263 research outputs found
Stability of periodic domain structures in a two-dimensional dipolar model
We investigate the energetic ground states of a model two-phase system with
1/r^3 dipolar interactions in two dimensions. The model exhibits spontaneous
formation of two kinds of periodic domain structure. A striped domain structure
is stable near half filling, but as the area fraction is changed, a transition
to a hexagonal lattice of almost-circular droplets occurs. The stability of the
equilibrium striped domain structure against distortions of the boundary is
demonstrated, and the importance of hexagonal distortions of the droplets is
quantified. The relevance of the theory for physical surface systems with
elastic, electrostatic, or magnetostatic 1/r^3 interactions is discussed.Comment: Revtex (preprint style, 19 pages) + 4 postscript figures. A version
in two-column article style with embedded figures is available at
http://electron.rutgers.edu/~dhv/preprints/index.html#ng_do
Interface dynamics for layered structures
We investigate dynamics of large scale and slow deformations of layered
structures. Starting from the respective model equations for a non-conserved
system, a conserved system and a binary fluid, we derive the interface
equations which are a coupled set of equations for deformations of the
boundaries of each domain. A further reduction of the degrees of freedom is
possible for a non-conserved system such that internal motion of each domain is
adiabatically eliminated. The resulting equation of motion contains only the
displacement of the center of gravity of domains, which is equivalent to the
phase variable of a periodic structure. Thus our formulation automatically
includes the phase dynamics of layered structures. In a conserved system and a
binary fluid, however, the internal motion of domains turns out to be a slow
variable in the long wavelength limit because of concentration conservation.
Therefore a reduced description only involving the phase variable is not
generally justified.Comment: 16 pages; Latex; revtex aps; one figure. Revision: screened coulomb
interaction with coulomb limi
Complex Patterns in Reaction-Diffusion Systems: A Tale of Two Front Instabilities
Two front instabilities in a reaction-diffusion system are shown to lead to
the formation of complex patterns. The first is an instability to transverse
modulations that drives the formation of labyrinthine patterns. The second is a
Nonequilibrium Ising-Bloch (NIB) bifurcation that renders a stationary planar
front unstable and gives rise to a pair of counterpropagating fronts. Near the
NIB bifurcation the relation of the front velocity to curvature is highly
nonlinear and transitions between counterpropagating fronts become feasible.
Nonuniformly curved fronts may undergo local front transitions that nucleate
spiral-vortex pairs. These nucleation events provide the ingredient needed to
initiate spot splitting and spiral turbulence. Similar spatio-temporal
processes have been observed recently in the ferrocyanide-iodate-sulfite
reaction.Comment: Text: 14 pages compressed Postscript (90kb) Figures: 9 pages
compressed Postscript (368kb
Interfaces of Modulated Phases
Numerically minimizing a continuous free-energy functional which yields
several modulated phases, we obtain the order-parameter profiles and
interfacial free energies of symmetric and non-symmetric tilt boundaries within
the lamellar phase, and of interfaces between coexisting lamellar, hexagonal,
and disordered phases. Our findings agree well with chevron, omega, and
T-junction tilt-boundary morphologies observed in diblock copolymers and
magnetic garnet films.Comment: 4 page
From Labyrinthine Patterns to Spiral Turbulence
A new mechanism for spiral vortex nucleation in nongradient reaction
diffusion systems is proposed. It involves two key ingredients: An Ising-Bloch
type front bifurcation and an instability of a planar front to transverse
perturbations. Vortex nucleation by this mechanism plays an important role in
inducing a transition from labyrinthine patterns to spiral turbulence. PACS
numbers: 05.45.+b, 82.20.MjComment: 4 pages uuencoded compressed postscrip
Self-replication and splitting of domain patterns in reaction-diffusion systems with fast inhibitor
An asymptotic equation of motion for the pattern interface in the
domain-forming reaction-diffusion systems is derived. The free boundary problem
is reduced to the universal equation of non-local contour dynamics in two
dimensions in the parameter region where a pattern is not far from the points
of the transverse instabilities of its walls. The contour dynamics is studied
numerically for the reaction-diffusion system of the FitzHugh-Nagumo type. It
is shown that in the asymptotic limit the transverse instability of the
localized domains leads to their splitting and formation of the multidomain
pattern rather than fingering and formation of the labyrinthine pattern.Comment: 9 pages (ReVTeX), 5 figures (postscript). To be published in Phys.
Rev.
Dynamical Ordering of Driven Stripe Phases in Quenched Disorder
We examine the dynamics and stripe formation in a system with competing short
and long range interactions in the presence of both an applied dc drive and
quenched disorder. Without disorder, the system forms stripes organized in a
labyrinth state. We find that, when the disorder strength exceeds a critical
value, an applied dc drive can induce a dynamical stripe ordering transition to
a state that is more ordered than the originating undriven, unpinned pattern.
We show that signatures in the structure factor and transport properties
correspond to this dynamical reordering transition, and we present the dynamic
phase diagram as a function of strengths of disorder and dc drive.Comment: 4 pages, 4 postscript figure
Topography and instability of monolayers near domain boundaries
We theoretically study the topography of a biphasic surfactant monolayer in
the vicinity of domain boundaries. The differing elastic properties of the two
phases generally lead to a nonflat topography of ``mesas'', where domains of
one phase are elevated with respect to the other phase. The mesas are steep but
low, having heights of up to 10 nm. As the monolayer is laterally compressed,
the mesas develop overhangs and eventually become unstable at a surface tension
of about K(dc)^2 (dc being the difference in spontaneous curvature and K a
bending modulus). In addition, the boundary is found to undergo a
topography-induced rippling instability upon compression, if its line tension
is smaller than about K(dc). The effect of diffuse boundaries on these features
and the topographic behavior near a critical point are also examined. We
discuss the relevance of our findings to several experimental observations
related to surfactant monolayers: (i) small topographic features recently found
near domain boundaries; (ii) folding behavior observed in mixed phospholipid
monolayers and model lung surfactants; (iii) roughening of domain boundaries
seen under lateral compression; (iv) the absence of biphasic structures in
tensionless surfactant films.Comment: 17 pages, 9 figures, using RevTeX and epsf, submitted to Phys Rev
Topological correlations in soap froths
Correlation in two-dimensional soap froth is analysed with an effective
potential for the first time. Cells with equal number of sides repel (with
linear correlation) while cells with different number of sides attract (with
NON-bilinear) for nearest neighbours, which cannot be explained by the maximum
entropy argument. Also, the analysis indicates that froth is correlated up to
the third shell neighbours at least, contradicting the conventional ideas that
froth is not strongly correlated.Comment: 10 Pages LaTeX, 6 Postscript figure
Ordering kinetics of stripe patterns
We study domain coarsening of two dimensional stripe patterns by numerically
solving the Swift-Hohenberg model of Rayleigh-Benard convection. Near the
bifurcation threshold, the evolution of disordered configurations is dominated
by grain boundary motion through a background of largely immobile curved
stripes. A numerical study of the distribution of local stripe curvatures, of
the structure factor of the order parameter, and a finite size scaling analysis
of the grain boundary perimeter, suggest that the linear scale of the structure
grows as a power law of time with a craracteristic exponent z=3. We interpret
theoretically the exponent z=3 from the law of grain boundary motion.Comment: 4 pages, 4 figure
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