Fluid Mechanics and Waves Seminar - Fall 2019

Seminars are held on Mondays from 2:30 - 3:30PM in Cullimore Hall, Room 611, unless noted otherwise.

Date	Speaker, Affiliation, Title, and Abstract	Host
September 23	Amir Sagiv, Department of Applied Physics and Applied Mathematics, Columbia University Prediction of Random and Chaotic Dynamics in Nonlinear Optics The prediction of interactions between nonlinear laser beams is a longstanding open problem. A traditional assumption is that these interactions are deterministic. We have shown, however, that in the nonlinear Schrodinger equation (NLS) model of laser propagation, beams lose their initial phase information in the presence of input noise. Thus, the interactions between beams become unpredictable as well. Not all is lost, however. The statistics of many interactions are predictable by a universal model. Computationally, the universal model is efficiently solved using a novel spline-based stochastic computational method. Our algorithm efficiently estimates probability density functions (PDF) that result from differential equations with random input. This is a new and general problem in numerical uncertainty-quantification (UQ), which leads to surprising results and analysis at the intersection of probability and approximation theory.	Roy Goodman
October 7	Eduardo Corona Department of Mathematics, New York Institute of Technology A Fast Algorithmic Framework for Dense Rigid Body Suspensions in Stokes Flow The study of dense particulate suspensions is of great interest in fundamental science and technological applications; Often, the physical phenomenon of interest happens at scales much larger than the constituent particle sizes e.g. collective motion in bacterial suspensions or material self-assembly. We thus require scalable and robust simulation methods to produce valuable insights on these systems. In this talk, I will describe a scalable computational framework for simulating suspensions of rigid bodies in Stokes flow: Our approach features a fast, parallel and spectrally accurate boundary integral method tailored to spherical particles which enables singular and near-singular evaluations. Particle collisions are efficiently detected and resolved via an optimization-based linear complementarity method. I will then discuss some of our recent work applying this framework to the study of particulate rotors and of material self-assembly for suspensions of Janus (dual-nature) particles.	Travis Askham
October 21	Scott Wunsch, Johns Hopkins University Internal Waves in Variable Stratification Internal waves are oscillatory motions of a density-stratified fluid. They are ubiquitous in Earth's oceans and atmosphere, transporting momentum and energy and playing an important role in ocean dynamics and climate. In varying stratification, internal waves transfer energy to harmonic modes. This nonlinear process may contribute to the transfer of internal wave energy from large to small scales in the ocean. This seminar will introduce basic concepts of internal wave propagation and explore harmonic generation in variable stratification using weakly nonlinear theory, laboratory experiment, and numerical simulation.	Yuan-nan Young
November 18	David Stein, Center for Computational Biology, Flatiron Institute High-Accuracy Simulations of Thousands of Deformable, Interacting, Active Droplets Coarse-grained continuum models of active fluids capture important aspects of self-organizing behavior seen in experiments while providing a computationally tractable basis for their simulation. Producing accurate solutions to these models is nevertheless challenging, and numerical schemes for their solution have been largely limited to simple, stationary geometries or low-accuracy methods. In this talk, I will describe a spectrally accurate method for the simulation of active fluids in complex geometries, and show how to use this method to simulate deformable droplets of active fluids. When multiple drops are immersed in a Stokesian fluid, their interactions are captured through a robust and scalable boundary integral method, allowing for the simulation of thousands of such particles which may come into near-contact with each other. We explore some of the emergent phenomenon that occurs with such large aggregates of active droplets.	Anand Oza

Date

Speaker, Affiliation, Title, and Abstract

Host

September 23

Amir Sagiv, Department of Applied Physics and Applied Mathematics, Columbia University

Prediction of Random and Chaotic Dynamics in Nonlinear Optics

The prediction of interactions between nonlinear laser beams is a longstanding open problem. A traditional assumption is that these interactions are deterministic. We have shown, however, that in the nonlinear Schrodinger equation (NLS) model of laser propagation, beams lose their initial phase information in the presence of input noise. Thus, the interactions between beams become unpredictable as well. Not all is lost, however. The statistics of many interactions are predictable by a universal model.

Computationally, the universal model is efficiently solved using a novel spline-based stochastic computational method. Our algorithm efficiently estimates probability density functions (PDF) that result from differential equations with random input. This is a new and general problem in numerical uncertainty-quantification (UQ), which leads to surprising results and analysis at the intersection of probability and approximation theory.

Roy Goodman

October 7

Eduardo Corona Department of Mathematics, New York Institute of Technology

A Fast Algorithmic Framework for Dense Rigid Body Suspensions in Stokes Flow

The study of dense particulate suspensions is of great interest in fundamental science and technological applications; Often, the physical phenomenon of interest happens at scales much larger than the constituent particle sizes e.g. collective motion in bacterial suspensions or material self-assembly. We thus require scalable and robust simulation methods to produce valuable insights on these systems.

In this talk, I will describe a scalable computational framework for simulating suspensions of rigid bodies in Stokes flow: Our approach features a fast, parallel and spectrally accurate boundary integral method tailored to spherical particles which enables singular and near-singular evaluations. Particle collisions are efficiently detected and resolved via an optimization-based linear complementarity method. I will then discuss some of our recent work applying this framework to the study of particulate rotors and of material self-assembly for suspensions of Janus (dual-nature) particles.

Travis Askham

October 21

Scott Wunsch, Johns Hopkins University

Internal Waves in Variable Stratification

Internal waves are oscillatory motions of a density-stratified fluid. They are ubiquitous in Earth's oceans and atmosphere, transporting momentum and energy and playing an important role in ocean dynamics and climate. In varying stratification, internal waves transfer energy to harmonic modes. This nonlinear process may contribute to the transfer of internal wave energy from large to small scales in the ocean. This seminar will introduce basic concepts of internal wave propagation and explore harmonic generation in variable stratification using weakly nonlinear theory, laboratory experiment, and numerical simulation.

Yuan-nan Young

November 18

David Stein, Center for Computational Biology, Flatiron Institute

High-Accuracy Simulations of Thousands of Deformable, Interacting, Active Droplets

Coarse-grained continuum models of active fluids capture important aspects of self-organizing behavior seen in experiments while providing a computationally tractable basis for their simulation. Producing accurate solutions to these models is nevertheless challenging, and numerical schemes for their solution have been largely limited to simple, stationary geometries or low-accuracy methods. In this talk, I will describe a spectrally accurate method for the simulation of active fluids in complex geometries, and show how to use this method to simulate deformable droplets of active fluids. When multiple drops are immersed in a Stokesian fluid, their interactions are captured through a robust and scalable boundary integral method, allowing for the simulation of thousands of such particles which may come into near-contact with each other. We explore some of the emergent phenomenon that occurs with such large aggregates of active droplets.

Anand Oza

Fluid Mechanics and Waves Seminar - Fall 2019

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