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Relevant bibliographies by topics / Conformal mapping. Functions of complex variables

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Academic literature on the topic 'Conformal mapping. Functions of complex variables'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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Journal articles on the topic "Conformal mapping. Functions of complex variables"

1

Yu, Li-yuan, Hong-wen Jing, and Ying-chao Wang. "Elastic Analysis for Subaqueous Tunnel Surrounding Rock via the Complex Variable Method." Mathematical Problems in Engineering 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/492745.

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Generally speaking, the subaqueous tunnels can be regarded as the shallow-buried ones. Consequently, the classical problem of an elastic half plane with a round cavity, loaded arbitrarily along the surface boundary, can be used to obtain the stress and displacement fields of the surrounding rock for this type of tunnels. The solution uses the complex variable method, with a conformal mapping onto a circular ring in the image plane. Because of the convergence of the complex potentials throughout the annular region, the coefficients in the Laurent series expansion form for complex functions can

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Li, Yansong, and Shougen Chen. "A Complex Variable Solution for Lining Stress and Deformation in a Non-Circular Deep Tunnel II Practical Application and Verification." Mathematical and Computational Applications 23, no. 3 (2018): 43. http://dx.doi.org/10.3390/mca23030043.

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A new complex variable method is presented for stress and displacement problems in a non-circular deep tunnel with certain given boundary conditions at infinity. In order to overcome the complex problems caused by non-circular geometric configurations and the multiply-connected region, a complex variable method and continuity boundary conditions are used to determine stress and displacement within the tunnel lining and within the surrounding rock. The coefficients in the conformal mapping function and stress functions are determined by the optimal design and complex variable method, respective

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Visser, F. C., J. J. H. Brouwers, and R. Badie. "Theoretical analysis of inertially irrotational and solenoidal flow in two-dimensional radial-flow pump and turbine impellers with equiangular blades." Journal of Fluid Mechanics 269 (June 25, 1994): 107–41. http://dx.doi.org/10.1017/s0022112094001503.

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Using the theory of functions of a complex variable, in particular the method of conformal mapping, the irrotational and solenoidal flow in two-dimensional radialflow pump and turbine impellers fitted with equiangular blades is analysed. Exact solutions are given for the fluid velocity along straight radial pump and turbine impeller blades, while for logarithmic spiral pump impeller blades solutions are given which hold asymptotically as (r1/r2)n→0, in whichr1is impeller inner radius,r2is impeller outer radius andnis the number of blades. Both solutions are given in terms of a Fourier series,

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Ulrych, S. "Conformal relativity with hypercomplex variables." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470, no. 2168 (2014): 20140027. http://dx.doi.org/10.1098/rspa.2014.0027.

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Majorana's arbitrary spin theory is considered in a hyperbolic complex representation. The underlying differential equation is embedded into the gauge field theories of Sachs and Carmeli. In particular, the approach of Sachs can serve as a unified theory of general relativity and electroweak interactions. The method is extended to conformal space with the intention to introduce the strong interaction. It is then possible to use the wave equation, operating on representation functions of the conformal group, to describe the dynamics of matter fields. The resulting gauge groups resemble closely

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He, Qiong, and Hai Yun Xiong. "Complex Potentials for Plane Problem of Two-Dimensional Quasicrystals with a Lip-Shape Crack." Advanced Materials Research 1004-1005 (August 2014): 1415–18. http://dx.doi.org/10.4028/www.scientific.net/amr.1004-1005.1415.

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By introducing a conformal mapping and applying the complex variable function method, two potential functions are determined for plane problem of two-dimensional quasicrystals with a lip-shape crack. When the height of the lip-shape crack approaches to zero, the results can be reduced to the solutions of the Griffith crack.

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Wang, Xian Feng, Feng Xing, Norio Hasebe, and P. B. N. Prasad. "A Point Dislocation Interacting with an Elliptical Hole Located at a Bi-Material Interface." Applied Mechanics and Materials 151 (January 2012): 75–79. http://dx.doi.org/10.4028/www.scientific.net/amm.151.75.

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The problem of a point dislocation interacting with an elliptical hole at the interface of two bonded half-planes is studied. Complex stress potentials are obtained by applying the methods of complex variables and conformal mapping. A rational mapping function that maps a half plane with a semi-elliptical notch onto a unit circle is used for mapping the bonded half-planes. The solution derived can serve as Green’s function to study internal cracks interacting with an elliptical interfacial cavity.

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Wang, Yung-Ming, and Jiann-Quo Tarn. "Green’s Functions for Generalized Plane Problems of Anisotropic Bodies With a Hole or a Rigid Inclusion." Journal of Applied Mechanics 60, no. 3 (1993): 583–88. http://dx.doi.org/10.1115/1.2900843.

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Green’s function solutions are presented for the generalized plane problems of a point force and an edge dislocation located in the general anisotropic elastic medium with a hole or with a rigid inclusion. The Lekhnitskii’s complex potential approach is used and a general expression of the solutions is obtained. Particular attention is paid to the determination of appropriate mapping functions that map the exterior of the hole or the inclusion onto the exterior of a unit circle. The conditions under which the conformal mapping is possible are explored. Examples using the Green’s functions for

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NIKOLOV, NIKOLAY M., and IVAN T. TODOROV. "ELLIPTIC THERMAL CORRELATION FUNCTIONS AND MODULAR FORMS IN A GLOBALLY CONFORMAL INVARIANT QFT." Reviews in Mathematical Physics 17, no. 06 (2005): 613–67. http://dx.doi.org/10.1142/s0129055x0500239x.

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Global conformal invariance (GCI) of quantum field theory (QFT) in two and higher space-time dimensions implies the Huygens' principle, and hence, rationality of correlation functions of observable fields [29]. The conformal Hamiltonian H has discrete spectrum assumed here to be finitely degenerate. We then prove that thermal expectation values of field products on compactified Minkowski space can be represented as finite linear combinations of basic (doubly periodic) elliptic functions in the conformal time variables (of periods 1 and τ) whose coefficients are, in general, formal power series

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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 ver

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N. Ivanshin, Pyotr, and . "Continued Fractions and Conformal Mappings for Domains with Angel Points." International Journal of Engineering & Technology 7, no. 4.7 (2018): 409. http://dx.doi.org/10.14419/ijet.v7i4.7.23039.

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Here we construct the conformal mappings with the help of the continued fraction approximations. We first show that the method of [19] works for conformal mappings of the unit disk onto domains with acute external angles at the boundary. We give certain illustrative examples of these constructions. Next we outline the problem with domains which boudary possesses acute internal angles. Then we construct the method of rational root approximation in the right complex half-plane. First we construct the square root approximation and consider approximative properties of the mapping sequence in Theor

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Dissertations / Theses on the topic "Conformal mapping. Functions of complex variables"

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Loganathan, Ramanan Mayoorathen. "Solutions for the flows induced by lazy, forced and pure turbulent plumes." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/273741.

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In this thesis an analytical modelling approach is employed to predict and gain insight into the flows induced by turbulent plumes and jets above slender horizontal slots, in otherwise quiescent uniform environments. To supplement the solutions, the effect on the environment of a plume driven by an off-source supply of buoyancy was also considered. The solutions derived provide an advancement on existing idealised models for the jet and plume induced flows, and moreover, complement a number of key advances that have been made in our understanding of plume flows in recent years. The theory of f

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Guo, Yunbo. "Multi-population genetic algorithm for the mapping of landscape of complex function /." View abstract or full-text, 2009. http://library.ust.hk/cgi/db/thesis.pl?PHYS%202009%20GUO.

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Cruz, Carla Maria. "Numerical and combinatorial applications of generalized Appell polynomials." Doctoral thesis, Universidade de Aveiro, 2014. http://hdl.handle.net/10773/13962.

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Doutoramento em Matemática<br>This thesis studies properties and applications of different generalized Appell polynomials in the framework of Clifford analysis. As an example of 3D-quasi-conformal mappings realized by generalized Appell polynomials, an analogue of the complex Joukowski transformation of order two is introduced. The consideration of a Pascal n-simplex with hypercomplex entries allows stressing the combinatorial relevance of hypercomplex Appell polynomials. The concept of totally regular variables and its relation to generalized Appell polynomials leads to the constructi

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Books on the topic "Conformal mapping. Functions of complex variables"

1

Kythe, Prem K. Computational Conformal Mapping. Birkhäuser Boston, 1998.

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Černý, Ilja. Foundations of analysis in the complex domain. Academia, 1992.

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Bell, Steven Robert. The Cauchy transform, potential theory, and conformal mapping. CRC Press, 1992.

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Pommerenke, Christian. Boundary Behaviour of Conformal Maps. Springer Berlin Heidelberg, 1992.

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5

Complex analysis: Conformal inequalities and the Bieberbach conjecture. Taylor & Francis, 2016.

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6

Andrievskii, V. V. Conformal invariants in constructive theory of functions of complex variable. World Federation Publishers Co., 1995.

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7

1941-, Hag Kari, and Broch Ole Jacob, eds. The ubiquitous quasidisk. American Mathematical Society, 2012.

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8

Conformal invariants: Topics in geometric function theory. AMS Chelsea Pub., 2010.

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9

Riemann surfaces by way of complex analytic geometry. American Mathematical Society, 2011.

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10

Ibragimov, Zair. Topics in several complex variables: First USA-Uzbekistan Conference on Analysis and Mathematical Physics, May 20-23, 2014, California State University, Fullerton, California. American Mathematical Society, 2016.

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Book chapters on the topic "Conformal mapping. Functions of complex variables"

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Curtiss, J. H. "Conformal Mapping." In Introduction to Functions of a Complex Variable. CRC Press, 2021. http://dx.doi.org/10.1201/9781003209072-13.

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Wunsch, A. David. "Harmonic Functions, Conformal Mapping, and Some Applications." In A MATLAB® Companion to Complex Variables. CRC Press, 2018. http://dx.doi.org/10.1201/9781315380339-4.

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Krantz, Steven G. "Applications that Depend on Conformal Mapping." In Complex Variables. Chapman and Hall/CRC, 2019. http://dx.doi.org/10.1201/9780429275166-12.

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Krantz, Steven G. "Applications that Depend on Conformal Mapping." In Handbook of Complex Variables. Birkhäuser Boston, 1999. http://dx.doi.org/10.1007/978-1-4612-1588-2_14.

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Svetunkov, Sergey. "Conformal Mappings of Functions of a Complex Variable." In Complex-Valued Modeling in Economics and Finance. Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-5876-0_3.

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Beals, Richard, and Roderick S. C. Wong. "Conformal maps and the Riemann mapping theorem." In Explorations in Complex Functions. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-54533-8_5.

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Biswas, P., and Bapi Karmakar. "Nonlinear Dynamic (Vibration) Analysis of Irregular-Shaped Sandwich Plates by the Method of Complex Variables and Conformal Mapping." In Lecture Notes in Mechanical Engineering. Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-8049-9_60.

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Biswas, Paritosh, and Bapi Karmakar. "Brief Review on the Use of Complex Variables and Conformal Mapping for Elastic Plate Problems—Application to Buckling of Sandwich Plates." In Lecture Notes in Mechanical Engineering. Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-8049-9_59.

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"4. Conformal Mapping." In Functions of a Complex Variable: Theory and Technique. Society for Industrial and Applied Mathematics, 2005. http://dx.doi.org/10.1137/1.9780898719116.ch4.

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"Chapter 8: Conformal Mappings." In Complex Variables and Analytic Functions: An Illustrated Introduction. Society for Industrial and Applied Mathematics, 2019. http://dx.doi.org/10.1137/1.9781611975987.ch8.

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Conference papers on the topic "Conformal mapping. Functions of complex variables"

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Jiang, Long, Shikui Chen, and Xianfeng David Gu. "Generative Design of Multi-Material Hierarchical Structures via Concurrent Topology Optimization and Conformal Geometry Method." In ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/detc2019-97617.

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Abstract Topology optimization has been proved to be an automatic, efficient and powerful tool for structural designs. In recent years, the focus of structural topology optimization has evolved from mono-scale, single material structural designs to hierarchical multimaterial structural designs. In this research, the multi-material structural design is carried out in a concurrent parametric level set framework so that the structural topologies in the macroscale and the corresponding material properties in mesoscale can be optimized simultaneously. The constructed cardinal basis function (CBF) i

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Megherbi, Dalila B., A. J. Boulenouar, and Y. Cheng. "Generalized technique for object-shape representation, classification, and recognition via complex variables and conformal mapping." In Aerospace/Defense Sensing, Simulation, and Controls, edited by Stephen K. Park, Zia-ur Rahman, and Robert A. Schowengerdt. SPIE, 2001. http://dx.doi.org/10.1117/12.438273.

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Song, Tianshu, Lili Sun, and Diankui Liu. "Dynamic Anti-Plane Characteristic of an Infinite Piezoelectric Medium With a Non-Circular Cavity." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-85695.

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In this paper, dynamic stress concentrations are studied in an infinite piezoelectric medium with a non-circular cavity under time harmonic incident anti-plane shear wave and inplane electric field. Based on complex variable and conformal mapping method, the dynamic stress concentration factors and the electric field concentration factors at the boundary of the non-circular cavity are obtained by applying the orthogonal function expansion technique. Numerical examples about an infinite piezoelectric medium with an elliptic cavity are provided with different elliptic axial length ratios, differ

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Panta Pazos, Rube´n. "Hybrid Methods Approach for Solving Problems in Transport Theory." In 16th International Conference on Nuclear Engineering. ASMEDC, 2008. http://dx.doi.org/10.1115/icone16-48400.

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In this work the hybrid methods approach is introduced in order to solve some problems in Transport Theory for different geometries. The transport equation is written as: ∂ψ∂t(x,v,t)+v·∇ψ(x,v,t)+h(x,μ)ψ(x,v,t)==∫Vk(x,v,v′)ψ(x,v′,t)dv′+q(x,v,t),inΩTψ(x,v,0)=φ0(x,v),in∂Ω×Vψ(x,v,t)=φ(x,v,t),in∂Ω×V×R(1) where x represents the spatial variable in a domain D, v an element of a compact set V, ψ is the angular flux, h(x, v) the collision frequency, k(x, v, v’) the scattering kernel function and q(x, v) the source function. If ψ does not depend on the time, it is said that the problem (1) is a steady t

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Wang, Xuesong, Jinju Sun, Changjiang Huo, Guilong Huo, and Peng Song. "Design and Flow Analysis of a Radial Outflow Turbo-Expander." In ASME Turbo Expo 2019: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/gt2019-90346.

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Abstract Radial-outflow turbo-expanders have emerged in the recent years to suit some special applications where complex multi-phase and multi-component flows (like liquid-rich gases and solid particle-laden gases) need to be expanded. This paper presents a systematic study on the design and flow behavior of a single stage radial-outflow turbo-expander, which is to be used in organic Rankine power system to covert the low-temperature heat into shaft power. A mean-line code coupled with the optimization algorithm is developed and used to carry out the one-dimensional preliminary design, where 7

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