Fluid Mechanics and Waves Seminar - Spring 2022

For questions about the seminar schedule, please contact Travis Askham.

To join the Fluid Mechanics and Waves seminar mailing list visit https://groups.google.com/a/njit.edu/forum/#!forum/math-fmws/join (Google Profile required). To join the mailing list without a Google Profile, submit the seminar request form.

February 14

Mykhailo Potomkin, University of California, Riverside

Location: WebEx

Orientation dynamics of a microswimmer in nematic liquid crystal

Microscopic swimmers, such as bacteria, often swim in biofluids with properties different from isotropic Newtonian fluid but rather those of liquid crystal. Understanding how a bacterium navigates itself in such an environment is important for treatment strategies of many infectious diseases. We developed a nonlinear PDE system coupling liquid crystal hydrodynamics with the model of active microswimmer. Our goal is to elucidate how the orientation order of liquid crystal affects the motion of an individual bacterium. In this talk, I will present this PDE system and show that it reveals how surface properties affect swimming direction. I will also discuss the emergence of topological defects around the microswimmer for large propulsion speeds. If time permits, I will present our recent results on analysis of the model, its well-posedness, existence of steady states, as well as collective swimming in liquid crystal and how it can be described with the help of homogenization theory. This work is done jointly with I. Aronson (Penn State U.), L. Berlyand (Penn State U.), H. Chi (Penn State U.), A. Yip (Purdue U.), and L. Zhang (Shanghai Jiao Tong U.).

Dr. Potomkin is an assistant professor at UC Riverside. He previously held a postdoctoral position at the Pennsylvania State University, and he received his Ph.D. from V.N. Karazin Kharkiv National University (Ukraine). Dr. Potomkin’s area of research includes modeling, analysis and numerical simulation of problems involving various types of differential equations, with the specific focus on problems arising in Mathematical Biology and Soft Matter Physics.

February 28

Carlos Borges, University of Central Florida

Location: WebEx

High-Fidelity Reconstructions of the Shape and Impedance using Scattered Data

The use of an impenetrable obstacle with an impedance boundary condition was proposed to simplify the modeling of scattering of an impinging source wave off of a penetrable obstacle, knowingly the transmission scattering problem. In this paper, we propose a framework to recover both the shape and the impedance function of an obstacle from measurements of the scattered field at multiple frequencies. In our framework, we apply the recursive linearization algorithm (RLA) framing at each frequency the inverse problem as a nonlinear optimization problem. The single frequency inverse problem to recover the shape and impedance is both nonlinear and ill-posed. To deal with the nonlinearity, we apply the Newton-like method advancing both variables, the shape and impedance function, using the Fréchet derivative of the forward operator. We treat ill-posedness by considering the approximation of the shape and impedance function to be bandlimited functions, where the limit is a function of the incident wave frequency. We present examples to demonstrate the feasibility of the method in different settings. The framework presented can recover the shape and impedance function with high accuracy when the scattered measurements used are generated by forward models with Dirichlet, Fourier-Robin or Neumann boundary conditions.

March 21

Canceled

April 4

Stephen Guimond, University of Maryland Baltimore County, Goddard Space Flight Center

Location: WebEx

*Please note that this seminar will begin at 2:00 pm*

Fluid Mechanics and Waves in Extreme Weather Systems

In this talk, I will discuss my research efforts to understand the fluid mechanics of extreme weather systems where vortex dynamics, convective heat transfer, turbulence and waves all play a role in the system evolution. While the focus of the talk is on hurricanes, current research into other systems will be briefly discussed.  The intensity of hurricanes is a balance between energy production, dissipation, and the nonlinear transfer of that energy across scales. The production of energy begins as a thermodynamic disequilibrium at the air-sea interface and ends as clusters of convective clouds that release large amounts of latent heat, which, in turn, generates a complex field of vorticity. The dissipation of energy primarily occurs in the boundary layer through frictional drag and a hierarchy of turbulent eddies that transfer energy to other scales. Numerical models calculate this energy balance by solving complicated equations that attempt to capture these physical processes. While sometimes they can do well, there is a long-standing, major problem of underpredicting, or a low-bias, in hurricane rapid intensity changes.

New research in the Geophysical Fluid Dynamics Group (GFDG) at UMBC shows that the community numerical models used to perform these predictions are overly dissipative in their design: from the dynamic core down to the turbulence parameterizations. I will explain this result using studies of advanced numerical methods and radar remote sensing observations.

April 18

Jason Kaye, Flatiron Institute

Location: CULM 611

Accelerating Green's function methods for time-dependent quantum many-body calculations: fast history integration for Dyson equations

By moving the focus from wavefunctions to particle correlations, many-body Green's function methods provide a controlled and tractable path towards describing truly many-body dynamics at a level of accuracy beyond that achieved by effective one-body methods like time-dependent density functional theory. This talk will focus on one of the many algorithmic difficulties associated with Green's function calculations: the problem of history dependence in real time single particle Green's functions.

These Green's functions satisfy real time Dyson equations, which are Volterra integro-differential equations in which the integral kernel depends nonlinearly on the solution itself. All Volterra equations suffer from an explicit history dependence, and the situation is no different here -- namely, advancing a single time step requires incorporating information from all previous time steps, leading to an apparent quadratic computational scaling. However, the kernel nonlinearity in the Dyson equations is unusual from the point of view of the applied mathematics literature, and existing fast history integration algorithms are not applicable. This talk will introduce new algorithms for the equilibrium and nonequilibrium Dyson equations, which treat quantum many-body systems without and with external forcing, respectively.

May 2

Daria Sushnikova, NYU

Location: WebEx

*Please note that this seminar will begin at 11:30 am instead of our usual time*

A fast linearly scaling direct solver for multiscale boundary integral equations

The FMM-based matrices (HSS, H2, etc.), and direct solvers for systems with such matrices are promising research directions as they give robust and very fast instruments for the solution of the 2d and 3d  multiscale integral equations. The FMM-LU algorithm and its implementation that I am going to present in my talk are based on the idea of the low-rank approximation of the fill-in that appears in the course of the direct solution. The proposed approach allows building direct solvers for the general case of the FMM-like matrices. It has linear scaling with sufficient constant and good accuracy for both 2d and 3d problems on complex geometries.

Updated April 18, 2022