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
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
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
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
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
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
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.
Rujeko Chinomona, Temple University
The simulation of multiphysics applications, for example, in climate or combustion engine models, is often challenging because of its large-scale nature and the presence of complex dynamics. Physical processes that evolve on disparate time scales, mixed stiff and nonstiff components, and combined linear and nonlinear terms pose unique challenges to traditional time-stepping methods. Although there might be optimal time integration methods for separate components, typically no single algorithm is suitable for the combined problem. Multirate integrators use at least two time step sizes to evolve coupled initial value problems (IVPs) and can tackle some of the temporal challenges in multiphysics simulations, providing solutions that are highly accurate and computationally efficient.
This talk will focus on three new classes of multirate time integrators with the characteristic that the slow dynamics are evolved using a traditional one step scheme and the fast dynamics are solved through a sequence of modified IVPs. These multirate schemes have high orders of accuracy (fourth order or greater) and allow flexibility in the choice of algorithm for both the fast and slow dynamics, including mixed implicit-explicit treatment of both time scales. Numerical results show their competitiveness with both legacy operator-splitting approaches commonly used in multiphysics simulations and other comparable multirate methods in the literature.
Mengsha Yao, Temple University
This research is motivated by the following two applications involving biosensor-measured transdermal alcohol concentration (TAC). A TAC biosensor measures the ethanol content in perspiration. The first application is the control of intravenously-infused alcohol studies based on a population model for the study participant or subject and TAC sensing, while the second application is estimating blood or breath alcohol concentration (respectively, BAC or BrAC) from TAC. A dynamical model for the underlying control system is established. It takes the form of a semi-linear, parabolic PDE/ODE hybrid system describing the transport of ethanol from the blood through the skin, its excretion within perspiration, and finally its measurement on the surface of the skin by an electro-chemical biosensor. Since the parameters of this dynamical model can vary with the individual wearing the sensor, the particular sensor being worn, and environmental factors such as ambient temperature and humidity, we allow the model parameters to be random with either known or estimated distribution. A state space formulation of the model set in an appropriately constructed Gelfand triple of Bochner spaces is derived wherein the random parameters are treated as additional spatial variables. The resulting population model takes the form of an abstract parabolic hybrid system involving coupled partial and ordinary differential equations with random parameters. A finite-dimensional Galerkin-based approximation and convergence theory and estimation of abstract parabolic systems with random parameters is developed.
Alberto Tenore, Temple University
This research concerns the mathematical modelling of complex biological systems, known in the literature as multispecies biofilms, in the field of Continuum Mechanics. Two are the primary objectives pursued. The first is the description of the dynamics of planar and granular biofilms, by modelling the main biological and ecological aspects of these ecosystems. Starting from this, the second objective consists in the modelling of innovative biofilm-based reactors devoted to wastewater treatment, by predicting and simulating the biological processes involved.
The first model presented has been formulated in a free boundary 1D planar domain with vanishing initial value, and describes the formation and evolution of biofilms attached to solid supports. The second model has been formulated as a spherical free boundary problem with radial symmetry, and focuses on the dynamics of granular biofilms. The free boundary domain expands due to various phenomena: attachment, detachment, invasion, microbial growth and decay. Hyperbolic PDEs model the growth of the sessile microbial species, while parabolic PDEs govern the dynamics of substrates and invading species within the biofilm. The granular biofilm model has been coupled with macroscopic reactor mass balances, to simulate the biological processes involved in granular-based bioreactors devoted to wastewater treatment. Two different bioreactor configurations have been considered, continuous stirred tank reactor (CSTR) and sequencing batch reactor (SBR), through first order ODEs and first order impulsive ODEs, respectively.
The models have been applied to relevant biological cases, such as phototrophic-heterotrophic biofilms, anaerobic granules and oxygenic photogranules. Due to the complexity and non-linearity of equations involved, these models have been numerically integrated through original software developed in MatLab platform. Numerical studies and results of relevant engineering, biological and ecological interest have been achieved.
Agnieszka Międlar, University of Kansas
Randomized NLA methods have recently gained popularity because of their easy implementation, computational efficiency, and numerical robustness. We propose a randomized version of a well-established FEAST eigenvalue algorithm that enables computing the eigenvalues of the Hermitian matrix pencil (A},B}) located in the given real interval I \ [lambda_min, lambda_max]. In this talk, we will present deterministic as well as probabilistic error analysis of the accuracy of approximate eigenpair and subspaces obtained using the randomized FEAST algorithm.
First, we derive bounds for the canonical angles between the exact and the approximate eigenspaces corresponding to the eigenvalues contained in the interval I. Then, we present bounds for the accuracy of the eigenvalues and the corresponding eigenvectors. This part of the analysis is independent of the particular distribution of an initial subspace, therefore we denote it as deterministic. In the case of the starting guess being a Gaussian random matrix, we provide more informative,probabilistic error bounds. Finally, we will illustrate numerically the effectiveness of all the proposed error bounds.
This is a joint work with Eric de Sturler (Virginia Tech), Nikita Kapur (University of Iowa) and Arvind K. Saibaba (NC State).
Mirjeta Pasha, Arizona State University
In this talk, we discuss various approaches that use learning from training data to solve inverse problems, following a bi-level learning approach. We consider a general framework for optimal inversion design, where training data can be used to learn optimalregularization parameters, data fidelity terms, and regularizers, thereby resulting in superior variational regularization methods. In particular, we describe methods to learn optimal p and q norms for L^p-L^q regularization and methods to learn optimal parametricregularization matrices. We exploit efficient algorithms based on Krylov projection methods for solving the regularized problems, both at training and validation stages, making these methods well-suited for large-scale problems. We experimentally show thatthe learned regularization methods perform well even when the data are corrupted by noise coming from different distributions, or when there is some inexactness in the forward operator. This is joint work with Julianne Chung, Matthias Chung and Silvia Gazzola.
Arvind Krishna Saibaba, NC State
Randomized Numerical Linear Algebra (RandNLA) is an emerging research area that uses randomization as an algorithmic resource to develop algorithms that are numerically robust, with strong theoretical guarantees, easy to implement,and well-suited for high-performance computing. There are two parts to this talk. In the first part, I will give a brief overview of RandNLA techniques for dimensionality reduction and give insight into their accuracy and computational costs. In the second part, I will present novel randomized algorithms for computing the truncated generalized singular value decomposition, and illustrate these algorithms on hyperdifferential sensitivity analysis, a technique to study the sensitivity of the solution of optimization problems with respect to parameters.
Joint work with Joseph Hart and Bart van Bloemen Waanders (both at Sandia National Labs).
Shahriar Afkhami, New Jersey Institute of Technology
Consider two fluids separated by an interface. Surface tension arises on the interface of two immiscible fluids as a result of the asymmetry in attractive forces between molecules of two fluids, which is the origin of the surface excess energy. For the fluid to minimize its energy state, the interface should then assume the smoothest shape possible. When deriving boundary conditions appropriate for a fluid-fluid interface, surface tension gives rise to a normal stress across the interface linearly proportional to the local curvature and a tangential stress associated with gradients in the surface tension. Here I describe a framework for direct numerical simulation of surface tension driven flows. I will present a numerical scheme we devised to include surface gradients into our Eulerian interface description, to discretize the tangential (Marangoni) stresses. Numerical validations and convergence of the method are discussed. We also show numerical examples, motivated by experimental observations, of the effect of the concentration-dependent surface tension on the flow field and the interface evolution. Time permitting, I will also discuss a semi-implicit discretization of the surface tension which involves discretizing the Laplace-Beltrami operator, to include surface diffusion, for improving the numerical stability.
Lee Ricketson, Lawrence Livermore National Laboratory
Magnetic confinement fusion devices attempt to confine a hot plasma using a strong magnetic field in order to create the conditions necessary for energy-producing fusion reactions. Simulation of such devices is complicated by many factors, prominent among which is the extremely short time-scale on which particles gyrate about magnetic field lines. Stepping over this time-scale is essential for practical simulation of the much longerscales of physical and engineering interest. In this talk we will review the elementary aspects of charged particle motion and the so-called “guiding center” asymptotic limit when the magnetic field is strong. Motivated by recent evidence that this asymptoticlimit is not universally valid in fusion devices, we present the development of a new asymptotic preserving time integrator that converges at second order in the small time-step limit while reproducing the guiding center limit when stepping over the gyrationscale. In contrast to previous efforts along these lines, we show that the new scheme conserves energy exactly, and demonstrate through examples that this property can be critical for long-time accuracy.
Casey Diekman, NJIT
Circadian rhythms are biological oscillations that align our physiology and behavior with the 24-hour environmental cycles conferred by the Earth’s rotation. In this talk, I will discuss two projects that focus on circadian clock cells in the brain and the entrainment of circadian rhythms to the light-dark cycle. Most of what we know about the electrical activity of circadian clock neurons comes from studies of nocturnal (night-active) rodents, hindering the translation of this knowledge to diurnal (day-active) humans. In the first part of the talk, we use data assimilation and patch-clamp recordings from the diurnal rodent Rhabdomys pumilio to build the first mathematical models of the electrophysiology of circadian neurons in a day-active species. We find that the electrical activity of circadian neurons is similar overall between nocturnal and diurnal rodents but that there are some interesting differences in their responses to inhibition. In the second part of the talk, we use tools from dynamical systems theory to study the reentrainment of a model of the human circadian pacemaker following perturbations that simulate jet lag. We show that the reentrainment dynamics are organized by invariant manifolds of fixed points of a 24-hour stroboscopic map and use these manifolds to explain a rapid reentrainment phenomenon that occurs under certain jet lag scenarios.