Random Packing of Equal Spheres on a Plane Surface

Nature ◽  
1963 ◽  
Vol 198 (4882) ◽  
pp. 747-749 ◽  
Author(s):  
G. F. ROUND ◽  
R. NEWTON
Keyword(s):  
Plane Surface ◽  
Random Packing

Random Packing Performance in Continuous Foam Fractionation

2021 ◽  
Author(s):  
Qianfeng Gu ◽  
Xiaochen Xue ◽  
Osama M. Darwesh ◽  
Pascal Habimana ◽  
Wei Liu ◽  
...  
Keyword(s):  
Random Packing ◽  
Foam Fractionation

scholarly journals Optimal Random Packing of Spheres and Extremal Effective Conductivity

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1063
Author(s):  
Vladimir Mityushev ◽  
Zhanat Zhunussova
Keyword(s):  
Effective Conductivity ◽  
Dimensional Space ◽  
Elementary Function ◽  
Voronoi Tessellation ◽  
Random Packing ◽  
Periodicity Cell ◽  
Algebraic Equations ◽  
Optimal Packing ◽  
Linear Algebraic Equations ◽  
Initial Location

A close relation between the optimal packing of spheres in Rd and minimal energy E (effective conductivity) of composites with ideally conducting spherical inclusions is established. The location of inclusions of the optimal-design problem yields the optimal packing of inclusions. The geometrical-packing and physical-conductivity problems are stated in a periodic toroidal d-dimensional space with an arbitrarily fixed number n of nonoverlapping spheres per periodicity cell. Energy E depends on Voronoi tessellation (Delaunay graph) associated with the centers of spheres ak (k=1,2,…,n). All Delaunay graphs are divided into classes of isomorphic periodic graphs. For any fixed n, the number of such classes is finite. Energy E is estimated in the framework of structural approximations and reduced to the study of an elementary function of n variables. The minimum of E over locations of spheres is attained at the optimal packing within a fixed class of graphs. The optimal-packing location is unique within a fixed class up to translations and can be found from linear algebraic equations. Such an approach is useful for random optimal packing where an initial location of balls is randomly chosen; hence, a class of graphs is fixed and can dynamically change following prescribed packing rules. A finite algorithm for any fixed n is constructed to determine the optimal random packing of spheres in Rd.

scholarly journals A Study of Moist Air Condensation Characteristics in a Transonic Flow System

Energies ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 4052
Author(s):  
Jie Wang ◽  
Hongfang Gu
Keyword(s):  
Mach Number ◽  
Relative Humidity ◽  
Transonic Flow ◽  
Flow System ◽  
Plane Surface ◽  
Droplet Growth ◽  
Moist Air ◽  
Dry Air ◽  
Hydraulic Equipment ◽  
Non Equilibrium

When water vapor in moist air reaches supersaturation in a transonic flow system, non-equilibrium condensation forms a large number of droplets which may adversely affect the operation of some thermal-hydraulic equipment. For a better understanding of this non-equilibrium condensing phenomenon, a numerical model is applied to analyze moist air condensation in a transonic flow system by using the theory of nucleation and droplet growth. The Benson model is adopted to correct the liquid-plane surface tension equation for realistic results. The results show that the distributions of pressure, temperature and Mach number in moist air are significantly different from those in dry air. The dry air model exaggerates the Mach number by 19% and reduces both the pressure and the temperature by 34% at the nozzle exit as compared with the moist air model. At a Laval nozzle, for example, the nucleation rate, droplet number and condensation rate increase significantly with increasing relative humidity. The results also reveal the fact that the number of condensate droplets increases rapidly when moist air reaches 60% relative humidity. These findings provide a fundamental approach to account for the effect of condensate droplet formation on moist gas in a transonic flow system.

Artifact Design and Measurement Error Analysis in the Evaluation of Lead Measurement Accuracy of Helical Gear Using Wedge Artifact

2010 ◽  
Vol 132 (7) ◽  
Author(s):  
Masaharu Komori ◽  
Fumi Takeoka ◽  
Aizoh Kubo ◽  
Kazuhiko Okamoto ◽  
Sonko Osawa ◽  
...  
Keyword(s):  
Evaluation Method ◽  
Plane Surface ◽  
Design Method ◽  
Measuring Instrument ◽  
Setting Error ◽  
Geometrical Form ◽  
Measurement Experiment ◽  
Mechanical Devices ◽  
Tooth Flank ◽  
Artifact Design

The reduction in the vibration and noise of gears is an important issue in mechanical devices such as vehicles and wind turbines. The characteristics of the vibration and noise of gears are markedly affected by deviations of the tooth flank form of micrometer order; therefore, strict quality control of the tooth flank form is required. The accuracy of the lead measurement for a gear-measuring instrument is usually evaluated using a helicoid artifact. However, it is difficult to manufacture it with high accuracy because the helix is a complicated geometrical form. To solve this problem, a method of evaluating a gear-measuring instrument using a wedge artifact, which includes a highly precise plane surface, has been proposed. In this research, to put the wedge artifact into practice, a design method of the wedge artifact is developed. In addition, the effects of the measuring condition and the setting error of the wedge artifact on the measurement result are investigated. The uncertainty for the evaluation method using a wedge artifact is assessed by a measurement experiment and simulation.

scholarly journals An introduction to Acoustic Emission Analysis (AEA) based medical diagnostic techniques: Screening and Monitoring of cartilage defects in knee joint osteoarthrosis

2020 ◽  
Vol 6 (3) ◽  
pp. 518-521
Author(s):  
Subke Joerg ◽  
Krueger Sabine ◽  
Junker Heinz-Otto ◽  
Schwalbe Hans-Joachim ◽  
Franke Ralf-Peter ◽  
...  
Keyword(s):  
Acoustic Emission ◽  
Load Transfer ◽  
Plane Surface ◽  
Cartilage Damage ◽  
Diagnostic Techniques ◽  
Outer Edge ◽  
Cartilage Defects ◽  
Emission Analysis ◽  
Medical Diagnostic ◽  
Therapeutic Measures

AbstractClinical studies have shown that during standardized movements the Acoustic Emission (AE) from lesions in articular cartilage can be assessed. Specific lesions produce specific acoustic signals, therefore it is possible to evaluate the character of cartilage damage. Consequently it is possible to evaluate the condition of the joint cartilage in order to enhance therapy. Patients performed series of knee bends, first on a plane surface in order to assess the cartilage lesions. Then patients performed knee bends on boards simulating orthopaedic insoles by means of inner and outer edge elevations. Insoles aim at relieving the lesioned areas of cartilage from loads and strain. AEA monitoring reveals the effects of a shift of the zone of load transfer immediately and is an adequate tool for the diagnosis as well as the monitoring of therapeutic measures.

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