Some Dual Problems of Geometric Probability in the Plane

1993 ◽  
Vol 2 (1) ◽  
pp. 11-23 ◽  
Author(s):  
John Gates
Keyword(s):  
Combinatorial Geometry ◽  
Chord Length ◽  
Geometric Probability ◽  
Dual Problems ◽  
Sylvester’S Problem

A definition is adopted for convexity of a set of directed lines in the plane. Following this, the duals of a number of standard problems of geometric probability are formulated. Problems considered in detail are the duals of Sylvester's problem, chord length distributions and Ambartzumian's combinatorial geometry. The paper suggests some questions for further work.

Results and Problems in Combinatorial Geometry

1985 ◽  
Author(s):  
Vladimir G. Boltjansky ◽  
Israel Gohberg
Keyword(s):  
Combinatorial Geometry

scholarly journals Use of Multi-Anionic Sodium Tripolyphosphate to Enhance Dispersion of Concentrated Kaolin Slurries in Seawater

Metals ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 1085
Author(s):  
Williams Leiva ◽  
Norman Toro ◽  
Pedro Robles ◽  
Edelmira Gálvez ◽  
Ricardo Ivan Jeldres
Keyword(s):  
Rheological Properties ◽  
Fine Particles ◽  
Sodium Tripolyphosphate ◽  
Mining Industry ◽  
Chord Length ◽  
Water Recovery ◽  
Reflectance Measurement ◽  
Anionic Charge ◽  
Free Environment ◽  
The Impact

This research aims to analyze the impact of sodium tripolyphosphate (STPP) as a rheological modifier of concentrated kaolin slurries in seawater at pH 8, which is characteristic of copper sulfide processing operations. The dispersion phenomenon was analyzed through chord length measurements using the focused beam reflectance measurement (FBRM) technique, complementing size distributions in unweighted and square-weighted modes. The reduction of the rheological properties was significant, decreasing from 231 Pa in a reagent-free environment to 80 Pa after the application of STPP. A frequency sweep in a linear viscoelastic regime indicated that by applying a characteristic dosage of 0.53 kg/t of STPP, the pulp before yielding increases its phase angle, which increases its liquid-like character. Measurements of the chord length verified the dispersion of particles, which showed an apparent increase in the proportion of fine particles and a reduction of the coarser aggregates when STPP was applied. Measurements of the zeta potential suggested that the high anionic charge of the reagent (pentavalent) increases the electrostatic repulsions between particles, overcoming the effect of cations in seawater. The results are relevant for the mining industry, especially when the deposits have high contents of complex gangues, such as clays, that increase the rheological properties. This increases the energy costs and water consumption needed for pumping the tailings from thickeners to the tailing storages facilities. The strategies that allow for the improvement of the fluidity and deformation of the tailings generate slack in order to maximize water recovery in the thickening stages.

scholarly journals Quantitative combinatorial geometry for concave functions

2021 ◽  
Vol 182 ◽  
pp. 105465
Author(s):  
Sherry Sarkar ◽  
Alexander Xue ◽  
Pablo Soberón
Keyword(s):  
Combinatorial Geometry ◽  
Concave Functions

Algorithms in Combinatorial Geometry.

1989 ◽  
Vol 96 (5) ◽  
pp. 457
Author(s):  
Jacob E. Goodman ◽  
Herbert Edelsbrunner
Keyword(s):  
Combinatorial Geometry

Geometric Probability.

1979 ◽  
Vol 142 (3) ◽  
pp. 386
Author(s):  
P. Holgate ◽  
H. Solomon
Keyword(s):  
Geometric Probability

Numerical Research on the Characteristics of Lift-Drag Type Vertical Axis Wind Turbine

2012 ◽  
Vol 189 ◽  
pp. 448-452
Author(s):  
Yan Jun Chen ◽  
Guo Qing Wu ◽  
Yang Cao ◽  
Dian Gui Huang ◽  
Qin Wang ◽  
...  
Keyword(s):  
Wind Turbine ◽  
Vertical Axis ◽  
Chord Length ◽  
Power Coefficient ◽  
Speed Ratio ◽  
Vertical Axis Wind Turbine ◽  
Tip Speed Ratio ◽  
Middle Range ◽  
Parabolic Form ◽  
Cfd Method

Numerical studies are conducted to research the performance of a kind of lift-drag type vertical axis wind turbine (VAWT) affected by solidity with the CFD method. Moving mesh technique is used to construct the model. The Spalart-Allmaras one equation turbulent model and the implicit coupled algorithm based on pressure are selected to solve the transient equations. In this research, how the tip speed ratio and the solidity of blade affect the power coefficient (Cp) of the small H-VAWT is analyzed. The results indicate that Cp curves exhibit approximate parabolic form with its maximum in the middle range of tip speed ratio. The two-blade wind turbine has the lowest Cp while the three-blade one is more powerful and the four-blade one brings the highest power. With the certain number of blades, there is a best chord length, and too long or too short chord length may reduce the Cp.

Sign in / Sign up

Export Citation Format

Share Document