7,618 research outputs found
Combined 3D thinning and greedy algorithm to approximate realistic particles with corrected mechanical properties
The shape of irregular particles has significant influence on micro- and
macro-scopic behavior of granular systems. This paper presents a combined 3D
thinning and greedy set-covering algorithm to approximate realistic particles
with a clump of overlapping spheres for discrete element method (DEM)
simulations. First, the particle medial surface (or surface skeleton), from
which all candidate (maximal inscribed) spheres can be generated, is computed
by the topological 3D thinning. Then, the clump generation procedure is
converted into a greedy set-covering (SCP) problem.
To correct the mass distribution due to highly overlapped spheres inside the
clump, linear programming (LP) is used to adjust the density of each component
sphere, such that the aggregate properties mass, center of mass and inertia
tensor are identical or close enough to the prototypical particle. In order to
find the optimal approximation accuracy (volume coverage: ratio of clump's
volume to the original particle's volume), particle flow of 3 different shapes
in a rotating drum are conducted. It was observed that the dynamic angle of
repose starts to converge for all particle shapes at 85% volume coverage
(spheres per clump < 30), which implies the possible optimal resolution to
capture the mechanical behavior of the system.Comment: 34 pages, 13 figure
Hyperfine Spin-Two (F=2) Atoms in Three-Dimensional Optical Lattices: Phase Diagrams and Phase Transitions
We consider ultracold matter of spin-2 atoms in optical lattices. We derive
an effective Hamiltonian for the studies of spin ordering in Mott states and
investigate hyperfine spin correlations. Particularly, we diagonalize the
Hamiltonian in an on-site Hilbert space taking into account spin-dependent
interactions and exchange between different sites. We obtain phase diagrams and
quantum phase transitions between various magnetic phases.Comment: 10 pages, 10 figures, published versio
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