Our
primary
research
objective
is
to
develop
rapid
and
accurate
numerical
algorithms
and
analytic
techniques
for
devices
and
systems.
In
the
past,
our
main
areas
of
research
have
encompassed
electromagnetic
field
modeling,
especially
electric
field
propagation
in
waveguides
and
fibers,
semiconductor
physics
with
emphasis
on
optical
and
transport
processes
in
heavily
doped
III-V
semiconductors,
underwater
acoustics,
numerical
boundary
conditions
and
wide-angle
methods
for
parabolic
partial
differential
equations.
From
2002-2014
our
research
additionally
centered
on
polarization
effects
in
optical
communications
with
emphasis
on
time
varying
polarization-dependent
component
of
the
transit
times
of
electric
fields
in
optical
fibers
(polarization
mode
dispersion).
These
were
modeled
by
introducing
an
analogy
between
the
probability
density
function
of
communication
systems
and
the
statistical
mechanical
density
of
states
that
led
to
new
methods
based
on
biased
sampling
for
finding
the
bit-error-rate
in
optical
fiber
systems.
Since,
however,
in
large-scale
systems
computing
the
physically
significant
outputs
for
even
a
single
realization
of
the
numerous
underlying
system
variables
often
requires
substantial
resources,
further
optimization
of
multicanonical
and
related
biased
sampling
procedures
is
highly
desirable.
This
motivated
us
to
examine
foundational
aspects
of
these
procedures
as
well
further
refinements
motivated
by
practical
applications.
Recently
we
have
clarified
subtle
issues
inherent
in
the
transition
matrix
method
reformulation
of
biased
sampling
and
have
introduced
several
novel
strategies
for
mitigating
these
accuracy
and
efficiency
problems.
In
particular,
we
have
quantified
the
relationship
between
the
accuracy
of
biased
sampling
procedures
and
the
degree
to
which
these
methods
evenly
sample
all
accessible
regions
of
state
(configuration)
space.
As
well,
my
group
has
recently
been
examining
related
numerical
modeling
issues
in
statistical
and
fluid
mechanics.