Beurling’s free boundary value problem in conformal geometry

A conformal mapping algorithm for the Bernoulli free boundary value problem

We propose a new numerical method for the solution of Bernoulli’s free boundary value problem for harmonic functions in a doubly connected domain D in R2 where an unknown free boundary Γ0 is determined by prescribed Cauchy data on Γ0 in addition to a Dirichlet condition on the known boundary Γ1. Our main idea is to involve the conformal mapping method as proposed and analyzed by Akduman, Haddar...

Conformal Fractal Geometry & Boundary Quantum Gravity

This article gives a comprehensive description of the fractal geometry of conformally-invariant (CI) scaling curves, in the plane or half-plane. It focuses on deriving critical exponents associated with interacting random paths, by exploiting an underlying quantum gravity (QG) structure, which uses KPZ maps relating exponents in the plane to those on a random lattice, i.e., in a fluctuating met...

Diffusion in Glassy Polymers: a Free Boundary Value Problem

A 2 - D Free Boundary Value Problem with Onset ofa

NON-POLYNOMIAL QUARTIC SPLINE SOLUTION OF BOUNDARY-VALUE PROBLEM

Quartic non-polynomial spline function approximation in off step points is developed, for the solution of fourth-order boundary value problems. Using consistency relation of such spline and suitable choice of parameter,we have obtained second, fourth and sixth orders methods. Convergence analysis of sixth order method has been given. The methods are illustrated by some examples, to verify the or...