Thursday, May 7, 20201PM, Location TBA
Optimizing the free energy and kinetic accessibility for systems of self-assembling colloids
Thursday, April 30, 20201PM, Location TBA
Hydrodynamics of magnetic chains, and flexible fibres with a twist
Thursday, April 23, 20201PM, Location TBA
A sharp interface version of the immersed boundary finite element method
Thursday, April 16, 20201PM, Location TBA
How can we estimate the slowest dynamics of a Markov process?
See presentation slides .
When analyzing a Markov process, a frequent goal is identifying the functions of the process that decorrelate most slowly in time. Slowly decorrelating functions are important for dimensionality reduction and prediction, since the values of these functions can be forecast far into the future. Moreover, because of their persistent nature, slowly decorrelating functions often have scientific significance. In biomolecular systems, for example, fluctuations of bond lengths and angles decorrelate quickly, while large-scale rearrangements that determine biological activity generally decorrelate slowly.
Dynamical spectral estimation is a rigorous approach for identifying slowly decorrelating functions. The approach uses sample trajectories to estimate the eigenfunctions of the Markov transition operator. Under appropriate assumptions, a small number of eigenfunctions span all the most slowly decorrelating functions of the process, and the corresponding eigenvalues determine the slowest decorrelation rates.
Despite the prevalence of dynamical spectral estimation in biomolecular simulation studies, estimated eigenfunctions and eigenvalues can have substantial error. The goal of this talk is to identify and bound the major error sources, thereby identifying opportunities where dynamical spectral estimation can produce accurate results.
Thursday, April 9, 20201PM, Warren Weaver Hall remote; zoom link sent via email
The Universal Route to Rogue Waves via Instanton Theory
Tobias Grafke (Warwick)
In stochastic systems, extreme events are known to be described by "instantons", saddle point configurations of the action of the associated stochastic field theory. In this talk, I will present experimental evidence of a hydrodynamic instanton in a real world fluid system: A 270m wave channel experiment in Norway. The experiment attempts to model conditions on the ocean in order to observe so-called rogue waves, realisations of extreme ocean surface elevation out of relatively calm surroundings. These rogue waves are also observed in the ocean, where they are rare and hard to predict but pose significant danger to naval vessels. We show that the instanton approach, which is rigorously grounded in large deviation theory, offers a unified description of rogue waves in the water tank, covering the entire range of parameters for deep water waves in the ocean. In particular, this approach allows for a unified description of both the predominantly linear and the highly nonlinear regimes, and is able to predict the experimental data in the tank regardless of the strength of the nonlinearity.
Thursday, April 2, 20201PM, Location TBA
Equilibrium statistical mechanics of semiflexible fibers (worm-like chains)
Aleksandar Donev, Courant Institute
Here are notes for the talk: WormLikeChains.pdf
Info for zoom meeting and recording sent by email.
Thursday, March 5, 202012:30PM, Warren Weaver Hall 1314
The Entropic Uncertainty Principle and the Fast Fourier Transform
The entropic uncertainty principle for the discrete Fourier transform
states that for any nonzero u in C^n, H(u) + H(F_n(u)) >= log(n),
where H(u) is the entropy of the discrete probability distribution
P_j = |u_j|^2/||u||^2, and where F_n is the discrete Fourier transform
of order n. This is a special case of a known result , but the
proof of the general case requires functional analysis. Here, we give
an elementary proof of the special case (and moreover only for n
as a power of 2). The proof is based on the Fast Fourier Transform
 Dembo A, Cover TM, and Thomas JA 1991: Information Theoretic
Inequalities. IEEE Transactions on Information Theory
37(6):1501-1517, see Theorem 23 on page 1513.
Thursday, February 27, 202012:30PM, Warren Weaver Hall 1314
"Data-driven optimization of an ocean turbulence model" & "Facing the multiscale problem in biomathematics with statistical physics and machine learning tools"
Justin Finkel & Rocio Vega Martinez
Thursday, February 20, 202012:30PM, Warren Weaver Hall 1314
Estimation of extreme tsunami waves using large deviation theory
Shanyin Tong, partner Chris Miles
Thursday, February 13, 202012:30PM, Warren Weaver Hall 1314
How to give a killer talk (a discussion)
Thursday, February 6, 202012:30PM, Location TBA
Monte Carlo festival
Tristan Goodwill, Miranda Holmes-Cerfon, Michael Lindsey, Robert Webber
A collection of 10-minute talks, each one presenting a Monte Carlo algorithm that was a game changer for a previously intractable sampling problem.
Thursday, January 30, 202012:30PM, Location TBA
Planning meeting -- everyone welcome!