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
October 24	Tóth János	Budapest University of Technology and Economics	The concept of reaction extent

Abstracts

Veronica Ciocanel

Actin filaments are polymers that interact with myosin motor proteins and play important roles in cell motility, shape, and development. Depending on its function, this dynamic network of interacting proteins reshapes and organizes in a variety of structures, including bundles, clusters, and contractile rings. Motivated by observations from the reproductive system of the roundworm C. elegans, we use an agent-based modeling framework to simulate interactions between actin filaments and myosin motor proteins inside cells. We also develop techniques based on topological data analysis to understand time-series data extracted from these filament network interactions. These measures allow us to compare the filament organization resulting from myosin motors with different properties. Recently, we have also studied how different models of myosin regulation predict actin network organization during the cell cycle. This work also raises questions about how to assess the significance of features in common topological summaries.

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.