1,403 research outputs found
Random projections and the optimization of an algorithm for phase retrieval
Iterative phase retrieval algorithms typically employ projections onto
constraint subspaces to recover the unknown phases in the Fourier transform of
an image, or, in the case of x-ray crystallography, the electron density of a
molecule. For a general class of algorithms, where the basic iteration is
specified by the difference map, solutions are associated with fixed points of
the map, the attractive character of which determines the effectiveness of the
algorithm. The behavior of the difference map near fixed points is controlled
by the relative orientation of the tangent spaces of the two constraint
subspaces employed by the map. Since the dimensionalities involved are always
large in practical applications, it is appropriate to use random matrix theory
ideas to analyze the average-case convergence at fixed points. Optimal values
of the gamma parameters of the difference map are found which differ somewhat
from the values previously obtained on the assumption of orthogonal tangent
spaces.Comment: 15 page
Interaction between static holes in a quantum dimer model on the kagome lattice
A quantum dimer model (QDM) on the kagome lattice with an extensive
ground-state entropy was recently introduced [Phys. Rev. B 67, 214413 (2003)].
The ground-state energy of this QDM in presence of one and two static holes is
investigated by means of exact diagonalizations on lattices containing up to
144 kagome sites. The interaction energy between the holes (at distances up to
7 lattice spacings) is evaluated and the results show no indication of
confinement at large hole separations.Comment: 6 pages, 3 figures. IOP style files included. To appear in J. Phys.:
Condens. Matter, Proceedings of the HFM2003 conference, Grenobl
Dense packing crystal structures of physical tetrahedra
We present a method for discovering dense packings of general convex hard
particles and apply it to study the dense packing behavior of a one-parameter
family of particles with tetrahedral symmetry representing a deformation of the
ideal mathematical tetrahedron into a less ideal, physical, tetrahedron and all
the way to the sphere. Thus, we also connect the two well studied problems of
sphere packing and tetrahedron packing on a single axis. Our numerical results
uncover a rich optimal-packing behavior, compared to that of other continuous
families of particles previously studied. We present four structures as
candidates for the optimal packing at different values of the parameter,
providing an atlas of crystal structures which might be observed in systems of
nano-particles with tetrahedral symmetry
The Entropy of Square-Free Words
Finite alphabets of at least three letters permit the construction of
square-free words of infinite length. We show that the entropy density is
strictly positive and derive reasonable lower and upper bounds. Finally, we
present an approximate formula which is asymptotically exact with rapid
convergence in the number of letters.Comment: 18 page
Stability of the hard-sphere icosahedral quasilattice
The stability of the hard-sphere icosahedral quasilattice is analyzed using
the differential formulation of the generalized effective liquid approximation.
We find that the icosahedral quasilattice is metastable with respect to the
hard-sphere crystal structures. Our results agree with recent findings by
McCarley and Ashcroft [Phys. Rev. B {\bf 49}, 15600 (1994)] carried out using
the modified weighted density approximation.Comment: 15 pages, 2 figures available from authors upon request, (revtex),
submitted to Phys. Rev.
A study of long range order in certain two-dimensional frustrated lattices
We have studied the Heisenberg antiferromagnets on two-dimensional frustrated
lattices, triangular and kagome lattices using linear spin-wave theory. A
collinear ground state ordering is possible if one of the three bonds in each
triangular plaquette of the lattice becomes weaker or frustrated. We study
spiral order in the Heisenberg model along with Dzyaloshinskii-Moriya (DM)
interaction and in the presence of a magnetic field. The quantum corrections to
the ground state energy and sublattice magnetization are calculated
analytically in the case of triangular lattice with nearesr-neighbour
interaction. The corrections depend on the DM interaction strength and the
magnetic field. We find that the DM interaction stabilizes the long-range
order, reducing the effect of quantum fluctuations. Similar conclusions are
reached for the kagome lattice. We work out the linear spin-wave theory at
first with only nearest-neighbour (nn) terms for the kagome lattice. We find
that the nn interaction is not sufficient to remove the effects of low energy
fluctuations. The flat branch in the excitation spectrum becomes dispersive on
addition of furthet neighbour interactions. The ground state energy and the
excitation spectrum have been obtained for various cases.Comment: 18 pages, 9 figure
Exact Solution of an Octagonal Random Tiling Model
We consider the two-dimensional random tiling model introduced by Cockayne,
i.e. the ensemble of all possible coverings of the plane without gaps or
overlaps with squares and various hexagons. At the appropriate relative
densities the correlations have eight-fold rotational symmetry. We reformulate
the model in terms of a random tiling ensemble with identical rectangles and
isosceles triangles. The partition function of this model can be calculated by
diagonalizing a transfer matrix using the Bethe Ansatz (BA). The BA equations
can be solved providing {\em exact} values of the entropy and elastic
constants.Comment: 4 pages,3 Postscript figures, uses revte
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