29,455 research outputs found
Maximum and Minimum Stable Random Packings of Platonic Solids
Motivated by the relation between particle shape and packing, we measure the
volume fraction occupied by the Platonic solids which are a class of
polyhedron with congruent sides, vertices and dihedral angles. Tetrahedron,
cube, octahedron, dodecahedron, and icosahedron shaped plastic dice were
fluidized or mechanically vibrated to find stable random loose packing
and densest packing , respectively with standard deviation . We find that obtained by all protocols peak at the cube, which is
the only Platonic solid that can tessellate space, and then monotonically
decrease with number of sides. This overall trend is similar but systematically
lower than the maximum reported for frictionless Platonic solids, and
below of spheres for the loose packings. Experiments with ceramic
tetrahedron were also conducted, and higher friction was observed to lead to
lower
Desain Pembelajaran Volume Kubus Dan Balok Menggunakan Filling Dan Packing Di Kelas V
This study was aimed at producing a learning design that can help the students to understand the concept of cube and cuboid volume using the filling and packing method in the fifth grade of the primary school. The approach used was PMRI. The subjects were the students of the fifth grade of MI Ma\u27had Islamy Palembang, South Sumatera. The study used validation study research design. The results show that the learning design is able to help students in understanding the concept of cube and cuboid volume; the contents of cube and cuboid through the activity of filling, the beams have more volume than the cube through comparing, the concept of the cubes and cuboid volume, the volume of a cube through the activity of packing, a formula of cube volume, the volume of the cuboid through the activity of packing, cuboid volume formula, and the conclusing out of cubes and cuboid formulas
A Cubical Flat Torus Theorem and the Bounded Packing Property
We prove the bounded packing property for any abelian subgroup of a group
acting properly and cocompactly on a CAT(0) cube complex. A main ingredient of
the proof is a cubical flat torus theorem. This ingredient is also used to show
that central HNN extensions of maximal free-abelian subgroups of compact
special groups are virtually special, and to produce various examples of groups
that are not cocompactly cubulated.Comment: 14 pages, 2 figures, submitted May 2015 Minor corrections and swapped
sections 2 and 3 Corrected an unfortunate typo in Theorem 2.1 - the
hypothesis that the cube complex be finite dimensional has now been adde
Packing subgroups in relatively hyperbolic groups
We introduce the bounded packing property for a subgroup of a countable
discrete group G. This property gives a finite upper bound on the number of
left cosets of the subgroup that are pairwise close in G. We establish basic
properties of bounded packing, and give many examples; for instance, every
subgroup of a countable, virtually nilpotent group has bounded packing. We
explain several natural connections between bounded packing and group actions
on CAT(0) cube complexes.
Our main result establishes the bounded packing of relatively quasiconvex
subgroups of a relatively hyperbolic group, under mild hypotheses. As an
application, we prove that relatively quasiconvex subgroups have finite height
and width, properties that strongly restrict the way families of distinct
conjugates of the subgroup can intersect. We prove that an infinite,
nonparabolic relatively quasiconvex subgroup of a relatively hyperbolic group
has finite index in its commensurator. We also prove a virtual malnormality
theorem for separable, relatively quasiconvex subgroups, which is new even in
the word hyperbolic case.Comment: 45 pages, 2 figures. To appear in Geom. Topol. v2: Updated to address
concerns of the referee. Added theorem that an infinite, nonparabolic
relatively quasiconvex subgroup H of a relatively hyperbolic group has finite
index in its commensurator. Added several new geometric results to Section 7.
Theorem 8.9 on packing relative to peripheral subgroups is ne
Heterogeneous packing and hydraulic stability of cube and cubipod armor units
This paper describes the heterogeneous packing (HEP) failure mode of breakwater armor. HEP reduces packing density in the armor layer near and above the mean water level and increases packing density below it. With HEP, armor units may move in the armor layer, although they are not actually extracted from it. Thus, when HEP occurs, armor-layer porosity is not constant, and measurements obtained with
conventional methods may underestimate armor damage. In this paper, the Virtual Net method is proposed to calculate armor damage considering both armor-unit extraction and HEP. The Cubipod concrete armor unit is then described as a solution to the effects of HEP on conventional cubic block armor. The hydraulic stability of cube and Cubipod armor units was compared in two-dimensional laboratory experiments. Cube and Cubipod armor layers were tested in two wave flumes under nonbreaking and non-overtopping conditions. The hydraulic stability was higher for double-layer Cubipod armor than for single-layer Cubipod armor, which had a higher hydraulic stability tan conventional double-layer cube armor.The authors are grateful for the financial support of CDTI (CUBIPOD Project), SATO Construction Co. (OHL Group), and Puertos del Estado (Convenio de Diques). The authors also thank Debra Westall for revising the manuscript.Gómez-MartÃn, ME.; Medina, JR. (2014). Heterogeneous packing and hydraulic stability of cube and cubipod armor units. Journal of Waterway, Port, Coastal, and Ocean Engineering. 140(1):100-108. doi:10.1061/(ASCE)WW.1943-5460.0000223S100108140
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