Abstract

Bias Fields and Pattern Complexity

Martin Glicksman
Florida Institute of Technology

Small
quantities
of
energy
or
mass
released,
or
removed,
at
evolving
interfaces
are
described
as
capillary
bias
fields.
These
scalar
fields
are
in
part
responsible
for
branching
during
dendritic
crystallization
and
for
the
development
of
`chaotic’
patterns
developed
when
immiscible
fluids
interpenetrate.
Bias
fields,
as
weak
energy
sources,
were
initially
discovered
from
crystallite
melting
experiments
in
microgravity,
and
derive
straightforwardly
from
the
well-­-known
Gibbs-­-Thomson-­-
Herring
(Euler-­-Lagrange)
local
equilibrium
condition.
Although
extremely
weak
compared
to
the
ordinary
transport
fields
responsible
for
heat
and
mass
transfer
during
diffusion-­-limited
phase
transformation,
bias
fields
are
found
to
be
deterministically
causal
for
the
onset
of
interfacial
branching
and
pattern
complexity.
Examples
of
capillary
bias
fields
derived
analytically
for
several
starting
shapes
and
comparisons
among
analysis,
simulation,
and
experiments
will
be
discussed.
Although
captured
by
most
numerical
models
of
pattern
forming
systems,
the
4th-­-order
nature
of
bias
fields,
as
the
surface
Laplacian
of
the
interface
potential,
has
obscured
their
identification
and
dynamic
role
in
pattern
formation.