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Office
5532-G
Boelter Hall
Phone
(310)
267-0169
Fax
(310)
206-4107
Email
makis@seas.ucla.edu
RESEARCH
RECENT
PAPERS |
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RESEARCH
Novel
algorithms for fluid simulation.
Monte Carlo
simulations are becoming increasingly important for investigating
systems with properties that cannot be easily obtained using
analytical techniques. The Metropolis method, samples phase space
through local moves of randomly selected particles. The random
selection of a particle ensures that the so-called principle of
detailed balance is satisfied at all times. However, strict detailed
balance is not necessary for Monte Carlo simulations to converge to
equilibrium. In addition, strict detailed balance poses difficulties
in parallel implementations of Monte Carlo simulations. In this
project, we develop new generic algorithms that converge faster than
Metropolis-type of algorithms with purely random moves. Our
algorithms are based on sequential or spatial component updates and
are characterized by the absence of strict detailed balance. The
main advantages of our methods are their simplicity, generality, and
the feasibility of large-scale, parallel processing. The increased
efficiency makes these algorithms ideal for numerical studies of
first- and second-order phase transitions.
Polyelectrolyte solutions.
In this project, we develop simulation techniques to understand the
physical behavior of polyelectrolyte solutions. Although
polyelectrolytes are water-soluble macromolecules, they are seen to
collapse and precipitate in the presence of multivalent counterions.
They also associate with mesoscopic particles (colloids, proteins,
micelles, dendrimers) of opposite charge and form nano-scale
aggregates. For example, negatively charged double-helix DNA wraps
around positively charged histone proteins and forms complexes (nucleosomes).
The key questions in understanding the behavior of polyelectrolyte
solutions include counterion valence, quality of solvent for the
hydrophobic chain backbone, and amount and valence of added salt.
Ionomer
melts.
Ionomers are copolymers containing a small fraction of partially or
fully neutralized ionic groups. Examples constitute lightly
sulfonated polystyrene and copolymers of ethylene with methacrylic
acid. Ionomers form nanometer-size ionic aggregates and network
structures and thus find numerous applications in adhesives,
packaging, thermoplastics and many more. While the existence of
ionic aggregates in ionomers is generally recognized, their size,
internal structure, and distribution are still matters of
considerable uncertainty. In this project, we address the issues of
morphology and network formation in ionomers using Monte Carlo and
Molecular Dynamics simulations. Although substantial progress has
been made in understanding gel formation in polymers with
short-range associating sites, very little is known about the
structures and types of networks formed via ionic cross-links.
Rigid
biopolymer dynamics.
Rigid
biopolymers such as microtubules, actin and intermediate filaments
are major components of the cytoskeleton and the cellular
environment. They play a fundamental role in biological systems by
facilitating cellular transport, cell motility, and reproduction.
Microtubules are rigid, cylindrical tubes of diameter ~ 24 nm that
are composed of 11-15 parallel protofilaments. Tubulins, the basic
subunits from which each protofilament is built, are composed of
alternating α- and β-tubulin monomers. Polymerization and
depolymerization processes of rigid biopolymers have been studied
extensively, both experimentally and theoretically. Most biopolymer
models are comprised of independent and non-interacting
protofilaments, hence lacking inspection on microscopic structure,
geometrical properties of the lattice, and lateral interactions
between adjacent protofilaments. In this project, we develop
stochastic simulation methods in order to understand the dynamic
behavior of these systems. The present research focuses on the
effects of the complex structure of the growing and shrinking end,
the geometrical properties, and the lateral interactions between
adjacent protofilaments on the dynamics of rigid biopolymers.
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