of the Dissertation The Ahlfors Iteration for Conformal Mapping by Christopher Michael Green Doctor of Philosophy in Mathematics Stony Brook University 2011 The Riemann Mapping Theorem states that for any proper, simply connected planar domain there exists a conformal mapping from the disk onto the domain. But can this map be explicitly described? For general domains, there is no obvious answer...

We describe a dielectric sensor that is used to measure several biological fluids and tissues. The device consists of an LTCC wafer with a PDMS ring on top. S-parameter measurements are made, TRL calibrated and de-embedded. Two extraction methods are used to obtain the relative permittivity: conformal mapping and a method based on 2D simulations. Results are given for ethanol, 50% ethanol-water...

Conformal mapping has been a familiar tool of science and engineering for generations. Determination of a conformal map from the unit disk onto the Jordan region is reduced to solving the Theodorsen equation, which is an integral equation for boundary correspondence functions. There are many methods for solving the Theodorsen equation. It is the goal of numerical conformal mapping to find metho...

We present the conformal magnifier, a novel interactive Focus+Context visualization technique to magnify a region of interest (ROI) using conformal mapping. Our framework allows the user to design an arbitrary magnifier to enlarge the features of interest while deforming part of the remaining areas without any cropping. By using conformal mapping, the ROI is magnified with minimal distortion, w...

The dispersion in an eccentric annulus region by taking blood as a Newtonian fluid with the investigation of oxygen transfer to the tissue cells in an eccentric catheterized artery is studied. The region bounded by eccentric circles in x-y plane is conformal mapping to concentric circles in   plane using a conformal mapping 1 . z c    The resulting governing equations are analytically solv...