Remark on the Harmonic Radius Vector

1970 ◽  
Vol 38 (3) ◽  
pp. 291-294
Author(s):  
H. A. Buchdahl
Keyword(s):  
Radius Vector ◽  
Harmonic Radius

scholarly journals A new catalogue of multiple galaxies in the Local Supercluster

2000 ◽  
Vol 174 ◽  
pp. 40-45
Author(s):  
D. I. Makarov ◽  
I. D. Karachentsev
Keyword(s):  
New Approach ◽  
Galaxy Groups ◽  
Closed Orbits ◽  
Crossing Time ◽  
Local Supercluster ◽  
Virial Mass ◽  
Nearby Galaxies ◽  
The Individual ◽  
Group Member ◽  
Harmonic Radius

AbstractA new approach is suggested which makes use of the individual properties of galaxies, for the identification of small galaxy groups in the Local Supercluster. The criterion is based on the assumption of closed orbits of the companions around the dominating group member within a zero velocity sphere.The criterion is applied to a sample of 6321 nearby galaxies with radial velocities V0 ≤ 3000 km s−1. These 3472 galaxies have been assigned to 839 groups that include 55% of the sample considered. For the groups identified by the new algorithm (with k ≥ 5 members) the median velocity dispersion is 86 km s−1, the median harmonic radius is 247 kpc, the median crossing time is 0.08(1/H), and the median virial-mass-to-light ratio is 56 M⊙/L⊙.

What can Observations of Comets Tell Us about the Solar Wind at the Maunder Minimum?

2018 ◽  
Vol 14 (A30) ◽  
pp. 181-183
Author(s):  
N. V. Zolotova ◽  
Y. V. Sizonenko ◽  
M. V. Vokhmyanin ◽  
I. S. Veselovsky
Keyword(s):  
Solar Wind ◽  
Spectral Composition ◽  
Maunder Minimum ◽  
Radius Vector ◽  
Physical Parameters ◽  
Historical Records ◽  
Made In ◽  
Visual Observations

AbstractThis paper discussed whether 17th Century observers left historical records of the plasma tails of comets that would be adequate to enable us to extract the physical parameters of the solar wind. The size of the aberration angle between a comet’s tail and its radius-vector defines the type of the tail: plasma or dust. We considered Bredikhin’s calculations of the parameters for 10 comet tails observed during the Maunder minimum (1645 – 1715). For those comets the angle between the tail’s axis and the radius-vector on average exceeded the value of 10° that is typical for dust tails. It was noted that visual observations of the ion tails of comets are very difficult to make owing to the spectral composition of their radiation, confirming the conclusion that observations of comet tails made in the 17th Century are not suitable for deriving past values of the physical parameters of the solar wind.

scholarly journals Physical Observations of the Short-Period Comet 1969 IV

1972 ◽  
Vol 45 ◽  
pp. 27-34
Author(s):  
K. I. Churyumov ◽  
S. I. Gerasimenko
Keyword(s):  
Spectral Region ◽  
Sunspot Area ◽  
Radius Vector ◽  
Short Period Comet ◽  
Short Period ◽  
Single Emission ◽  
The Continuum ◽  
Period Comet

The new short-period comet Churyumov-Gerasimenko, discovered by the authors on plates taken by the Kiev University cometary expedition to Alma-Ata in September 1969, was systematically photographed with fast telescopes at Byurakan and Alma-Ata until March 1970. Measurements were made of the photographic magnitude of the photometric nucleus, as well as of the photographic and photovisual integral magnitudes. The variations in nuclear magnitude were found to be well correlated with changes in the total sunspot area. The integral photometric parameters are Hy = 11.91±0m.54 and n=4.0±0.8 (in the photographic spectral region). Deviations of the tail axis from the prolonged radius vector were considerable. A spectrogram shows the continuum and emission of CN, C2 and C3 in the head, the continuum and a single emission (perhaps CO+) in the tail.

Hypercube-Based Crowding Differential Evolution with Neighborhood Mutation for Multimodal Optimization

2018 ◽  
Vol 9 (2) ◽  
pp. 15-27
Author(s):  
Haihuang Huang ◽  
Liwei Jiang ◽  
Xue Yu ◽  
Dongqing Xie
Keyword(s):  
Differential Evolution ◽  
Euclidean Distance ◽  
Optimization Problems ◽  
Random Search ◽  
Adaptive Method ◽  
Radius Vector ◽  
Multimodal Optimization ◽  
Optimal Solutions ◽  
Reasonable Range ◽  
Neighborhood Mutation

In reality, multiple optimal solutions are often necessary to provide alternative options in different occasions. Thus, multimodal optimization is important as well as challenging to find multiple optimal solutions of a given objective function simultaneously. For solving multimodal optimization problems, various differential evolution (DE) algorithms with niching and neighborhood strategies have been developed. In this article, a hypercube-based crowding DE with neighborhood mutation is proposed for such problems as well. It is characterized by the use of hypercube-based neighborhoods instead of Euclidean-distance-based neighborhoods or other simpler neighborhoods. Moreover, a self-adaptive method is additionally adopted to control the radius vector of a hypercube so as to guarantee the neighborhood size always in a reasonable range. In this way, the algorithm will perform a more accurate search in the sub-regions with dense individuals, but perform a random search in the sub-regions with only sparse individuals. Experiments are conducted in comparison with an outstanding DE with neighborhood mutation, namely NCDE. The results show that the proposed algorithm is promising and computationally inexpensive.

scholarly journals IV. On the figure and stability of a liquid satellite

1906 ◽  
Vol 206 (402-412) ◽  
pp. 161-248 ◽  
Keyword(s):  
Relative Motion ◽  
Radius Vector ◽  
Numerical Results ◽  
Graphical Methods ◽  
True Value

More than half a century ago Édouard Roche wrote his celebrated paper on the form assumed by a liquid satellite when revolving, without relative motion, about a solid planet. In consequence of the singular modesty of Roche’s style, and also because the publication was made at Montpellier, this paper seems to have remained almost unnoticed for many years, but it has ultimately attained its due position as a classical memoir. The laborious computations necessary for obtaining numerical results were carried out, partly at least, by graphical methods. Verification of the calculations, which as far as I know have never been repeated, forms part of the work of the present paper. The distance from a spherical planet which has been called “Roche’s limit” is expressed by the number of planetary radii in the radius vector of the nearest possible infinitesimal liquid satellite, of the same density as the planet, revolving so as always to present the same aspect to the planet. Our moon, if it were homo­geneous, would have the form of one of Roche’s ellipsoids; but its present radius vector is of course far greater than the limit. Roche assigned to the limit in question the numerical value 2·44; in the present paper I show that the true value is 2·455, and the closeness of the agreement with the previously accepted value affords a remarkable testimony to the accuracy with which he must have drawn his figures.

On: “The reflection, refraction, and diffraction of waves in media with an elliptical velocity dependence”, by Franklyn K. Levin (GEOPHYSICS, April 1978, p. 528–537.)

Geophysics ◽  
1979 ◽  
Vol 44 (5) ◽  
pp. 987-990 ◽  
Author(s):  
K. Helbig
Keyword(s):  
Phase Velocity ◽  
Radius Vector ◽  
Wave Surface ◽  
Slowness Surface ◽  
Slowness Vector ◽  
Velocity Surface ◽  
Snell’S Law ◽  
Snell's Law ◽  
Wave Surfaces ◽  
Second Degree

Levin treats the subject concisely and exhaustively. Nevertheless, I feel a few comments to be indicated. My first point is rather general: of the three surfaces mentioned in the Appendix, the phase velocity surface (or normal surface) is easiest to calculate, since it is nothing but the graphical representation of the plane‐wave solutions for each direction. The wave surface has the greatest intuitive appeal, since it has the shape of the far‐field wavefront generated by an impulsive point source. The slowness surface, though apparently an insignificant transformation of the phase‐velocity surface, has the greatest significance for two reasons: (1) The projection of the slowness vector on a plane (the “component” of the slowness vector) is the apparent slowness, a quantity directly observed in seismic measurement. Continuity of wave‐fronts across an interface—the idea on which Snell’s law is based—is synonymous with continuity of apparent (or trace) slownesses; and (2) the slowness surface is the polar reciprocal of the wave surface; that is to say, not only has the radius vector of the slowness surface the direction of the normal to the wave surface (which follows from the definition of the two surfaces), but the inverse is also true. That is, the normal to the slowness surface has the direction of the corresponding ray (the radius vector of the wave surface). The fact that this surface so conveniently embodies all relevant information—direction of wave normal and ray, inverse phase velocity, inverse ray velocity (projection of the slowness vector on the ray direction), and the trace slowness along an interface—was the main reason for its introduction by Hamilton (1837) and McCullagh (1837). It is true that this information also can be obtained from the other surfaces, but only in a somewhat roundabout way, which can lead to serious complications. That only few of these complications are apparent in Levin’s article is a consequence of the fact that the polar reciprocal of a surface of second degree is another surface of second degree, in this case an ellipsoid. For more complicated and realistic types of anisotropy, one has to expect much more complicated surfaces. For transverse anisotropy, the slowness surface consists of one ellipsoid (SH‐waves) and a two‐leaved surface of fourth degree, the wave surface of an ellipsoid and a two‐leaved surface of degree 36. More general types of elastic anisotropy can lead to wave surfaces of up to degree 150, while the slowness surface is at most of degree six. It is, therefore, in the interest of a unified theory of wave propagation in anisotropic media to use, wherever possible, the slowness surface. The advantages of this are exemplified by Snell’s law in its general form. While it is impossible to base a concise formulation on the wave surface (reflected and refracted rays do not always lie in the plane containing the incident ray and the normal to the interface), the use of the slowness surface allows the following simple statement (Helbig 1965): “The slowness vectors of all waves in a reflection/refraction process have their end points on a common normal to the interface; the direction of the rays is parallel to the corresponding normals to the slowness surfaces”. A method to interpret refraction seismic data with an anisotropic overburden based on this form of Snell’s law has been described in Helbig (1964).

Composite Spherical Pressure Vessels With Hardening Metal Liners

1979 ◽  
Vol 101 (3) ◽  
pp. 200-206 ◽  
Author(s):  
R. F. Foral
Keyword(s):  
Transverse Isotropy ◽  
Pressure Vessels ◽  
Radius Vector ◽  
Linear Strain ◽  
Composite Sphere ◽  
Liner Material ◽  
Form Analysis ◽  
Linear Elastic ◽  
Spherical Pressure ◽  
Incremental Theory Of Plasticity

This paper presents a closed form analysis of behavior of a metal-lined composite sphere under internal pressure. Generic behavior, away from discontinuities, is considered. The composite is assumed to be linear elastic throughout, with transverse isotropy with respect to a radius vector. The liner material is elastic-plastic with assumed linear strain hardening. The analysis utilizes the J2 incremental theory of plasticity and is structured so that a typical pressurization history can be described, with proof, release, and cyclic pressurization. Numerical results are presented. The solution is used to relate performance with design parameter variation and design efficiency charts are presented.

Asymptotic dipole expansions for small horizontal angles

1932 ◽  
Vol 28 (4) ◽  
pp. 433-441 ◽  
Author(s):  
F. H. Murray
Keyword(s):  
Electromagnetic Field ◽  
Approximate Calculation ◽  
Radius Vector

An approximate calculation of the electromagnetic field of a vertical dipole at the surface of a conducting earth, for small angles of the radius vector with the horizontal, was given by Sommerfield; the case of large angles with the horizontal has been studied by a number of writers. It is proposed here to develop formulae for the vertical dipole by a method which takes into account the singularities of the integrand of a certain integral more accurately than is done by Sommerfield; the analysis is developed especially for small horizontal angles and small numerical distances.

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