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Current contacts: Benjamin Seibold or Daniel B. Szyld
The Seminar usually takes place on Wednesdays at 4:00 PM in Room 617 on the sixth floor of Wachman Hall. Click on title for abstract.
Stephan Grein, Department of Mathematics, Temple University
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Computational Neuroscience has to deal with a vast diversity of morphologically distinct brain cells which display a complicated three-dimensional topology and architecture and contain nested distinct structures within the cell which have implications for the cellular function. In particular time-dependent ion dynamics in the intracellular space of the cell have ramifications for learning and memory formation in the brain and are thus of crucial interest to the researcher who describes the dynamics by models using partial differential equations. The intracellular space of the cell however it typically not fully accounted for in detail by current mesh generation tools or the degrees of freedom of the generated computational mesh skyrocket thus rendering the meshes as an inappropriate substrate for hierarchical numerical solvers for HPC infrastructure. In this talk a novel mesh generation pipeline is described allowing reconstruction of a large body of neurons stored in publicly available neuroscientific databases which allows one the one hand a control of the degrees of freedom and on the other hand large-scale batch processing for parameter studies compiled into a reusable automatic and versatile toolbox for multi-physics simulations on HPC systems.
Nour Khoudari, Department of Mathematics, Temple University
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Real traffic flow develops instabilities and traffic waves. Traffic waves are traveling disturbances in the distribution of vehicles on a highway. They travel backwards relative to the vehicles themselves. Low density autonomous vehicles, acting as Lagrangian flow actuators, have the potential to dampen and prevent these undesirable non-equilibrium phenomena. By connecting traffic models from micro to macro scales, we outline some of the key macroscopic flow consequences of microscopic traffic waves, discuss AV-based flow smoothing, and derive continuum models from microscopic car-following models.
Anyone interested in Applied Math (in particular first-year graduate students), in talking about research or potential research opportunities, or just wants to enjoy their coffee in the company of fellow students and faculty is invited to join this week's Applied Math Seminar Social.
After brewing your coffee you can join HERE.
Brandi Henry, Temple University
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Biofilms are communities of microorganisms that form when these microorganisms attach to surfaces, secrete a sticky substance, and reproduce within this sticky extracellular matrix. We are interested in how the structure of the biofilms within the human microbiota affects these interactions, and specifically how structural changes relate to antibiotic resistance. Structural changes can occur when biofilms are stressed. Hydrogen peroxide can trigger a stress response that causes rigid, dense towers to grow within the biofilm, resulting in a highly heterogeneous structure. We will discuss our recent work in reconstructing the biofilm environments from microscopy data and modeling and simulating movement of antibiotics through the biofilm environments when put under flow.
Yoichiro Mori, Applied Mathematics and Computational Science, University of Pennsylvania
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Systems in which thin filaments interact with the surrounding fluid abound in science and engineering. The computational and analytical difficulties associated with treating thin filaments as 3D objects has led to the development of slender body theory, in which filaments are approximated as 1D curves in a 3D fluid. In the 70-80s, Keller, Rubinow, Johnson and others derived an expression for the Stokesian flow field around a thin filament given a one-dimensional force density along the center-line curve. Through the work of Shelley, Tornberg and others, this slender body approximation has become firmly established as an important computational tool for the study of filament dynamics in Stokes flow. An issue with slender body approximation has been that it is unclear what it is an approximation to. As is well-known, it is not possible to specify some value along a 1D curve to solve the 3D exterior Stokes problem. What is the PDE problem that slender body approximation is approximating? Here, we answer this question by formulating a physically natural PDE problem with non-conventional boundary conditions on the filament surface, which incorporates the idea that the filament must maintain its integrity (velocity along filament cross sections must be constant). We prove that this PDE problem is well-posed, and show furthermore that the slender body approximation does indeed provide an approximation to this PDE problem by proving error estimates. This is joint work with Laurel Ohm, Will Mitchell and Dan Spirn.
Bruce Ayati, Department of Mathematics, University of Iowa
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This talk will cover an arc of work done with the Martin Lab at the University of Iowa Department of Orthopedics & Rehabilitation. We will go over some of our models and simulations, and the role they played in advancing the work of our collaborators.
Greg Forest, Mathematics, Applied Physical Sciences, & Biomedical Engineering, UNC Chapel Hill
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Insights into the mechanisms and dynamics of human respiratory tract (HRT) infections from the SARS-CoV-2 virus can inform public awareness as well as guide medical prevention and treatment for COVID-19 disease. Yet, the complex physiology of the human lung and the inability to sample diverse regions of the HRT pose fundamental roadblocks, both to discern among potential mechanisms for infection and disease and to monitor progression of infection. My group has explored lung biology and disease for over 2 decades in an effort called the UNC Virtual Lung Project, spanning many disciplines. We further explored how viruses “traffic” in mucosal barriers coating human organs, including the upper and lower respiratory tract, for the last decade, focusing on natural and synthetic antibody protection.
Then along came the novel coronavirus SARS-CoV-2, for which we have no immune protection, requiring a step back to a pre-immunity scenario. We developed a computational model that incorporates: detailed physiology of the HRT, and best current knowledge about the mobility of SARS-CoV-2 virions in airway surface liquids (ASL) as well as epithelial cell infectability and replication of infectious virions throughout the HRT. The model simulates outcomes from any dynamic deposition profile of SARS-CoV-2 throughout the HRT, and tracks the propagation of infectious virions in the ASL and infected epithelial cells. We focus this lecture on two clinical observations, their respective likelihoods, and open questions raised: an upper respiratory tract infection following inhaled exposure to SARS-CoV-2; and, progression to alveolar pneumonia. Our baseline modeling platform is poised to superimpose interventions, from adaptive immune responses to any form of medical or drug treatment, at any point from pre-exposure to disease progression, with several new collaborations to do so. The results presented highlight the urgency to understand the underlying physical and physiological conditions that facilitate transmission, including self-transmission, which we absolutely do not yet understand.
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