161,901 research outputs found
Melting of Hard Cubes
The melting transition of a system of hard cubes is studied numerically both
in the case of freely rotating cubes and when there is a fixed orientation of
the particles (parallel cubes). It is shown that freelly rotating cubes melt
through a first-order transition, whereas parallel cubes have a continuous
transition in which positional order is lost but bond-orientational order
remains finite. This is interpreted in terms of a defect-mediated theory of
meltingComment: 5 pages, 3 figures included. To appear in Phys. Rev.
Toric Cubes
A toric cube is a subset of the standard cube defined by binomial
inequalities. These basic semialgebraic sets are precisely the images of
standard cubes under monomial maps. We study toric cubes from the perspective
of topological combinatorics. Explicit decompositions as CW-complexes are
constructed. Their open cells are interiors of toric cubes and their boundaries
are subcomplexes. The motivating example of a toric cube is the edge-product
space in phylogenetics, and our work generalizes results known for that space.Comment: to appear in Rendiconti del Circolo Matematico di Palermo (special
issue on Algebraic Geometry
EPW Cubes
We construct a new 20-dimensional family of projective 6-dimensional
irreducible holomorphic symplectic manifolds. The elements of this family are
deformation equivalent with the Hilbert scheme of three points on a K3 surface
and are constructed as natural double covers of special codimension 3
subvarieties of the Grassmanian G(3,6). These codimension 3 subvarieties are
defined as Lagrangian degeneracy loci and their construction is parallel to
that of EPW sextics, we call them the EPW cubes. As a consequence we prove that
the moduli space of polarized IHS sixfolds of K3-type, Beauville-Bogomolov
degree 4 and divisibility 2 is unirational.Comment: minor corrections, 25 pages, to appear in J. Reine Angew. Mat
Complexities of Bi-Colored Rubik\u27s Cubes
Which of two bi-colored cubes is the simpler puzzle? The differences in the coloring of the cubes creates different symmetries that dramatically reduce the number of states each cube can reach. Which of the symmetries is most reductive? The answer to these questions can be achieved by discovering and comparing the “God’s Number” for these cubes
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