Zeros of the isomonodromic tau functions in constructive conformal mapping of polycircular arc domains: the n-vertex case
| Autor: | Bruno Carneiro da Cunha, Salman Abarghouei Nejad, Tiago Anselmo, Rhodri Nelson, Darren G Crowdy |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Statistics and Probability
Science & Technology 02 Physical Sciences conformal mapping Physics Physics Multidisciplinary General Physics and Astronomy Statistical and Nonlinear Physics Physics Mathematical isomonodromic tau functions ORDINARY DIFFERENTIAL-EQUATIONS DEFORMATION Modeling and Simulation Physical Sciences Mathematical Physics 01 Mathematical Sciences Fredholm determinants |
| Popis: | The prevertices of the conformal map between a generic, n-vertex, simply connected, polycircular arc domain and the upper half plane are determined by finding the zeros of an isomonodromic tau function. The accessory parameters of the associated Fuchsian equation are then found in terms of logarithmic derivatives of this tau function. Using these theoretical results a constructive approach to the determination of the conformal map is given and the particular case of five vertices is considered in detail. A computer implementation of a construction of the isomonodromic tau function described by Gavrylenko and Lisovyy (2018 Commun. Math. Phys. 363 1–58) is used to calculate some illustrative examples. A procedural guide to constructing the conformal map to a given polycircular arc domain using the method presented here is also set out. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|