Applied Math Seminar

Fall 2025

All talks are from 1240-1330 in the Seminar Room unless otherwise specified.

• Oct

  22
• Two Inverse Problem Applications

  Alex Sheranko

  UMBC

  Time: 12:40 PM

  View Abstract

  The talk will focus on two topics related to solving the inverse problem through optimal control. The first is a spatial extension to the SIR model that calculates infection rates using integral operators. The goal is to perform parameter estimation on historical epidemics. The model is continuous and could be more amenable to such methods. Currently, the project focuses on the analysis of the equation and simulations of the variety of infection dynamics that can be modeled. The second project develops a multigrid preconditioner for inverting the heat equation for a spatially varying heat conductivity. This uses an optimal control framework with the preconditioner applied to the Gauss-Newton algorithm to solve for the heat conductivity.

• Oct

  01
• Data assimilation and inverse problems for the Navier--Stokes equations

  Josh Hudson

  USNA-Math

  Time: 12:40 PM

  View Abstract

  Many natural phenomena are governed by differential equations, which we solve to make predictions. However, even when the model precisely describes the physics, we may only expect to compute predictions with finite accuracy because the full initial state is never known exactly. Data assimilation leverages the past measurement information with the model to better approximate the system state, and from there make better predictions. In this talk, we will discuss a data assimilation technique developed by Azouani Olson and Titi (AOT), which applies naturally to the Navier--Stokes equations (the prototypical model for fluid flow). It turns out their method is robust with respect to error in the viscosity parameter, and in fact, we can use the observable part of the prediction and measurement discrepancy to infer the true viscosity of the fluid. Our approach constitutes a new way to fit models by identifying parameters from data, which can be rigorously justified for nonlinear dissipative systems.

• Sep

  24
• Added mass effect in coupled Brownian particles

  Long Him

  UMD-Physics

  Time: 12:40 PM

  View Abstract

  The added mass effect is the contribution to a Brownian particle’s effective mass arising from the hydrodynamic flow its motion induces. For a spherical particle in an incompressible fluid, the added mass is half the fluid’s displaced mass, but in a compressible fluid its value depends on a competition between timescales. Here we illustrate this behavior with a solvable model of two harmonically coupled Brownian particles of mass m, one representing the sphere, the other the immediately surrounding fluid. Solving analytically for the effective mass m∗, we find that its value is determined by three relevant timescales: the momentum relaxation time, the harmonic oscillation period, and the velocity measurement time resolution. In limiting cases of large time-scale separations, m∗ reduces to m or 2m. The model exhibits similar behavior when generalized to the case of unequal masses.

• Sep

  17
• Correlation Measurements in Fission

  Ron Malone

  USNA-Physics

  Time: 12:40 PM

  View Abstract

  Nuclear fission is a violent phenomenon which proceeds from a small deformation of an atomic nucleus to its eventual split. The accompanying release of large amounts of energy has applications relevant to energy and national security. In spite of nearly 80 years of work, no comprehensive theory of fission exists. In this talk, I will discuss measurements of correlations between observables from fission. I will briefly discuss the motivation for these measurements and the experiment setup. The main focus of the talk will be on the mathematical techniques used to transform raw signals into meaningful physics quantities and then compare them against theory.

• Sep

  03
• Uniform Error Control in Online Change Diagnosis

  Austin Warner

  USNA-Math

  Time: 12:40 PM

  View Abstract

  In this talk I will describe the problem of online change diagnosis, where observations are obtained on-line, an abrupt change occurs in their distribution, and the goal is to quickly detect the change and accurately identify the post-change distribution, while controlling the false alarm rate. It is critical that algorithms deployed for this problem perform well even when the change occurs after monitoring for some time. However, many algorithms that have been proposed for this problem implicitly use pre-change data for determining the post-change distribution. This can lead to very large conditional probabilities of misidentification, given that there was no false alarm, unless the change occurs soon after monitoring begins. I will outline recent developments towards uniform error control---i.e., controlling the misidentification rate uniformly with respect to the time of the change---including (i) a simple change-point detection algorithm, that does not directly address the identification aspect, can actually control misidentifications uniformly for all possible change points in some problems, and (ii) uniform error control in general settings can be achieved by making modifications to existing algorithms.