Construction Of Conformal Mappings Research Articles

Construction of conformal mappings between several rotating surfaces

Construction of conformal mappings between several rotating surfaces

Construction of conformal mappings by generalized polarization tensors

We present a new systematic method to compute the Riemann mapping from the outside of the unit disc to the outside of a simply connected domain. We derive explicit relations between the coefficients of the Riemann mapping and the generalized polarization tensors associated with the domain. Because the generalized polarization tensors can be computed numerically, we are able to compute the coefficients of the Riemann mapping using these relations. Effectiveness of the method is validated by numerical examples. Copyright © 2014 John Wiley & Sons, Ltd.

Conformal mappings of multiply connected domains onto canonical domains using the Green and Neumann functions

In this study, some properties of the Green and Neumann functions associated with boundary value problems for elliptic equations are analysed. The described Green and Neumann functions are used for the construction of conformal mappings of multiply connected domains onto some canonical domains.

The motion of a point vortex through gaps in walls

New analytical techniques for studying the motion of a point vortex in fluid domains bounded by straight walls having an arbitrary number of gaps are presented. By exploiting explicit formulae for the Kirchhoff–Routh path function in multiply connected circular domains, combined with a novel construction of conformal mappings from such circular domains to multiply connected slit domains, the governing Hamiltonians for the motion of a point vortex in a number of physically interesting fluid regions involving walls with gaps are derived. The vortex trajectories in several illustrative cases are computed. These examples include finding the vortex paths around a chain of islands sitting off an infinite coastline, around islands in an unbounded ocean and around a sequence of islands situated between two headlands.

Analytic construction of conformal mappings for simply-connected regions of a particular class

Analytic construction of conformal mappings for simply-connected regions of a particular class