July 21 - 25, 2025
Mathematical Modeling, Computational Methods, and Biological Fluid Dynamics: Research and Training
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Overview
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 encouraging participation in the 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 ensuring that everyone can thrive in the mathematical sciences. The workshop is also designed to promote the training and mentorship of students and early-career researchers. It will uniquely integrate research in mathematical modeling with education and facilitate discussions on promoting participation within the field.
Participants
Speaker
Attendee
Cynthia Anhalt - University of Arizona (Speaker & Panelist)
Vivian Aranda - Universidad Técnica Federico Santa María
Aaron Barrett - University of Utah (Tutorialist)
J. Thomas Beale - Duke University (Speaker)
Francesca Bernardi - Worcester Polytechnic Institute (Panelist)
Sarah Bogen - Florida International University
Amy Buchmann - University of California, San Diego (Panelist)
Hongfei Chen - Tulane University
Zixiao Chen - Worcester Polytechnic Institute
David Chopp - Northwestern University (Organizer)
John Chrispell - Indiana University of Pennsylvania
Keisha Cook - Clemson University (Speaker)
Ricardo Cortez - Tulane University (Speaker & Panel Moderator)
Breschine Cummins - Montana State University (Panelist)
Yash Deodhar - Northwestern University
Irene Erazo - Tulane University
Ege Eren - University of Chicago
Thomas Fai - Brandeis University (Panelist)
Lisa Fauci - Tulane University (Speaker & Panel Moderator)
Dana Ferranti - Worcester Polytechnic Institute (Tutorialist)
Greg Forest - University of North Carolina at Chapel Hill (Panel Moderator)
Jake Grdadolnik - University of North Carolina at Chapel Hill
Boyce Griffith - University of North Carolina at Chapel Hill (Tutorialist & Panelist)
Venkatesh Gopal - Elmhurst University
Rochelle Gutierrez - University of Illinois Urbana-Champaign
Christina Hamlet - Bucknell University (Panelist)
Alexander Hoover - Cleveland State University (Panelist)
Shilpa Khatri - University of California, Merced (Organizer, Tutorialist)
Brynja Kohler - Utah State University (Speaker & Panel Moderator)
Michaela Kubacki - Middlebury College
Brittany Leathers - University of California, Merced
Sang-Eun Lee - Tulane University
Karin Leiderman - University of North Carolina at Chapel Hill (Speaker)
Owen Lewis - University of New Mexico (Panelist)
Sergi Leyva - Northwestern University
Sookkyung Lim - University of Cincinnati (Organizer, Speaker)
Lulu Lu - Michigan State University
Hailey Lynch - University of Notre Dame
Jane Shaw MacDonald - Oregon State University
Cameron MacKenzie - Northwestern University
Ondrej Maxian - University of Notre Dame
Scott McKinley - Tulane University
Yoichiro Mori - University of Pennsylvania (Panelist)
Adnan Morshed - Tulane University
Annah Naturinda - Worcester Polytechnic Institute
Irma Nelson - Northwestern University
Hoa Nguyen - Trinity University (Organizer)
Nhan Nguyen - University of Chicago
Jasmine Nirody - University of Chicago
Alex Nisbet - Tulane University
Sarah Olson - Worcester Polytechnic Institute (Organizer, Tutorialist)
Kayode Oluwasegun - Drexel University
Jeungeun Park - State University of New York at New Paltz
Terrance Pendleton - Drake University
Sayandeepa Raha - University of Notre Dame
Owen Richfield - Yale University (Speaker)
Bhavneet Singh Saini - University of South Florida, Tampa
Rudi Schuech - Santa Clara University
Sergei Shmakov - University of Chicago
Henry Shum - University of Waterloo (Panelist)
Julie Simons - University of California, Santa Cruz (Speaker)
John Stockie - Simon Fraser University (Speaker)
Nils Strand - University of Chicago
Becca Thomases - Smith College (Speaker)
William Tidwell - Morehead State University
Conrad Triebold - University of Chicago
David Uminsky - University of Chicago
Douglas Varela - DVC Academic Consulting (Panelist)
Petia Vlahovska - Northwestern University
Zheng Wang - Tulane University
Nathaniel Whitaker - ICERM/University of Massachusetts Amherst (Speaker)
Stephen Williams - University of California, Merced (Tutorialist)
Yanfeng Xing - University of Chicago
Longhua Zhao - Case Western Reserve University
Han Zhou - University of Pennsylvania
July
21
2025
Monday
Chairs: Shilpa Khatri (morning) & Hoa Nguyen (afternoon)
Speakers: Ricardo Cortez, Karin Leiderman, Shilpa Khatri, Stephen Williams, Sarah Olson & Dana Ferranti
8:30 am - 8:50 am
Light Breakfast
8:50 am - 8:55 am
Welcome & Introduction of Institute
8:55 am - 9:00 am
Welcome to Workshop & Housekeeping
9:00 am - 9:30 am
Vignettes of Stokes Flows in and Around Circles and Spheres - Ricardo Cortez
Abstract: This opening presentation of the workshop will describe recent work on regularized Stokeslets in which the regularization depends on the co-dimension of the body where the forces are supported. At scattered points in 3D, traditional regularized Stokeslet are used. Along curves in 3D, we may use regularized Stokeslet segments, Kirchhoff rod theory, or slender-body theory. Finally, on surfaces in 3D, no regularization is needed. I will focus on simple shapes, namely circles in 2D and spheres in 3D, and show a method for computing the flow based on single- and double-layer potentials to machine precision in a simple way. The extension to more general shapes (i.e. star shape domains) will be described. The talk will focus on the main ideas, examples and open problems.
9:30 am - 10:00 am
A discrete platelet-bonding model for simulating platelet aggregation under flow - Karin Leiderman
Abstract: Hemostasis is the healthy clotting response to a blood vessel injury. A major component of clotting is platelet aggregation, which involves the formation of platelet-platelet and platelet-wall bonds between platelet receptors (GPVI and GP1b), and platelet integrins ($\alpha_2\beta_1$ and $\alpha_{IIb}\beta_3$) with plasma-borne molecules (von Willebrand factor and fibrinogen) and wall adherent collagen. There are platelet disorders that decrease the number and/or functionality of $\alpha_{IIb}\beta_3$, which results in excessive bleeding. Current treatments exist but are not evidence based and are not always successful in restoring hemostasis. In the cases where hemostasis is restored, the aggregation mechanism without $\alpha_{IIb}\beta_3$ remains speculative. Our long-term goal is to uncover this mechanism with a mathematical and computational approach. As a first step, we simulated platelet aggregation using the molecular dynamics software, LAMMPS. We considered individual platelets and tracked the platelet-platelet and platelet-wall bonds that formed during aggregation. Currently, the strength of the bonds depends on the local shear rate of a prescribed background flow. Simulations show stable aggregation for healthy platelets under flow. Future work is to improve our modeling framework by parameterizing with experimental measurements and computationally coupling our platelet model to a dynamic flow.
10:00 am - 10:30 am
Coffee Break
10:30 am - 12:00 pm
One-slide Introductions & Group Photo
12:00 pm - 1:30 pm
Lunch
1:30 pm - 3:00 pm
Tutorial: MRS Part 1 - Shilpa Khatri & Stephen Williams
3:00 pm - 3:30 pm
Coffee Break
3:30 pm - 5:00 pm
Tutorial: MRS Part 2 - Sarah Olson & Dana Ferranti
July
22
2025
Tuesday
Chairs: Sarah Olson (morning) & Shilpa Khatri (afternoon)
Speakers: Thomas Beale, Sookkyung Lim, Brynja Kohler, Ricardo Cortez, Henry Shum, Amy Buchmann & Alexander Hoover, Aaron Barrett & Boyce Griffith
8:30 am - 8:55 am
Light Breakfast
8:55 am - 9:00 am
Welcome to Workshop & Housekeeping
9:00 am - 9:30 am
Computing nearly singular surface integrals and solving p.d.e.'s on surfaces - Thomas Beale
Abstract: We describe two numerical methods which could be useful in continuum modeling. The first is a method for computing nearly singular integrals, i.e., integrals such as single or double layer potentials for harmonic functions, or integrals in Stokes flow with Stokeslet or stresslet kernel, when evaluated at points near the surface. Such integrals are more general than the case of evaluation on the surface and could be needed when surfaces are close to each other, or to evaluate at grid points near the surface. Values at all grid points can be recovered efficiently from those near the surface by a technique introduced by A. Mayo. We use regularized versions of the integral kernel as in the method of regularized Stokeslets. In recent work with S. Tlupova (Adv. Comput. Math. 2024) we derive analytic expressions for the error due to regularization, and these allow us to improve this error to higher order, giving better control of the discretization error. The second topic is a method for solving p.d.e.'s on a surface, such as diffusion determined by the Laplace-Beltrami operator, or transport equations (SIAM J. Sci. Comput. 2020). We use a clever discretization of the surface due to W. Ying and W.-C. Wang. The surface is represented by points where it intersects intervals in a three-dimensional grid. The selected points are projected onto regular grid points in coordinate planes, allowing standard numerical methods to be used. The discretization technique allows for seamless transition between coordinate planes. Extension beyond the surface is not required.
9:30 am - 10:00 am
Mathematical modeling of cell motility: bacterial swimming & glioblastoma migration - Sookkyung Lim
Abstract: Cell motility is fundamental to various biological processes, from bacterial navigation in fluid environments to glioblastoma invasion in brain tissue. Mathematical modeling and simulations provide a useful framework for analyzing and predicting the underlying mechanisms governing these distinct modes of movement. In this talk, I will present mathematical models that describe swimming of C. jejuni in 3D using the method of regularized Stokeslet combined with the Kirchhoff rod theory and glioblastoma migration along blood vessels in 2D using the immersed boundary method. These computational simulations not only demonstrate strong agreement with experimental data but also provide novel insights into the biophysical principles governing cell motility.
10:00 am - 10:30 am
Coffee Break
10:30 am - 11:00 am
Community-Engaged Learning in an Interdisciplinary Math-Biology Course - Brynja Kohler
Abstract: This talk describes a junior-level interdisciplinary Math/Biology course that integrates mathematical modeling with community-engaged learning. Students explore complex social and environmental systems through project-based learning, applying modeling approaches from ecology, public health, conservation, and sociology. The course emphasizes modeling as a tool for understanding and addressing real-world issues and as a disposition for approaching complex problems. For the final project, students collaborate with local partners—such as a municipal landfill, a regional zoo, and conservation nonprofits—to propose data-informed solutions to problems. Examples from Spring 2023 and Spring 2025 illustrate how students engage with stakeholders, develop teamwork and communication skills, and connect mathematical modeling to civic and scientific contexts. The course builds on institutional support for community-engaged learning and draws on research in team science and project-based learning.
11:00 am - 12:00 pm
Panel Discussion: MRS + Advances – Ricardo Cortez (moderator), Henry Shum, Amy Buchmann & Alexander Hoover
12:00 pm - 1:30 pm
Lunch
1:30 pm - 3:00 pm
Tutorial: IBM Part 1 – Aaron Barrett
3:00 pm - 3:30 pm
Coffee Break
3:30 pm - 5:00 pm
Tutorial: IBM Part 2 - Boyce Griffith
July
23
2025
Wednesday
Chairs: Sookkyung Lim (morning) & Sarah Olson (afternoon)
Speakers: John Stockie, Becca Thomases, Lisa Fauci, Thomas Fai, Christina Hamlet, Boyce Griffith,
Greg Forest, Breschine Cummins, Yoichiro Mori & Owen Lewis
8:30 am - 8:55 am
Light Breakfast
8:55 am - 9:00 am
Welcome to Workshop & Housekeeping
9:00 am - 9:30 am
Immersed boundary simulations of worm-like, inertial swimmers - John Stockie
Abstract: The swimming dynamics of marine organisms has been the subject of many theoretical and computational studies, especially for microscopic organisms (such as bacteria, spermatozoa or plankton) that exist in the viscous-dominated Stokes flow regime where the Reynolds number (Re) is very small. This previous work has focused on individual microswimmers, although there has been a surge of recent interest in simulating suspensions of such swimmers using algorithms that exploit approximate analytical solutions and fast solvers tailored for Stokesian dynamics. Computational studies of higher-Re swimmers are also well-represented in the literature, for organisms such as fish, eels, jellyfish, etc. However, less attention has been paid to creatures like nematodes that swim in an intermediate regime where inertial and viscous effects are comparable, with 0.1 < Re
9:30 am - 10:00 am
How to swim through goo - Becca Thomases
Many microorganisms and cells function in complex (non-Newtonian) fluids, which are mixtures of different materials that exhibit both viscous and elastic stresses. For example, mammalian sperm swim through cervical mucus on their journey through the female reproductive tract, and they must penetrate the viscoelastic gel outside the ovum to fertilize. In micro-scale swimming the dynamics emerge from the coupled interactions between the complex rheology of the surrounding media and the passive and active body dynamics of the swimmer. We use computational and analytical models of swimmers in viscoelastic fluids to investigate and provide mechanistic explanations for emergent swimming behaviors. I will discuss a few examples that highlight the role of fluid elasticity in micro-organism locomotion.
10:00 am - 10:30 am
Coffee Break
10:30 am - 11:30 am
Panel Discussion: IBM + Advances - Lisa Fauci (moderator), Thomas Fai, Christina Hamlet
& Boyce Griffith
11:30 am - 12:00 pm
Lightning Talks
Breschine Cummins
Venkatesh Gopal
Sang-Eun Lee
Scott McKinley
12:00 pm - 1:30 pm
Lunch
1:30 pm - 2:30 pm
Lightning Talks
Vivian Aranda
Sarah Bogen
Hongfei Chen
Sergi G. Leyva
Jane Shaw MacDonald
Kayode Oluwasegun
Sayandeepa Raha
Rudi Schuech
Stephen Williams
2:30 pm - 3:00 pm
Coffee Break
3:00 pm - 4:00 pm
Panel Discussion: Math Modeling - Greg Forest (moderator), Breschine Cummins, Yoichiro Mori, & Owen Lewis
4:00 pm - 5:00 pm
Poster Session & Drinks
Aaron Barrett
Zixiao Chen
Breschine Cummins
Dana Ferranti
Jake Grdadolnik
Boyce Griffith
Sang-Eun Lee
Sergi G. Leyva
Lulu Lu
Hailey Lynch
Scott McKinley
Hoa Nguyen
Kayode Oluwasegun
Sayandeepa Raha
Rudi Schuech
Stephen Williams
Han Zhou
July
24
2025
Thursday
Chairs: Hoa Nguyen (morning) & Sookkyung Lim (afternoon)
Speakers: Cynthia Anhalt, Julie Simons, Brynja Kohler, Francesca Bernardi, Douglas Varela,
Nathaniel Whitaker & Owen Richfield
8:30 am - 8:55 am
Light Breakfast
8:55 am - 9:00 am
Welcome to Workshop & Housekeeping
9:00 am - 9:30 am
Mathematical Modeling and Prospective Teacher Education: Collaborative Research Findings and Promising Opportunities - Cynthia Anhalt
Abstract: This presentation on mathematics education will focus on the infusion of mathematical modeling into the K-12 mathematics curriculum, collaborative efforts, and research in teacher preparation in mathematical modeling. Secondary mathematics teacher education programs are generally positioned in either mathematics departments or in colleges of education. In preparing to become secondary teachers, it is common for students to take courses from mathematics educators and mathematicians, so there is a need and opportunities for research collaborations between these two groups on how students learn to do mathematical modeling and how they develop ideas for teaching mathematical modeling. A challenge arises when prospective teachers are initially learning to do mathematical modeling, and almost instantaneously must learn and develop ideas for teaching modeling. This presentation will elaborate on mathematical modeling tasks with connections between undergraduate level mathematics and secondary settings, collaborative research efforts, and the role of mathematicians in secondary teacher preparation.
9:30 am - 10:00 am
From Biofluids to genAI: Gateways for Undergraduate Research – Julie Simons
Abstract: Mathematical modeling is an exciting framework to engage undergraduate students in interdisciplinary research. In this talk, I’ll highlight the work of several projects involving undergraduate researchers, including prior work in low Reynolds number biofluid mechanics and more recent work in generative AI literacy in the calculus classroom. Biofluid mechanics offers students a visually rich and mathematically rigorous context for exploring complex processes like flagellar motility or micro-swimmer dynamics. In contrast, generative AI activities provide opportunities to reframe word problems, critique machine-generated solutions, and analyze graphical representations—all within a modeling context. Teaching students to critically engage with AI tools is essential for promoting equity and deeper learning, both in mathematics and beyond. We will present some preliminary data from recent cohorts of students in introductory calculus courses where AI activities have been incorporated. These projects show how mathematical modeling can open doors to domain-specific inquiry as well as broader societal questions about technology, education, and ethics that are impacting our students already.
10:00 am - 10:15 am
Workshop Survey
10:15 am - 10:45 am
Coffee Break
10:45 am - 12:00 pm
Panel Discussion: Math Education + Mock Classroom – Brynja Kohler (moderator), Cynthia Anhalt, Douglas Varela & Francesca Bernardi
12:00 pm - 1:30 pm
Lunch
1:30 pm - 2:00 pm
Computing Coherent Structures in 2-Dimensional Turbulence - Nathaniel Whitaker
Abstract: I will present some of my earlier work in fluids dynamics. In particular, I will discuss longtime equilibrium solutions of the two-dimensional Euler equations for ideal fluid flow using statistical mechanics. Statistical mechanics transforms the problem into a constrained optimization problem. This problem is solved using a novel numerical method. Using this method, we model such phenomena as the merger of vortex patches and the axisymmetrization of an elliptical patch.
2:00 pm - 2:30 pm
Mathematical Modeling of Glomerular Hemodynamics and Associated Nanoparticle-Based Drug Delivery - Owen Richfield
Abstract: The kidney is a vital organ responsible for maintaining fluid, solute and electrolyte homeostasis in the body. Importantly, recent efforts in drug development have focused on targeting kidney disease, which currently affects >10% of the global population and continues to rise. The glomerulus, the specialized microvascular bed in the kidney responsible for filtering the blood to create urine, represents a unique biological niche in terms of its anatomy, physiology and cellular composition. Importantly, glomerular injury is a crucial factor in the progression of overall kidney disease, but few drugs target the glomerular cells directly. Our work expands a 1-dimensional mathematical model of blood flow through a filtering capillary to a network of interconnected capillaries to predict individual capillary filtration rates and mechanical stresses on different glomerular cell types. In this work, we build on this model to predict the binding dynamics of antibody-functionalized nanoparticles for drug delivery in the context of ex vivo perfused human kidneys for transplant. Utilizing data generated in the laboratory and meta-analyses of literature regarding nanoparticle binding and uptake to endothelial cells, the model reproduces experimental results and presents a scheme for rational nanoparticle design in the context of ex vivo pretreatment of kidney grafts for transplant.
2:30 pm - 3:00 pm
Coffee Break
3:00 pm - 3:55 pm
Lightning Talks
Francesca Bernardi
Amy Buchmann
John Chrispell
Irene Erazo
Thomas Fai
Christina Hamlet
Alexander Hoover
Michaela Kubacki
3:55 pm - 4:05 pm
Coffee Break
4:05 pm - 5:00 pm
Lightning Talks
Brittany Leathers
Adnan Morshed
Jeungeun Park
Henry Shum
William Tidwell
Zheng Wang
Longhua Zhao
5:00 pm - 6:30 pm
Break
6:30 pm - 8:30 pm
Reception, Group Photo & Slideshow
July
25
2025
Friday
Chairs: Shilpa Khatri
Speakers: Keisha Cook & Lisa Fauci
8:30 am - 8:55 am
Light Breakfast
8:55 am - 9:00 am
Welcome to Workshop & Housekeeping
9:00 am - 9:30 am
Mathematical Model of Peptide-Mediated Endosomal Escape – Keisha Cook
Abstract: We developed a novel method to quantify endosomal escape of designed fusogenic peptides that electrostatically bind with siRNAs and promote their endosomal escape and delivery into the cytosol. The novel fusogenic peptides enable efficient knockdown of target oncogenes in epithelial ovarian cancer, resulting in decreased cell migration and recolonization in vitro. siRNAs are also known to degrade rapidly in the endosome. Rapid degradation is avoided due to a combination of cationic and hydrophobic amino acid residues, which allows disruption of the endosome and release of siRNAs into the cytosol. Studies regarding the use of the peptides complexed with siRNAs targeting and silencing oncogenes demonstrate the technology's therapeutic potential in ovarian cancer and strategies to reduce ovarian cancer aggressiveness. More information is needed about endosomal escape after successful delivery. Combining kinetic modeling of biochemical systems and stochastic modeling of intracellular organelles for analysis will enable the development of novel strategies to understand the complexity of in vitro delivery and intracellular processes.
9:30 am - 10:00 am
Biofluid dynamics: lessons learned and unfinished tails – Lisa Fauci
Abstract: Given the luxury of the ‘final word’, I will share some thoughts about choices that we have made in modeling biological systems, with their accompanying successes and challenges. Looking forward, I will also share some thoughts about systems that could be exciting research avenues that will benefit from mathematical and computational investigation.
10:00 am - 10:30 am
Coffee Break
10:30 am - 11:45 am
Small Group Discussions
11:45 am - 12:00 pm
Closing Remarks & Highlights Reel of the Workshop
12:00 pm - 1:30 pm
Lunch
Ricardo Cortez
Recorded on 7/21/2025
Title: Vignettes of Stokes Flows in and Around Circles and Spheres
Abstract: This opening presentation of the workshop will describe recent work on regularized Stokeslets in which the regularization depends on the co-dimension of the body where the forces are supported. At scattered points in 3D, traditional regularized Stokeslet are used. Along curves in 3D, we may use regularized Stokeslet segments, Kirchhoff rod theory, or slender-body theory. Finally, on surfaces in 3D, no regularization is needed. I will focus on simple shapes, namely circles in 2D and spheres in 3D, and show a method for computing the flow based on single- and double-layer potentials to machine precision in a simple way. The extension to more general shapes (i.e. star shape domains) will be described. The talk will focus on the main ideas, examples and open problems.
Karin Leiderman
Recorded on 7/21/2025
Title: A discrete platelet-bonding model for simulating platelet aggregation under flow
Abstract: Hemostasis is the healthy clotting response to a blood vessel injury. A major component of clotting is platelet aggregation, which involves the formation of platelet-platelet and platelet-wall bonds between platelet receptors (GPVI and GP1b), and platelet integrins ($\alpha_2\beta_1$ and $\alpha_{IIb}\beta_3$) with plasma-borne molecules (von Willebrand factor and fibrinogen) and wall adherent collagen. There are platelet disorders that decrease the number and/or functionality of $\alpha_{IIb}\beta_3$, which results in excessive bleeding. Current treatments exist but are not evidence based and are not always successful in restoring hemostasis. In the cases where hemostasis is restored, the aggregation mechanism without $\alpha_{IIb}\beta_3$ remains speculative. Our long-term goal is to uncover this mechanism with a mathematical and computational approach. As a first step, we simulated platelet aggregation using the molecular dynamics software, LAMMPS. We considered individual platelets and tracked the platelet-platelet and platelet-wall bonds that formed during aggregation. Currently, the strength of the bonds depends on the local shear rate of a prescribed background flow. Simulations show stable aggregation for healthy platelets under flow. Future work is to improve our modeling framework by parameterizing with experimental measurements and computationally coupling our platelet model to a dynamic flow.
Shilpa Khatri & Stephen Williams
Recorded on 7/21/2025
Title: Tutorial: MRS Part 1
Sarah Olson & Dana Ferranti
Recorded on 7/21/2025
Title: Tutorial: MRS Part 2
Thomas Beale
Recorded on 7/22/2025
Title: Computing nearly singular surface integrals and solving p.d.e.'s on surfaces
Abstract: We describe two numerical methods which could be useful in continuum modeling. The first is a method for computing nearly singular integrals, i.e., integrals such as single or double layer potentials for harmonic functions, or integrals in Stokes flow with Stokeslet or stresslet kernel, when evaluated at points near the surface. Such integrals are more general than the case of evaluation on the surface and could be needed when surfaces are close to each other, or to evaluate at grid points near the surface. Values at all grid points can be recovered efficiently from those near the surface by a technique introduced by A. Mayo. We use regularized versions of the integral kernel as in the method of regularized Stokeslets. In recent work with S. Tlupova (Adv. Comput. Math. 2024) we derive analytic expressions for the error due to regularization, and these allow us to improve this error to higher order, giving better control of the discretization error. The second topic is a method for solving p.d.e.'s on a surface, such as diffusion determined by the Laplace-Beltrami operator, or transport equations (SIAM J. Sci. Comput. 2020). We use a clever discretization of the surface due to W. Ying and W.-C. Wang. The surface is represented by points where it intersects intervals in a three-dimensional grid. The selected points are projected onto regular grid points in coordinate planes, allowing standard numerical methods to be used. The discretization technique allows for seamless transition between coordinate planes. Extension beyond the surface is not required.
Brynja Kohler
Recorded on 7/22/2025
Title: Community-Engaged Learning in an Interdisciplinary Math-Biology Course
Abstract: This talk describes a junior-level interdisciplinary Math/Biology course that integrates mathematical modeling with community-engaged learning. Students explore complex social and environmental systems through project-based learning, applying modeling approaches from ecology, public health, conservation, and sociology. The course emphasizes modeling as a tool for understanding and addressing real-world issues and as a disposition for approaching complex problems. For the final project, students collaborate with local partners—such as a municipal landfill, a regional zoo, and conservation nonprofits—to propose data-informed solutions to problems. Examples from Spring 2023 and Spring 2025 illustrate how students engage with stakeholders, develop teamwork and communication skills, and connect mathematical modeling to civic and scientific contexts. The course builds on institutional support for community-engaged learning and draws on research in team science and project-based learning.
Boyce Griffith
Recorded on 7/22/2025
Title: Tutorial: IBM Part 2
John Stockie
Recorded on 7/23/2025
Title: Immersed boundary simulations of worm-like, inertial swimmers
Abstract: The swimming dynamics of marine organisms has been the subject of many theoretical and computational studies, especially for microscopic organisms (such as bacteria, spermatozoa or plankton) that exist in the viscous-dominated Stokes flow regime where the Reynolds number (Re) is very small. This previous work has focused on individual microswimmers, although there has been a surge of recent interest in simulating suspensions of such swimmers using algorithms that exploit approximate analytical solutions and fast solvers tailored for Stokesian dynamics. Computational studies of higher-Re swimmers are also well-represented in the literature, for organisms such as fish, eels, jellyfish, etc. However, less attention has been paid to creatures like nematodes that swim in an intermediate regime where inertial and viscous effects are comparable, with 0.1
Becca Thomases
Recorded on 7/23/2025
Title: How to swim through goo
Abstract: Many microorganisms and cells function in complex (non-Newtonian) fluids, which are mixtures of different materials that exhibit both viscous and elastic stresses. For example, mammalian sperm swim through cervical mucus on their journey through the female reproductive tract, and they must penetrate the viscoelastic gel outside the ovum to fertilize. In micro-scale swimming the dynamics emerge from the coupled interactions between the complex rheology of the surrounding media and the passive and active body dynamics of the swimmer. We use computational and analytical models of swimmers in viscoelastic fluids to investigate and provide mechanistic explanations for emergent swimming behaviors. I will discuss a few examples that highlight the role of fluid elasticity in micro-organism locomotion.