Victor Roytburd DMS Division Of Mathematical Sciences
MPS Direct For Mathematical & Physical Scien
September 15, 2010
August 31, 2014 (Estimated)
Awarded Amount to Date:
Kenneth Golden email@example.com (Principal Investigator)
University of Utah
75 S 2000 E
SALT LAKE CITY, UT
CONDENSED MATTER & MAT THEORY
Program Reference Code(s):
Program Element Code(s):
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
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.