Quasidefinite sesquilinear forms for Laurent polynomials in the complex plane and corresponding CMV biorthogonal Laurent polynomial families are studied. Bivariate linear functionals encompass large families of orthogonalities like Sobolev and discrete Sobolev types. Two possible Christoffel transformations of these linear functionals are discussed. Either the linear functionals are multiplied ...

We define a family of natural decompositions of Sturmian words in Christoffel words, called reversible Christoffel (RC) factorizations. They arise from the observation that two Sturmian words with the same language have (almost always) arbitrarily long Abelian equivalent prefixes. Using the three gap theorem, we prove that in each RC factorization, only 2 or 3 distinct Christoffel words may occ...

In this paper, two-dimensional turbulent flows in different and complex geometries are simulated by using an accurate grid generation method. In order to analyze the fluid flow, numerical solution of the continuity and Navier-Stokes equations are solved using CFD techniques. Considering the complexity of the physical geometry, conformal mapping is used to generate an orthogonal grid by means of...

The numerical computation of a conformal map from a disk or a half plane onto an elongated region is frequently difficult, or impossible, because of the so-called crowding phenomenon. This paper shows that this problem can often be avoided by using another elongated region, an infinite strip, as the standard domain. A transformation similar to the Schwarz-Christoffel formula maps this strip ont...

The classical Schwarz-Christoffel transformation provides a formula for the conformal mapping of the half-plane onto a plane polygon. A generalization enlarging the class of image domains to include many-sheeted plane polygons with interior winding points was known already to at least Schwarz and Schlifli.' This note is concerned with a further simple extension of the formula which delivers a u...

The flow field, velocity and pressure coefficient distribution of some 2-D ideal flows are presented. Conformal mapping is used to simulate two-dimensional ideal flow for a variety of complex internal and external configurations, based on the numerical integration of Schwarz-Christoffel transformation. The advantages of this method are simplicity and high accuracy. The method presented in this ...

Empirical Similitude Method (ESM) is a technique developed to address the concerns of non – linear similitude. The process disconnects the scaling of material and shape response by assuming them to be independent to form a system transformation. Such a transformation requires modeling using three representative models instead of just one as is used in the Buckingham π theorem. In an effort to g...