Complex Materials and Industrial Mathematics (CMIM)

An opportunity to meet and discuss research ideas. More detail to follow.

Abstract
In this study, the real-world application is concerned with the determination of a space-dependent index of refraction of an optical anti-reflection coating. The model is based on solving an inverse coefficient identification problem for the 1D Helmholtz equation. The additional data necessary for the inversion can be the full complex reflection coefficient or its absolute value only, measured for many wavenumbers. The numerical method is based on a FDM
direct solver combined with a nonlinear Tikhonov regularization. It is shown that, in general, the knowledge of the full complex reflection coefficient is necessary to determine uniquely a spacewise continuous index of refraction. When only the absolute value of the reflection coefficient is used as input data, constraints need to be imposed, e.g., the knowledge of the full integrated refraction index, additional smoothness assumptions on the index of refraction, or more reflectance data measured for many wavelengths. Apart from this insight into the uniqueness of solution of the inverse problem, the principal conclusion is that a better fit of the reflectance measured data is obtained by using a continuously varying index of refraction than when this coefficient is sought as a piecewise constant function.

An opportunity to meet and discuss research ideas. More detail to follow.

Pelin Senel*^
*Karadeniz Technical University, Department of Mathematics, Trabzon, Türkiye
^University of Leeds, Department of Applied Mathematics, Leeds, UK
(Visiting Research Fellow)

Abstract

In this talk, unsteady flow of an electrically conducting fluid in a wavy channel subjected to an external magnetic field will be presented. The influences of the slip, the amplitude and the undulation of the wavy wall on the fluid flow and numerical stability of solutions will be discussed.

An opportunity to meet and discuss research ideas. More detail to follow.

Chalk and talk.

An opportunity to meet and discuss research ideas.

Kicking off the CMIM group's series of seminars to review our past and current research, Mike Evans will revisit work on the XY model. A remarkably simple dynamical model exhibits many of the complex flow regimes and non-equilibrium phase transitions characteristic of complex fluids. By removing extraneous detail, this simplest microscopic model of non-Newtonian flow has the potential to reveal universal principles relevant to all complex fluids.