169 research outputs found
Wind tunnel model surface gauge for measuring roughness
The optical inspection of surface roughness research has proceeded along two different lines. First, research into a quantitative understanding of light scattering from metal surfaces and into the appropriate models to describe the surfaces themselves. Second, the development of a practical instrument for the measurement of rms roughness of high performance wind tunnel models with smooth finishes. The research is summarized, with emphasis on the second avenue of research
Competition Between Exchange and Anisotropy in a Pyrochlore Ferromagnet
The Ising-like spin ice model, with a macroscopically degenerate ground
state, has been shown to be approximated by several real materials. Here we
investigate a model related to spin ice, in which the Ising spins are replaced
by classical Heisenberg spins. These populate a cubic pyrochlore lattice and
are coupled to nearest neighbours by a ferromagnetic exchange term J and to the
local axes by a single-ion anisotropy term D. The near neighbour spin
ice model corresponds to the case D/J infinite. For finite D/J we find that the
macroscopic degeneracy of spin ice is broken and the ground state is
magnetically ordered into a four-sublattice structure. The transition to this
state is first-order for D/J > 5 and second-order for D/J < 5 with the two
regions separated by a tricritical point. We investigate the magnetic phase
diagram with an applied field along [1,0,0] and show that it can be considered
analogous to that of a ferroelectric.Comment: 7 pages, 4 figure
Lower Bounds and Series for the Ground State Entropy of the Potts Antiferromagnet on Archimedean Lattices and their Duals
We prove a general rigorous lower bound for
, the exponent of the ground state
entropy of the -state Potts antiferromagnet, on an arbitrary Archimedean
lattice . We calculate large- series expansions for the exact
and compare these with our lower bounds on
this function on the various Archimedean lattices. It is shown that the lower
bounds coincide with a number of terms in the large- expansions and hence
serve not just as bounds but also as very good approximations to the respective
exact functions for large on the various lattices
. Plots of are given, and the general dependence on
lattice coordination number is noted. Lower bounds and series are also
presented for the duals of Archimedean lattices. As part of the study, the
chromatic number is determined for all Archimedean lattices and their duals.
Finally, we report calculations of chromatic zeros for several lattices; these
provide further support for our earlier conjecture that a sufficient condition
for to be analytic at is that is a regular
lattice.Comment: 39 pages, Revtex, 9 encapsulated postscript figures, to appear in
Phys. Rev.
Topology by Design in Magnetic nano-Materials: Artificial Spin Ice
Artificial Spin Ices are two dimensional arrays of magnetic, interacting
nano-structures whose geometry can be chosen at will, and whose elementary
degrees of freedom can be characterized directly. They were introduced at first
to study frustration in a controllable setting, to mimic the behavior of spin
ice rare earth pyrochlores, but at more useful temperature and field ranges and
with direct characterization, and to provide practical implementation to
celebrated, exactly solvable models of statistical mechanics previously devised
to gain an understanding of degenerate ensembles with residual entropy. With
the evolution of nano--fabrication and of experimental protocols it is now
possible to characterize the material in real-time, real-space, and to realize
virtually any geometry, for direct control over the collective dynamics. This
has recently opened a path toward the deliberate design of novel, exotic
states, not found in natural materials, and often characterized by topological
properties. Without any pretense of exhaustiveness, we will provide an
introduction to the material, the early works, and then, by reporting on more
recent results, we will proceed to describe the new direction, which includes
the design of desired topological states and their implications to kinetics.Comment: 29 pages, 13 figures, 116 references, Book Chapte
Asymptotic Limits and Zeros of Chromatic Polynomials and Ground State Entropy of Potts Antiferromagnets
We study the asymptotic limiting function , where is the chromatic polynomial for a graph
with vertices. We first discuss a subtlety in the definition of
resulting from the fact that at certain special points , the
following limits do not commute: . We then
present exact calculations of and determine the corresponding
analytic structure in the complex plane for a number of families of graphs
, including circuits, wheels, biwheels, bipyramids, and (cyclic and
twisted) ladders. We study the zeros of the corresponding chromatic polynomials
and prove a theorem that for certain families of graphs, all but a finite
number of the zeros lie exactly on a unit circle, whose position depends on the
family. Using the connection of with the zero-temperature Potts
antiferromagnet, we derive a theorem concerning the maximal finite real point
of non-analyticity in , denoted and apply this theorem to
deduce that and for the square and
honeycomb lattices. Finally, numerical calculations of and
are presented and compared with series expansions and bounds.Comment: 33 pages, Latex, 5 postscript figures, published version; includes
further comments on large-q serie
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