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Joint Dynamics and PDE Seminar

The Boston University Department of Mathematics and Statistics, Brown University's Department of Mathematics and Division of Applied Mathematics, and the University of Massachusetts Amherst Department of Mathematics and Statistics hold joint seminars on topics in dynamics and PDE. The schedule and locations for these events can be found below. For a list of all past events of the seminar please visit the BU/Brown/UMass PDE Seminar Archive.

The organizers for the Brown/BU/UMass Seminars are Jason Bramburger, Ryan Goh, and Stathis Charalampidis. Please contact them at jason_bramburger@Brown.edu, rgoh@bu.edu, or charalamp@math.umass.edu.

Fall 2018

Using Diffusion Maps in Equation-Free Modeling

Rebecca Santorella

In many high-dimensional dynamical systems interactions between microscopic particles lead to low-dimensional macroscopic behaviors. Equation-free modeling estimates this macro-level behavior through a coarse time stepper in three steps: (1) lift: build the microstate from the macrostate, (2), evolve: simulate the microsystem for short bursts, and (3) restrict: estimate the macrostate from the evolved microstate.

No equations, no variables, no parameters, no space, no time: Data and the modeling of complex systems

Yannis G. Kevrekidis

Obtaining predictive dynamical equations from data lies at the heart of
science and engineering modeling, and is the linchpin of our technology.
In mathematical modeling one typically progresses from observations of
the world (and some serious thinking!) first to equations for a model,
and then to the analysis of the model to make predictions. Good mathematical
models give good predictions (and inaccurate ones do not) - but the computational
tools for analyzing them are the same: algorithms that are typically based
on closed form equations.

Waves and gradients on chemically-driven active surfaces

Pearson Miller

Fundamental biological and biomimetic processes, from tissue morphogenesis to soft robotics, rely on spatiotemporally varying chemical patterns to coordinate active force generation. In this talk, I describe recent investigations into the mechanics of chemically-driven active surfaces from the perspective of non-Euclidean elastic shell theory.

Solitons in ring-shaped Bose-Einstein Condensates

Mareike Haberichter

We construct stationary soliton states in a one-component, two dimensional nonlinear Schroedinger equation with a ring-shaped trap and repulsive interatomic interactions.

Some Asymptotic Solutions of the Camassa-Holm Nonlinear Schrödinger Equation

Cory Ward

In this informal talk, we look at a recently published deformation of the Nonlinear Schrödinger Equation, known as the Camassa-Holm Nonlinear Schrödinger Equation. Using multiscale expansion techniques as well as numerical methods, we show that both the (1+1) and (2+1) variants have soliton solutions of both the dark and antidark varieties. We also highlight some recent work concerning the Camassa-Holm Derivative Nonlinear Schrodinger Equation.

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Brown University

Joint Dynamics and PDE Seminar

Fall 2018

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