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Dr. Marilyn F. Bishop
Theoretical Condensed Matter Physics, Theoretical Biophysics
In the area of condensed matter physics, the two major thrusts have been (1)
theoretical studies of charge density waves and spin density waves in simple
metals and (2) the theory of superconductivity. The importance of understanding
the properties of simple metals extends well beyond the explanation of a few
phenomena. Different theoretical treatments of electron-electron interactions of
exchange and correlation in an electron gas will lead to different ground
states, and the choice of the ground state one uses can lead to various
predictions of optical and transport properties of a simple metal. This implies
that the simple metals, especially the alkali metals, are a testing ground for
theories of electron gas interactions. Comparison of theory with a large number
of experiments shows that the correct ground state of simple metals must be that
of a charge density wave. Until one can explain the properties of the alkali
metals, the predictions for more complicated systems will also be in question.
In fact, the understanding of the electronic interactions in superconductors
must rely on some of the same principles as found in simple metals.
The work on simple metals has included a theory of the residual resistivity
anisotropy determined in potassium by induced torque measurements, a theory of
electron-phason scattering and an explanation of the low temperature resistivity
of potassium below 1.3 K, including variability from sample to sample,
localization effects in thin potassium wire, effects of charge density waves on
the x-ray band spectra of alkali metals, and the calculation of the Bloch-Grüneisen
functions by the use of series expansions. Current and future work include
Hartree-Fock calculations of spin density waves in one and three dimensional
systems, including the study of spiral and canted spiral spin density wave
states. In the study of superconductivity, my work has involved a study of the
phonon-mediated electron-electron interaction, which is integral to the BCS
theory of superconductivity and is important in the theory of bipolaronic
superconductors, and a theory of the proximity-induced superconducting
transition temperature.
The research in biophysics involves the theoretical study of the kinetics of
polymerization, light scattering, and optical properties of biological polymers.
Kinetic theories, which include the nucleation and growth of polymers, have been
applied to sickle hemoglobin, actin, and collagen. Actin, a fibrous tissue in
muscle and an important component in the structure of cells, undergoes a
polymerization that is complicated by the hydrolysis of ATP to ADP during the
polymerization process. Sickle hemoglobin, which is a mutation of normal
hemoglobin but transports oxygen as does normal hemoglobin, polymerizes only
when deoxygenated, which occurs when delivering oxygen in the capillaries.
Polymerization proceeds through a double nucleation process in which nuclei form
from a solution of hemoglobin molecules (monomers) and once polymers are formed,
nuclei are formed on the surfaces of existing polymers. The work on light
scattering and optical properties of polymers focusses on sickle hemoglobin but
could equally apply to any system in which the polymers are rigid straight
fibers. These include actin, tubulin, intermediate filaments, myosin, collagen,
crystallin, fibrin, and amyloid. Most formulations of light scattering from
particles assume that those particles are dilute, i.e. well separated compared
with the wavelength of light. This work is developing a theoretical formulation
whose validity will range from the dilute to dense concentrations of polymers.
This is especially important in the study of the sickle hemoglobin because the
most physiologically significant regime ranges from intermediate to high
concentration. In sickle hemoglobin, polymers are known to form in spherulitic
arrays known as domains. Recent studies involve calculations of the expected
light scattering from these domains as compared to scattering form individual
polymers, in order to determine the processes involved in the growth and
alignment of polymers in the formation of domains.
Marilyn F. Bishop and Frank A. Ferrone, "Kinetics of Nucleation-Controlled
Polymerization", Biophys. J. 46, 631-644 (1984).
Marilyn F. Bishop, "Calculations of Scattered Light from Rigid Polymers
by Shifrin and Rayleigh- Debye Approximations", Biophys. J. 56,
911-925 (1989).
Mary Eileen Farrell, Marilyn F. Bishop, "Theory of the Proximity-Induced
Superconducting Transition Temperature", Phys. Rev. B 40,
10786-10795 (1989).
Mary Eileen Farrell, Marilyn F. Bishop, N. Kumar, and W.E. Lawrence,
"Theory of the Effects of the Destruction of Localization by Inelastic
Scattering in the Resistivity of Pure Thin Potassium Wires", Phys. Rev.
B 42, 3260-3270 (1990).
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