Applied math seminar
Title: Finite-time blowup for the restricted Euler equation
Speaker: Evan Miller, UBC, PIMS
Date and time:
10 May 2023,
2:30pm -
3:30pm
Location: MacLaurin D 207
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Abstract: I will discuss finite-time blowup for a model of the 3D Euler
equation where the Helmholtz projection is replaced by a projection onto a
more restrictive constraint space. The model preserves the structure of the
self-advection nonlinearity entirely, and also conserves energy and
helicity.
Title: Anticipate the Surge: A Predictive Learning Model for Forecasting Acute Care Admissions during Infectious Disease Outbreaks
Speaker: Adel Guitouni, Gustavson School of Business, UVic
Date and time:
03 May 2023,
2:30pm -
3:30pm
Location: MacLaurin D 207
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Abstract: The COVID-19 pandemic has placed an unprecedented strain on healthcare systems worldwide, making it difficult to accurately predict demand surge for acute care and allocate resources effectively. This paper proposes a novel predictive learning model that combines a differential equation model with delays and a multi-objective learning genetic algorithm to forecast hospitalizations and intensive care admissions based on predicted infections in a given population. Using data from Canada, Alberta, and Edmonton, we demonstrate the effectiveness of our model in significantly improving the ability to predict acute care capacity and manage resources during emergent infectious disease outbreaks such as COVID-19. Our approach is tailored to different population segments and considers various factors, such as variant strains of the virus and vaccination campaigns. Our model represents a significant contribution to the field, providing healthcare managers and decision-makers with a powerful tool to plan resources in the face of epidemics and major disasters. We contribute to the conversation on how we respond to public health emergencies, enabling more accurate predictions of demand for care and allocation of resources, ultimately saving lives and limiting the impact of these crises on our communities.
This is a joint work with Y. Bahri, N. Gilani, S. Ibrahim, A. Park and O. Chakroun
Title: Continuous Data Assimilation: Insights and Connections to Understanding Turbulent Flows
Speaker: Elizabeth Carlson, University of Victoria
Date and time:
19 Apr 2023,
2:30pm -
3:30pm
Location: MacLaurin D 207
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Abstract: One of the challenges of the accurate simulation of turbulent flows is that initial data is often incomplete, which is a significant difficulty when modeling chaotic systems whose solutions are sensitive to initial conditions. If one instead has snapshots of a system, i.e. data, one can make a better guess at the true state by incorporating the data via data assimilation. Many of the most popular data assimilation methods were developed for general physical systems, not just turbulent flows or chaotic systems. However, in the context of fluids, data assimilation works better than would be anticipated for a general physical system. In particular, turbulent fluid flows have been proven to have the property that, given enough perfect observations, one can recover the full state irrespective of the choice of initial condition. This property is unique to turbulent fluid flows, a consequence of their finite dimensionality. In this presentation, we will discuss the continuous data assimilation algorithm that was used to prove the convergence in the original, perfect data setting, present various robustness results of the continuous data assimilation algorithm, and discuss how continuous data assimilation can be used to identify and correct model error. Moreover, we will highlight the efforts of our other current research into long-standing problems in the stability of fluid flows, and how we have discovered some very interesting connections to our data assimilation research.
Title: Beltrami fields: mathematical aspects and applications to equilibrium models in solar physics and in fusion
Speaker: T. Boulmezouad , University of Victoria
Date and time:
12 Apr 2023,
2:30pm -
3:30pm
Location: MacLaurin D 207
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The aim of this talk is to present some theoretical and numerical results
concerning Beltrami fields, called force-free fields in solar and fusion physics.
The talk will be divided into three parts. In the first part, we will recall the
physical context of the appearance of these fields, i .e. essentially the modeling
of magnetic equilibria in solar physics. In the second part, we will
recall some mathematical theoretical results concerning the existence
and properties of fields in any three-dimensional domain.
In the third and last part, we will expose some methods to compute these
3D fields and the associated physical equilibria, as well as some
numerical results obtained with our codes.
Title: Phase Transition threshold and stability of magnetic skyrmions
Speaker: Slim Ibrahim, University of Victoria
Date and time:
05 Apr 2023,
2:30pm -
3:30pm
Location: COR A125
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After a very brief intro to chiral magnets, I will examine the stability of vortex-like configurations known as magnetic skyrmions. These correspond to critical points of the Landau-Lifshitz energy with the Dzyaloshinskii-Moriya (DM) interactions. From an earlier work of Doring and Melcher, it is known that the skyrmion is a ground state when the coefficient of the DM term is small. In this work, we quantify an explicit critical threshold of that coefficient above which the skyrmion becomes unstable, while stable below it. In addition, in the unstable regime, I will show how the infimum of energy is not bounded from below, by giving an explicit counterexample with a sort of helical-shape configuration. This mathematically explains the occurrence of phase transition observed in some experiments. This is a joint work with I. Shimizu (Osaka, U.)
Title: Modelling SARS-CoV-2 immuno-epidemiological dynamics
Speaker: Chadi M. Saad-Roy, University of Berkeley
Date and time:
29 Mar 2023,
2:30pm -
3:30pm
Location: COR A125
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Abstract: The COVID-19 pandemic is a global emergency with significant morbidity and mortality. In this talk, we use models to investigate the potential future SARS-CoV-2 transmission dynamics, landscapes of immunity, and the effect of vaccination. Since there are substantial uncertainty on the strength and duration of immunity following natural infection or vaccination, we examine a range of scenarios. Through a general framework, we also explore the potential epidemiological and evolutionary considerations of various vaccine dosing regimes. We then examine the impact of vaccine nationalism on SARS-CoV-2 immuno-epidemiological dynamics and control. Finally, using a simple model, we examine the invasion dynamics of SARS-CoV-2 variants and the impacts of vaccine breakthrough infections.
Title: The Relativistic Vlasov-Maxwell System: local smooth solvability for weak topologies
Speaker: Slim Ibrahim, University of Victoria
Date and time:
15 Mar 2023,
2:30pm -
3:30pm
Location: COR A125
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Abstract:
This talk is devoted to the Relativistic Vlasov-Maxwell system in space
dimension three. We prove the local smooth solvability for weak topologies. This result is derived from a representation formula informing about the momentum spread, showing that the domain of influence in momentum is controlled by mild information in the sense that derivatives are not (or less than before) implied. In doing so, we develop a Radon Fourier analysis on the RVM system, which leads to the study of a class of singular weighted integrals. The end of my talk, I show how this method is applied in order to construct smooth solutions to the RVM system in the regime of hot, dense and strongly magnetized plasmas. This is a joint work with C. Cheverrey.
Title: Growth rates for some axisymmetric Euler flows
Speaker: Stephen Gustafson, UBC
Date and time:
25 Jan 2023,
2:30pm -
3:30pm
Location: COR A125
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Abstract: We discuss solutions of the Euler equations of fluid mechanics in three (and higher) dimensions which describe, roughly speaking, colliding pairs of vortex tubes. More precisely, they are axisymmetric and swirl-free, with vorticity satisfying certain sign, oddness, and decay properties. We show rigorous upper and lower bounds on the growth of the vorticity which generalize and improve on recent estimates of Choi and Jeong. This is joint work with Evan Miller and Tai-Peng Tsai.
Title: Verifying global stability of fluid flows despite transient growth of energy
Speaker: David Goluskin, University of Victoria
Date and time:
18 Jan 2023,
2:30pm -
3:30pm
Location: COR A125
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Abstract: Verifying nonlinear stability of a laminar fluid flow against all perturbations is a classic challenge in fluid dynamics. All past results rely on monotonic decrease of a perturbation energy or a similar quadratic generalized energy. This "energy method" cannot show global stability of any flow in which perturbation energy may grow transiently. For the many flows that allow transient energy growth but seem to be globally stable (e.g. pipe flow and other parallel shear flows at certain Reynolds numbers) there has been no way to mathematically verify global stability. After explaining why the energy method was the only way to verify global stability of fluid flows for over 100 years, I will describe a different approach that is broadly applicable but more technical. This approach, proposed in 2012 by Goulart and Chernyshenko, uses sum-of-squares polynomials to computationally construct non-quadratic Lyapunov functions that decrease monotonically for all flow perturbations. I will present a computational implementation of this approach for the example of 2D plane Couette flow, where we have verified global stability at Reynolds numbers above the energy stability threshold. This energy stability result for 2D Couette flow had not been improved upon since being found by Orr in 1907. The results I will present are the first verification of global stability – for any fluid flow – that surpasses the energy method. This is joint work with Federico Fuentes (Universidad Católica de Chile) and Sergei Chernyshenko (Imperial College London).
Title: Singularly perturbed differential operators and the stochastic analytic counterparts
Speaker: Yu-Ting Chen, University of Victoria
Date and time:
11 Jan 2023,
2:30pm -
3:30pm
Location: COR A125
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Abstract: Schrödinger operators with delta potentials are of longstanding interest for admitting closed analytic solutions, and they receive renewed attention for connections to the Kardar–Parisi–Zhang equation. Along with a review of this background, the talk will discuss a standard model of the operators in 2D and its counterpart in Feynman–Kac formulas.