Group Meeting
Past Events

Thursday, December 17, 202012:30PM, Warren Weaver Hall 1314
Generalized ConstantinLaxMajda equation: Collapse vs. blow up and global existence
Denis SilantyevSynopsis:
We investigate the behavior of the generalized ConstantinLaxMajda (CLM) which is a 1D model for the advection and stretching of vorticity in a 3D incompressible Euler fluid. Similar to Euler equations the vortex stretching term is quadratic in vorticity, and therefore is destabilizing and has the potential to generate singular behavior, while the advection term does not cause any growth of vorticity and provides a stabilizing effect. We study the influence of a parameter a which controls the strength of advection, distinguishing a finite time singularity formation (collapse or blowup) vs. global existence of solutions. For solutions on the infinite domain we find a new critical value a_c=0.6890665337007457... below which there is finite time singularity formation that has a form of selfsimilar collapse, with the spatial extent of blowup shrinking to zero. We identify the leading order complex singularity for general values of a which controls the leading order behavior of the collapsing solution. We also rederive a known exact collapsing solution for a=0 and we find a new exact analytical collapsing solution at a= 1/2. For a_c<a≤1, we find a blowup solution on the real line in which the spatial extent of the blowup region expands infinitely fast at the singularity time. For a>1, we find that the solution exists globally with exponentiallike growth of the solution amplitude in time.

Thursday, December 10, 202012:30PM, Warren Weaver Hall 1314
Two Research Talks
Mariya Savinov, Yuhsuan ShihSynopsis:
Mariya will discuss oscillating systems with flexible periods, as those observed in fireflies. Motivated by a recent forced oscillator model of Loehr et al., we explored the behaviors of a pair of twodimensional maps with freerunning phase and period, focusing on characterizing the stability of N:M locking regimes (in which an oscillator produces N cycles for M stimulus cycles). Even with the inclusion of a natural period (a common quality of biological oscillating systems), we find that there is a great deal of multistability and the basins of attraction can be complex and riddled. Yuhsuan will introduce a viscoplastic rheology that can be used to model localization through a yield stress, e.g., in solid earth or sea ice applications. Then, she will present a novel Newton method for solving the nonlinear Stokes flow equations with viscoplastic rheology, which is observed to converge much faster and robustly than traditional fixed point and standard Newton methods.

Thursday, December 3, 202012:30PM, Warren Weaver Hall 1314
Shape dynamics of ice melting in cold water
Scott WeadySynopsis:
Water is an unusual fluid in that it is densest above its freezing point, at about 4 degrees Celsius. In this talk, we'll discuss experiments in the Applied Math Lab, supplemented by numerical simulations, that show how this property writes itself onto melting ice in surprising ways.

Thursday, November 19, 202012:30PM, Warren Weaver Hall 1314
Two Paper Review Talks: Simulated Annealing and Simulated Tempering
Frederick Law, Terrence Alsup, CIMSSynopsis:
"Optimization by Simulated Annealing" (1983) by Kirkpatrick et al. and "Simulated Tempering: a New Monte Carlo Scheme" (1992) by Marinari et al

Monday, November 16, 20205AM, Warren Weaver Hall 1314
Discussion of film "Picture a Scientist"
Synopsis:
We will discuss the documentary Picture a Scientist and the issues of gender discrimination, harrasment, and diversity, as they affect our department and science and math more broadly.

Thursday, November 12, 202012:30PM, Warren Weaver Hall 1314
Mathematical foundations of slender body theory
Laurel OhmSynopsis:
Slender body theory is a popular tool for modeling the interaction between a thin fiber and a 3D viscous fluid. In this talk, we develop a PDE framework for analyzing the error introduced by this approximation and thereby place slender body theory on firm theoretical footing.

Thursday, November 5, 202012:30PM, Warren Weaver Hall 1314
The nanoscale caterpillar: or how to achieve precise motion with random sticky feet
Sophie Marbach, CIMSSynopsis:
I will be talking about particles with sticky feet, trying to understand how they stick and how they move. Particles with sticky feet are minimalistic models of specific physical systems such as DNA coated colloids or white blood cells.

Thursday, October 29, 202012:30PM, Warren Weaver Hall 1314
Geometrical and topological strategies for pumping
Leif Ristroph, CIMSSynopsis:
I'll talk about ways to pump fluids and direct flows using either pipes with complex geometries or simple pipes hooked up to form complex networks. I'll focus on two systems that we've studied experimentally in the Applied Math Lab but still don't really understand. One story involves a curious creation by Nikola Tesla and the other is about the loopy layout of bird lungs.

Thursday, October 22, 202012:30PM, Warren Weaver Hall 1314
Numerical methods for doublyperiodic electrostatics and Stokes flow
Ondrej Maxian, Zecheng Gan, Partner: Aleksandar Donev, CIMSSynopsis:
Donev will give a brief intro and conclusions as a "partner". Lipid bilayer membranes, thin liquid crystal films, confined electrolytes, and colloidal monolayers on fluidfluid interfaces or sedimented above a bottom wall, are all effectively quasi twodimensional, periodic in two out of the three spatial directions, and open or confined in the third direction  a doubly periodic geometry. We describe numerical techniques based on the Fast Fourier Transform (FFT) and Chebyshev polynomials that can compute electrostatic and hydrodynamic interactions in doublyperiodic geometries in linear time in the number of particles.
Here are presentation slides:
Poisson (Ondrej) andStokes (Zecheng) 
Thursday, October 15, 202012:30PM, Warren Weaver Hall 1314
PDEconstrained optimization problems
Yunan Yang, Florian Weschung, CIMSSynopsis:
Yunan will discuss optimizethendiscretize and the discretizethenoptimize approaches for optimization problems constrained by the nonlinear Boltzmann equation. The two developed Monte Carlo methods can compute the gradient efficiently despite the sevendimensional forward and adjoint equations. Florian will discuss shape optimization using nearly conformal mappings. He will show that the standard mesh deformation methods can be augmented in a way so that they preserve angles in a finite element mesh, enabling larger deformations while preserving mesh quality.

Thursday, October 8, 202012:30PM, Warren Weaver Hall 1314
Toy models for the many faces of magnetized plasma turbulence
Antoine Cerfon, CIMSSynopsis:
In this talk, I will present the many facets of magnetized plasma turbulence, explain why they must be understood for the design of efficient fusion reactors, and introduce toy fluid models which capture a surprisingly large fraction of these complex turbulent features.

Thursday, October 1, 202012:30PM, Warren Weaver Hall 1314
Collisions of billiard balls in 3D with spin and friction
Charlie Peskin, CIMSSynopsis:
The collision of billiard balls is influenced by their spin. This influence is a consequence of friction that acts during the very brief time that the balls are in contact. Here we use the Coulomb friction law, which is especially convenient because it does not require knowledge of the area of contact. In centerofmass coordinates, we solve the general problem of the collision of identical billiard balls in 3D. When sliding friction is the only dissipative mechanism, we are able to express the outgoing state of the balls unambiguously in terms of their incoming state. When there is additional dissipation associated with compression of the balls during the collision, there is a oneparameter family of solutions depending on the extent of this additional dissipation.
Notes:
https://www.math.nyu.edu/faculty/peskin/Collision_of_Billiard_Balls_in_3D_with_Spin_and_Friction.pdf

Thursday, September 17, 202012:30PM, Warren Weaver Hall Zoom
A cavalcade of short research talks from Professors
Miranda HolmesCerfon, Aleks Donev, Alex Mogilner, Charlie Peskin, Marsha Berger, and Georg Stadler, CIMSSynopsis:
This week will be an introductory meeting where selected faculty (click on name for the PDF of the presentation): Miranda HolmesCerfon, Aleks Donev, Alex Mogilner, Charlie Peskin, Marsha Berger, and Georg Stadler, will give a brief overview of their ongoing research.

Thursday, September 10, 202012:30PM, Warren Weaver Hall zoom
Organizational meeting
Synopsis:
This first meeting will be both an organizational meeting, and a social meeting; we will decide on presenters and activities for the fall semester. Everyone is welcome, whether you plan on participating regularly or not. New PhD students are especially welcome and the organizers have planned activities to get to know each other.