Special Lefschetz Center for Dynamical Systems Seminar
Abstract: We present an approach to emulating a complicated reaction/chemotaxis/diffusion model describing the spatial dispersal of Mountain Pine Beetles and their effect on host pines. The approach depends on separation of scales between chemical diffusion and beetle movement, which reduces the dispersal problem to a linear partial differential equation with complicated, spatially varying coefficients. We develop an approximation procedure for solving this linear system in general circumstances and analyze its errors. Finally, we analyze the behavior of the system, using the previous procedure to take extremely large numerical time steps. We show that the qualitative dynamics are preserved even when the pointwise error may be large, which leads us to propose this approach as a general emulation technique for similar systems.
Lefschetz Center for Dynamical Systems Seminar
Abstract:
First part of this talk deals with discrete nonlinear gyroscopic
systems which can be obtained either in the context of rigid-body motions
or by applying the Galerkin approximation to continuous systems. Gyroscopic
systems are an important class of systems which include such problems as
rotating shafts, supported pipes conveying fluid, systems subject to Lorenz
forces, structures moving in fluid media, transverse vibrations of moving
belts, etc. The problem considered in this paper is motivated by the whirling
motion of a rotating shaft which is a fundamental component of many mechanical
systems.
The second part investigates the effects of nonlinearities on the dynamics of flat panels in supersonic flow. The interaction of aerodynamic forces with a flexible structure such as a panel can create complicated vibrational effects that may adversely affect the overall performance of an aircraft. Phenomena such as large amplitude flutter, buckling, and fatigue failure are all possible results of flow-induced dynamics.
Stochastic Systems Seminar
Abstract:
The standard approach in the theory of linear partial or pseudo-differential equations consists of two steps. First one considers a
sufficiently large space in which the solution exists in some weak
sense. Then one identifies a smaller linear subspace in which there is
only one solution. This uniqueness subspace is usually specified in
terms of local smoothness properties (e.g. a Sobolev space) and is the
same for a wide range of equations irrespective of the specific values
of the coefficients, etc.
We will show on the example of the first order Hamilton-Jacobi
-Bellman equation that this approach can be extended to nonlinear
equations. The only necessary modification is that the uniqueness
class has to be specified as a cone rather than a linear subspace of
functions. Examples of such uniqueness cones are the sums of all smooth
and concave functions or the cone of all Lipschitz functions with upper
semi-continuous directional derivatives. Conceptually this approach is
closer to the classical linear theory than to the widely used viscosity solutions method.
The proofs will be guided by control theoretic intuition and will depend on a key lemma on the solvability of ODEs with substantially discontinuous right hand sides.
LEMS and Electrical Science Seminar
General Electric Research & Development Center | |
Abstract:
Advances in medical imaging provide an opportunity for improving the
effectiveness and productivity of health care. Both diagnostic techniques and
interventional (therapeutic) procedures are developing rapidly. A summary of
recent results in MR, CT, and ultrasound will be presented, and prospects for
future diagnostic systems will be listed. Image-guided therapy techniques
will be described, and their future potential projected. Recent results and
prospects in image analysis and display will be presented.
Biographical sketch:
Dr. Vosburgh obtained his BS/MS in Engineering Physics from
Cornell University and holds a PhD in Physics from Rutgers University and
a post-doctoral fellowship at Princeton University.
After joining GE R+D in 1972, he contributed to the development of the first
GE CT scanners, the storage of radiographic information, and various energy
sources and storage systems. Dr. Vosburgh has served as the Project Manager
for the research and
development teams at GE Corporate R+D for image-guided therapies, including
enhanced reality, MR-guided surgery, and MR-guided focused ultrasound therapy.
Dr. Vosburgh has published over 30 papers, holds three US Patents and is a
member of the American Physical Society, the Society for Minimally Invasive
Therapy, and the IEEE.
GE Corp. Research and Development, Bldg. KW, Room C300, P.O. Box 8, Schenectady, NY 12301
Brown Applied Mathematics Pattern Theory and Vision Seminar
(Joint work with Anthony R. Cassandra and Michael L. Littman.) | |
Abstract:
In this talk, I will describe the partially observable Markov decision
process (POMDP) approach to finding optimal or near-optimal control
strategies for partially observable stochastic environments, given a
complete model of the environment. The POMDP approach was originally
developed in the operations research community and provides a formal
basis for high-level planning and reasoning under uncertainty when
continuous uncertainty models, such as Kalman filters, are
inappropriate.
We found the existing algorithms for computing optimal control strategies to be highly computationally inefficient and have developed a new algorithm that is more efficient, both theoretically and empirically. However, exact solution of POMDPs of moderate size remains intractable. I will conclude with a discussion of our recent research on approximation methods that allow us to solve medium-sized problems and an application to mobile-robot navigation.
Brown Analysis Seminar
Special Department of Mathematics Lecture
Scientific Computing Seminar
Abstract: We present a new formulation of the incompressible Navier-Stokes equation in terms of an auxiliary field that differs from the velocity by a gauge transformation. The gauge freedom allows us to assign simple and specific boundary conditions for both the auxiliary field and the gauge field, thus eliminating the issue of pressure boundary condition in the usual primitive variable formulation. Although it closely resembles the projection method, the gauge method has the advantage that the gauge Poisson equation in the projection step can be solved by standard Poisson solvers including the five-point formula. This is in contrast to the projection method in which the pressure Poisson equation has to be solved using special Poisson solvers.
P.D.E./Lefschetz Center Seminar
Department of Mathematics Colloquium
<--- 1997 Index