18 research outputs found
1991 Summer Study Program in Geophysical Fluid Dynamics : patterns in fluid flow
The GFD program in 1991 focused on pattern forming processes in physics and geophysics. The pricipallecturer, Stephan
Fauve, discussed a variety of systems, including our old favorite, Rayleigh-Bénard convection, but passing on to exotic
examples such as vertically vibrated granular layers. Fauve's lectures emphasize a unified theoretical viewpoint based on
symmetry arguments. Patterns produced by instabilties can be described by amplitude equations, whose form can be deduced
by symmetry arguments, rather than the asymptotic expansions that have been the staple of past Summer GFD Programs. The
amplitude equations are far simpler than the complete equations of motion, and symetry arguments are easier than
asymptotic expansions. Symmetry arguments also explain why diverse systems are often described by the same amplitude
equation. Even for granular layers, where there is not a universaly accepted continuum description, the appropnate amplitude
equation can often be found using symmetry arguments and then compared with experiment.
Our second speaker, Daniel Rothan, surveyed the state of the art in lattice gas computations. His lectures illustrate the
great utility of these methods in simulating the flow of complex multiphase fluids, particularly at low Reynolds numbers. The
lattice gas simulations reveal a complicated phenomenology much of which awaits analytic exploration.
The fellowship lectures cover broad ground and reflect the interests of the staff members associated with the program. They
range from the formation of sand dunes, though the theory of lattice gases, and on to two dimensional-turbulence and
convection on planetary scales. Readers desiring to quote from these report should seek the permission of the authors (a
partial list of electronic mail addresses is included on page v). As in previous years, these reports are extensively reworked for
publication or appear as chapters in doctoral theses. The task of assembling the volume in 1991 was at first faciltated by our
newly acquired computers, only to be complicated by hurricane Bob which severed electric power to Walsh Cottage in the
final hectic days of the Summer.Funding was provided by the National Science Foundation
through Grant No. OCE 8901012
Generalized averaged Gaussian quadrature and applications
A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal
MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications
Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described
Theoretical Approaches in Non-Linear Dynamical Systems
From Preface: The 15th International Conference „Dynamical Systems - Theory and Applications” (DSTA 2019, 2-5 December, 2019, Lodz, Poland) gathered a numerous group of outstanding scientists and engineers who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without great effort of the staff of the Department of Automation, Biomechanics and Mechatronics of the Lodz University of Technology. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and Ministry of Science and Higher Education of Poland. It is a great pleasure that our event was attended by over 180 researchers from 35 countries all over the world, who decided to share the results of their research and experience in different fields related to dynamical systems. This year, the DSTA Conference Proceedings were split into two volumes entitled „Theoretical Approaches in Non-Linear Dynamical Systems” and „Applicable Solutions in Non-Linear Dynamical Systems”. In addition, DSTA 2019 resulted in three volumes of Springer Proceedings in Mathematics and Statistics entitled „Control and Stability of Dynamical Systems”, „Mathematical and Numerical Approaches in Dynamical Systems” and „Dynamical Systems in Mechatronics and Life Sciences”. Also, many outstanding papers will be recommended to special issues of renowned scientific journals.Cover design: Kaźmierczak, MarekTechnical editor: Kaźmierczak, Mare