PDE & Applied Mathematics seminar

Wednesday 10:00 -10:50 am, https://ucr.zoom.us/j/97606227247 

Organizers :  Weitao Chen / Heyrim Cho / Yat Tin Chow / Qixuan Wang / Jia Gou / Mykhailo Potomkin / Yiwei Wang / Maziar Raissi /

Past Organizers :  Mark Alber / James Kelliher / Amir Moradifam

In Spring 2024, the PDE & Applied Math seminar will be held through Zoom or in person (Skye 268). Specific information about the format of each talk will be provided in the email announcement and posted below. If you're interested in attending the seminar, please contact Dr. Qixuan Wang (qixuan.wang@ucr.edu) and Dr. Jia Gou (jia.gou@ucr.edu).


Spring 2024 Schedule 

Apr 03 10:00 AM (Wed) Organizational meeting

Apr 09 02:00 PM (Tue) Dr. Xiaochuan Tian (University of California, San Diego)

Apr 10 10:00 AM (Wed) Dr. Xiaoyu Shi (University of California, Irvine) , in joint with ICQMB seminar

Apr 17 10:00 AM (Wed) Dr. Elena Koslover (University of California, San Diego)

Apr 24 10:00 AM (Wed) Dr. Mykhailo Potomkin (University of California, Riverside)

May 01 10:00 AM (Wed) Dr. Paola Vera-Licona (University of Connecticut)

May 08 10:00 AM (Wed) Dr. Sean Lawley (University of Utah)

May 15  10:00 AM (Wed) Dr. Mikhail Blinov (University of Connecticut)

May 22 10:00 AM (Wed) Dr. Sui Tang (University of California, Santa Barbara)

May 29 10:00 AM (Wed) Dr. Paul Macklin (Indiana University)

Jun 05 10:00 AM (Wed) Mingye Gao & Minh Vu (University of California, Riverside)

Upcoming Talks:

Apr 17, 2024, 10:00 AM - 10:50 AM PT 

Dr. Elena Koslover (Department of Physics, University of California, San Diego)

Title: Tunneling Through the Cell: Structure and Transport in Organelle Networks


Abstract: Eukaryotic cells contain a variety of complex architectures that modulate the transport, distribution, and encounter kinetics of molecular components. In this talk we will explore the emergent structure and transport properties of the peripheral endoplasmic reticulum (ER), which forms an interconnected network of tubules spanning throughout the cell.  Analytic calculations of mean first passage times, numerical reaction-diffusion simulations, and analysis of live-cell imaging data are used to demonstrate how the reticulated architecture of this organelle supports its ability to rapidly disperse and deliver proteins and calcium ions. Furthermore, we will show how a novel liquid network model, incorporating edge tension and new tubule growth, describes the emergent steady-state structure and dynamic rearrangements of the peripheral ER. The specific intracellular system discussed here highlights the role of mathematical modeling in elucidating interplay of structure and function in living cells.


Bio: Elena Koslover is a professor of physics at the University of California, San Diego. She obtained her undergraduate degrees in biology and mathematics at the California Institute of Technology, an MPhil in Chemistry from the University of Cambridge, and a PhD in Biophysics at Stanford University, where she worked on modeling genome mechanics and intracellular fluid dynamics. Her research group uses theoretical and computational techniques, together with analysis of quantitative data provided by collaborating groups, to understand how the morphology and organization of cellular structures determine the spatiotemporal distribution and interaction kinetics of intracellular components.



April 24th, 2024, 10:00 AM - 10:50 AM PT 

Dr. Mykhailo Potomkin (Department of Mathematics, University of California, Riverside)

Title: Well-posedness of orientational dynamics of a microswimmer in nematic liquid crystal


Abstract: I will present the analysis of a nonlinear partial differential equation system describing the motion of a microswimmer in a nematic liquid crystal environment. The model was developed to elucidate how a bacterium navigates itself in biofluids with properties different from isotropic Newtonian fluid but rather those of liquid crystal. First, I will discuss the existence of the steady state corresponding to the traveling wave solution. Next, the finite-time existence of the time-dependent problem in a periodic domain will be presented. Finally, I will show how the homogenization theory can be used to capture the dynamics of a squirmer colony. This work was done jointly with L. Berlyand (Penn State U.), H. Chi (Penn State U.), and A. Yip (Purdue U.).


Bio: Dr. Potomkin is an assistant professor at UC Riverside. He previously held a postdoctoral position at the Pennsylvania State University, and he received his Ph.D. from V.N. Karazin Kharkiv National University (Ukraine). Dr. Potomkin’s area of research includes modeling, analysis, and numerical simulation of problems involving various types of differential equations, with a specific focus on problems arising in Mathematical Biology and Soft Matter Physics.    


  

May 08, 2024, 10:00 AM - 10:50 AM PT 

Dr. Sean Lawley (Mathematics Department, University of Utah)

Title: Stochastics in medicine: Delaying menopause and missing drug doses


Abstract: Stochastic modeling and analysis can help answer pressing medical questions. In this talk, I will attempt to justify this claim by describing recent work on two problems in medicine. The first problem concerns ovarian tissue cryopreservation, which is a proven tool to preserve ovarian follicles prior to gonadotoxic treatments. Can this procedure be applied to healthy women to delay or eliminate menopause? How can it be optimized? The second problem concerns medication nonadherence. What should you do if you miss a dose of medication? How can physicians design dosing regimens that are robust to missed/late doses? I will describe (a) how stochastics theory offers insights into these questions and (b) the mathematical questions that emerge from this investigation. The first problem is based on joint work with Joshua Johnson (University of Colorado School of Medicine), John Emerson (Yale University), and Kutluk Oktay (Yale School of Medicine).

Past Talks:


April 09, 2024, 02:00 PM - 02:50 PM PT

Dr. Xiaochuan Tian (Department of Mathematics, University of California, San Diego)

Title: Enhancing Meshfree Methods for Solving PDEs through Nonlocal Analysis


Abstract: Meshfree and particle methods are widely used in computational studies of partial differential equations, offering many advantages compared to traditional mesh- or grid-based numerical methods.  Nevertheless, many practical questions revolve around meshfree methods, encompassing concerns about stability and accuracy.  We propose a new paradigm of designing meshfree methods for solving partial differential equations (PDEs) through nonlocal analysis, inspired by the recent development of nonlocal calculus and its applications.  We propose that the development of stable, accurate, and efficient meshfree methods relies on two key factors: (1) the formulation of well-posed continuum nonlocal models to approximate the PDE models and (2) the development of asymptotically compatible schemes for robust discretization of nonlocal models that allow a flexible coupling of the modeling and discretization parameters.  We will review several aspects of nonlocal calculus and asymptotically compatible schemes and demonstrate the idea with a monotone meshfree method for solving linear elliptic equations in non-divergence form.


April 10, 2024, 10:00 AM - 10:50 AM PT 

in joint with ICQMB seminar 

Dr. Xiaoyu Shi (Department of Developmental & Cell Biology, University of California, Irvine)

Title: Super-resolution Visualization of Organelle-organelle Interactions with Expansion Microscopy


Abstract: Expansion microscopy has revolutionized cell biology and neuroscience by unveiling intricate spatial relationships in organelles since 2015. In this talk, we'll delve into two new methods from the Xiaoyu Shi lab that enhance detection resolution in imaging organelle-organelle and protein-protein interactions. One technique is the Label-Retention Expansion Microscopy (LR-ExM), which captures molecular-resolution images of structures like the nuclear envelope, microtubules, clathrin-coated pits, mitochondria, nucleolus, and ER. The other method is the Proximity-Labeling Expansion Microscopy (PL-ExM), revealing the 3D structure of protein interactome within cells and tissues at resolutions up to 12 nm. Remarkably, these chemical techniques enable super-resolution using conventional microscopes, such as confocal and Airyscan. The Shi lab pledges to provide the science community with LR-ExM probes and protocols at no cost from now to 2025.