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.
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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
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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.
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