11,067 research outputs found
Geometry of polycrystals and microstructure
We investigate the geometry of polycrystals, showing that for polycrystals
formed of convex grains the interior grains are polyhedral, while for
polycrystals with general grain geometry the set of triple points is small.
Then we investigate possible martensitic morphologies resulting from intergrain
contact. For cubic-to-tetragonal transformations we show that homogeneous
zero-energy microstructures matching a pure dilatation on a grain boundary
necessarily involve more than four deformation gradients. We discuss the
relevance of this result for observations of microstructures involving second
and third-order laminates in various materials. Finally we consider the more
specialized situation of bicrystals formed from materials having two
martensitic energy wells (such as for orthorhombic to monoclinic
transformations), but without any restrictions on the possible microstructure,
showing how a generalization of the Hadamard jump condition can be applied at
the intergrain boundary to show that a pure phase in either grain is impossible
at minimum energy.Comment: ESOMAT 2015 Proceedings, to appea
On generalized Kneser hypergraph colorings
In Ziegler (2002), the second author presented a lower bound for the
chromatic numbers of hypergraphs \KG{r}{\pmb s}{\calS}, "generalized
-uniform Kneser hypergraphs with intersection multiplicities ." It
generalized previous lower bounds by Kriz (1992/2000) for the case without intersection multiplicities, and by Sarkaria (1990) for
\calS=\tbinom{[n]}k. Here we discuss subtleties and difficulties that arise
for intersection multiplicities :
1. In the presence of intersection multiplicities, there are two different
versions of a "Kneser hypergraph," depending on whether one admits hypergraph
edges that are multisets rather than sets. We show that the chromatic numbers
are substantially different for the two concepts of hypergraphs. The lower
bounds of Sarkaria (1990) and Ziegler (2002) apply only to the multiset
version.
2. The reductions to the case of prime in the proofs Sarkaria and by
Ziegler work only if the intersection multiplicities are strictly smaller than
the largest prime factor of . Currently we have no valid proof for the lower
bound result in the other cases.
We also show that all uniform hypergraphs without multiset edges can be
represented as generalized Kneser hypergraphs.Comment: 9 pages; added examples in Section 2; added reference ([11]),
corrected minor typos; to appear in J. Combinatorial Theory, Series
Chiral d-wave superconductivity in doped graphene
A highly unconventional superconducting state with a spin-singlet
-wave, or chiral d-wave, symmetry has recently been
proposed to emerge from electron-electron interactions in doped graphene.
Especially graphene doped to the van Hove singularity at 1/4 doping, where the
density of states diverges, has been argued to likely be a chiral d-wave
superconductor. In this review we summarize the currently mounting theoretical
evidence for the existence of a chiral d-wave superconducting state in
graphene, obtained with methods ranging from mean-field studies of effective
Hamiltonians to angle-resolved renormalization group calculations. We further
discuss multiple distinctive properties of the chiral d-wave superconducting
state in graphene, as well as its stability in the presence of disorder. We
also review means of enhancing the chiral d-wave state using proximity-induced
superconductivity. The appearance of chiral d-wave superconductivity is
intimately linked to the hexagonal crystal lattice and we also offer a brief
overview of other materials which have also been proposed to be chiral d-wave
superconductors.Comment: 51 pages, 8 figures. Invited topical review in J. Phys.:Condens.
Matte
Effects of different closures for thickness diffusivity
The effects of spatial variations of the thickness diffusivity (K) appropriate to the parameterisation of [Gent, P.R. and McWilliams, J.C., 1990. Isopycnal mixing in ocean circulation models. J. Phys. Oceanogr., 20, 150–155.] are assessed in a coarse resolution global ocean general circulation model. Simulations using three closures yielding different lateral and/or vertical variations in K are compared with a simulation using a constant value. Although the effects of changing K are in general small and all simulations remain biased compared to observations, we find systematic local sensitivities of the simulated circulation on K. In particular, increasing K near the surface in the tropical ocean lifts the depth of the equatorial thermocline, the strength of the Antarctic Circumpolar Current decreases while the subpolar and subtropical gyre transports in the North Atlantic increase by increasing K locally. We also find that the lateral and vertical structure of K given by a recently proposed closure reduces the negative temperature biases in the western North Atlantic by adjusting the pathways of the Gulf Stream and the North Atlantic Current to a more realistic position
Data depth and floating body
Little known relations of the renown concept of the halfspace depth for
multivariate data with notions from convex and affine geometry are discussed.
Halfspace depth may be regarded as a measure of symmetry for random vectors. As
such, the depth stands as a generalization of a measure of symmetry for convex
sets, well studied in geometry. Under a mild assumption, the upper level sets
of the halfspace depth coincide with the convex floating bodies used in the
definition of the affine surface area for convex bodies in Euclidean spaces.
These connections enable us to partially resolve some persistent open problems
regarding theoretical properties of the depth
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