Brown University Center for Statistical Sciences Seminar
Abstract:
Part 1: Motivational problems from neuroscience. My collaborators collect brain
signals to study their frequency properties at each site and how activity at
one site may be associated with another site. One goal in these studies is to
compare the frequency and connectivity properties across patient groups (e.g.,
schizophrenics vs control) or experimental conditions (e.g., right vs left).
Part 2: Review of some basic ideas of Fourier analysis of stationary time
series and highlights of its connection to analysis of variance and regression.
Since most biological signals display non-stationarity, the Fourier approach
may not be sufficient. My active area of research is developing tools, methods
and theory for non-stationary processes. My approach is based on the SLEX
(smooth localized complex exponentials) which is a generalized localized
Fourier transform.
Part 3: Application of my methods to the EEG data set collected by Jerome Sanes,
PhD, a collaborator in Neuroscience at Brown. In this experiment, the
participants were instructed to move the joystick from the center to the
right side when they see a cursor flashing on the right side of the screen
(and to the left when the cursor flashes on the left side). In this study,
the goal was to use the EEGs to predict the participants' motor intent. That
is, using the trial-specific EEGs, can we tell if the participant intended to
move the joystick to the right or the left side in response to the visual
stimulus.
The goal of this talk to give the students and colleagues some introduction to
my research and thus throughout the talk I will be happy to answer as many
questions as possible.
Lefschetz Center for Dynamical Systems Seminar
Abstract: Burgers turbulence (Burgers equation with random initial data or forcing) is a nonlinear, out of equilibrium system with applications ranging from cosmology to interface dynamics. In the forceless case, shocks act as particles that cluster through ballistic aggregation and the system exhibits coarsening. Motivated by previous results in the limit cases of Levy process and white noise data, we will demonstrate that 1-D Burgers turbulence with spectrally negative Markov initial data is a completely integrable system. Specifically, we demonstrate that (i) the entropy solution remains of this type and (ii) the time evolution of the solution's infinitesimal generator is given by a Lax pair. These results also hold true in the case of general 1-D scalar conservation laws. The evolution equation is shown to have a rich family of solutions as evidenced by a highly nontrivial, explicit solution derived in the 1980's through entirely probabilistic methods.
Center for Fluid Mechanics Seminar
Abstract: Active flow control via oscillatory forcing or synthetic jets has experimentally been shown to increase aerodynamic performance of naturally separating flows. However, development of accurate computational tools for unsteady separation and control remains a challenge, especially at high Reynolds numbers. This work presents compressible large-eddy simulations (LES) over a wall-mounted hump geometry, which exhibits turbulent, unsteady separation and reattachment. Flow control via steady suction and oscillatory zero mass-flux forcing is applied just before the natural separation point. Results are compared with previous experiments for uncontrolled and controlled flows over a range of subsonic Mach numbers. Compared with the baseline flow, control shortens the separation bubble length, but is generally found to be less effective at compressible Mach numbers. The effect of forcing frequency, and a comparison between steady suction and oscillatory forcing are also presented. The LES is shown to capture the major flow physics of the large-scale shedding of vortical structures, creating a testbed for future closed-loop control developments.
Scientific Computing Seminar
Abstract: In this presentation , we systematically investigate adaptive Runge-Kutta discontinuous Galerkin (RKDG) methods for hyperbolic conservation laws with different indicators which were based on the troubled cell indicators studied by Qiu and Shu [SIAM J. Sci. Comput., 27 (2005), 995-1013], with an objective of obtaining efficient and reliable indicators to obtain better performance for adaptive computation to save computational cost. Both $h$-version and $r$-version adaptive methods are considered in the paper. The idea is to first identify ``troubled cells'' by different troubled-cell indicators, namely those cells where limiting might be needed and discontinuities might appear, then adopt an adaptive approach in these cells. A detailed numerical study in one dimensional case is performed, addressing the issues of CPU cost, accuracy, non-oscillatory property, and resolution of discontinuities.
PDE Seminar
Brown Analysis Seminar
Abstract: In 1971 Charles Fefferman identified the dual of the Hardy space H^1 with the space BMO of functions of bounded mean oscillation. The dual pairing is somewhat subtle, because the product of an H^1 function and a BMO function need not be integrable. In a recent paper Bonami, Iwaniec, Jones and Zinsmeister (BIJZ) give meaning to this product as a distribution. In the setting of the unit disk, they identify the product of an H^1 function and an analytic BMO function with a function in a certain Hardy-Orlicz space. I will give an exposition of this and other results in the BIJZ paper.
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