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DTSTART;TZID=America/Los_Angeles:20210201T150000
DTEND;TZID=America/Los_Angeles:20210201T160000
DTSTAMP:20260519T015727
CREATED:20210112T175201Z
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SUMMARY:Applied math. talk: Searching for singularities in Navier-Stokes flows using variational optimization methods by Di Kang\, McMaster University\, Canada
DESCRIPTION:Abstract: In the presentation we will discuss our research program\nconcerning the search for the most singular behaviors possible in viscous\nincompressible flows. These events are characterized by extremal growth of \nvarious quantities\, such as the enstrophy\, which control the regularity of the solution. \nThey are therefore intimately related to the question of possible singularity formation \nin the 3D Navier-Stokes system\, known as the\nhydrodynamic blow-up problem. We demonstrate how new insights\nconcerning such questions can be obtained by formulating them as\nvariational PDE optimization problems which can be solved\ncomputationally using suitable discrete gradient flows. More\nspecifically\, such an optimization formulation allows one to identify\n"extreme" initial data which\, subject to certain constraints\, leads to\nthe most singular flow evolution.  In offering a systematic approach\nto finding flow solutions which may saturate known estimates\, the\nproposed paradigm provides a bridge between mathematical analysis and\nscientific computation. In particular\, it makes it possible to\ndetermine whether or not certain mathematical estimates are "sharp"\,\nin the sense that they can be realized by actual vector fields\, or if\nthese estimates may still be improved. In the presentation we will\nreview a number of results concerning 1D and 2D flows characterized by\nthe maximum possible growth of different Sobolev norms of the\nsolutions.  As regards 3D flows\, we focus on the enstrophy which is a\nwell-known indicator of the regularity of the solution. We find a family of initial \ndata with fixed enstrophy which leads to the largest possible growth of this quantity \nat some prescribed final time. Since even with such worst-case initial data the\nenstrophy remains finite\, this indicates that the 3D Navier-Stokes\nsystem reveals no tendency for singularity formation in finite time.\n\n[joint work with Dongfang Yun and Bartosz Protas]
URL:https://colleges.claremont.edu/ccms/event/applied-math-talk-searching-for-singularities-in-navier-stokes-flows-using-variational-optimization-methods-by-di-kang-mcmaster-university-canada/
LOCATION:Zoom meeting\, United States
CATEGORIES:Applied Math Seminar
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BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20210208T150000
DTEND;TZID=America/Los_Angeles:20210208T160000
DTSTAMP:20260519T015727
CREATED:20210126T021149Z
LAST-MODIFIED:20210201T225414Z
UID:2147-1612796400-1612800000@colleges.claremont.edu
SUMMARY:Applied Math. Talk: Complex Fluids in the Immersed Boundary Method: From Viscoelasticity to Blood Clots by Aaron Barrett\, Department of Mathematics\, University of Utah
DESCRIPTION:The immersed boundary method was first developed in the 1970s to model the motion of heart valves and has since been utilized to study many different biological systems. While the IB method has seen countless modifications and advancements from the perspective of fluid-structure interaction\, the use of a Newtonian fluid model remains a fundamental component of many implementations. However\, many biological fluids exhibit non-Newtonian responses to stresses\, and as such\, a Newtonian fluid model falls short to fully describe the system. In this talk\, we will discuss models of two different systems: polymeric fluids and blood clotting\, and we will address the numerical challenges associated with each system.
URL:https://colleges.claremont.edu/ccms/event/applied-math-talk-by-aaron-barrett-department-of-mathematics-university-of-utah/
LOCATION:CA
CATEGORIES:Applied Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20210215T150000
DTEND;TZID=America/Los_Angeles:20210215T160000
DTSTAMP:20260519T015727
CREATED:20210114T013414Z
LAST-MODIFIED:20210127T210557Z
UID:2120-1613401200-1613404800@colleges.claremont.edu
SUMMARY:Applied Math. Talk:  Modeling and Simulation of Ultrasound-mediated Drug Delivery to the Brain  by Peter Hinow\, University of Wisconsin\, Milwaukee
DESCRIPTION:We use a mathematical model to describe the delivery of a drug to a specific region of the brain. The drug is carried by liposomes that can release their cargo by application of focused ultrasound. Thereupon\, the drug is absorbed through the endothelial cells that line the brain capillaries and form the physiologically important blood-brain barrier. We present a compartmental model of a capillary that is able to capture the complex binding and transport processes the drug undergoes in the blood plasma and at the blood-brain barrier. We apply this model to the delivery of L-dopa\, (used to treat Parkinson’s disease) and doxorubicin (an anticancer agent). The goal is to optimize the delivery of drug while at the same time minimizing possible side effects of the ultrasound. In a second project\, we present a mathematical model for drug delivery through capillary networks with increasingly complex topologies with the goal to understand the scaling behavior of model predictions on a coarse-to-fine sequence of grids.
URL:https://colleges.claremont.edu/ccms/event/applied-math-talk-by-peter-hinow-university-of-wisconsin-milwaukee/
LOCATION:Zoom meeting\, United States
CATEGORIES:Applied Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20210222T150000
DTEND;TZID=America/Los_Angeles:20210222T160000
DTSTAMP:20260519T015727
CREATED:20210112T175752Z
LAST-MODIFIED:20210213T053831Z
UID:2102-1614006000-1614009600@colleges.claremont.edu
SUMMARY:Applied math. talk: Heatmap centrality: a new measure to identify super-spreader nodes in scale-free networks by Christina Duron\, the University of Arizona
DESCRIPTION:Abstract: The identification of potential super-spreader nodes within a network is a critical part of the study and analysis of real-world networks. Motivated by a new interpretation of the “shortest path” between two nodes\, this talk will explore the properties of the recently proposed measure\, the heatmap centrality\, by comparing the farness of a node with the average sum of farness of its adjacent nodes in order to identify influential nodes within the network. As many real-world networks are often claimed to be scale-free\, numerical experiments based upon both simulated and real-world undirected and unweighted scale-free networks are used to illustrate the effectiveness of the new “shortest path” based measure with regards to its CPU run time and ranking of influential nodes.
URL:https://colleges.claremont.edu/ccms/event/applied-math-talk-heatmap-centrality-a-new-measure-to-identify-super-spreader-nodes-in-scale-free-networks-by-christina-duron-the-university-of-arizona/
LOCATION:Zoom meeting\, United States
CATEGORIES:Applied Math Seminar
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