17,547 research outputs found
Atomic scale lattice distortions and domain wall profiles
We present an atomic scale theory of lattice distortions using strain related
variables and their constraint equations. Our approach connects constrained
{\it atomic length} scale variations to {\it continuum} elasticity and
describes elasticity at several length scales. We apply the approach to a
two-dimensional square lattice with a monatomic basis, and find the elastic
deformations and hierarchical atomic relaxations in the vicinity of a domain
wall between two different homogeneous strain states. We clarify the
microscopic origin of gradient terms, some of which are included
phenomenologically in Ginzburg-Landau theory, by showing that they are
anisotropic.Comment: 6 figure
The one-round Voronoi game replayed
We consider the one-round Voronoi game, where player one (``White'', called
``Wilma'') places a set of n points in a rectangular area of aspect ratio r
<=1, followed by the second player (``Black'', called ``Barney''), who places
the same number of points. Each player wins the fraction of the board closest
to one of his points, and the goal is to win more than half of the total area.
This problem has been studied by Cheong et al., who showed that for large
enough and r=1, Barney has a strategy that guarantees a fraction of 1/2+a,
for some small fixed a.
We resolve a number of open problems raised by that paper. In particular, we
give a precise characterization of the outcome of the game for optimal play: We
show that Barney has a winning strategy for n>2 and r>sqrt{2}/n, and for n=2
and r>sqrt{3}/2. Wilma wins in all remaining cases, i.e., for n>=3 and
r<=sqrt{2}/n, for n=2 and r<=sqrt{3}/2, and for n=1. We also discuss complexity
aspects of the game on more general boards, by proving that for a polygon with
holes, it is NP-hard to maximize the area Barney can win against a given set of
points by Wilma.Comment: 14 pages, 6 figures, Latex; revised for journal version, to appear in
Computational Geometry: Theory and Applications. Extended abstract version
appeared in Workshop on Algorithms and Data Structures, Springer Lecture
Notes in Computer Science, vol.2748, 2003, pp. 150-16
Spin-Coupled Local Distortions in Multiferroic Hexagonal HoMnO3
Local structural measurements have been performed on hexagonal HoMnO3 in
order to ascertain the specific changes in bond distances which accompany
magnetic ordering transitions. The transition from paramagnetic to the
antiferromagetic (noncollinear) phase near ~70 K is dominated by changes in the
a-b plane Mn-Mn bond distances. The spin rotation transition near ~40 K
involves both Mn-Mn and nearest neighbor Ho-Mn interactions while the low
temperature transition below 10 K involves all interactions, Mn-Mn, Ho-Mn
(nearest and next nearest) and Ho-Ho correlations. These changes in bond
distances reveal strong spin-lattice coupling. The similarity in magnitude of
the change in J(Mn-Mn) and J(Ho-Mn) enhances the system frustration. The
structural changes are interpreted in terms of a model of competing spin order
and local structural distortions. Density functional calculations are used to
estimate the energies associated with ionic displacements. The calculations
also reveal asymmetric polarization of the charge density of Ho, O3 and O4
sites along the z-axis in the ferroelectric phase. This polarization
facilitates coupling between Ho atoms on neighboring planes normal to the
z-axis.Comment: 8 figure
The Operator Product Expansion of the Lowest Higher Spin Current at Finite N
For the N=2 Kazama-Suzuki(KS) model on CP^3, the lowest higher spin current
with spins (2, 5/2, 5/2,3) is obtained from the generalized GKO coset
construction. By computing the operator product expansion of this current and
itself, the next higher spin current with spins (3, 7/2, 7/2, 4) is also
derived. This is a realization of the N=2 W_{N+1} algebra with N=3 in the
supersymmetric WZW model. By incorporating the self-coupling constant of lowest
higher spin current which is known for the general (N,k), we present the
complete nonlinear operator product expansion of the lowest higher spin current
with spins (2, 5/2, 5/2, 3) in the N=2 KS model on CP^N space. This should
coincide with the asymptotic symmetry of the higher spin AdS_3 supergravity at
the quantum level. The large (N,k) 't Hooft limit and the corresponding
classical nonlinear algebra are also discussed.Comment: 62 pages; the footnotes added, some redundant appendices removed, the
presentations in the whole paper improved and to appear in JHE
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