Recent zbMATH articles in MSC 30C35https://zbmath.org/atom/cc/30C352023-05-31T16:32:50.898670ZWerkzeugNumerical computation of a preimage domain for an infinite strip with rectilinear slitshttps://zbmath.org/1508.300182023-05-31T16:32:50.898670Z"Kalmoun, El Mostafa"https://zbmath.org/authors/?q=ai:kalmoun.el-mostafa"Nasser, Mohamed M. S."https://zbmath.org/authors/?q=ai:nasser.mohamed-m-s"Vuorinen, Matti"https://zbmath.org/authors/?q=ai:vuorinen.matti-kSummary: Let \(\varOmega\) be the multiply connected domain in the extended complex plane \(\overline{\mathbb{C}}\) obtained by removing \(m\) non-overlapping rectilinear segments from the infinite strip \(S=\{z : |\mathrm{Im} z|<\pi /2\}\). In this paper, we present an iterative method for numerical computation of a conformally equivalent bounded multiply connected domain \(G\) in the interior of the unit disk \(\mathbb{D}\) and the exterior of \(m\) non-overlapping smooth Jordan curves. We demonstrate the utility of the proposed method through two applications. First, we estimate the capacity of condensers of the form \((S,E)\) where \(E \subset S\) is a union of disjoint segments. Second, we determine the streamlines associated with uniform incompressible, inviscid and irrotational flow past disjoint segments in the strip \(S\).Phase transition for a family of complex-driven Loewner hullshttps://zbmath.org/1508.300192023-05-31T16:32:50.898670Z"Lind, Joan"https://zbmath.org/authors/?q=ai:lind.joan-r"Utley, Jeffrey"https://zbmath.org/authors/?q=ai:utley.jeffreySummary: Building on H. Tran's study of Loewner hulls generated by complex-valued driving functions, which showed the existence of a phase transition, we answer the question of whether the phase transition for complex-driven hulls matches the phase transition for real-driven hulls. This is accomplished through a detailed study of the Loewner hulls generated by driving functions \(c\sqrt{1-t}\) and \(c\sqrt{\tau + t}\) for \(c \in \mathbb{C}\) and \(\tau \geq 0\). This family also provides examples of new geometric behavior that is possible for complex-driven hulls but prohibited for real-driven hulls. \looseness-1A free boundary problem of elasticity in an angle and a vector Riemann-Hilbert problem on a torushttps://zbmath.org/1508.300792023-05-31T16:32:50.898670Z"Antipov, Y. A."https://zbmath.org/authors/?q=ai:antipov.yuri-aSummary: An inverse problem of elasticity of reconstructing the shape of an inclusion placed in a wedge, when the whole inclusion is subjected to a prescribed antiplane uniform stress, is considered. The doubly connected physical domain is conformally mapped onto a parametric plane cut along two finite segments on the real axis. Determination of such a map requires solving a vector Riemann-Hilbert problem of the theory of holomorphic functions on a symmetric genus-1 Riemann surface. The main steps of the method include factorization of a discontinuous function on a torus, solution of the associated Jacobi inversion problem, representation of the unknown vector-functions in terms of Weierstrass integrals, and reduction of the vector Riemann-Hilbert problem to a single integral kernel of the second kind with a discontinuous kernel on the elliptic surface. An integral representation of the conformal map in terms of the solution to the integral equation is given. In addition to four dimensionless problem parameters, the conformal map possesses five free parameters. Numerical results, which reconstruct the inclusion shape for sample sets of the parameters, are reported and discussed.