| NSF Org: |
DMS Division Of Mathematical Sciences |
| Recipient: |
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| Initial Amendment Date: | August 11, 2011 |
| Latest Amendment Date: | August 11, 2011 |
| Award Number: | 1109030 |
| Award Instrument: | Standard Grant |
| Program Manager: |
Eugene Gartland
DMS Division Of Mathematical Sciences MPS Directorate for Mathematical and Physical Sciences |
| Start Date: | August 15, 2011 |
| End Date: | July 31, 2015 (Estimated) |
| Total Intended Award Amount: | $160,822.00 |
| Total Awarded Amount to Date: | $160,822.00 |
| Funds Obligated to Date: |
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| History of Investigator: |
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| Recipient Sponsored Research Office: |
202 HIMES HALL BATON ROUGE LA US 70803-0001 (225)578-2760 |
| Sponsor Congressional District: |
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| Primary Place of Performance: |
202 HIMES HALL BATON ROUGE LA US 70803-0001 |
| 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: |
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| 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
Almog
1109030
The investigator studies several fundamental theoretical problems of superconductivity. Through analysis of the time-dependent Ginzburg-Landau model, he examines:
1. Critical currents, and bounds on them, associated with the loss of stability of the normal and superconducting states in two and three dimensions.
2. Phase transitions between these states in various circumstances.
3. Critical currents under magnetic field effects near the normal state.
4. Highly nonlinear effects of induced magnetic fields.
Superconductors are metals that at a sufficiently low temperature exhibit two important properties:
1. They lose entirely their electrical resistivity.
2. The magnetic field is excluded from the superconducting area.
Superconductors have great technological potential for applications ranging from magnetic sensors, through generators of large magnetic fields, to high power transmitters. The investigator studies the behavior of superconducting materials near the critical current, the maximum current density which can flow through a superconducting wire with (practically) zero resistance. He focuses on the transition between the normal and superconducting states, how stable these states are, and effects of induced magnetic fields on the critical current. Of particular interest is the disparity between experimental measures of the critical current and theoretical predictions of the critical current in the absence of magnetic fields. Determining the maximal current a superconductor can carry before reverting to the normal state where material resistivity causes energy losses is an important consideration in superconductor technologies. The project sheds light on both the nucleation of superconductivity for decreasing currents, and on the loss of superconducting properties when the electric current increases.
PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH
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PROJECT OUTCOMES REPORT
Disclaimer
This Project Outcomes Report for the General Public is displayed verbatim as submitted by the Principal Investigator (PI) for this award. Any opinions, findings, and conclusions or recommendations expressed in this Report are those of the PI and do not necessarily reflect the views of the National Science Foundation; NSF has not approved or endorsed its content.
It is well known from experimental observations that when a
sufficiently strong current is bing flown through a superconducting
wire the material would revert to the normal state. I have (together
with B. Helffer and X.B. Pan) demonstrated that this fact can be
theoretically explained) by using the time-dependent Ginzburg-Landau
equations: a popular model used in the theoretical study of
superconductivity. Our explanation offers two physical mechanisms that
generate the transition to the normal state. The first of them is the
effect of the magnetic field which the electric current induces, and
the second is the direct effect of the potential. The negative effect
of the magnetic field on superconductivituy has been extensively
studied both theoretically and experimentally, but not when its being
induced by an electric current.
The induced magnetic field plays a significant role in the transition
between the normal and the superconducting states, when the current is
being decreased. I have established (together with B. Helffer and
X. B. Pan) that for electric current densities that are much weaker than the
critical current density at which the normal state looses its stability the
superconducting sample still exhibits significant electrical
resistivity. These results suggest that the overall current a that a
superconducting wire can carry with no (or insignificant) potential
drop, grows proportinally with the wire's cross section perimeter and
not the area as one might expect.
Finally, (together with L. Berlyand, D. Golovaty, and I. Shafrir) I
have established the existence and stability of a fully
superconducting solution to the Ginzburg-Landau equations. So far
these results were proved only when magnetic field effects are
negligible.
Last Modified: 09/23/2015
Modified by: Yaniv Almog
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