Center for Statistical Sciences Seminar
In many experiments, time series data can be collected from multiple units and multiple time series segments can be collected from the same unit. This article introduces a mixed effects Cramer spectral representation which can be used to model the effects of design covariates on the second-order power spectrum while accounting for potential correlations among the time series segments collected from the same unit. The transfer function is composed of a deterministic component to account for the population-average effects and a random component to account for the unit-specific deviations. The resulting log-spectrum has a functional mixed effects representation where both the fixed effects and random effects are functions in the frequency domain. It is shown that, when the replicate-specific spectra are smooth, the log-periodograms converge to a functional mixed effects model. A data-driven iterative estimation procedure is offered for the periodic smoothing spline estimation of the fixed effects, penalized estimation of the functional covariance of the random effects, and unit-specific random effects prediction via the best linear unbiased predictor.
Based on the Biometrika paper of Krafty, Hall and Guo (2011) 98(3): 583-98
Lefschetz Center for Dynamical Systems Seminar
Abstract: We propose to derive rigorously asymptotic models for the propagation of gravity waves at the interface between two layers of immiscible fluids of different densities (modeling fresh and salt water interface). We will focus on unidirectional models, such as Kortweg-de Vries, Gardner or Camassa-Holm equations.
Center for Fluid Mechanics, Division of Applied Mathematics Fluid, Thermal and Chemical Processes Group, School of Engineering Joint Seminar Series
Abstract: Consider a large cloud of particles which are moved around in space by a random transport process such as diffusion. If these particles are ``sticky'' so that they clump together irreversibly upon contact then the resulting distribution of cluster sizes evolves in time since smaller clusters stick to each other to produce larger ones. The statistical dynamics of such sticky particles has applications in surface physics, colloids, granular materials, bio-physics and atmospheric science. It also provides a rich variety of non-equilibrium phenomena for theoretical analysis. One of the most striking of these phenomena is the so-called gelation transition which, roughly speaking, corresponds to the generation of clusters of infinite size in a finite time. In this talk, I will discuss the scaling theory of cluster aggregation at the level of mean field theory and explain the meaning of the gelation transition. At the end I will discuss the somewhat mysterious phenomenon of "instantaneous" gelation and its relation to some problems in cloud physics.
Scientific Computing Seminar
Abstract: We shall present several applications of efficient and fast algorithms based on Multigrid Methods to simulate the non-Newtonian fluid flows. We discuss a novel numerical method designed by Xu and Lee (2004) and its improvement due to Li and Lee (2011) that can be used to handle the rate-type non-Newtonian equations in a unified and stable manner. We show how multigrid methods can be effectively used to solve the resulting discrete models. Various real-life applications as well as theoretical results will be presented. We shall present some enhancement of the methods developed using the parallel computing techniques as well jointly done with Leng Wei, Chensong Zhang.
Abstract: We consider the solitary water wave problem with vorticity. Small amplitude solutions have been constructed by Hur and later by Groves and Wahlén. We use degree theory to prove a continuation result, constructing a global connected set of solutions. We also discuss some properties of this connected set.
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