3 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
Striped periodic minimizers of a two-dimensional model for martensitic phase transitions
In this paper we consider a simplified two-dimensional scalar model for the
formation of mesoscopic domain patterns in martensitic shape-memory alloys at
the interface between a region occupied by the parent (austenite) phase and a
region occupied by the product (martensite) phase, which can occur in two
variants (twins). The model, first proposed by Kohn and Mueller, is defined by
the following functional: where
is periodic in and almost everywhere.
Conti proved that if then the minimal specific
energy scales like ,
as . In the regime , we improve Conti's results, by computing exactly the
minimal energy and by proving that minimizers are periodic one-dimensional
sawtooth functions.Comment: 29 pages, 3 figure
On the absence of ferromagnetism in typical 2D ferromagnets
We consider the Ising systems in dimensions with nearest-neighbor
ferromagnetic interactions and long-range repulsive (antiferromagnetic)
interactions which decay with a power, , of the distance. The physical
context of such models is discussed; primarily this is and where,
at long distances, genuine magnetic interactions between genuine magnetic
dipoles are of this form. We prove that when the power of decay lies above
and does not exceed , then for all temperatures, the spontaneous
magnetization is zero. In contrast, we also show that for powers exceeding
(with ) magnetic order can occur.Comment: 15 pages, CMP style fil