Over billions of years, single-celled and simple multicellular organisms have evolved motility mechanisms particularly suited for locomotion in their fluid environment. In the past century, considerable progress has been made in understanding biological processes and fluid dynamics at various scales. In particular, locomotion strategies, from single cells to multicellular large animals in Newtonian and non-Newtonian fluids have motivated the development of new modeling frameworks and numerical methods while also leading to new bio-inspired designs for different applications. Specifically, advances in mathematical models and methods relating to fluid-structure interactions, including the method of regularized Stokeslets (MRS) and the immersed boundary (IB) method, are being highly leveraged to answer biological questions about animal interactions with their surrounding fluid. 

 

This workshop will delve into the development and analysis of mathematical models, numerical methods, computational simulations, theoretical fluid dynamics, and the integration of biological experimental data into modeling, simulations, and data analysis. It will focus on recent and ongoing advancements in fluid-structure interactions, the development of computational libraries, and the incorporation of experimental data to improve biological predictions. Presentations and discussions will also address education, training, and topics related to diversity, equity, and inclusion in mathematical sciences. A unique feature of the workshop is the inclusion of research findings in mathematical modeling within K–16 education. A special highlight of the event will be a tribute to Dr. Ricardo Cortez of Tulane University, recognizing his groundbreaking contributions to research, including the development of the Method of Regularized Stokeslets, as well as his outstanding service to the mathematics community.

 

The workshop will emphasize interdisciplinary research, demonstrating the critical role of mathematics and fluid dynamics in understanding biological phenomena. This will be showcased through invited talks, panel discussions, and poster presentations. Tutorials on the MRS and IB methods will provide hands-on demonstrations of how these tools and their variations can be applied to contemporary scientific challenges. Additionally, the workshop will encourage collaboration in research and training, with a particular focus on supporting underrepresented groups in mathematical sciences. The workshop is also designed to promote the training and mentorship of students and early-career researchers in mathematical sciences. It will uniquely integrate research in mathematical modeling for education and facilitate discussions on DEI advancements within the field.