scholarly journals Algorithms of optimal ball packing into ellipsoids

2018 ◽  
Vol 52 ◽  
pp. 59-74
Author(s):  
P.L. Lebebev ◽  
◽  
N.G. Lavrov ◽  
◽  
◽  
...  
Keyword(s):  
Ball Packing

scholarly journals Top dense hyperbolic ball packings and coverings for complete coxeter orthoscheme groups

2018 ◽  
Vol 103 (117) ◽  
pp. 129-146
Author(s):  
Emil Molnár ◽  
Jenő Szirmai
Keyword(s):  
Hyperbolic Space ◽  
Coxeter Group ◽  
Upper Bound ◽  
Dihedral Angles ◽  
Ball Packings ◽  
Ball Packing ◽  
Packing Densities

In n-dimensional hyperbolic space Hn (n > 2), there are three types of spheres (balls): the sphere, horosphere and hypersphere. If n = 2, 3 we know a universal upper bound of the ball packing densities, where each ball?s volume is related to the volume of the corresponding Dirichlet-Voronoi (D-V) cell. E.g., in H3 a densest (not unique) horoball packing is derived from the {3,3,6} Coxeter tiling consisting of ideal regular simplices T? reg with dihedral angles ?/3. The density of this packing is ??3 ? 0.85328 and this provides a very rough upper bound for the ball packing densities as well. However, there are no ?essential" results regarding the ?classical" ball packings with congruent balls, and for ball coverings either. The goal of this paper is to find the extremal ball arrangements in H3 with ?classical balls". We consider only periodic congruent ball arrangements (for simplicity) related to the generalized, so-called complete Coxeter orthoschemes and their extended groups. In Theorems 1.1 and 1.2 we formulate also conjectures for the densest ball packing with density 0.77147... and the loosest ball covering with density 1.36893..., respectively. Both are related with the extended Coxeter group (5,3,5) and the so-called hyperbolic football manifold. These facts can have important relations with fullerenes in crystallography.

Bestimmung der transitiven optimalen Kugelpackungen

2002 ◽  
Vol 39 (3-4) ◽  
pp. 443-483
Author(s):  
I. Molnár ◽  
I. Prok ◽  
J. Szirmai
Keyword(s):  
Fundamental Domain ◽  
Complete List ◽  
Orbit Type ◽  
Space Group ◽  
Space Groups ◽  
Wyckoff Position ◽  
Ball Packing ◽  
Orbit Types

Each of the 7 Coxeter space groups in BE3 can be extended by the possible symmetries of its fundamental domain. Thus, we get a space group G in the title. For any orbit type (Wyckoff position) of G the optimal ball packing and its D-V cell have been determined, described and enumerated in tables and figures. We make a complete list for all the orbit types of the 29 generalized Coxeter space groups above.

PEMEKATAN ETANOL DENGAN METODE STRIPPING MENGGUNAKAN GAS NITROGEN DAN UDARA

EKUILIBIUM ◽  
2014 ◽  
Vol 13 (2) ◽  
Author(s):  
Enny Kriswiyanti
Keyword(s):  
Flow Rate ◽  
Gas Flow ◽  
Average Diameter ◽  
Gas Stripping ◽  
Gas Flow Rate ◽  
Packing Materials ◽  
Optimum Result ◽  
Raschig Ring ◽  
Ball Packing ◽  
Fuel Grade Ethanol

<p>Abstract: Nowadays, the use of ethanol as an alternative fuel in Indonesia is less attractive than<br />fossil fuel because its price is relatively high due to the high cost of purification process. While<br />the fuel grade ethanol must have a very high purity. That’s why another low costed way to purify<br />ethanol is needed, in this research we used stripping method. The focus of this research are the<br />optimum conditions such as the type of stripping gas, stripping gas flow rate, and the type of<br />packing material. The research was conducted with a packed stripper. The variables used in this<br />research is the type of stripping gas (nitrogen and air), stripping gas flow rate (air : 67,5 ml/s; 90<br />ml/s; 112,5 ml/s and nitrogen: 61,16 ml/s; 70,02 ml/s; 92,87ml/s), the type of packing materials<br />(ball packing with average diameter of 1,5 cm and a 5/12 inch diameter raschig ring; average<br />length of 1,5 cm), while the ethanol flow rate of 29,14 ml/s and 48 cm packing height are not<br />changed during the process. The optimum result shown in the nitrogen gas flow rate of 77,02<br />ml/s with packing materials raschig ring, for 85,31%.<br />Keywords: ethanol, stripping, nitrogen, packed stripper</p>

scholarly journals Computer 3D-simulation of the temperature and diffusion kinetics of SHS in the closest packing of Ni@Al “core-shell” mesocells for modes with variable values of the key ignition parameters

2021 ◽  
Vol 2142 (1) ◽  
pp. 012015
Author(s):  
I A Shmakov ◽  
V I Jordan
Keyword(s):  
Combustion Wave ◽  
3D Simulation ◽  
Core Shell ◽  
Test Model ◽  
Diffusion Kinetics ◽  
Preliminary Heating ◽  
Model Cluster ◽  
Ball Packing ◽  
Kinetics Of ◽  
And Diffusion

Abstract The paper presents the results of computer 3D-simulation of the temperature and diffusion kinetics of SHS in a test model cluster of Ni-Al particles for modes with variable values of the key parameters of the SHS combustion wave ignition. The key parameters for the SHS combustion wave ignition were chosen as follows: the initial temperature for preliminary heating of the Ni-Al particles mixture, the ignition temperature of the combustion wave in the mixture of Ni-Al particles, the duration of the action of the heat pulse until the combustion wave ignition, and the thickness of the ignited layer in the mixture of particles. A program has been created to generate a test model cluster in the form of the closest ball packing of the Ni@Al “core-shell” mesocells (CBP-structure cluster of the Ni@Al “core-shell” mesocells). Using such a CBP-structure cluster, was continued a testing of created software package intended for 3D-simulation of SHS macrokinetics in a heterogeneous particle mixture, taking into account parallel MPI-calculations. In addition, the value ranges of the key parameters of the SHS combustion wave ignition for which the simulation results are in adequate agreement with the experimental data are determined as the parameters of the program model for SHS-simulation. The results of computational experiments have shown that diffusion kinetics is interrelated with temperature kinetics, and in mesocells with different locations within the CBP-structure cluster, the formation of intermetallic phases occurs inhomogeneously.

scholarly journals Pemodelan perpindahan massa ekstraksi kolom isian dengan distribusi ukuran tetesan

2018 ◽  
Vol 10 (2) ◽  
pp. 81
Author(s):  
Iwan Ridwan
Keyword(s):  
Mass Transfer ◽  
Droplet Size ◽  
Packed Column ◽  
Distribution Model ◽  
Transfer Model ◽  
Glass Ball ◽  
Dispersion Phase ◽  
Raschig Ring ◽  
Droplet Distribution ◽  
Ball Packing

Mass transfer modeling of extraction in a packed bed with droplet size distribution The evaluation of liquid extraction packed column is not able yet to give a satisfying result caused by constant spherical droplet size assumption. Droplet size from dispersion phase that is not homogeneous causes column calculation approach with assumption form of droplet haves the character of constant cannot be applied again. The goal of this research is to build droplet distribution model and mass transfer model at various heights of extraction column both in continuous phase and in dispersion phase. Droplet distribution model is more accurately applied to describe droplet breaks distribution for extraction in glass ball packed column with average of errors 4.53% compared to raschig ring packed column with average error of 11.52 %. At glass ball packing, the mass transfer modeling with total droplet has errors average to 57.67% while at raschig ring packing the model has errors average to 121.38%. Glass ball packing column model has smaller mean errors compared to raschig ring packing column because the glass ball packing form is more regular than the raschig ring packing. The amount of error between the mass transfer models and the experiment is caused by difference of the initial number of droplets that exit from the nozzle in the half circle column and in the full circle column. Keyword: extraction, packed column, droplet distribution model, mass transfer model AbstrakUkuran tetesan dari fasa dispersi yang tidak homogen menyebabkan pendekatan perhitungan kolom dengan asumsi bentuk tetesan bersifat konstan tidak dapat digunakan lagi. Tujuan dari penelitian ini adalah untuk membangun model distribusi tetesan dan model perpindahan massa pada berbagai ketinggian kolom ekstraksi baik di fasa kontinu maupun di fasa dispersi. Model distribusi tetesan lebih tepat digunakan untuk memodelkan fraksi tetesan pecah hasil penelitian pada ekstraksi kolom isian bola kaca dengan rata-rata error sebesar 4,53% dibandingkan dengan kolom isian raschig ring yang mempunyai error sebesar 11,52 Pada isian bola kaca pemodelan perpindahan massa dengan tetesan total mempunyai error rata-rata sebesar 57,67% sedangkan pada isian raschig ring mempunyai error rata-rata sebesar 121,38%. Model kolom isian bola kaca mempunyai error rata-rata yang lebih kecil dibandingkan dengan kolom kolom isian raschig ring, dikarenakan model isian bola kaca bentuknya lebih beraturan dibanding dengan kolom isian raschig ring yang bentuknya lebih tidak beraturan. Besarnya error perpindahan massa antara model dengan percobaan disebabkan oleh tidak samanya jumlah tetesan awal pada kolom setengah lingkaran dengan jumlah tetesan awal pada kolom lingkaran penuh.Kata kunci : ekstraksi,kolom isian, model distribusi tetesan, model perpindahan massa

scholarly journals New Lower Bound for the Optimal Ball Packing Density in Hyperbolic 4-Space

2014 ◽  
Vol 53 (1) ◽  
pp. 182-198 ◽  
Author(s):  
Robert Thijs Kozma ◽  
Jenő Szirmai
Keyword(s):  
Lower Bound ◽  
Packing Density ◽  
Ball Packing
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