scholarly journals On the Existence of Central Configurations of2k+2p+2l-Body Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Yueyong Jiang ◽  
Furong Zhao
Keyword(s):  
Central Configurations ◽  
The Masses

We prove the existence of central configurations of the2k+2p+2l-body problems with Newtonian potentials inR3. In such configuration,2kmasses are symmetrically located on thez-axis,2pmasses are symmetrically located on they-axis, and2lmasses are symmetrically located on thex-axis, respectively; the masses symmetrically about the origin are equal.

scholarly journals Central Configurations for NewtonianN+2p+1-Body Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Furong Zhao ◽  
Jian Chen
Keyword(s):  
Central Configurations ◽  
Straight Line ◽  
Spatial Central Configurations ◽  
The Masses

We show the existence of spatial central configurations for theN+2p+1-body problems. In theN+2p+1-body problems,Nbodies are at the vertices of a regularN-gonT;2pbodies are symmetric with respect to the center ofT, and located on the straight line which is perpendicular to the regularN-gonTand passes through the center ofT; theN+2p+1th is located at the the center ofT. The masses located on the vertices of the regularN-gon are assumed to be equal; the masses located on the same line and symmetric with respect to the center ofTare equal.

scholarly journals Spatial Central Configurations with Two Twisted Regular 4-Gons

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Sen Zhang ◽  
Furong Zhao
Keyword(s):  
Twist Angle ◽  
Central Configurations ◽  
Central Configuration ◽  
Spatial Central Configurations ◽  
The Masses ◽  
Axis Passing

We study the configuration formed by two squares in two parallel layers separated by a distance. We picture the two layers horizontally with thez-axis passing through the centers of the two squares. The masses located on the vertices of each square are equal, but we do not assume that the masses of the top square are equal to the masses of the bottom square. We prove that the above configuration of two squares forms a central configuration if and only if the twist angle is equal tokπ/2or (π/4+kπ/2)(k=1,2,3,4).

scholarly journals Symmetry of planar four-body convex central configurations

2008 ◽  
Vol 464 (2093) ◽  
pp. 1355-1365 ◽  
Author(s):  
Alain Albouy ◽  
Yanning Fu ◽  
Shanzhong Sun
Keyword(s):  
Body Problem ◽  
The Other ◽  
Central Configurations ◽  
Central Configuration ◽  
Geometric Properties ◽  
Four Body Problem ◽  
Planar Central Configurations ◽  
The Masses ◽  
The Relationship ◽  
Convex Central Configuration

We study the relationship between the masses and the geometric properties of central configurations. We prove that, in the planar four-body problem, a convex central configuration is symmetric with respect to one diagonal if and only if the masses of the two particles on the other diagonal are equal. If these two masses are unequal, then the less massive one is closer to the former diagonal. Finally, we extend these results to the case of non-planar central configurations of five particles.

scholarly journals Regions of Central Configurations in a Symmetric 4 + 1-Body Problem

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Muhammad Shoaib
Keyword(s):  
Inverse Problem ◽  
Body Problem ◽  
Center Of Mass ◽  
Central Configurations ◽  
Central Configuration ◽  
Isosceles Trapezoid ◽  
The Masses

The inverse problem of central configuration of the trapezoidal 5-body problems is investigated. In this 5-body setup, one of the masses is chosen to be stationary at the center of mass of the system and four-point masses are placed on the vertices of an isosceles trapezoid with two equal massesm1=m4at positions∓0.5, rBandm2=m3at positions∓α/2,rA. The regions of central configurations where it is possible to choose positive masses are derived both analytically and numerically. It is also shown that in the complement of these regions no central configurations are possible.

In situ irradiation effects studies in medium- and high-voltage TEM

1995 ◽  
Vol 53 ◽  
pp. 234-235
Author(s):  
Charles W. Allen
Keyword(s):  
Cross Section ◽  
Particle Flux ◽  
Threshold Value ◽  
High Energy ◽  
Irradiation Damage ◽  
Defect Complexes ◽  
Lattice Position ◽  
Electrons And Ions ◽  
The Masses

With respect to structural consequences within a material, energetic electrons, above a threshold value of energy characteristic of a particular material, produce vacancy-interstial pairs (Frenkel pairs) by displacement of individual atoms, as illustrated for several materials in Table 1. Ion projectiles produce cascades of Frenkel pairs. Such displacement cascades result from high energy primary knock-on atoms which produce many secondary defects. These defects rearrange to form a variety of defect complexes on the time scale of tens of picoseconds following the primary displacement. A convenient measure of the extent of irradiation damage, both for electrons and ions, is the number of displacements per atom (dpa). 1 dpa means, on average, each atom in the irradiated region of material has been displaced once from its original lattice position. Displacement rate (dpa/s) is proportional to particle flux (cm-2s-1), the proportionality factor being the “displacement cross-section” σD (cm2). The cross-section σD depends mainly on the masses of target and projectile and on the kinetic energy of the projectile particle.

Mass Media Misleading the Masses: The Propagation of Nonscientifically Supported Autism Treatments

2012 ◽  
Author(s):  
Kimberly A. Schreck ◽  
Melissa Russell ◽  
Luis Vargas ◽  
Tanya Brucie ◽  
Jennifer Hall
Keyword(s):  
Mass Media ◽  
The Masses ◽  
Autism Treatments
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