Central configurations of four bodies with an axis of symmetry

2016 ◽  
Vol 125 (1) ◽  
pp. 33-70 ◽  
Author(s):  
Bálint Érdi ◽  
Zalán Czirják
2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Muhammad Shoaib ◽  
Abdul Rehman Kashif ◽  
Anoop Sivasankaran

We study central configuration of a set of symmetric planar five-body problems where(1)the five masses are arranged in such a way thatm1,m2, andm4are collinear andm2,m3, andm5are collinear; the two sets of collinear masses form a triangle withm2at the intersection of the two sets of collinear masses;(2)four of the bodies are on the vertices of an isosceles trapezoid and the fifth body can take various positions on the axis of symmetry both outside and inside the trapezoid. We form expressions for mass ratios and identify regions in the phase space where it is possible to choose positive masses which will make the configuration central. We also show that the triangular configuration is not possible.


Climate ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 39
Author(s):  
Oleg Onishchenko ◽  
Viktor Fedun ◽  
Wendell Horton ◽  
Oleg Pokhotelov ◽  
Natalia Astafieva ◽  
...  

A new model of an axially-symmetric stationary concentrated vortex for an inviscid incompressible flow is presented as an exact solution of the Euler equations. In this new model, the vortex is exponentially localised, not only in the radial direction, but also in height. This new model of stationary concentrated vortex arises when the radial flow, which concentrates vorticity in a narrow column around the axis of symmetry, is balanced by vortex advection along the symmetry axis. Unlike previous models, vortex velocity, vorticity and pressure are characterised not only by a characteristic vortex radius, but also by a characteristic vortex height. The vortex structure in the radial direction has two distinct regions defined by the internal and external parts: in the inner part the vortex flow is directed upward, and in the outer part it is downward. The vortex structure in the vertical direction can be divided into the bottom and top regions. At the bottom of the vortex the flow is centripetal and at the top it is centrifugal. Furthermore, at the top of the vortex the previously ascending fluid starts to descend. It is shown that this new model of a vortex is in good agreement with the results of field observations of dust vortices in the Earth’s atmosphere.


2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
B. Benhammouda ◽  
A. Mansur ◽  
M. Shoaib ◽  
I. Szücs-Csillik ◽  
D. Offin

In the current article, we study the kite four-body problems with the goal of identifying global regions in the mass parameter space which admits a corresponding central configuration of the four masses. We consider two different types of symmetrical configurations. In each of the two cases, the existence of a continuous family of central configurations for positive masses is shown. We address the dynamical aspect of periodic solutions in the settings considered and show that the minimizers of the classical action functional restricted to the homographic solutions are the Keplerian elliptical solutions. Finally, we provide numerical explorations via Poincaré cross-sections, to show the existence of periodic and quasiperiodic solutions within the broader dynamical context of the four-body problem.


1967 ◽  
Vol 29 (3) ◽  
pp. 485-494 ◽  
Author(s):  
M. I. G. Bloor

Using the grey gas approximation, the effect of radiative heat loss on axially symmetric flows is studied. Using an expansion procedure about the axis of symmetry, a numerical solution for the stagnation region is found taking the shock to be spherical. The results of this calculation are compared with the results of Lighthill's non-radiative constant density solution.


2007 ◽  
Vol 81 (16) ◽  
pp. 8648-8655 ◽  
Author(s):  
Melissa Stewart Kim ◽  
Vincent R. Racaniello

ABSTRACT Enterovirus type 70, an etiologic agent of acute hemorrhagic conjunctivitis, may bind different cellular receptors depending on cell type. To understand how EV70-receptor interaction is controlled, we studied two variants of the virus with distinct receptor utilization. EV70-Rmk, derived by passage in rhesus monkey kidney cells, replicates poorly in HeLa cells and does not cause cytopathic effects. Decay accelerating factor (DAF) is not a cell receptor for EV70-Rmk. Passage of EV70-Rmk in HeLa cells lead to isolation of EV70-Dne, which does not replicate in rhesus monkey kidney cells but grows to high titers in HeLa cells and causes cytopathic effects. DAF is sufficient for cell entry of EV70-Dne. EV70-Rmk replicates in human eye and brain-derived cell lines, whereas the Dne strain replicates only in HeLa cells and in conjunctiva-derived 15C4 cells. The two EV70 strains differ by five amino acid changes in the viral capsid. Single substitution of four of the five EV70-Rmk amino acids with the residue from EV70-Dne leads to lytic replication in HeLa cells. Conversely, substitution of any of the five EV70-Dne amino acids with the EV70-Rmk amino acid does not alter replication in HeLa cells. Three of these capsid amino acids are predicted to be located in the canyon encircling the fivefold axis of symmetry, one amino acid is found at the fivefold axis of symmetry, and one is located the interior of the capsid. The five EV70 residues define a region of the capsid that controls viral host range, DAF utilization, and cytopathogenicity.


1966 ◽  
Vol 24 (2) ◽  
pp. 275-284
Author(s):  
R. A. Wentzell

Plumpton & Ferraro (1955) considered the torsional oscillations of an infinitely conducting sphere in a uniform magnetic field. They showed that if the fluid and magnetic viscosity were assumed to be zero in the governing differential equations, then a continuous spectrum of eigenvalues could be obtained. This novel feature was clarified by Stewartson (1957) when he obtained the exact solution and showed that in the correct limit of a perfect conductor the eigen-values are discrete. Furthermore, in the limit of infinite conductivity the oscillations occur only on the axis of symmetry (figure 1).


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