Results 11 to 20 of about 930 (251)

Constructions of Dense Lattices of Full Diversity

Trends in Computational and Applied Mathematics, 2020
A lattice construction using Z-submodules of rings of integers of number fields is presented. The construction yields rotated versions of the laminated lattices A_n for n = 2,3,4,5,6, which are the densest lattices in their respective dimensions.
A. A. Andrade, A. J. Ferrari, J. C. Interlando, R. R. Araujo   +3 more
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A colloidal viewpoint on the sausage catastrophe and the finite sphere packing problem

Nature Communications, 2023
It is commonly believed that the most efficient way to pack a finite number of equal-sized spheres is by arranging them tightly in a cluster. However, mathematicians have conjectured that a linear arrangement may actually result in the densest packing ...
Susana Marín-Aguilar, Fabrizio Camerin, Stijn van der Ham, Andréa Feasson, Hanumantha Rao Vutukuri, Marjolein Dijkstra   +5 more
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Finite sphere packing and sphere covering [PDF]

Discrete & Computational Geometry, 1989
By a convex body we mean a compact convex subset of Euclidean d-space with non-empty interior. Let k be a given positive integer. A central problem of finite packing and covering is to find (A) the minimum volume of all convex bodies containing a packing of k unit balls, and (B) the maximum volume of all convex bodies that can be covered by k unit ...
Wills, J.M., Tóth, Fejes G., Gritzmann, P.   +2 more
openaire   +1 more source

ON THE HARD SPHERE MODEL AND SPHERE PACKINGS IN HIGH DIMENSIONS

Forum of Mathematics, Sigma, 2019
We prove a lower bound on the entropy of sphere packings of $\mathbb{R}^{d}$ of density $\unicode[STIX]{x1D6E9}(d\cdot 2^{-d})$. The entropy measures how plentiful such packings are, and our result is significantly stronger than the trivial lower bound ...
MATTHEW JENSSEN, FELIX JOOS, WILL PERKINS   +2 more
doaj   +1 more source

Online circle and sphere packing [PDF]

Theoretical Computer Science, 2018
In the Online Circle Packing in Squares, circles arrive one at a time and we need to pack them into the minimum number of unit square bins. We improve the previous best-known competitive ratio for the bounded space version from 2.439 to 2.3536 and we also give an unbounded space algorithm.
Carla Negri Lintzmayer, Flávio Keidi Miyazawa, Eduardo Candido Xavier   +2 more
openaire   +3 more sources

Investigation of pore-scale random porous media using lattice boltzmann method [PDF]

Journal of Heat and Mass Transfer Research, 2015
The permeability and tortuosity of pore-scale two and three-dimensional random porous media were calculated using the Lattice Boltzmann method (LBM). Effects of geometrical parameters of medium on permeability and tortuosity were investigated as well ...
Alireza Azhdari Heravi, Farhad Talebi, Mohmmad Sadegh Valipour   +2 more
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A FORMAL PROOF OF THE KEPLER CONJECTURE

Forum of Mathematics, Pi, 2017
This article describes a formal proof of the Kepler conjecture on dense sphere packings in a combination of the HOL Light and Isabelle proof assistants. This paper constitutes the official published account of the now completed Flyspeck project.
THOMAS HALES, MARK ADAMS, GERTRUD BAUER, TAT DAT DANG, JOHN HARRISON, LE TRUONG HOANG, CEZARY KALISZYK, VICTOR MAGRON, SEAN MCLAUGHLIN, TAT THANG NGUYEN, QUANG TRUONG NGUYEN, TOBIAS NIPKOW, STEVEN OBUA, JOSEPH PLESO, JASON RUTE, ALEXEY SOLOVYEV, THI HOAI AN TA, NAM TRUNG TRAN, THI DIEP TRIEU, JOSEF URBAN, KY VU, ROLAND ZUMKELLER   +21 more
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Simulation of Ultrasonic Backscattering in Polycrystalline Microstructures

Acoustics, 2022
Ultrasonic testing of polycrystalline media relies heavily on simulation of the expected signals in order to detect and correctly interpret deviations due to defects. Many effects disturb ultrasonic waves propagating in polycrystalline media. One of them
Dascha Dobrovolskij, Katja Schladitz
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(Dis)continuous shear thickening in frictionless granular media? [PDF]

EPJ Web of Conferences
Continuous and discontinuous shear thickening are commonly observed in sheared dense suspensions but are still not fully understood. Although micro-friction at particle-particle contacts is widely accepted as the dominating origin of discontinuous shear ...
Shi Hao, Ilhan Beybin, Duits Michael H.G., Luding Stefan   +3 more
doaj   +1 more source

Methodology to Solve Multi-Dimentional Sphere Packing Problems [PDF]

Journal of Mechanical Engineering, 2019
This paper discusses the problem of optimally packing spheres of various dimensions into containers of arbitrary geometrical shapes. According to the international classification, this problem belongs to Sphere Packing Problems (SPPs).
Georgiy N. Yaskov
doaj   +1 more source