Statistics & Probability Seminar (Fall 07)
Krzysztof Podgorski - Lund University, Sweden
Friday, February 8, 1:00 in AB201
Title: Envelope Crossing Distributions for Gaussian Fields
Abstract: The envelope process is an analytical tool often used to study extremes
and wave groups. In an approach to approximate the first passage
probability for the underlying response the average number of envelope
crossings is used to obtain an upper bound. The method of sampling
distribution is applied to the envelope field that is a generalization of
the envelope process. As oppose to the one dimensional version, the
envelope field is not uniquely defined and its statistical properties
depend on a chosen version. We utilize convenient envelope sampling
distributions to decide for a version that has desired smoothing
properties. The spatial-temporal Gaussian sea-surface model is used to
illustrate this approach. One intrinsically multivariate problem is
studying velocities of moving spatial records. Under the Gaussian model we
derive sampling properties of the envelope velocity measured at the level
contours. By associating the properties of envelope with the properties of
group waves we present differences between statistical distributions of
individual waves and waves groups.
Matt Reeves - Desert Research Institute
Friday, November 30, 1:00 in AB109
Title: Stochastic simulation of fracture networks for ground water flow and transport model
Abstract: Numerical simulations are commonly used to guide decisions on water resource issues such as the transport of contaminants through subsurface flow systems. The incorporation of physically realistic geological structures, along with appropriate parameterization of these features, is essential in constructing models that adequately simulate key flow and transport processes. In the case of low-permeability rock masses, fractures provide primary pathways for both fluid flow and solutes transport, and thus, the likelihood of a dissolved contaminant reaching a distant receptor depends on physical and hydraulic properties of an interconnected network of fractures. The generation of fracture networks that honor fracture statistics, collected during field characterization efforts, is of paramount importance in capturing the high degree of heterogeneity that fractures impart on a ground water flow system.
This talk will focus on the use of a probabilistic framework to generate fracture networks that will provide the foundation for numerical simulations designed for radionuclide transport predictions at the Rainier Mesa T-Tunnel Complex, Nevada Test Site. Site-specific statistics of fracture properties, such as orientation, length, density and spatial variability, will be presented, along with stochastic methods used to reproduce synthetic networks with these statistical properties. An emphasis will be placed on stochastic methods that can reproduce the fractal clustering of fractures observed along tunnel transects. For this purpose, a multiplicative cascade process that conditions on deterministic features (large faults), has been developed. As an alternative, a negative binomial process could also potentially reproduce networks with the observed fracture clustering. Time will be allowed at the end to discuss the utility of these methods and the stochastic generation of fracture networks in general.
Boris Baeumer - University of Otago, NZ
Friday, November 16, 1:00 in AB109
Title: Fractional (or non-local) diffusion and reaction
Abstract: Using scaling limit laws we derive a fractional dispersal equation to model seed/viral dispersion of organisms. Combining the dispersal equation with a growth equation yields a non-local reaction diffusion
(growth-dispersal) equation which we use to model Hawthorn growth and
spread at Porters Pass, New Zealand.
Erick Luerken - UNR Math&Stat
Friday, November 2, 1:00 in AB109
Title: Reinsurance with pareto claims: Aggregate-XL models
John Sutko (joint work with Josh Larkin) - UNR CMB
Friday, October 12, 1:00 in AB109
Title: Analysis of images from laser scanning light microscope - Part II
John Sutko (joint work with Josh Larkin) - UNR CMB
Friday, October 12, 1:00 in AB109
Title: Analysis of images from laser scanning light microscope - Part I