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Applied and Computational Mathematics Seminar

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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.

Body

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.

Body

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.

Body

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.

Body

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.

Body

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.

Body

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.

Body

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.

Body

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.

Body

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.

Body

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.

Body

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.

Body

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.

Body

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.

Body

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.

Body

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.

Body
  • Wednesday January 27, 2021 at 16:00, Virtual Meeting

    A novel hierarchical mesh generation pipeline for the numerical simulation of neurons

    Stephan Grein, Department of Mathematics, Temple University

    Join HERE

    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.
     

  • Wednesday February 10, 2021 at 16:00, Virtual Meeting

    Macroscopic Interpretation of Microscopic Car-following Models with Traffic Waves

    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.
     

  • Wednesday February 24, 2021 at 16:00, Virtual Meeting

    Applied Math Social

     
    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.
     

  • Wednesday March 10, 2021 at 16:00, Virtual Meeting

    Antibiotic Movement in Heterogeneous Biofilm Environments

    Brandi Henry, Temple University

    Join HERE

    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. 
     

  • Wednesday March 24, 2021 at 16:00, Virtual Meeting

    Mathematical Justification of Slender Body Theory

    Yoichiro Mori, Applied Mathematics and Computational Science, University of Pennsylvania

    Join HERE

    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.
     

  • Wednesday April 7, 2021 at 16:00, Virtual Meeting

    Mathematics as a conduit for translational research in post-traumatic osteoarthritis

    Bruce Ayati, Department of Mathematics, University of Iowa

    Join HERE

    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.
     

  • Wednesday April 21, 2021 at 16:00, Virtual Meeting

    Modeling insights into SARS-CoV-2 respiratory tract infections

    Greg Forest, Mathematics, Applied Physical Sciences, & Biomedical Engineering, UNC Chapel Hill

    Join HERE

    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. 
     

  • Wednesday September 1, 2021 at 16:00, Virtual Meeting

    Flexible and accurate multirate time-stepping methods for differential equations

    Rujeko Chinomona, Temple University

    Join HERE

    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.
     

  • Wednesday September 29, 2021 at 16:00, Virtual Meeting

    Linear Quadratic Control, Estimation, and Tracking for Random Abstract Parabolic Systems with Application to Transdermal Alcohol Biosensing

    Mengsha Yao, Temple University

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    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. 
     

  • Wednesday October 6, 2021 at 16:00, Virtual Meeting

    Free boundary problems for mixed-species biofilms: modelling and simulation

    Alberto Tenore, Temple University

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    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.

     

  • Wednesday October 20, 2021 at 16:00, Virtual Meeting

    Randomized FEAST Algorithm for Generalized Hermitian Eigenvalue Problems with Probabilistic Error Analysis

    Agnieszka Międlar, University of Kansas

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    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).

  • Wednesday October 27, 2021 at 16:00, Virtual Meeting

    Efficient learning methods for large-scale optimal inversion design

    Mirjeta Pasha, Arizona State University

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    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.

  • Monday November 1, 2021 at 16:00, Virtual Meeting

    Randomized algorithms for hyperdifferential sensitivity analysis 

    Arvind Krishna Saibaba, NC State   

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    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).

  • Wednesday November 3, 2021 at 16:00, Virtual Meeting

    An Eulerian Discretization of Surface Tension Driven Flows

    Shahriar Afkhami, New Jersey Institute of Technology 

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    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.

  • Wednesday November 17, 2021 at 16:00, Virtual meeting

    Asymptotic-Preserving Time Integration for Charged Particle Motion in Strong Magnetic Fields

    Lee Ricketson, Lawrence Livermore National Laboratory

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    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.

  • Wednesday December 1, 2021 at 16:00, Virtual Meeting

    Data Assimilation and Dynamical Systems Analysis of Circadian Rhythmicity and Entrainment

    Casey Diekman, NJIT

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    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.
     

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  • Wednesday February 2, 2022 at 16:00, Virtual event

    Optimal Size of the Block in Block GMRES on GPUs: Computational Model and Experiments

    Andrew Higgins, Temple University

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    The block version of GMRES (BGMRES) is most advantageous over the single right hand side (RHS) counterpart when the cost of communication is high while the cost of floating point operations is not. This is the case on modern Graphics Processing Units(GPUs), while it is generally not the case on traditional Central Processing Units (CPUs). In this talk, experiments on both GPUs and CPUs are shown that compare the performance of BGMRES against GMRES as the number of RHS increases. The experiments indicatethat there are many cases in which BGMRES is slower than GMRES on CPUs, but faster on GPUs. Furthermore, when varying the number of RHS on the GPU, there is an optimal number of RHS where BGMRES is clearly most advantageous over GMRES. A computational modelis developed using hardware specific parameters, showing qualitatively where this optimal number of RHS is, and this model also helps explain the phenomena observed in the experiments.
     

  • Wednesday February 16, 2022 at 16:00, Virtual event

    An Agent-Based Model of Pain-Related Neurons in the Amygdala

    Rachael Miller Neilan, Duquesne University

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    In this talk, I will present an agent-based model (ABM) that simulates the behavior and interactions of neurons in the amygdala for the purpose of studying their impact on pain. 
    In the ABM, agents represent individual neurons that express either protein kinase C delta (PKC) or somatostatin (SOM). Neurons that express PKC are known to increase pain whereas neurons that express SOM are known to decrease pain. During the model’s initialization, neurons are assigned type-specific parameters based on laboratory data and a location in either the right or left amygdala. A network of directed links is established to allow for the transmission of inhibitory signals between neurons. During each model timestep, neurons accrue damage and the firing rates all of neurons are updated based on the intensity of the external stimulus and the strength of signals transmitted through the network. The ABM outputs an emergent measure of pain, which is calculated in terms of the cumulative pro-nociceptive activity of the PKC neurons and anti-nociceptive activity of the SOM neurons. Results demonstrate the ability of the model to produce changes in pain that are consistent with published studies and highlight the importance of several model parameters. 

    Undergraduate students contributed to the development and programming of the ABM using NetLogo software.
     

  • Wednesday April 6, 2022 at 16:00, Virtual event

    Bridging the Biophysics and Evolution of Viruses

    Antoni Luque, San Diego State

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    Viruses are the most abundant biological entity on Earth and play a pivotal role in regulating the evolution of organisms and the planet's biogeochemistry. Most viruses protect their genome in icosahedral shells made of multiple copies of the same protein. Viral icosahedral shells span two orders of magnitude in size and thousands of different architectures. Yet, the physical mechanisms that have selected such diverse viral structures are unknown. Here, I will share my most recent contributions to this fundamental problem. First, I will introduce the generalized quasi-equivalence theory of icosahedral architectures as a framework to investigate systematically viral architectures and their protein components. Second, I will show how the physical relationship between the protein shell and genome of viruses has opened the door to characterize uncultured viruses, predict the existence of unknown viruses, and engineer new viruses from the environment. Finally, I will discuss a novel physical mechanism that may hold the key to how viruses explore different viral architectures.
     

  • Wednesday April 20, 2022 at 16:00, Virtual event

    Subaerial biofilms: confocal microscopy imaging and theoretical model on the availability of water via microbially-induced condensation 

    Alberto Tenore, Temple University

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    Subaerial biofilms (SABs) are thin layers of densely packed microorganisms, that live in self-organized structures on soil and rock surfaces exposed to the air. Microbial life within these ecosystems is very hard and mainly dependent on the availability of liquid water, essential for microbial metabolic activities. That’s why SAB inhabitants are special microorganisms, able to resist long desiccation periods and loosen the thermodynamic constraints to the water vapor condensation into the SAB. 

    Here, I will present a multidisciplinary study on subaerial biofilms. First, I will show some confocal microscopy images of SAB microbial colonies, the result of multiple sampling campaigns conducted on the marble surfaces of the Merchants’ Exchange Building (Philadelphia, USA) and on the stone railing of my house in Naples (Italy). Then, I will present a novel theoretical model to predict liquid water availability via microbially-induced condensation and estimate the maximum SAB thickness thermodynamically supported under specific temperature and humidity conditions. Finally, I will apply the present model to a year-long data campaign about temperature and humidity, conducted on the marble roof of the portico of the Thomas Jefferson Memorial (Washington D.C., USA). 

     

  • Wednesday August 31, 2022 at 16:00, 617 Wachman Hall

    On the Prandtl-Kolmogorov 1-Equation Model

    Kiera Kean, Temple University

    Turbulence modeling in practice requires predicting averages of solutions of the Navier-Stokes equations. We examine eddy viscosity RANS models based on the 1-equation model of Prandtl and Kolmogorov. Many of these models fail due to overdissipation in the near wall region. For general eddy viscosity models, we show that the ratio of the near wall average viscosity to the effective global viscosity is the key parameter. This result is then applied to the 1-equation, URANS model of turbulence for which this ratio depends on the specification of the turbulence length scale. We propose a modification to traditional choices of l: away from walls, interpreting an early suggestion of Prandtl, we set l=√2k+1/2τ, where τ=selected time scale. In the near wall region analysis suggests replacing the traditional l=0.41d (d=wall normal distance) with l=0.41d√(d/L)giving, e.g., l=min{√2k+1/2τ, 0.41d√(d/L)}. This l(⋅) results in a simpler model with correct near wall asymptotics. Its energy dissipation rate scales no larger than the physically correct O(U3/L), balancing energy input with energy dissipation.

     

  • Wednesday September 7, 2022 at 16:00, 617 Wachman Hall

    Resonance-based mechanisms of generation of oscillations in networks of non-oscillatory neurons

    Horacio Rotstein, New Jersey Institute of Technology
     

    Several neuron types have been shown to exhibit (subthreshold) membrane potential resonance (MPR), defined as the occurrence of a peak in their voltage amplitude response to oscillatory input currents at a preferred (resonant) frequency. MPR has been investigated both experimentally and theoretically. However, whether MPR is simply an epiphenomenon or it plays a functional role for the generation of neuronal network oscillations, and how the latent time scales present in individual, non-oscillatory cells affect the properties of the oscillatory networks in which they are embedded are open questions. We address these issues by investigating a minimal network model consisting of (i) a non-oscillatory linear resonator (band-pass filter) with 2D dynamics, (ii) a passive cell (low-pass filter) with 1D linear dynamics, and (iii) nonlinear graded synaptic connections (excitatory or inhibitory) with instantaneous dynamics. We demonstrate that (i) the network oscillations crucially depend on the presence of MPR in the resonator, (ii) they are amplified by the network connectivity, (iii) they develop relaxation oscillations for high enough levels of mutual inhibition/excitation, and (iv) the network frequency monotonically depends on the resonator’s resonant frequency. We explain these phenomena using a reduced adapted version of the classical phase-plane analysis that helps uncovering the type of effective network nonlinearities that contribute to the generation of network oscillations. We extend our results to the so-called firing rate models with adaption. Our results have direct implications for neuronal network oscillations in more complex systems and other biological oscillatory networks (e.g, biochemical, genetic).

     

  • Wednesday September 14, 2022 at 16:00, 617 Wachman Hall

    Optimal local approximation spaces in multiscale methods and their application in domain decomposition methods

    Kathrin Smetana, Stevens Institute Technology 

    Heterogeneous problems that take place at multiple scales are ubiquitous in science and engineering. Examples are wind turbines made from composites or groundwater flow relevant e.g., for the design of flood prevention measures. However, finite element or finite volume methods require an often prohibitively large amount of computational time for such tasks. Multiscale methods that are based on ansatz functions which incorporate the local behavior of the (numerical) solution of the partial differential equations (PDEs) have been developed to tackle these heterogeneous problems. Heterogeneous problems also pose a challenge for iterative linear system of equations solvers as the condition number of the preconditioned system generally depends on the contrast of the coefficient function leading to a deterioration of convergence.Two-level domain decomposition preconditioners with so-called adaptive coarse spaces constructed from suitable local eigenvalue problems restore robust, contrast-independent convergence. However, these eigenvalue problems typically rely on non-algebraic information, such that the adaptive coarse spaces cannot be constructed from the fully assembled system matrix

    In this talk we will present optimal local approximation spaces for multiscale methods, whose local ansatz functions can be constructed by solving the PDE on small subdomains, and that allow controlling the error due to localization and the (global) approximation error at a (quasi-optimal) rate without relying on structural assumptions such as scale separation or periodicity. In addition, we will show how these optimal local approximation spaces can be used to generate two-level overlapping Schwarz preconditioners that are both fully algebraic and robust in the sense that we can show an upper bound for the condition number that is independent of the contrast.
     

     

  • Wednesday September 21, 2022 at 16:00, 617 Wachman Hall

    Efficient Time Integration Approaches for the Dispersive Shallow Water Equations

    David Shirokoff, New Jersey Institute of Technology
     

    This talk focuses on developing time integration strategies for thedispersive shallow water equations (DSWE)—which are fluid models, applicable tocoastal regions that include additional physics (such as dispersion) to thewell-known shallow water equations. The DSWEs contain nonlinear,"mixed" space and time derivatives that create computational challengesin the numerical time integration of the equations. We devise a constantcoefficient preconditioner that may be used to handle the time integration ofthe mixed derivative terms in the DSWE via preconditioned Krylov methods. A key feature of the approach is that the results may be applied to varyingbottom topographies. Concepts from the preconditioner also enablethe development of computationally advantageous IMEX approaches that treat someterms in the time integration implicitly (Im) and others explicitly (Ex).

     

  • Wednesday September 28, 2022 at 16:00, 617 Wachman Hall

    Importance of the Antarctic Slope Current in the Southern Ocean Response to Ice Sheet Melt and Wind Stress Change

    Rebecca Beadling, Temple University
     

    Two coupled climate models, GFDL-CM4and GFDL-ESM4, are used to investigate the physical response of the SouthernOcean to changes in surface wind stress, increased Antarctic meltwater, and thecombined forcing of the two in a pre-industrial control simulation. Themeltwater cools the ocean surface in all regions except the Weddell Sea, wherethe wind stress drives a warming of the near-surface layer. The limitedsensitivity of the Weddell Sea surface layer to the meltwater is a result ofthe spatial distribution of the imposed meltwater fluxes, regional bathymetry,and large-scale circulation patterns. The models yield strikingly differentresponses on the West Antarctic shelf. The disagreement is attributable to themean-state representation and meltwater-driven acceleration of the AntarcticSlope Current (ASC). In CM4, the meltwater is efficiently trapped on the shelfby a strong, and accelerating ASC which isolates the West Antarctic shelf fromwarm offshore waters, leading to strong subsurface cooling. In ESM4, a weakerand diffuse ASC allows more meltwater to escape from the shelf and there is noisolation mechanism in West Antarctica. Instead, the subsurface warms in thisregion in ESM4. The CM4 results suggest a possible negative feedback mechanismthat acts to limit future melting, while the ESM4 results suggest a possiblepositive feedback mechanism that acts to accelerate melt. Our resultsdemonstrate the strong influence the ASC has on governing changes along theshelf, highlighting the importance of coupling interactive ice sheet models toocean models that can resolve these dynamical processes.

     

  • Wednesday October 19, 2022 at 16:00,

    Multiscale modeling and simulation of neuronal processes in the context of medical applications

    Gillian Queisser, Temple University
     
    Repetitive transcranial magnetic stimulation (rTMS) is a treatment modality for neurological disorders, such as schizophrenia and depression. A coil is positioned close to the patient’s skull, through which a time-varying magnetic field induces an electric field which penetrates brain tissue. By this extracellular stimulation neurons are activated and ideally promote long-term cellular changes that improve the neurological condition. Although rTMS has been in clinical use for over a decade, the mechanisms by which a specific treatment protocol operates are far from understood. The complexity of understanding and optimizing rTMS lies in the multiscale nature of the biophysical problem, where macroscopic electric fields affect individual neurons and these in turn translate electrical signals into biochemical responses. We therefore developed a multiscale framework with which rTMS parameters, such as coil position and stimulation frequency, can be modified and effects of rTMS can be measured at the cellular level. The novelty of this framework is the incorporation of cellular calcium dynamics, which are critical for inducing long-term responses using a short rTMS window. In this talk, we will introduce the general problem and the calcium problem in particular. Numerical analysis of the calcium problem shows existence and uniqueness, and careful linearization of the nonlinear problem gives rise to fast, efficient, and scalable time-stepping methods for solving the calcium problem on complex three-dimensional cellular domains. As examples we will show simulation results of calcium dynamics in human dendritic spines and on full 3D neurons, which are synaptically activated in concert with rTMS stimuli. These results demonstrate how different rTMS protocols and the spatial organization of neurons control intracellular calcium signaling and they pave the way for patient-specific rTMS optimization. Additionally, a similar framework can be used to study calcium dynamics under neuropathological states, such as Alzheimer’s disease. Here we show the effect of Alzheimer’s disease on intracellular calcium dynamics.  
     

  • Friday October 28, 2022 at 10:15, 617 Wachman Hall

    Mid-Atlantic Numerical Analysis Day

    A conference on numerical analysis and scientific computingfor graduate students and postdocs in the Mid-Atlantic region.

  • Wednesday November 2, 2022 at 16:00, 617 Wachman Hall

    Sea Life in Sea Ice

    Isaac Klapper, Temple University

    Sea ice, which covers a significant portion of the earth's surface, is a
    interestingly complicated material consisting of a mixture of solid
    ice and liquid brine phases which are coupled by thermodynamic considerations.
    It also is a platform for microbial life, lots of
    it in fact, that uses the ice as a sort of shelter though eventually
    becoming part of the local food chain. A model will be presented that
    hypothesizes that, in turn, the resident microbial population might
    impact sea ice structure.

  • Wednesday November 9, 2022 at 16:00,

    Lifted Newton methods, with application to nonlinear fluid dynamics 

    Georg Stadler, Courant Institute, NYU
     
    I will review basic properties of Newton's method for solving
    nonlinear equations. For difficult nonlinearities it can be beneficial
    to lift the nonlinear systems to a higher-dimensional space, linearize
    there and reduce the linearization to the original space before
    solving the linearized system.  The resulting algorithms may yield
    favorable convergence properties.  I will illustrate the ideas on a
    simple example, and show connections to primal-dual interior point
    methods. The resulting Newton solvers will be used for the solution of
    flow problems with visco-plastic constitutive relations arising in the
    geosciences.  This is joint work with Johann Rudi (Virginia Tech) and
    Melody Shih (NYU).

  • Wednesday November 16, 2022 at 16:00, 617 Wachman Hall

    Synergy of Algorithms, High-Performance Computing and Nuclear Physics to Resolve Long-standing Puzzles: The Proton Spin and Mass

    Martha Constantinou, Temple University

    More than 99% of the mass of the visible matter resides in hadrons
    which are bound states of quarks and gluons, collectively called
    partons. These are the fundamental constituents of Quantum
    Chromodynamics (QCD), the theory of strong interactions. While QCD is
    a very elegant theory, it is highly non-linear and cannot be solved
    analytically, posing severe limitations on our knowledge of the
    structure of the hadrons. Lattice QCD is a powerful first-principle
    formulation that enables the study of hadrons numerically, which is
    done by defining the continuous equations on a discrete Euclidean
    four-dimensional lattice.

    Hadron structure is among the frontiers of Nuclear and Particle
    Physics. Among the high-priority science questions identified by 
    the  National Academies of Sciences, Engineering, and Medicine
    are:
    1. How does the mass of the nucleon arise?
    2. How does the spin of the nucleon arise?

    In this talk, I will discuss how mathematical methods, 
    algorithms and access to large-scale computational resources
    are critical in addressing the above questions.

     

  • Wednesday November 30, 2022 at 16:00,

    Research in Computational and Applied Mathematics at the National Institute of Standards and Technology (NIST): NIST’s DLMF and More 

    Bonita Saunders, National Institute of Standards and Technology
     
     

    The National Institute of Standards and Technology (NIST), founded in 1901, is a government agency under the Department of Commerce that conducts research in measurement science and other areas of the mathematical and physical sciences to enhance US industrial competitiveness. Researchers in the Applied and Computational Mathematics Division (ACMD), located in the Information Technology Laboratory(ITL) at NIST, work with members of the division, collaborate with scientists from other NIST labs, and often foster interdisciplinary collaborations at research institutions and universities external to NIST. The speaker will discuss her involvement, research and outside collaborations related to the NIST Digital Library of Mathematical Functions (DLMF), https://dlmf.nist.gov , one of the signature projects ofACMD, and  look at additional projects in ACMD that showcase the breadth of research being conducted. Opportunities for internships and postdocs at NIST will also be discussed.

     

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  • Wednesday February 1, 2023 at 16:00, 617 Wachman Hall

    Ion channels in Critical Membranes: Clustering, Cooperativity, and Memory effects 

    Vincenzo Carnevale, Temple University

    The response and conformational changes of voltage-gated ion channels are well understood at a single-molecule level, but there is limited knowledge about how these channels interact with the lipids and with one another in their native environment. In particular, current models cannot accommodate recent experimental observations that highlight a dramatic and so far unsuspected collective behavior: voltage gated ion channels in physiological membranes form clusters, gate cooperatively, and show pronounced hysteresis effects suspected to give rise to multistability of membrane-potentials and thus to"cellular memory". To reconcile these seemingly conflicting views and bridge these two vastly different length scales, I will present a quantitative model based on the statistical mechanics of interacting, diffusing agents with internal degrees of freedom and subject to an external field. I will thus show that channels embedded in membranes close to a miscibility transition develop attractive long-range interactions and hysteresis. This model sheds light on several poorly understood aspects of ion channels behavior, including the non-Markovian character of single channel currents.

  • Wednesday February 8, 2023 at 16:00, 617 Wachman Hall

    Free boundary approach to model granular biofilms: application to wastewater treatment 

    Fabiana Russo, Temple University

    The application of granular biofilms in engineered systems for wastewater treatment and valorisation has significantly increased over the past years. Granular biofilms have a regular, dense structure and allow the coexistence of a high number of microbial trophic groups. A mathematical model is presented to describing the de novo granulation, and the evolution of multispecies granular biofilms, in a continuously fed bioreactor. The granular biofilm is modeled as a spherical free boundary domain with radial symmetry and a vanishing initial value. All main phenomena involved in the process are accounted: initial attachment by pioneer planktonic cells, biomass growth and decay, substrates diffusion and conversion, invasion by planktonic cells and detachment. Specifically, non-linear hyperbolic PDEs govern the advective transport and growth of sessile biomasses which constitute the biofilm matrix, and quasi-linear parabolic PDEs model the diffusive transport and conversion of dissolved substrates and planktonic species within the biofilm granule. Non-linear ODEs describe the dynamics of substrates and planktonic biomass within the bulk liquid. The free boundary evolution is governed by an ordinary differential equation which accounts for microbial growth, attachment and detachment phenomena. The model is applied to cases of biological and engineering interest. Numerical simulations are performed to test its qualitative behavior and explore the main aspects of the de novo granulation: ecology, microbial species distribution within the granules, dimensional evolution of the granules, and dynamics of dissolved substrates and planktonic biomass within the bioreactor.

  • Wednesday February 22, 2023 at 16:00, 617 Wachman Hall

    Spatial Manifestations of Order Reduction, and Remedies via Weak Stage Order

    Benjamin Seibold, Temple University

    Order reduction, i.e., the convergence of the solution at a lower rate than the formal order of the chosen time-stepping scheme, is a fundamental challenge in stiff problems. Runge-Kutta schemes with high stage order provide a remedy, but unfortunately high stage order is incompatible with DIRK schemes. We first highlight the spatial manifestations of order reduction in PDE IBVPs. Then we introduce the concept of weak stage order, and (a) demonstrate how it overcomes order reduction in important linear PDE problems; and (b) how high-order DIRK schemes can be constructed that are devoid of order reduction.

  • Wednesday March 15, 2023 at 16:00, 617 Wachman Hall

    Contour integral methods for convection diffusion equations 

    Nicola Guglielmi, Gran Sasso Science Institute, L'Aquila, Italy

    We present a new class of contour integral methods for linear convection-diffusion parametric PDEs and in particular those arising from modeling in finance. These methods aim to provide a numerical approximation of the solution by computing its inverse Laplace transform. The choice of the integration contour is determined by a pseudospectral roaming technique, which depends on few (weighted) pseudo-spectral level sets of the operator in the equation. Next we discuss how to deal efficiently with parametric problems. The main advantage of the proposed method is that, differently from time stepping methods as Runge-Kutta integrators, the Laplace transform allows to compute the solution directly at a given instant or in a given time window. In terms of the reduced basis methodology, this determines a significant improvement in the reduction phase. Some illustrative examples arising from finance will be presented to show the effectiveness of the method. This talk is based on joint work with Maria Lopez Fernandez and Mattia.

  • Wednesday April 5, 2023 at 16:00, 617 Wachman Hall

    Herglotz-Nevanlinna functions in the properties of poroelastic/porous materials 

    Yvonne Ou, University of Delaware

    In physics applications, we can encounter a Herglotz-Nevanlinna (H-N) function that does not decay fast enough along the imaginary axis to be classified as a Stieltjes function, which is well-known to have a simplified integral representation formula. However, in these applications the corresponding Nevanlinna functions might have certain nice properties along the real axis and hence can possess useful integral representation formulas. In this talk, I will present two examples of H-N functions in the context of two-phase porous/poroelastic materials. In the first example, H-N arises because of the causality encoded in the viscodynamic response of poroelastic materials; it is applied to create an effective numerical scheme for handling the memory terms in the poroelastic wave equations. In the second example, the technique of H-N functions is used to treat the effective permeability of a mixture of fluid with tiny bubbles inclusions and that of the mixture of fluid and solid inclusions in a unified framework.

  • Wednesday April 12, 2023 at 16:00, 617 Wachman Hall

    Preconditioning the Stage Equations of Implicit Runge Kutta Methods 

    Michal Outrata, Virginia Tech

    When using implicit Runge-Kutta methods for solving parabolic PDEs, solving the stage equations is often the computational bottleneck, as the dimension of the stage equations Mk=b for an s-stage Runge-Kutta method becomes sn

where the spatial discretization dimension n can be very large. Hence the solution process often requires the use of iterative solvers, whose convergence can be less than satisfactory. Moreover, due to the structure of the stage equations, the matrix M

  • does not necessarily inherit any of the preferable properties of the spatial operator, making GMRES the go-to solver and hence there is a need for a preconditioner.  Recently in [3] and also [1, 2] a new block preconditioner was proposed and numerically tested with promising results. Using spectral analysis and the particular structure of M , we study the properties of this class of preconditioners, focusing on the eigenproperties of the preconditioned system, and we obtain interesting results for the eigenvalues of the preconditioned system for a general Butcher matrix. In particular, for low number of stages, i.e., s = 2, 3, we obtain explicit formulas for the eigenproperties of the preconditioned system and for general s we can explain and predict the characteristic features of the spectrum of the preconditioned system observed in [1]. As the eigenvalues alone are known to not be sufficient to predict the GMRES convergence behavior in general, we also focus on the eigenvectors, which altogether allows us to give descriptive bounds of the GMRES convergence behavior for the preconditioned system. We then numerically optimize the Butcher tableau for the performance of the entire solution process, rather than only the order of convergence of the Runge-Kutta method. To do so requires careful balancing of the numerical stability of the Runge-Kutta method, its order of convergence and the convergence of the iterative solver for the stage equations. (Joint work with Martin Gander)

    References
    [1] M. M. Rana, V. E. Howle, K. Long, A. Meek, W. Milestone. A New Block Preconditioner
    for Implicit Runge-Kutta Methods for Parabolic PDE Problems. SIAM Journal on Scientific
    Computing, vol (43): S475–S495, 2021
    [2] M. R. Clines, V. E. Howle, K. R. Long. Efficient order-optimal preconditioners for implicit
    Runge-Kutta and Runge-Kutta-Nystr ̈om methods applicable to a large class of parabolic and
    hyperbolic PDEs. arXiv: https: // arxiv. org/ abs/ 2206. 08991 , 2022
    [3] M. Neytcheva, O. Axelsson. Numerical solution methods for implicit Runge-Kutta methods of
    arbitrarily high order. Proceedings of ALGORITHMY 2020, ISBN : 978-80-227-5032-5, 2020 
     
  • Wednesday April 19, 2023 at 16:00, 617 Wachman Hall

    Adventures in the brain jungle: from neuronal trees to functional circuits

    Giorgio Ascoli, George Mason University

    Santiago Ramon y Cajal, widely hailed for ushering neuroscience into the modern era, described the brain jungle as impenetrable. Indeed, a century after his seminal call to arms, our understanding of neural architecture is still partial. Nevertheless, groundbreaking neuroinformatics progress in the past decades opened exciting new possibilities to test and refine the theoretical foundations of neural function with large-scale, data-driven computer simulations. This talk will highlight two open-access computational neuroanatomy resources fostering collaborative research. NeuroMorpho.Org is a database of digital reconstructions of neuronal and glial morphology from any animal species, developmental stage, and experimental methods. Hippocampome.org is a knowledge base of neuron types in the mammalian hippocampus enabling the implementation of biologically detailed spiking neural network models of associative memory and spatial navigation.

  • Wednesday August 30, 2023 at 16:00, 617 Wachman Hall

    Sparse-grid fast sweeping WENO methods for eikonal equations

    Zachary Miksis, Temple University

    Fast sweeping WENO methods are a class of explicit iterative methods for solving steady-state hyperbolic PDEs. While they are able to produce high-order accurate solutions, WENO methods can be computationally expensive due to the use of multiple approximating interpolation stencils. This problem is compounded in multi-dimensional settings, and the computational cost of the iterative scheme can become enormous. In this talk, I will present the recent application of the sparse-grid combination technique, which has shown to be and effective approximation tool for high-dimensional problems, to fast sweeping WENO methods in order to reduce their computational cost.
     

  • Wednesday September 13, 2023 at 16:00, 617 Wachman Hall

    Nonlocal Boundary Value Problems with Local Boundary Conditions

    James M. Scott, Columbia University
     
    In recent years nonlocal models have seen a sharp increase in use across a variety of applications, such as continuum mechanics, image processing, and nonlocal diffusion. These models are often characterized by integro-differential equations, which hold on a bounded domain. An outstanding challenge in their implementation is to  incorporate given boundary data into the problems.We address this challenge by considering a special class of nonlocal operators which allow us to state and analyze classical boundary value problems. The model takes its horizon parameter to be spatially dependent, vanishing near the boundary of the domain. We show the variational convergence of solutions to the nonlocal problem with mollified Poisson data to the solution of the localized classical Poisson problem with rough data as the horizon uniformly converges to zero. Several classes of boundary conditions are considered.

  • Wednesday September 20, 2023 at 16:00, 617 Wachman Hall

    How to Model Sea Ice at Different Scales: From Microstructure to Effective Properties

    Noa Kraitzman, Macquarie University

    Sea ice is a crucial component of the Earth’s climate system, affecting the ocean circulation, the atmospheric temperature, and the marine ecosystems. However, sea ice is not a simple solid material; it is a complex mixture of ice crystals, brine pockets, and air bubbles, that changes its structure and properties depending on the environmental conditions. In this talk, I will explore how we can model and understand the behaviour of sea ice at different scales, from the microscopic interactions of ice and salt to the macroscopic effects of heat transfer and fluid flow.  I will present two mathematical models: a thermodynamically consistent model for the liquid-solid phase change in sea ice that incorporates the effects of salt, using multiscale analysis to derive a quasi-equilibrium Stefan-type problem. And a new rigorous derivation of bounds on the sea ice effective thermal conductivity obtained through Padé approximates and using Stieltjes integrals.

  • Wednesday October 11, 2023 at 16:00, 617 Wachman Hall

    Regularization Methods for Inverse Problems in Imaging 

    Malena Espanol, Arizona State University
     
    Discrete linear and nonlinear inverse problems arise from many different imaging systems, exhibiting inherent ill-posedness wherein solution sensitivity to data perturbations prevails. This sensitivity is exacerbated by errors arising from imaging system components (e.g., cameras, sensors, etc.), necessitating the development of robust regularization methods to attain meaningful solutions. Our presentation commences with the exposition of distinct imaging systems, and their mathematical formalism, and subsequently introduces regularization techniques tailored for linear inverse problems. Then, we delve into the variable projection method, a powerful tool to address separable nonlinear least squares problems.

  • Wednesday October 18, 2023 at 16:00, 617 Wachman Hall

    Nonlinear model reduction with adaptive bases and adaptive sampling

    Benjamin Peherstorfer, Courant Institute, New York University
     
    We introduce an online-adaptive model reduction approach
    that can efficiently reduce convection-dominated problems. It exploits
    that solution manifolds are low dimensional in a local sense in time
    and iteratively learns and adapts reduced spaces from randomly sampled
    data of the full models to locally approximate the solution manifolds.
    Numerical experiments to predict pressure waves in combustion dynamics
    demonstrate that our approach achieves about one order of magnitude
    speedups in contrast to classical, static reduced models.

  • Wednesday November 1, 2023 at 16:00,

    No seminar today. Grosswald Lectures

     

  • Wednesday November 29, 2023 at 16:00, 617 Wachman Hall

    Convergence of randomized and greedy relaxation schemes for solving nonsingular linear systems of equations 

    Daniel B Szyld, Temple University

    We extend results known for the randomized Gauss-Seidel and the Gauss-Southwell methods for the case of a Hermitian and positive definite matrix to certain classes of non-Hermitian matrices. We obtain convergence results for a whole range of parameters describing the probabilities in the randomized method or the greedy choice strategy in the Gauss-Southwell-type methods. We identify those choices which make our convergence bounds best possible. Our main tool is to use weighted 1

  • -norms to measure the residuals. A major result is that the best convergence bounds that we obtain for the expected values in the randomized algorithm are as good as the best for the deterministic, but more costly algorithms of Gauss-Southwell type.
  • Wednesday December 6, 2023 at 16:00, 617 Wachman Hall

    The Order of Runge-Kutta Methods in Theory and Practice

    Steven Byram Roberts, Lawrence Livermore National Laboratory
     
    Runge-Kutta methods are one of the most popular families of integrators for solving ordinary differential equations, essential in simulating dynamic systems arising in physics, engineering, biology, and various other fields.Unfortunately, classical error analysis for Runge-Kutta methods relies on assumptions that rarely hold when solving stiff ordinary differential equations (ODEs): an asymptotically small timestep and a right-hand side function with a moderate Lipschitz constant. Without idyllic assumptions, Runge-Kutta methods can experience a problematic degradation in accuracy known as order reduction.While high stage order remedies order reduction, it is only viable for expensive, fully implicit Runge-Kutta methods. In this talk, I will discuss some recent advancements in deriving practical Runge-Kutta methods that avoid order reduction. Initially, the focus will be on explicit methods applied to linear ODEs, where we have found a systematic approach to construct schemes of arbitrarily high order. Then, we will expand to classes of nonlinear ODEs where I will present new, stiff order conditions with a rich and interesting connection to rooted trees.

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  • Wednesday January 31, 2024 at 16:00, 617 Wachman Hall

    Low rank time integrators for solving time-dependent PDEs

    Jingmei Qiu, University of Delaware

    I will provide overview of low rank time integrators for time dependent PDEs.These include an explicit scheme that involves a time stepping followed by a SVD truncation procedure with application to the Vlasov equations; two implicit schemes: Reduced Augmentation Implicit Low rank (RAIL) scheme and a Krylov subspace low rank scheme with applications to the heat equation and the Fokker-Planck equation; as well as implicit-explicit low rank integrators for advection-diffusion equations.

  • Wednesday February 7, 2024 at 16:00, 617 Wachman Hall

    Minimal Quantization Model for an Active System

    Rodolfo Ruben Rosales, Massachusetts Institute of Technology

    A small liquid drop placed above the vibrating surface of a liquid, will not (under appropriate conditions) fall and merge. In fact it will bounce from the surface, and can be made to do so for very many bounces (hundreds of thousands). If the liquid below is just under the Faraday threshold, the drop excites waves with each bounce, and via these waves it can extract momentum from the fluid underneath it, and starts moving "walking" at some preferred speed. The drop-wave system then becomes a peculiar active system, where the active elements interact with each other (if there are many drops) via waves, as well as with their own past via the waves generated earlier in their history. This system have many special properties, some reminiscent of quantum mechanics. In this talk I will focus on one such property:
    If the drop is constrained to move in a bounded region by some external force (e.g.: Coriolis), then its path exhibits radial quantization: the statistics for the radius of curvature along the drop path is concentrated on a discrete set of values. The question is why? There are various models that predict this, but the question is not about the model(s), but about what is the mechanism behind the behavior. An obvious answer is that it is because the drop motion is caused via waves. This is, basically, correct; but too vague, even misleading. First of all, the drop does not move on some "external" wave field, but on a self-generated one. Second, the waves decay, hence the wave field is dominated by the waves produced in the recent path. Yet, if one discards all but the recent past, the quantization disappears --- the recent past selects the preferred speed, but does not quantize. It turns out that the effect is caused by (exponentially suppressed) waves emitted in the past at "special" regions where constructive interference magnifies their effect. As I hope to show, this gives a simple and intuitive explanation of how the radii selection occurs.

  • Wednesday February 14, 2024 at 16:00, 617 Wachman Hall

    Combining metabolic models, large data sets, and deep learning to improve systems biology simulators

    Sean McQuade, Rutgers University Camden

    Chemical networks, such as metabolism, can be simulated to assist in an array of research including new drug discovery, personalized medicine, and testing high-risk treatment before applying it to humans. Improved biochemical simulations can also reduce our dependence on animal testing before clinical trials. This talk demonstrates a mathematical framework for biochemical systems that was designed with two goals in mind: 1. improved early phase drug discovery and 2. personalized medicine. The talk also addresses a particular contribution that can be made by deep learning models.

  • Wednesday February 28, 2024 at 16:00, 617 Wachman Hall

    Dynamic Boundary Conditions and Motion of Grain Boundaries 

    Chun Liu, Illinois Institute of Technology

    I will present the dynamic boundary conditions in the general
    energetic variational approaches. The focus is on the coupling between
    the bulk effects with the active boundary conditions.
    In particular, we will study applications in the evolution of grain
    boundary networks, in particular, the drag of trip junctions. This is a
    joint work with Yekaterina Epshteyn (University of Utah) and Masashi
    Mizuno (Nihon University).

  • Monday March 11, 2024 at 16:00,

    Randomized Numerical Linear Algebra

    Erik Boman, Sandia National Laboratory

    Randomization has become a popular technique in numerical linear algebra in recent years, with applications in several areas from scientific computing to machine learning. We review some problems where it works well. Sketching is a powerful way to reduce a high-dimensional problem to a lower-dimensional problem. Sketch-and-solve and sketch-and-precondition are the two main approaches for linear systems and least squares problems. Finally, we describe two recent applications in more detail: Fast and stable orthogonalization (QR on tall, skinny matrices), and spectral graph partitioning.

  • Wednesday March 27, 2024 at 16:00, 617 Wachman Hall

    Numerical Solution of Double Saddle-Point Systems

    Chen Greif, University of British Columbia

    Double saddle-point systems are drawing increasing attention in the past few years, due to the importance of multiphysics and other relevant applications and the challenge in developing efficient iterative numerical solvers. In this talk we describe some of the numerical properties of the matrices arising from these problems. We derive eigenvalue bounds and analyze the spectrum of preconditioned matrices, and it is shown that if Schur complements are effectively approximated, the eigenvalue structure gives rise to rapid convergence of Krylov subspace solvers. A few numerical experiments illustrate our findings.

  • Wednesday April 3, 2024 at 16:00, 617 Wachman Hall

    Decentralized Stochastic Bilevel Optimization

    Hongchang Gao, Temple University

    Stochastic Bilevel Optimization (SBO) has widespread applications in machine learning, such as meta learning, hyperparameter optimization, and network architecture search. To train those machine learning models on large-scale distributed data, it is necessary to develop distributed SBO algorithms. Therefore, Decentralized Stochastic Bilevel Optimization (DSBO) has been actively studied in recent years due to the efficiency and robustness of decentralized communication. However, it is challenging to estimate the stochastic hypergradient on each worker due to the loss function's bilevelstructure and decentralized communication.
    In this talk, I will present our recent work on decentralized stochastic bilevel gradient descent algorithms. On the algorithmic design side, I will talk about how to estimate the hypergradient without incurring large communication overhead under both homogeneous and heterogeneous settings. On the theoretical analysis side, I will describe the convergence rate of our algorithms, showing how the communication topology, the number of workers, and heterogeneity affect the theoretical convergence rate. Finally, I will show the empirical performance of our algorithms.

  • Wednesday April 10, 2024 at 16:00, 617 Wachman Hall

    New Perspectives on Multiscale Modeling, Simulation, and Analysis of Grain Growth in Polycrystalline Materials

    Yekaterina Epshteyn, University of Utah

    Many technologically useful materials are polycrystals composed of small monocrystalline grains that are separated by grain boundaries of crystallites with different lattice orientations. One of the central problems in materials science is to design technologies capable of producing an arrangement of grains that delivers a desired set of material properties.
    A method by which the grain structure can be engineered in polycrystalline materials is through grain growth (coarsening) of a starting structure. Grain growth in polycrystals is a very complex multiscale multiphysics process. It can be regarded as the anisotropic evolution of a large cellular network and can be described by a set of deterministic local evolution laws for the growth of individual grains combined with stochastic models for the interaction between them. In this talk, we will present new perspectives on mathematical modeling, numerical simulation, and analysis of the evolution of the grain boundary network in polycrystalline materials. Relevant recent experiments will be discussed as well.

  • Wednesday April 17, 2024 at 16:00, 617 Wachman Hall

    A Mixed Sparse-Dense BLR Solver for Electromagnetics

    Francois-Henry Rouet, Ansys

    Element-by-element preconditioners were an active area of research in the 80s and 90s, and they found some success for problems arising from Finite Element discretizations, in particular in structural mechanics and fluid dynamics (e.g., the "EBE" preconditioner of Hughes, Levit, and Winget). Here we consider problems arising from Boundary Element Methods, in particular the discretization of Maxwell's equations in electromagnetism. The matrix comes from a collection of elemental matrices defined over all pairs of elements in the problem and is therefore dense. Inspired by the EBE idea, we select subsets of elemental matrices to define different sparse preconditioners that we can factor with a direct method. Furthermore, the input matrix is rank-structured ("data sparse") and is compressed to accelerate the matrix-vector products. We use the Block Low-Rank approach (BLR). In the BLR approach, a given dense matrix (or submatrix, in the sparse case) is partitioned into blocks following a simple, flat tiling; off-diagonal blocks are compressed into low-rank form using a rank-revealing factorization, which reduces storage and the cost of operating with the matrix. We demonstrate results for industrial problems coming from the LS-DYNA multiphysics software.
    Joint work with Cleve Ashcraft and Pierre L'Eplattenier

  • Wednesday September 4, 2024 at 16:00, 617 Wachman Hall

    Mathematical and computational epidemiology of antimalarial drug resistance evolution

    Maciej Boni, Temple University

  • Wednesday September 11, 2024 at 16:00, 617 Wachman Hall

    Trustworthy Machine Learning for Biomedicine

    Xinghua (Mindy) Shi, Temple University

    Recent biomedical data deluge has fundamentally transformed biomedical research into a data science frontier. The unprecedented accumulation of biomedical data presents a unique yet challenging opportunity to develop novel methods leveraging artificial intelligence and machine learning to further our understanding of biology and advance medicine. In this talk, I will first introduce the cutting-edge research in characterizing human genetic variation and their associations with disease. I will then present statistical and machine learning methods for robust modeling of medical data. Finally, I will overview recent development in trustworthy machine learning to combat model overfitting, privacy and biases.

  • Wednesday September 18, 2024 at 16:00, 617 Wachman Hall

    On the lack of external response of a nonlinear medium in the second-harmonic generation process.

    Narek Hovsepyan, Rutgers University 

    Second Harmonic Generation (SHG) is a process inwhich the input wave (e.g. laser beam) interacts with a nonlinearmedium and generates a new wave, called the second harmonic, atdouble the frequency of the original input wave. Weinvestigate whether there are situations in which the generatedsecond harmonic wave does not scatter and is localizedinside the medium, i.e., the nonlinearinteraction of the medium with the probing wave isinvisible to an outside observer. This leadsto the analysis of a semilinear elliptic system formulatedinside the medium with non-standard boundary conditions. Moregenerally, we set up a mathematical framework needed to investigate amultitude of questions related to the nonlinear scatteringproblem associated with SHG (or other similar multi-frequency opticalphenomena). This is based on a joint work with Fioralba Cakoni, MattiLassas and Michael Vogelius. 

  • Wednesday September 25, 2024 at 16:00, 617 Wachman Hall

    Mode switching in organisms for solving explore-versus-exploit problems

    Kathleen Hoffman, University of Maryland Baltimore County

    Fish use active sensing to constantly re-evaluate their position in space. The weakly electric glass knifefish, Eigenmannia virescens, incorporates an electric field as one of its active sensing mechanisms. The motion of the knifefish in a stationary refuge is captured using high-resolution motion tracking and illustrates many small amplitude oscillations inside the refuge coupled with high amplitude “jumps”. We show that this active sensing mechanism is not reflected by a Gaussian distribution of the velocities. Instead, we show that the velocities are more accurately reflected by a mixture of Gaussians because of the number of high amplitude jumps in the tails of the velocity distribution. The experimental position measurements were taken in both the light and the dark showing more frequent bursts of faster movement in the dark, where presumably the fish are relying more on their electric sensor than their vision. Computational models of active state estimation with noise injected into the system based on threshold triggers exhibit velocity distributions that resemble those of the experimental data, more so than with pure noise or zero noise inputs. Similar distributions have been observed in a variety of different senses and species. 
    This is joint work with Debojyoti Biswas (JHU), Noah Cowan (JHU), John Guckenheimer (Cornell), Andrew Lamperski (UMN), Yu Yang (JHU)

  • Wednesday October 2, 2024 at 16:00, 617 Wachman Hall

    The Average Rate of Convergence of the Exact Line Search Gradient Descent Method, with applications to polynomial optimization problems in data sciences 

    Thomas P.Y. Yu, Drexel University.
     
     

    It is very well known that when the exact line search gradient descent method is applied to a convex quadratic objective, the worst-case rate of convergence (ROC), among all seed vectors, deteriorates as the condition number of the Hessian of the objective grows. By an elegant analysis due to H. Akaike, it is generally believed -- but not proved -- that in the ill-conditioned regime the ROC for almost all initial vectors, and hence also the average ROC, is close to the worst-case ROC. We complete Akaike's analysis using the theorem of center and stable manifolds. Our analysis also makes apparent the effect of an intermediate eigenvalue in the Hessian by establishing the following somewhat amusing result: In the absence of an intermediate eigenvalue, the average ROC gets arbitrarily fast -- not slow -- as the Hessian gets increasingly ill-conditioned.

    This work is motivated by contemporary applications in data sciences. We shall discuss some of the surprising properties of the polynomial optimization problems involved in these applications.

     

  • Wednesday October 16, 2024 at 16:00, 617 Wachman Hall

    Seminar postponed

     

  • Wednesday October 23, 2024 at 16:00, 617 Wachman Hall

    Modified Patankar-Runge-Kutta Methods: Introduction, Analysis and Numerical Applications

    Andreas Meister, University of Kassel

    Mathematical modeling leads to so-called convection-diffusion-reaction equations in the form of systems of partial differential equations in numerous practical applications. Examples are turbulent air flows or algae growth in oceans orlakes. After discretization of the spatial derivatives, an extremely large systemof ordinary differential equations occurs. A reasonable numerical time integration scheme must reflect present properties like the positivity of single balancequantities or also the conservativity of the initial model.In the talk we will present so-called modified Patankar-Runge-Kutta (MPRK)schemes. They adapt explicit Runge-Kutta schemes in a way to ensure positivity and conservativity irrespective of the time step size. Thereby, we introducea general definition of MPRK schemes and present a thorough investigationof necessary as well as sufficient conditions to derive first, second and thirdorder accurate MPRK schemes. The theoretical results will be confirmed bynumerical experiments in which MPRK schemes are applied to solve non-stiffand stiff systems of ordinary differential equations. Furthermore, we investigatethe efficiency of MPRK schemes in the context of convection-diffusion-reactionequations with source terms of production-destruction type.

  • Wednesday November 20, 2024 at 16:00, 617 Wachman Hall

    Smart Data, Smarter Models: Enhancing the Predictive Power of Mathematical Models of Cancer

    Jana Gevertz, The College of New Jersey

    Mathematical models are powerful tools that can vastly improve our understanding of cancer dynamics and treatment response. However, to be useful, experimental or clinical data are necessary to both train and validate such predictive models, and not all data are created equal. Here I present two methodologies that improve upon model-informed experimental design and model-based predictions. First, I will introduce a multi-objective optimization algorithm to identify combination protocols that maximize synergy from the perspective of both efficacy and potency (toxicity), while simultaneously reconciling sometimes contradictory assessments made by different synergy metrics. Second, using the notion of parameter identifiability, I will address the question of what is the minimal amount of experimental data that needs to be collected, and when it should be collected, to have confidence in a model's predictions. Real-world applications of both methodologies will be presented.

Body
  • Wednesday September 22, 2004 at 16:00, Wachman 617

    David Fritzsche, "Graph theory and permutation of matrices."

  • Wednesday October 6, 2004 at 16:00, Wachman 617

    David Fritzsche, "Graph theory, permutation of matrices, and preconditioning."

  • Wednesday October 20, 2004 at 16:00, Wachman 617

    David Fritzsche, "Graph theoretical methods for preconditioning."

  • Wednesday November 3, 2004 at 16:00, Wachman 617

    Omar Hijab, "An Explicitly Solvable Free-Boundary Problem in R^d."

  • Wednesday November 17, 2004 at 16:00, Wachman 617

    Michael Dobbins, "Packing the simplex with its images."

  • Wednesday December 1, 2004 at 16:00, Wachman 617

    Sergio Serrano, Civil and Environmental Engineering Dept., "Exploration of Nonlinear Environmental Dynamics."

Lisa Davis, Montana State University and NSF/DMS

Event Date
2025-02-19
Event Time
04:00 pm ~ 05:00 pm
Event Location
Wachman Hall

Françoise Tisseur, University of Manchester

Event Date
2025-02-24
Event Time
04:00 pm ~ 05:00 pm
Event Location
617 Wachman Hall

Petr Plechac, University of Delaware

Event Date
2025-03-12
Event Time
04:00 pm ~ 05:00 pm
Event Location
617 Wachman Hall