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

Topological defects, pattern evolution, and hysteresis in thin magnetic films

Nature of the magnetic hysteresis for thin films is studied by the Monte-Carlo simulations. It is shown that a reconstruction of the magnetization pattern with external field occurs via the creation of vortex-antivortex pairs of a special kind at the boundaries of stripe domains. It is demonstrated that the symmetry of order parameter is of primary importance for this problem, in particular, the in-plane magnetic anisotropy is necessary for the hysteresis.Comment: Accepted to EPL; 7 pages, 3 color figure

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

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

Non-equilibrium raft-like membrane domains under continuous recycling

We present a model for the kinetics of spontaneous membrane domain (raft) assembly that includes the effect of membrane recycling ubiquitous in living cells. We show that the domains have a broad power-law distribution with an average radius that scales with the 1/4 power of the domain lifetime when the line tension at the domain edges is large. For biologically reasonable recycling and diffusion rates the average domain radius is in the tens of nm range, consistent with observations. This represents one possible link between signaling (involving rafts) and traffic (recycling) in cells. Finally, we present evidence that suggests that the average raft size may be the same for all scale-free recycling schemes.Comment: 8 pages, 5 figure

Surface states in nearly modulated systems

A Landau model is used to study the phase behavior of the surface layer for magnetic and cholesteric liquid crystal systems that are at or near a Lifshitz point marking the boundary between modulated and homogeneous bulk phases. The model incorporates surface and bulk fields and includes a term in the free energy proportional to the square of the second derivative of the order parameter in addition to the usual term involving the square of the first derivative. In the limit of vanishing bulk field, three distinct types of surface ordering are possible: a wetting layer, a non-wet layer having a small deviation from bulk order, and a different non-wet layer with a large deviation from bulk order which decays non-monotonically as distance from the wall increases. In particular the large deviation non-wet layer is a feature of systems at the Lifshitz point and also those having only homogeneous bulk phases.Comment: 6 pages, 7 figures, submitted to 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

Interfaces and Grain Boundaries of Lamellar Phases

Interfaces between lamellar and disordered phases, and grain boundaries within lamellar phases, are investigated employing a simple Landau free energy functional. The former are examined using analytic, approximate methods in the weak segregation limit, leading to density profiles which can extend over many wavelengths of the lamellar phase. The latter are studied numerically and exactly. We find a change from smooth chevron configurations typical of small tilt angles to distorted omega configurations at large tilt angles in agreement with experiment.Comment: 9 pages, 6 figures 9 pages, 6 figure

Magnetic Domain Patterns Depending on the Sweeping Rate of Magnetic Fields

The domain patterns in a thin ferromagnetic film are investigated in both experiments and numerical simulations. Magnetic domain patterns under a zero field are usually observed after an external magnetic field is removed. It is demonstrated that the characteristics of the domain patterns depend on the decreasing rate of the external field, although it can also depend on other factors. Our numerical simulations and experiments show the following properties of domain patterns: a sea-island structure appears when the field decreases rapidly from the saturating field to the zero field, while a labyrinth structure is observed for a slowly decreasing field. The mechanism of the dependence on the field sweeping rate is discussed in terms of the concepts of crystallization.Comment: 4 pages, 3 figure

Stable crystalline lattices in two-dimensional binary mixtures of dipolar particles

The phase diagram of binary mixtures of particles interacting via a pair potential of parallel dipoles is computed at zero temperature as a function of composition and the ratio of their magnetic susceptibilities. Using lattice sums, a rich variety of different stable crystalline structures is identified including $A_mB_n$ structures. [$A$ $(B)$ particles correspond to large (small) dipolar moments.] Their elementary cells consist of triangular, square, rectangular or rhombic lattices of the $A$ particles with a basis comprising various structures of $A$ and $B$ particles. For small (dipolar) asymmetry there are intermediate $AB_2$ and $A_2B$ crystals besides the pure $A$ and $B$ triangular crystals. These structures are detectable in experiments on granular and colloidal matter.Comment: 6 pages - 2 figs - phase diagram update