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Award Abstract #1009704

Phase Transitions in Composite Media

NSF Org: DMS
Division Of Mathematical Sciences
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Initial Amendment Date: September 18, 2010
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Latest Amendment Date: September 18, 2010
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Award Number: 1009704
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Award Instrument: Standard Grant
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Program Manager: Victor Roytburd
DMS Division Of Mathematical Sciences
MPS Direct For Mathematical & Physical Scien
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Start Date: September 15, 2010
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End Date: August 31, 2014 (Estimated)
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Awarded Amount to Date: $307,000.00
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Investigator(s): Kenneth Golden golden@math.utah.edu (Principal Investigator)
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Sponsor: University of Utah
75 S 2000 E
SALT LAKE CITY, UT 84112-8930 (801)581-6903
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NSF Program(s): APPLIED MATHEMATICS,
CONDENSED MATTER & MAT THEORY
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Program Reference Code(s): 1303, 9162
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Program Element Code(s): 1266, 1765

ABSTRACT

Golden

DMS-1009704

The investigator and his colleagues conduct fundamental

mathematical and numerical studies of phase transitions in

composite materials, with applications to electrorheological (ER)

fluids and sea ice, which share similar microstructural features.

They develop a statistical mechanics framework in which such

transitions can be studied, and explore random matrix

characterizations of composite microstructures and their

evolution. One central problem to be addressed is the existence

of a critical electric field necessary to induce the fluid/solid

transition in ER fluids. They anticipate that this phenomenon

goes beyond classical phase transitions in statistical mechanics,

representing a new type of transitional mechanism that depends on

a competition between geometrical entropy and electrical energy.

They also study the fluid transport and related microstructural

transition in sea ice, which plays a key role in Earth's climate

system. Such microstructures can be identified with random

matrices, and the investigators study the evolution of

microstructural features with such techniques.

Composite materials arise throughout the physical and

biological sciences and across most types of engineering. One of

the key features of these types of problems is the critical

dependence of the effective material properties on the parameters

characterizing the system. For example, an electrorheological

(ER) fluid is a suspension of particles in a viscous fluid such

as oil. If an applied electric field exceeds a critical value

then the particles form chains and the suspension undergoes a

fluid/solid transition within milliseconds. This electrically

induced transition has been used in applications including next

generation clutches, brakes, micro-fluidic valves, and human

prosthetics. Another example is sea ice, a composite of pure ice

with brine inclusions, which plays a key role in Earth's climate

system. If the temperature exceeds a critical value, then fluid

can flow through the ice. This transition mediates a broad range

of processes in the polar ice packs that are fundamental to

making better predictions of climate change. The investigator

and colleagues conduct fundamental mathematical and numerical

studies of these transitions in ER fluids and sea ice. They

bring to bear sophisticated techniques of theoretical statistical

physics to better understand the behavior of these types of

materials. Through these studies, the investigator anticipates

the development of applications to other high-tech composites and

to other areas critical to our understanding of polar climate

change.

The project is cofunded by the Division of Mathematical Sciences

and the Division of Materials Research.


PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH

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N. B. Murphy and K. M. Golden. "The Ising model and critical behavior of transport in binary composite media," J. Mathematical Physics, v.53, 2012, p. 063506. 

N. B. Murphy and K. M. Golden. "The Ising model and critical behavior of transport in binary composite media," J. Mathematical Physics, v.53, 2012. 

A. Gully, J. Lin, E. Cherkaev, and K. M. Golden. "Bounds on the complex permittivity of polycrystalline composites by analytic continuation," Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences, v.471, 2015, p. 20140702.

C. Hohenegger, B. Alali, K. R. Steffen,D. K. Perovich, and K. M. Golden. "Transition in the fractal geometry of Arctic melt ponds," The Cryosphere, v.6, 2012, p. 1157--116. 

C. Orum, E. Cherkaev and K. M. Golden. "Recovery of inclusion separations in strongly heterogeneous composites from effective property measurements," Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences, v.468, 2012, p. 784-809. 

K. M. Golden, N. B. Murphy, and E. Cherkaev. "Spectral analysis and connectivity of porous microstructures in bone," Journal of Biomechanics, v.44, 2011, p. 337.

N. B. Murphy and K. M. Golden. "The Ising model and critical behavior of transport in binary composite media," J. Mathematical Physics, v.53, 2012, p. 1-25. 

 

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