• Jan. 11 (Friday) 3:00-4:00 pm. Jones 131

Speaker: Nancy Sundell, Cornell University.
Title: Dynamics of a Multi-Patch Herbivory System: Herbivore Enhancement, Adaptive Behavior and Trophic Cascades
Abtract: A mathematical model was developed describing an herbivore grazing system in the Arctic and sub-Arctic regions of North America. This system is of interest both mathematically and biologically because of the complex interactions between the herbivores, the plants they eat and the nitrogen levels and salinity of the soil. The herbivores (Snow Geese) affect the plants in two contrasting ways: they directly decrease the above ground biomass of the plants by consumption and they indirectly increase the net above ground primary productivity of the plants by increasing the nitrogen levels of the soil. The benefit to the plants is not felt immediately, but is constrained by the time necessary for nitrogen to decay into the soil. The overall growth rate of the plants is limited by the level of inorganic salts which are drawn to the surface of the soil when plant biomass drops too low. The dynamics of a two patch ordinary differential equations model are examined both analytically and numerically for a variety of different parameter values and a large array of asymptotic behaviors and bifurcations are observed. The system is found to be very sensitive to initial conditions, nitrogen decay time, and changes in the total number of geese, suggesting the fragility of the ecosystem to changes in the environment.
• Jan 14 (Monday) 3:30-4:30 pm. Jones 131

Speaker: Peter Blomgren, Stanford University
Title: Time Reversal and Imaging in Random Media
Abstract: In time reversal acoustics, a signal is recorded on an array of transducers and then re-transmitted in last-in-first-out order. The signal propagates back through the medium and refocuses approximately on the originating source. In a homogeneous medium the refocusing resolution of the time-reversed signal is limited by diffraction. When the medium has random inhomogeneities, the resolution of the refocused signal can in some circumstances beat the diffraction limit. This is called super-resolution. I will discuss theoretical and numerical results that explain how super-resolution occurs, and why it is a stable physical phenomenon. Further, I will talk about how we use the lessons learned in the super-resolution study to construct statistically stable imaging functionals, and I will show numerical results of imaging in random media using an array of active transducers.
• Jan 18 (Friday) 2:00-3:00 pm. Jones 307 (Note the usual time and place)

Speaker: Sebastian Schreiber, Western Washington University
Title: Chaotic transients and unexpected extinction: Lessons from simple population models with an Allee effect.
Abstract A population exhibits an Allee effect when at low densities individuals benefit from the presence of conspecifics. Allee effects occur for a wide variety of reasons including the presence of conspecifics reducing predation risk or increasing the likelihood of mating success. Allee effects often lead to a critical population density below which extinction is unavoidable. Population with fluctuating dynamics and an Allee effect are especially vulnerable to extinction as the fluctuations may dip below this critical density. Since populations with discrete generations and overcompensating density dependence can exhibit fluctuating demographics, I will discuss the complex interaction between Allee effects and overcompensating density dependence. Under certain technical assumptions, models combining these effects exhibit six possible behaviors: persistence, semistability, bistability, extinction for all initial population densities, chaotic semistability, and essential extinction in which almost every initial condition leads to extinction. Essential extinction can be preceded by long-term chaotic transients. It also results in extinction times that are highly sensitive to initial conditions and that are approximately exponentially distributed with respect to randomly chosen initial conditions. Applying these analytic results to specific models, I will discuss some unexpected ecological and evolutionary implications (e.g., lowering predation/harvesting rates resulting in extinction, evolutionary suicide).

To see two figures related to the talk, click Figure 1 and Figure 2 .

• Jan 18 (Monday) 3:30-4:30 pm. Jones 131

Speaker: Boris Diskin ICASE, NASA Langley Research Center
Title: Textbook Multigrid Efficiency in Computational Fluid Dynamics
Abstract Full multigrid (FMG) algorithms are the fastest solvers for elliptic problems. These algorithms can solve a general discretized elliptic problem to the discretization accuracy in a computational work that is a small (less than 10) multiple of the operation count in one target-grid residual evaluation. Such efficiency is known as textbook multigrid efficiency (TME). The difficulties associated with extending TME for solution of the Reynolds-averaged Navier-Stokes (RANS) equations relate to the fact that the RANS equations are a system of coupled nonlinear equations that is not, even for subsonic Mach numbers, fully elliptic, but contain hyperbolic partitions. TME for the RANS simulations can be achieved if the different factors contributing to the system could be separated and treated optimally, e.g., by multigrid for elliptic factors and by downstream marching for hyperbolic factors. One of the ways to separate the factors is the distributed relaxation approach. Earlier demonstrations of TME solvers with distributed relaxation have already been performed for relatively simple subsets of RANS equations in simple geometries (incompressible free-stream inviscid and viscous flows without boundary layers).

In this talk, I am going to briefly outline the basic multigrid ideas and their applications to solution of PDE. The concept of distributed relaxation will be discussed in more details. A general framework for achieving TME in solution of the Navier-Stokes equations will be presented. Some numerical results confirming TME for distributed-relaxation solvers will be demonstrated for viscous incompressible and subsonic compressible flows with boundary layers and for inviscid compressible transonic flows with shocks.

• Jan 22 (Tuesday) 3:30-4:30 pm. Jones 131

Speaker: Julie Raye, North Carolina State University
Title: An electromagnetic interrogation technique utilizing pressure-dependent poloarization
Abstract Electromagnetic interrogation techniques have many useful applications, including foliage pentration, identification of underground objects, and noninvasive tumor detection. We consider a technique in which a traveling acoustic wave acts as a virtual interface for an oncoming electromagnetic wave. We suggest that the interaction between the electromagnetic wave and the acoustic wave can be described using a pressure-dependent model for electric polarization. We present both theoretical and computational results.
• Jan 28 (Monday) 2:00-3:00 pm. Jones 301 (Note the usual time and place)

Speaker: Sorin Mitran, University of Washington
Title: The Third Way - Computational Science and Engineering, Multiscale and Multiphysics Tools
Abstract Computational Science and Engineering (CSE) has emerged as a third mode of scientific investigation and engineering practice. CSE involves an interdisciplinary approach using techniques from applied mathematics and computer science to construct general solution tools aimed at classes of problems in science or engineering. This talk presents the development and application of two such computational tools, designed for simulation of phenomena governed by partial differential equations and that exhibit a wide variety of scales. Applications from acoustics, elasticity, fluid dynamics, magneto-hydrodynamics, cosmology show the wide range of problems that may be analyzed. An abstract underlying data structure allows simultaneous solution of different sets of physical laws; these may be a priori associated with some subdomain, or applied as required in response to the attainment of specified local conditions. The associated subdomains may have a different number of dimensions. Different numerical algorithms may also be applied on each subdomain and changed dynamically during the computation. Adaptive mesh refinement is provided to allow tracking of localized phenomena. Parallelization at various levels is employed in order to enable large-scale computation. Standardized output of results to scientific data formats permits the use of a number of visualization packages.

The interplay between CSE, theory and experiment is exemplified in the development of turbulence models for bubbly flow, a problem of considerable practical interest.

• Feb. 1 (Friday) 2:30-3:30 pm. Jones 131

Speaker: Maia Martcheva, Polytechnic University
Title: Forward Bifurcation and Backward Bifurcation of Equilibria in Epidemic Models
Abstract The use of mathematical modeling as a tool for disease control has historically relied on threshold results, in which a certain factor related to disease transmission must be changed beyond a given level in order to eradicate the disease. The most well-known threshold criterion is the {\it basic reproductive number} of a disease, typically denoted ${\Cal R}_0$, which represents the average number of secondary infections caused by one infective in a pool of susceptibles. In simple epidemic models when ${\Cal R}_0 <1$ the disease-free equilibrium is often globally stable which suggests that it is sufficient to reduce ${\Cal R}_0$ below one and the disease will disappear from the population. I consider a simple ODE model of hepatitis C as an illustration. However, several recent studies have shown that the ${\Cal R}_0<1$ criterion is not always sufficient to control the spread of a disease. Dynamically it is possible that the transcritical bifurcation that occurs at ${\Cal R}_0=1$ may change directions, creating what has become known in the literature as a ``backward'' bifurcation, in which the endemic equilibrium arises from the disease-free equilibrium for ${\Cal R}_0<1$ rather than for ${\Cal R}_0>1$ as in the simplest cases. From a control point of view when backward bifurcation occurs it is not sufficient to lower ${\Cal R}_0$ below one but below another threshold value which is the leftmost point on the bifurcation curve for which an endemic equilibrium exists. I consider a structured model for a disease with a progressing and a quiescent exposed class and variable susceptibility to super-infection. The model exhibits backward bifurcations under certain conditions, which allow for both stable and unstable endemic states when the basic reproduction number is smaller than one.
• Feb. 8 (Friday) 3:00-4:00 pm. Jones 131

Speaker:
Title:
• Feb. 14 (Thursday) 3:30-4:30 pm. Jones 301

Speaker: Erik M. Bollt, US Naval Academy
Title: Transport and Global Control of Deterministic and Stochastic Dynamical Systems
Abstract Associated with a dynamical system, which evolves single initial conditions, the Frobenius-Perron operator evolves ensemble densities of initial conditions. Including a brief tutorial on the topic, we will present our new applications of this global and statistical point of view:

1) The inverse Frobenius-Perron problem (IFPP) is a global open-loop strategy to control chaos by constructing a "nearby" dynamical system with desirable invariant density. We reduce the question of stabilizing an arbitrary invariant density to the question of a hyperplane intersecting a unit hyperbox; several controllability theorems follow. Applications will be described.

2) Well-known models have been found to exhibit new and interesting dynamics under the addition of stochastic perturbations. Using the Frobenius-Perron operator for stochastic dynamical systems, we develop new tools designed to predict the effects of noise and to pinpoint stochastic transport regions in phase space. As an example, we study a model from population dynamics for which chaos-like behavior can be induced, as the standard deviation of the noise is increased. We identify how stochastic perturbations destabilize two attracting orbits, effectively completing a heteroclinic orbit, to create chaos-like behavior. Other physical applications will also be discussed.

• Feb. 15 (Friday) 3:00-4:00 pm. Jones 131

Speaker: Boris Mityagin, Ohio State University
Title: Spectral triangles of one-dimensional periodic Schrodinger and Dirac operators.
Abstract

Computer Science Colloquium:
===========================================================================

Computer Science Colloquium Series
McGlothin-Street Hall, Room 020
February 15, 2002, Friday 3 p.m.

 Jill R. Hardin, Assistant Professor
 Virginia Commonwealth University
 Department of Statistical Sciences and Operations Research

Title: Using Integer Programming Formulations to Solve Scheduling Problems
 
Abstract:
 The classical, nonpreemptive, single-machine scheduling problem is as 
 follows: given a set of jobs, each with a processing time, sequence them 
 without interruption in order to optimize some objective criterion (for 
 example, minimize total schedule duration). This problem can be solved 
 easily for many objective criteria, but the addition of seemingly simple 
 restrictions can often make finding optimal solutions difficult. We 
 present  a typical integer programming formulation for the classical 
 problem, and we discuss how this formulation is used in obtaining 
 approximate solutions for more difficult scheduling problems. We then 
 discuss how the given integer programming formulation can be strengthened 
 and show how these results can be extended in the presence of more 
 general resource constraints.
=================================================

March

• March 1 (Friday) 3:00-4:00 pm. Jones 131

Speaker: Barry Peyton,Oak Ridge National Laboratory
Title: Practical Minimal Orderings
Abstract When minimum orderings proved too difficult to deal with, Rose, Tarjan, and Leuker instead studied minimal orderings and how to compute them (Algorithmic aspects of vertex elimination on graphs, SIAM J. Comput., 5:266-283, 1976). This talk discusses an algorithm that is capable of computing much better minimal orderings much more efficiently than the algorithm in Rose et al. The new insight is a way to use certain structures and concepts from modern Cholesky solvers to re-express one of the basic results in Rose et al. The new algorithm begins with any initial ordering and then refines it until a minimal ordering is obtained. It is simple to obtain high-quality low-cost minimal orderings by using fill-reducing heuristic orderings as initial orderings for the algorithm. We examine minimum degree and nested dissection initial orderings in some detail.

Blair, Heggernes, and Telle were the first to take this overall approach to finding good minimal orderings. The approach taken here is much more practical, however, because in general the final minimal ordering is obtained from the initial heuristic ordering very fast. This is especially the case when three enhancements are incorporated into the implementation of the algorithm. Time permitting, we will describe these enhancements and observe the improvements they are responsible for in the runtimes.

• March 5 (Tuesday) 3:00-4:00 pm. Jones 131

Speaker: Beatrix Jones, Penn State University
Title: Using genetic marker data to look at mating and dispersal patterns: inference when nuisance parameters live in a large, discrete space.
Abstract Many questions about fertility and dispersal in natural populations would be easy inference problems if parent-child relationships were known with certainty. However, in many natural (wild) populations, it is not possible to directly observe which offspring belong to which parents. These parent assignments are essentially nuisance parameters. Collecting genetic marker data can provide some information about which individuals are likely to be relatives. The likelihood for the mating and dispersal parameters is then a sum over possible parent assignments for the offspring in the population, where each summand is weighted by the likelihood of the observed genetic information under that set of parent assignments. We then use computational techniques such as importance sampling and Markov chain Monte Carlo to perform inference in a maximum likelihood framework. The talk will be illustrated with examples from plant and insect populations.
• March 6 (Wednesday) 3:00-4:00 pm. Jones 131

Speaker: Danny Walsh, Penn State University
Title: Accurate and Efficient Curve Detection in Images: The Importance Sampling Hough Transform
Abstract The Hough transform is a well known technique for detecting parametric curves in images. We place a particular group of Hough transforms, the probabilistic Hough transforms, in the framework of importance sampling. This framework suggests a way in which probabilistic Hough transforms can be improved: by specifying a target distribution and weighting the sampled parameters accordingly to make identification of curves easier. We investigate the use of clustering techniques to simultaneously identify multiple curves in an image. We also use probabilistic arguments to develop stopping conditions for the algorithm. The resulting methodology is called the Importance Sampling Hough Transform (ISHT). We apply our method to both simulated and real data, and compare its performance with that of two much used versions of the Hough transform: the standard Hough transform and the randomized Hough transform. In our experiments, it is more accurate than either of these common methods, and it is faster than the randomized Hough transform.
• March 15 (Friday) 3:00-4:00 pm. Jones 131

Speaker: Chongchun Zeng, Univ. of Virginia
Title: Wave equations under strong constraining forces
Abstract In this talk, we consider wave equations of $u(t,x) \in R^n$ where there is a strong constraining potential. This potential achieves its minimum on a submanifold $M \subset R^n$. We study the limit of solutions with $u(0, x) \in M$ as the constraining potential tends to infinity. On the other hand, this problem can also be viewed as realizing a holomophic constraint (to a submanifold in the configuration space) to a Hamiltonian motion by using a strong constraining potential.

Applied Science Colloquium
--------------------------
Monday, 18 March 2002, 1:00 pm, Physics Conference Room, Small Hall

SLIPS, TRIPS, AND TUGS!
EXPLORING DISTURBANCES TO BALANCE AND FALLS

Elizabeth T. Hsiao-Wecksler, Ph.D.
Integrated Rehabilitation Engineering Program
Department of Biomedical Engineering
Boston University and Harvard Medical School

Falls are a major health problem for older adults. It has been estimated
that one-third of senior citizens living in the community experience a 
fall
each year, and one-half of these will suffer from multiple falls.  During
this talk, I will discuss a variety of experimental and computational 
tools
that use unexpected disturbances to balance to better understand the 
effect
of aging on human postural control and balance recovery ability. Simulated
slipping experiments on young adult subjects explored movement strategies
used while attempting to prevent a fall or land safely in the event of a
fall. Simulated tripping experiments on young and elderly adult subjects
investigated the biomechanical and neuromuscular factors associated with 
the
ability to restore balance with one or more steps. The relationship 
between
static and dynamic postural control in young and elderly adult subjects 
was
examined using postural sway data collected while standing quietly or 
after
a mild disturbance or tug at the waist. Movement analysis data and
mathematical models, derived from the single-link inverted pendulum
paradigm, random walk theory, and the fluctuation-dissipation theorem, 
will
be discussed.

• March 20 (Wednesday) 2:00-3:00 pm. Jones 131

Speaker: Speaker: L. Sakhnovich (Courant Institute, New York).
Title: Finite zones potentials.
• March 26 (Tuesday)

Speaker: S. Novikov
Title: Discretization and Integrability. Discrete spectral analysis.

Cissy Patterson Lecture

Speaker: Tasha R. Inniss, Clare Boothe Luce Professor of Mathematics, Trinity College, Washington, D.C.
Title: Inclement Weather: Major Threat to Air Traffic Management Prior to 9-11
Abstract Inclement weather reduces an airport arrival capacity, which results in the institution of a ground delay program (GDP). The stochastic nature of weather precludes determining arrival capacities deterministically. In this talk, I will present statistical models that I developed using a seasonal clustering technique. These models are used to estimate capacity scenario distributions based on historical data from a given airport and are required inputs into a class of stochastic ground holding models that determine optimal ground delay to assign to incoming flights.

Brief Bio of Speaker: Dr. Tasha Inniss is an applied mathematician who specializes in aviation operations research and statistics. She received a BS in mathematics, summa cum laude, from Xavier University of Louisiana in 1993 and attended the Georgia Institute of Technology as a David and Lucile Packard Foundation Scholar where she received an MS in applied mathematics in 1995. In August of 2000, she completed her Ph.D. in applied mathematics at the University of Maryland. She was one of the first three African-American women to receive a Ph.D. in mathematics from the University of Maryland. The title of her dissertation is "Stochastic Models for the Estimation of Airport Arrival Capacity Distributions." The research was funded by the National Center of Excellence for Aviation Operations Research (NEXTOR), which was commissioned by the Federal Aviation Administration (FAA). Due to the relevance of the issues in her dissertation, she was awarded the FAA Centers of Excellence Student-of-the-Year Award. She is currently a Clare Boothe Luce Professor of Mathematics at Trinity College in Washington D.C. and a visiting researcher at the FAA.

April

• April 5 (Friday) 3:00-4:00 pm. Jones 131

Speaker:
Title:
• April 12 (Friday) 3:00-4:00 pm. Jones 131

Speaker:
Title:
• April 19 (Friday) 3:00-4:00 pm. Jones 131

Speaker:
Title:
• April 26 (Friday) 3:00-4:00 pm. Jones 131

Speaker:
Title:

• Sept. 14 (Fri) 3:00-4:00 pm. Jones 131, Byungik Kahng, William and Mary.

Title: Piecewise Elliptic Dynamical Systems
Abstract: We investigate the iterative dynamics of symplectic piecewise-affine elliptic rotation maps associated with matrices with non-integer entries,

             [  0   -1  
                1    a]

where $-2 < a < 2$. We explain how their singularity and periodicity structures develop in general. In a special case, $a = \pm \sqrt 2$, we completely determine the orbit structure, the singularity structure, the invariant fractal and the ergodicity on the invariant fractal with respect to its Hausdorff measure. We also report an example of a period tripling cascade that arises from this system.
• Sept. 28 (Fri) 3:00-4:00 pm. Jones 131, Sasha Kheifets, William and Mary.

Title: Abstract interpolation scheme in the Schur class.
 
 

• Oct 2 (Tue) 3:30-4:30 pm. Jones 131, Arlene Moore, NASA.

Title: Applications of Mathematical Modeling at NASA.
(Abstract outside the dept. office.)
• Oct 5 (Fri) 3:00-4:00 pm. Jones 131, Ed Poon, William and Mary.

Title: Angles between subspaces
• Oct 10 (Wed) 3:00-4:00 pm. Jones 131, S. Furtado, Portugal

Title: Products of matrices with prescribed invariants for similarity
• Oct 19 (Fri) 3:00-4:00 pm. Jones 131, Gregory D. Smith, Department of Applied Science, W&M.

Title: The shape of Ca2+ microdomains: Asymptotic analysis of the buffered diffusion of intracellular Ca2+ near open Ca2+ channels
 
 

• Nov. 30 (Fri) 3:00-4:00 pm. Jones 131, Byungik Kahng, William and Mary.

Title: Dynamics of Kaleidoscopic Maps