WVU Math Colloquia

Wednesdays at 4pm EDT
zoom link (pass mathAdi2)

The 2021-2022 Applied Mathematics Seminar is organized by Adrian Tudorascu and Casian Pantea. The talks are on zoom until further notice. The regular time for the Seminar is on Wednesday at 4:00 p.m. (in some cases we will schedule the seminar at different times, to accommodate speakers).

If you'd like to suggest speakers for the fall semester please contact Adrian or Casian.

Schedule

date	speaker	institution	title	notes
September 15	Dehua Wang	University of Pittsburgh	Elastic effects on vortex sheets and vanishing viscosity	2:30pm, 315 ARM
October 17	Farhad Jafari	University of Minnesota	TBA
October 24	Tóth János	Budapest University of Technology and Economics	The concept of reaction extent

Abstracts

Dehua Wang

Elastic effects on vortex sheets and vanishing viscosity

Elasticity is important in continuum mechanics with a wide range of applications and is challenging in analysis. In this talk we shall first review some basic mathematical results and then discuss some special elastic effects in fluid flows. The first elastic effect is the stabilizing effect of elasticity on the vortex sheets in compressible elastic flows. Some recent results on linear and nonlinear stability of compressible vortex sheets will be presented. The second effect is on the vanishing viscosity process of compressible viscoelastic flows in the half plane under the no-slip boundary condition. Our results show that the deformation tensor can prevent the formation of strong boundary layers. The talk is based on the recent joint works with several collaborators.

Tóth János

The concept of reaction extent

The concept of reaction extent or the progress of a reaction, advancement of the reaction, conversion, etc. was introduced around 100 years ago. Most of the literature provides a definition for the exceptional case of a single reaction step or gives an implicit definition that cannot be made explicit. Starting from the standard definition we extend the classic definition of the reaction extent in explicit form for an arbitrary number of species and of reaction steps and arbitrary kinetics. Then, we study the mathematical properties (evolution equation, continuity, monotony, differentiability, etc.) of the defined quantity, and connect them to the formalism of modern reaction kinetics. Our approach tries to adhere to the customs of chemists and be mathematically correct simultaneously.

We also show how to apply this concept to exotic reactions: reactions with more than one stationary state, oscillatory reactions, and reactions showing chaotic behavior. With the new definition, one can calculate not only the time evolution of the concentration of each reacting species but also the number of occurrences of the individual reaction events.