Math Awareness Week 1992

MAW 92 Theme Postcard

 Table of Contents ``` MATHEMATICS & THE ENVIRONMENT We see a diversity of waves in our everyday experience. Electromagnetic waves carry television and radio to our homes, ultrasound waves are used to monitor the growth of a baby in the mother's womb, and a variety of waves on the surfaces of rivers, lakes and oceans affect the coastal environment. Mathematical models help us understand these disparate phenomena. Many wave phenomena are characterized by a simple oscillation like a hand-waving greeting. Seen from across a football stadium, such a wave executed by human bodies appears to propagate around the stadium, and this is how sound waves carry your voice across a room. Other wave phenomena are more complex, often involving nonlinear interactions. A special type of wave which can propagate over long distances without significant dispersal, the solitary wave, was first observed by Scott Russell in 1844 on the surface of a canal. Often initiated by mid-ocean earthquakes, but also susceptible to creation by human error, similar waves propagate across oceans at the speed of a commercial jet and cause devastation when they collide with solid shores. Dubbed the tsunami by the Japanese who must contend with their destructive effects, these waves can propagate undetected due to their large wavelength and small amplitude. However, decreasing depth near a shoreline causes them to transform into huge waves that can inundate a coastal region. Their special form allows them to move over great distances without being dispersed as quickly as other waves. Solitary waves were found by Korteweg and de Vries in 1895 to be governed by the equation Not surprisingly, the model has been found to be appropriate for waves in other media, including fiber optic cables and plasma in aa fusion reactor, reflecting the universality of mathematical models. Remarkable properties of the equation itself have led to deep connections with fields of pure mathematics. Until recently, critical questions about the mathematical theory for the existence of solutions for the equation were unresolved, and solution of this equation strained the resources of the most powerful completers. However, mathematical advances have now made its solution routine, allowing accurate predictions of wave evolution. Early numerical techniques to solve the equation were slow and cumbersome. But now, several efficient techniques exist which can yield reliable results. Not only has the mathematical theory of water waves helped us to understand and protect our environment, but its insights have also had a significant impact on technological development. Although the solitary wave is now well understood, other water waves still have mysterious effects on our environment and remain objects of active mathematical research. [Back to top] MATHEMATICS, MATHEMATICIANS, & THE ENVIRONMENT Mathematics plays a key role in environmental studies, modeling, etc. Basic mathematics - calculus, percents, ratios, graphs and charts, sequences, sampling, averages, a population growth model, variability and probability - all relate to current, critical issues such as pollution, the availability of resources, environmental clean-up, recycling, CFC's, and population growth. In January of this year the annual winter meeting of the national mathematics societies held theme sessions on Mathematics and the Environment. Several presentations were made. Papers are available on request as described below. Fred Roberts - Department of Mathematics, Rutgers University Moving Traffic So As To Use Less Fuel and Reduce Pollution Two of the ways in which mathematics is used in traffic management are in the phasing of traffic lights and in the design of patterns of one-way streets. Mathematical methods first developed in the early stages of sequencing the DNA molecule have turned out to be useful in deciding when to give different streams of traffic a green light. Related mathematical methods are useful in deciding how to make streets one-way so as to move traffic more efficiently. Robert McKelvey - Department of Mathematics, Univ. of Montana Global Climate Change: How We Set Policy How we deal with uncertainty in making environmental decisions, focusing on some of the interlocking environmental problems of today: 1) global warming; 2) biodiversity and genetic diversity (loss of species); and 3)impending losses of resources (land, energy, clean air, water). Mary Wheeler - Department of Mathematics, Rice University, and Kyle Roberson, Pacific Northwest Laboratories Bio-remediation Modeling: Using Indigenous Organisms to Eliminate Soil Contaminants An explanation of laboratory, field, and simulation work to validate remediation strategies at U.S. Department of Energy sites, such as Hanford, WA. A project goal is to formulate and implement accurate and efficient algorithms for modeling biodegradation processes. Numerical simulation results that utilize realistic data and parallel computational complexity issues are discussed. Simon Levin - Section of Ecology and Systematics, Cornel The Problem of Scale in Ecology: Why this is Important in Resolving Global Problems Global environmental problems have local and regional causes and consequences, such as, linkages between photosynthetic dynamics at the leaf level, regional shifts in forest composition, and global changes in climate and the distribution of greenhouse gases. The fundamental problem is relating processes that are operating on very different scales of space and time. Mathematical methods provide the only way such problems can be approached, and techniques of scaling, aggregation, and simplification are critical. Mathematicians to Contact About the Mathematics of Ocean Waves Mark Ablowitz (303) 492-5502 (direct) Program in Applied Mathematics (303) 492-1411 (univ.) University of Colorado Campus Box 526 Boulder, CO 80309-0526 Jerry Bona (814) 865-7527 (direct) Dept. of Mathematics Pennsylvania State University (814) 865-3735 (fax) 215 McAllister Bldg. University Park, PA 16802 Peter Lax (212) 998-3231 NYU-Courant (212) 998-3000 251 Mercer St., Rm. 912 New York, NY 10012 Alan Newell (602) 621-6893 (dept.) Dept. of Mathematics (602) 621-2868 (direct) University of Arizona (602) 621-8322 (FAX) Tucson, AZ 85721 Norm Zabusky (908) 932-5869 (direct) Dept. of Mechanical & Aero. Engineering (908) 932-0278 Rutgers University P.O. Box 909 Piscataway, NJ 08855-0909 Donald Saari (708) 491-5580 Dept. of Mathematics (708) 491-8906 (fax) Northwestern University Evanston, IL 60201 Susan Freidlander (312) 996-3041 University of Illinois (312) 413-2167 Department of Mathematics Chicago, IL [Back to top] FOR IMMEDIATE RELEASE CONTACT: Kathleen Holmay Date Mailed: April, 1992 MATHEMATICS AWARENESS WEEK, April 26 - May 2, 1992 (Washington, DC) . . . . . Mathematics & The Environment is the theme for Mathematics Awareness Week, which will be observed on college and university campuses, in research laboratories, and in many other places nationwide from April 26 - May 2, 1992. The environmental emphasis is in recognition of the national and international increase in awareness of environmental issues and the key role mathematics plays in analyzing and interpreting environmental data. The health and welfare of Earth relies in large part on the ability to accurately understand and interpret mathematical environmental data in critical areas, such as pollution, global warming, recycling, population growth, and weather predicting. At a national mathematics conference held earlier this year, mathematicians reported on their research in these and other environmental areas. They also reported on new undergraduate courses being offered at mathematics departments which focus on how to study environmental issues. Celebrations of Mathematics Awareness Week will feature proclamations from many of the nation's governors, legislators, and mayors. Colleges and universities across the country have planned competitions, exhibits, demonstrations, lectures and other events to mark the week. The power and beauty of mathematics and the environment are symbolized in the ocean wave, featured on this year's poster and accompanying card. Included is the solitary wave equation, based on Scott Russell's observations of the surface of a canal in 1844. Mathematics Awareness Week is coordinated by the Joint Policy Board for Mathematics which represents three national mathematics organizations, the American Mathematical Society, the Mathematical Association of America, and the Society for Industrial and Applied Mathematics. [Back to top] ```