
NSF Org: |
DMS Division Of Mathematical Sciences |
Recipient: |
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Initial Amendment Date: | March 25, 1999 |
Latest Amendment Date: | April 25, 2001 |
Award Number: | 9876820 |
Award Instrument: | Continuing Grant |
Program Manager: |
Henry Warchall
DMS Division Of Mathematical Sciences MPS Directorate for Mathematical and Physical Sciences |
Start Date: | July 1, 1999 |
End Date: | June 30, 2002 (Estimated) |
Total Intended Award Amount: | $115,499.00 |
Total Awarded Amount to Date: | $115,499.00 |
Funds Obligated to Date: |
FY 2000 = $38,500.00 FY 2001 = $38,499.00 |
History of Investigator: |
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Recipient Sponsored Research Office: |
107 S INDIANA AVE BLOOMINGTON IN US 47405-7000 (317)278-3473 |
Sponsor Congressional District: |
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Primary Place of Performance: |
107 S INDIANA AVE BLOOMINGTON IN US 47405-7000 |
Primary Place of
Performance Congressional District: |
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Unique Entity Identifier (UEI): |
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Parent UEI: |
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NSF Program(s): | APPLIED MATHEMATICS |
Primary Program Source: |
01000102DB NSF RESEARCH & RELATED ACTIVIT app-0199 |
Program Reference Code(s): |
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Program Element Code(s): |
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Award Agency Code: | 4900 |
Fund Agency Code: | 4900 |
Assistance Listing Number(s): | 47.049 |
ABSTRACT
A "collisionless" plasma is a fully ionized gas in which
electromagnetic forces dominate collisional effects. The motion of a
high temperature, low density collisionless plasma is described by
the Vlasov-Maxwell equations, a nonlinear system of partial
differential equations. The major question to be addressed is this:
are there shocks in a collisionless plasma? That is, could a
singularity develop from smoothly prescribed initial values as time
progresses? Additionally, "induction heating" will be studied. In
this area one investigates how a conductive material is heated by
using electromagnetic waves. Microwave heating is a particular
example.
"Plasmas" are often called the fourth state of matter (after solids,
liquids and gases). Plasmas account for a huge proportion of the
material in the universe. Famous examples of plasmas include the
solar wind, the ionosphere, galactic nebulae and comet tails. The
motion of a plasma is described by a number of complicated equations
dictated by physics. The mathematician's goal is to show that these
equations have solutions, at least under certain conditions. This is
the main thrust of the proposal. A completely different application
to be studied is called "induction heating." Here one tries to
determine how various materials can be heated by passing
electromagnetic waves through them. The microwave heating of food
is a particular example.
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