conformal transformation, a coefficient to quantify the effect of curvature is proposed. Findings Neglecting the effect of curvature can produce significant errors in the calculation of no-load rotor losses when the ratio between the air-gap length and the rotor diameter is large. Originality/value The appropriate transformation of PM cylindrical domains into the rectangular domain is deduced. The proportional-logarithmic transformation proposed provides an insight into the effect of curvature on the magnetic field distribution in the air-gap and no-load rotor losses. Furthermore, the proposed curvature coefficient gives a notion of the effect of curvature for any particular geometry without the necessity of any complicated calculation. The case study shows that neglecting the effect of curvature underestimates the rotor eddy-current losses significantly in machines with large gap-to-rotor diameter ratios.

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9

CHAUDHRY, Maqsood A., and Roland SCHINZINGER. "NUMERICAL COMPUTATION OF THE SCHWARZ‐CHRISTOFFEL TRANSFORMATION PARAMETERS FOR CONFORMAL MAPPING OF ARBITRARILY SHAPED POLYGONS WITH FINITE VERTICES." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 11, no. 2 (February 1992): 263–75. http://dx.doi.org/10.1108/eb010091.

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10

Crowdy, Darren, and Jonathan Marshall. "Analytical formulae for the Kirchhoff–Routh path function in multiply connected domains." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 461, no. 2060 (June 23, 2005): 2477–501. http://dx.doi.org/10.1098/rspa.2005.1492.

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Explicit formulae for the Kirchhoff–Routh path functions (or Hamiltonians) governing the motion of N -point vortices in multiply connected domains are derived when all circulations around the holes in the domain are zero. The method uses the Schottky–Klein prime function to find representations of the hydrodynamic Green's function in multiply connected circular domains. The Green's function is then used to construct the associated Kirchhoff–Routh path function. The path function in more general multiply connected domains then follows from a transformation property of the path function under conformal mapping of the canonical circular domains. Illustrative examples are presented for the case of single vortex motion in multiply connected domains.

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11

Lin, De-Hone. "The Magnetic Hooke-Newton Transmutation in Momentum Space." Symmetry 13, no. 4 (April 6, 2021): 608. http://dx.doi.org/10.3390/sym13040608.

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The magnetic Hooke-Newton transmutation, which emerges from the transformation design of the quadratic conformal mapping for the system of charged particles moving in the uniform magnetic field, is investigated in the momentum space. It is shown that there are two ways to turn the linear interaction force of the system into the inverse square interaction. The first one, which involves simply applying the mapping to the system, has the spectrum with the Landau levels of even angular momentum quantum number. The second one considers the geometric structure of the mapping as an effective potential which leads us to the transmuted Coulomb system with the novel quantum spectrum. The wave functions of momentum for the bound and scattering states of the transmutation system are given. It is also shown that the effective potential due to the geometric structure can be generalized to a general 2D surface, and the Schrödinger equation of a particle moving on the surface while under the action of the potential can be solved by the form-invariant Schrödinger equation of the free particle. The solution of a particle moving on the hyperbolic surface under the potential is given with the conclusion. The presentation manifests the transformation design of the quantum state, depending mainly on the geometric structure of the representation space, not on the action of the specific potential field. This characteristic makes it possible for us to use the geometric structure of different representation spaces to explore some novel behaviors of quantum particles.

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12

Ma, Yaocai, Aizhong Lu, and Hui Cai. "An analytical method for determining the non-enclosed elastoplastic interface of a circular hole." Mathematics and Mechanics of Solids 25, no. 5 (February 26, 2020): 1199–213. http://dx.doi.org/10.1177/1081286520909489.

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Based on the Mohr–Coulomb yield criterion, an analytical method is presented to determine the plastic zone in an infinite plate weakened by a circular hole and subjected to non-hydrostatic stresses at infinity. It is worth noting that this paper considers the more complicated case that the plastic zone cannot completely surround the hole, namely the elastoplastic interface is non-enclosed. Initially, the non-circular elastic zone in the physical plane is mapped onto the outer region of a unit circle in the image plane by the conformal transformation in the complex variable method. Thereby, determining the elastoplastic interface is equivalent to solving the mapping function coefficients. The nonlinear equations for solving the coefficients are established by considering both the stress continuity conditions along the elastoplastic interface and the stress boundary conditions along the elastic part of the hole. Naturally, the problem can be further transformed into an optimization problem, which is ultimately achieved by the differential-evolution algorithm; what is more, an analytical solution with high accuracy is obtained. Based on the programmed computing, the influences of various parameters on the shape and size of the plastic zone are given.

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13

Bomba, A. Ya, I. P. Moroz, and M. V. Boichura. "THE OPTIMIZATION OF THE SHAPE AND SIZE OF THE INJECTION CONTACTS OF THE INTEGRATED P-I-N-STRUCTURES ON THE BASE OF USING THE CONFORMAL MAPPING METHOD." Radio Electronics, Computer Science, Control 1, no. 1 (April 2, 2021): 14–28. http://dx.doi.org/10.15588/1607-3274-2021-1-2.

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Context. P-i-n-diodes are widely used in a microwave technology to control the electromagnetic field. The field is controlled by the formation of an electron-hole plasma in the region of an intrinsic semiconductor (i-region) under the influence of a control current. The development of control devices on p-i-n-diodes has led to the emergence of integral p-i-n-structures of various types, the characteristics of which (for example, switching speed, switched power level, etc.) exceed the similar characteristics of volume diodes. The properties of p-i-n-structures are determined by a number of processes: the diffusion-drift charge transfer process, the recombination-generation, thermal, injection, and the so on. Obviously, these processes should be taken into account (are displayed) in the mathematical model of the computer-aided design system for control devices of a microwave systems. Integrated process accounting leads to the formulation of complex tasks. One of them is the task of optimizing the shape, geometric dimensions and placement of the injected contacts (an active region). Objective. The goal of the work is the development of a mathematical model and the corresponding software of the process of a microwave waves interaction with electron-hole plasma in an active region of the surface-oriented integral p-i-n-structures with ribbon-type freeform contacts to optimize an active region shape and its geometric dimensions. Method. The main idea of the developed algorithm is to use the conformal mapping method to bring the physical domain of the problem to canonical form, followed by solving internal boundary value problems in this area for the ambipolar diffusion equation and the wave equation using numerical-analytical methods (the finite difference method; partial domains method using projection boundary conditions similar to the Galerkin method). The optimization algorithm is based on a phased solution of the following problems (the shape and geometric dimensions of the active region are specified at each stage): a computational grid of nodes for the physical regions of the problem is being found, in an active region the carriers concentration distribution is being determined and the energy transmitted coefficient in the system under study is being calculated, which is used in the proposed optimization functional. The extreme values of the functional are found by the uniform search method. Results. The proposed mathematical model and the corresponding algorithm for optimizing the shape and geometric dimensions of the active region (i-region) of integrated surface-oriented p-i-n-structures expands the tool base for the design of semiconductor circuits of microwave frequencies (for example, similar to CST MICROWAVE STUDIO). Conclusions. An algorithm has been developed to optimize the shape and geometrical dimensions of the active region of integrated surface-oriented p-i-n-structures with in-depth contacts intended for switching millimeter-wave electromagnetic signals. The universality of the algorithm is ensured by applying the method of conformal transformations of spatial domains. The example of the application of the proposed algorithm to search for the optimal sizes of wedge-shaped (in cross-section) contacts of silicon structures is considered.

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14

Hansraj, S., K. S. Govinder, and N. Mewalal. "Conformal Mappings in Relativistic Astrophysics." Journal of Applied Mathematics 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/196385.

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We describe the use of conformal mappings as a mathematical mechanism to obtain exact solutions of the Einstein field equations in general relativity. The behaviour of the spacetime geometry quantities is given under a conformal transformation, and the Einstein field equations are exhibited for a perfect fluid distribution matter configuration. The field equations are simplified and then exact static and nonstatic solutions are found. We investigate the solutions as candidates to represent realistic distributions of matter. In particular, we consider the positive definiteness of the energy density and pressure and the causality criterion, as well as the existence of a vanishing pressure hypersurface to mark the boundary of the astrophysical fluid.

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15

Kobayashi, Osamu. "Yamabe metrics and conformal transformations." Tohoku Mathematical Journal 44, no. 2 (1992): 251–58. http://dx.doi.org/10.2748/tmj/1178227341.

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16

Ledet, Arne, and Alexander Yu Solynin. "Conformal mapping and ellipses." Proceedings of the American Mathematical Society 134, no. 12 (June 27, 2006): 3507–13. http://dx.doi.org/10.1090/s0002-9939-06-08482-6.

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17

Smith, Wayne, and Alexander Volberg. "A conformal mapping example." Comptes Rendus Mathematique 349, no. 9-10 (May 2011): 511–14. http://dx.doi.org/10.1016/j.crma.2011.04.010.

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18

Singh, U. P., and A. K. Singh. "On conformal transformations of kropina metric." Periodica Mathematica Hungarica 16, no. 3 (September 1985): 187–92. http://dx.doi.org/10.1007/bf01849841.

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19

González-Matesanz, F. J., and J. A. Malpica. "Quasi-conformal mapping with genetic algorithms applied to coordinate transformations." Computers & Geosciences 32, no. 9 (November 2006): 1432–41. http://dx.doi.org/10.1016/j.cageo.2006.01.002.

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20

Aflalo, Yonathan, Ron Kimmel, and Michael Zibulevsky. "Conformal Mapping with as Uniform as Possible Conformal Factor." SIAM Journal on Imaging Sciences 6, no. 1 (January 2013): 78–101. http://dx.doi.org/10.1137/110845860.

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21

Flinn, Barbara Brown, and Brad G. Osgood. "Hyperbolic Curvature and Conformal Mapping." Bulletin of the London Mathematical Society 18, no. 3 (May 1986): 272–76. http://dx.doi.org/10.1112/blms/18.3.272.

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22

Makarov, N. G. "Conformal mapping and Hausdorff measures." Arkiv för Matematik 25, no. 1-2 (December 1987): 41–89. http://dx.doi.org/10.1007/bf02384436.

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23

Bourguignon, Jean-Pierre, and Jean-Pierre Ezin. "Scalar curvature functions in a conformal class of metrics and conformal transformations." Transactions of the American Mathematical Society 301, no. 2 (February 1, 1987): 723. http://dx.doi.org/10.1090/s0002-9947-1987-0882712-7.

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24

Kress, Rainer. "Inverse problems and conformal mapping." Complex Variables and Elliptic Equations 57, no. 2-4 (February 2012): 301–16. http://dx.doi.org/10.1080/17476933.2011.605446.

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25

KIM, BYUNG-HAK, SEOUNG-DAL JUNG, TAE-HO KANG, and HONG-KYUNG PAK. "CONFORMAL TRANSFORMATIONS IN A TWISTED PRODUCT SPACE." Bulletin of the Korean Mathematical Society 42, no. 1 (February 1, 2005): 5–15. http://dx.doi.org/10.4134/bkms.2005.42.1.005.

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26

POON, Y. S. "CONFORMAL TRANSFORMATIONS OF COMPACT SELF-DUAL MANIFOLDS." International Journal of Mathematics 05, no. 01 (February 1994): 125–40. http://dx.doi.org/10.1142/s0129167x94000061.

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We prove that when the dimension of the group of conformal transformations of a compact self-dual manifold is at least three, the conformal class contains either a metric with positive constant scalar curvature or a metric with zero scalar curvature. This result is combined with a topological classification of 4-manifolds to provide a complete geometrical classification of the compact self-dual manifolds whose symmetry group is at least three-dimensional.

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27

Gottlieb, H. P. W. "Transformations between isospectral membranes yield conformal maps." IMA Journal of Applied Mathematics 70, no. 6 (December 1, 2005): 748–52. http://dx.doi.org/10.1093/imamat/hxh067.

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28

Jensen, Gerd, and Christian Pommerenke. "Shabat polynomials and conformal mapping." Acta Scientiarum Mathematicarum 85, no. 12 (2019): 147–70. http://dx.doi.org/10.14232/actasm-017-821-6.

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29

Wegmann, Rudolf. "An iterative method for conformal mapping." Journal of Computational and Applied Mathematics 14, no. 1-2 (February 1986): 7–18. http://dx.doi.org/10.1016/0377-0427(86)90128-7.

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30

Shiue, Sham‐Tsong, and Sanboh Lee. "Conformal mapping functions between different slits." International Journal of Mathematical Education in Science and Technology 21, no. 4 (July 1990): 595–98. http://dx.doi.org/10.1080/0020739900210413.

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31

Lopera, J. F. Torres. "Geodesics and Conformal Transformations of Heisenberg-Reiter Spaces." Transactions of the American Mathematical Society 306, no. 2 (April 1988): 489. http://dx.doi.org/10.2307/2000808.

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32

Torres Lopera, J. F. "Geodesics and conformal transformations of Heisenberg-Reiter spaces." Transactions of the American Mathematical Society 306, no. 2 (February 1, 1988): 489. http://dx.doi.org/10.1090/s0002-9947-1988-0933303-1.

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33

Iglesias, José A., Kevin Sturm, and Florian Wechsung. "Two-Dimensional Shape Optimization with Nearly Conformal Transformations." SIAM Journal on Scientific Computing 40, no. 6 (January 2018): A3807—A3830. http://dx.doi.org/10.1137/17m1152711.

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34

Pommerenke, Ch. "On Graphical Representation and Conformal Mapping." Journal of the London Mathematical Society s2-35, no. 3 (June 1987): 481–88. http://dx.doi.org/10.1112/jlms/s2-35.3.481.

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35

Koenig, Kenneth D., and Loredana Lanzani. "Bergman versus Szego via conformal mapping." Indiana University Mathematics Journal 58, no. 2 (2009): 969–98. http://dx.doi.org/10.1512/iumj.2009.58.3841.

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36

Ivrii, Oleg. "On Makarov’s Principle in Conformal Mapping." International Mathematics Research Notices 2019, no. 5 (August 9, 2017): 1543–67. http://dx.doi.org/10.1093/imrn/rnx129.

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37

Roussarie, Robert. "Quasi-conformal mapping theorem and bifurcations." Boletim da Sociedade Brasileira de Matem�tica 29, no. 2 (September 1998): 229–51. http://dx.doi.org/10.1007/bf01237650.

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38

Gutlyanskii, V. Ya, and A. O. Zaidan. "On conformal mapping of polygonal regions." Ukrainian Mathematical Journal 45, no. 11 (November 1993): 1669–80. http://dx.doi.org/10.1007/bf01060857.

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39

Kravchenko, Vladislav V., and R. Michael Porter. "Conformal mapping of right circular quadrilaterals." Complex Variables and Elliptic Equations 56, no. 5 (May 2011): 399–415. http://dx.doi.org/10.1080/17476930903276100.

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40

Papamichael, Nicolas. "P. K. Kythe, Computational Conformal Mapping." Journal of Approximation Theory 106, no. 2 (October 2000): 292–93. http://dx.doi.org/10.1006/jath.2000.3519.

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41

Bishop, Christopher J. "Conformal Mapping in Linear Time." Discrete & Computational Geometry 44, no. 2 (June 15, 2010): 330–428. http://dx.doi.org/10.1007/s00454-010-9269-9.

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42

Pommerenke, Ch. "On conformal mapping and linear measure." Journal d'Analyse Mathématique 46, no. 1 (December 1986): 231–38. http://dx.doi.org/10.1007/bf02796587.

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43

Wegmann, Rudolf. "Fast conformal mapping of multiply connected regions." Journal of Computational and Applied Mathematics 130, no. 1-2 (May 2001): 119–38. http://dx.doi.org/10.1016/s0377-0427(99)00387-8.

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44

Kerzman, Norberto, and Manfred R. Trummer. "Numerical conformal mapping via the Szegö kernel." Journal of Computational and Applied Mathematics 14, no. 1-2 (February 1986): 111–23. http://dx.doi.org/10.1016/0377-0427(86)90133-0.

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45

Yabuki, Yasuhiro. "Nayatani's metric and conformal transformations of a Kleinian manifold." Proceedings of the American Mathematical Society 136, no. 01 (January 1, 2008): 301–11. http://dx.doi.org/10.1090/s0002-9939-07-09022-3.

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46

FLEURY and DETRAUBENBERG. "Extended Complex Number Analysis and Conformal-like Transformations." Journal of Mathematical Analysis and Applications 191, no. 1 (April 1, 1995): 118–36. http://dx.doi.org/10.1016/s0022-247x(85)71123-7.

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47

Fleury, N., and M. R. Detraubenberg. "Extended Complex Number Analysis and Conformal-like Transformations." Journal of Mathematical Analysis and Applications 191, no. 1 (April 1995): 118–36. http://dx.doi.org/10.1006/jmaa.1995.1123.

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48

Shen, Bin. "S-closed conformal transformations in Finsler geometry." Differential Geometry and its Applications 58 (June 2018): 254–63. http://dx.doi.org/10.1016/j.difgeo.2018.02.004.

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49

Gong, Xianghong. "Conformal maps, monodromy transformations, and non-reversible Hamiltonian systems." Mathematical Research Letters 7, no. 4 (2000): 471–76. http://dx.doi.org/10.4310/mrl.2000.v7.n4.a13.

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50

Kirichenko, V. F., and I. V. Uskorev. "Invariants of conformal transformations of almost contact metric structures." Mathematical Notes 84, no. 5-6 (December 2008): 783–94. http://dx.doi.org/10.1134/s0001434608110229.

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