Nonlinear Waves Seminar... Continuation
Brown Analysis Seminar
Stochastic Systems Seminar
Abstract: The problem is to minimize probabilities of large end-to-end delays in a multiclass queueing network with each customer class having its own route through the network. The main result is that the Largest Weighted Delay First scheduling discipline is an optimal solution to this problem in the asymptotic (Large Deviations) regime. Moreover, we show that the LWDF network possesses a remarkable Critical Node Property: there exists a most likely (fluid) path to build "large delays," which is a most likely path to do so in one of the nodes in isolation. We will discuss these and related results, and their implications.
Interdisciplinary Lecture Series
Simulation and Visualization of Physical Phenomena
*Funded by the Wayland Collegium for Liberal Learning |
Special Lefschetz Center for Dynamical Systems Seminar
*Please Note: Change of Day, Time and Room for This Week Only |
Abstract: A detailed and comprehensive study in numerically simulating the mixing processes of a lobed mixer flow field via a Reynolds-averaged solution method has been conducted. Mixed-unstructured grids were employed to assess their suitability in capturing the convoluted mixing layers found downstream of the lobed mixer's trailing edge. In addition, two varients of the high Reynolds number k-epsilon model, a linear and a quadratic model, were employed. The relative merits of these two models was assessed through detailed comparisons with experimental data complemented by an analysis of the streamwise vorticity equation. The study revealed that capturing the initial mixing region proved to be most difficult. Firstly, unstructured meshes employing non-hexahedral elements were very inefficient at simulating the mixing layer in the early stages. Secondly, the initial mixing region revealed significant drawbacks in the use of a Reynolds-averaged solution method in which neither turbulence model was capable of correctly reproducing the turbulence field. Despite this, global parameters such as momentum thickness and streamwise circulation were well captured in the predictioms.
Brown Applied Mathematics Pattern Theory and Vision Seminar
Abstract: Recent proposals that information in cortical neurons may be encoded by precise spike timing have been challenged by the assumption that neurons in vivo can only operate in a noisy fashion, due to the large fluctuations in synaptic input activity. We studied the response properties of the integrate-and-fire neuron model focusing on spike responses to transient membrane potential excursions, implied by the physiological findings. Transients can be interpreted in terms of local network structure: a group of neurons receiving shared convergent input is at the same time the receiver (transients) and the generator of synchronized spikes. By repeating this arrangement in a "locally feed-forward" network, each group can act as the source of synchronous input to a consecutive group (formalized in the "synfire chain"). We performed a two-dimensional state space analysis of the synchronization dynamics of the system by constructing an iterative mapping based on the neuron groups' transmission function. An attractor, yielding a stable spiking precision in the (sub-)millisecond range governs the dynamics of synchronization. In this framework we discuss the number of neurons per group, the amount of background fluctuations, and the rise time of the post- synaptic potential as bifurcation parameters.
Applied Mathematics Colloquium
**Refreshments at 4:00 p.m. in Room 110, 182 George Street, Division of Applied Mathematics |
Abstract: Lift acting on a fluidized particle plays a central role in many inportant applications, such as the removal of drill cuttings in horizontal drill holes in the oil industry, sand transport in fractured reservoirs, and the cleaning of particles from surfaces. The levitation of 300 particles in a Poiseuille flow was numerically studied, from which a data bank was obtained. The method of correlations is a link between direct simulation and engineering application. The roles of slip and slip-angular velocity in the lift off of particles will be elucidated in the lecture.
PDE Seminar
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