scholarly journals Modeling of spatial variations of growth within apical domes by means of the growth tensor. II. Growth specified on dome surface

2014 ◽  
Vol 53 (3) ◽  
pp. 301-316 ◽  
Author(s):  
Zygmunt Hejnowicz ◽  
Jerzy Nakielski ◽  
Krystyna Hejnowicz
Keyword(s):  
Growth Rate ◽  
Coordinate System ◽  
Growth Rates ◽  
Relative Rate ◽  
Spatial Variations ◽  
Curvilinear Coordinate System ◽  
Volumetric Growth ◽  
Shoot Apices ◽  
Curvilinear Coordinate ◽  
Area Growth

Variations of the elemental relative rate of growth are modeled for parabolic, elliptic and hyperbolic domes of shoot apices by using the growth tensor in a suitable curvilinear coordinate system when the mode of area growth on the dome surface is known. Variations of growth rates within the domes are obtained in forms of computer-made maps for the following variants of growth on the dome surface: (1) constant meridional growth rate, (2) isotropic area growth, (3) anisotropy of area growth which becomes more intensive with increasing distance from the vertex. In variants 1 and 2 a maximum of volumetric growth rate appears in the center of the dome. Such a distribution of growth seems to be unrealistic. However, the corresponding growth tensors are interesting because they can be used in combination with other growth tensors to get the expected minimum volumetric growth rate in the dome center.

scholarly journals Spatial variations of growth within domes having different patterns of principal growth directions

2014 ◽  
Vol 56 (4) ◽  
pp. 611-623 ◽  
Author(s):  
Jerzy Nakielski
Keyword(s):  
Growth Rate ◽  
Coordinate System ◽  
Growth Rates ◽  
Relative Rate ◽  
Spatial Variations ◽  
Coordinate Systems ◽  
Dome A ◽  
Rate Of Growth ◽  
Natural Coordinate System ◽  
Natural Coordinate

Growth rate variations for two paraboloidal domes: A and B, identical when seen from the outside but differing in the internal pattern of principal growth directions, were modeled by means of the growth tensor and a natural coordinate system. In dome A periclinal trajectories in the axial plane were given by confocal parabolas (as in a tunical dome), in dome B by parabolas converging to the vertex (as in a dome without a tunica). Accordingly, two natural coordinate systems, namely paraboloidal for A and convergent parabolic for B, were used. In both cases, the rate of growth in area on the surfaces of domes was assumed to be isotropic and identical in corresponding points. It appears that distributions of growth rates within domes A and B are similar in their peripheral and central parts and different only in their distal regions. In the latter, growth rates are relatively large; the maximum relative rate of growth in volume is around the geometric focus in dome A, and on the surface around the vertex in dome B.

Flow Over a Cylinder at a Plane Boundary—A Model Based Upon (k–ε) Turbulence

1989 ◽  
Vol 111 (4) ◽  
pp. 414-419 ◽  
Author(s):  
T. Solberg ◽  
K. J. Eidsvik
Keyword(s):  
Pressure Gradient ◽  
Coordinate System ◽  
Adverse Pressure Gradient ◽  
Plane Boundary ◽  
Length Scale ◽  
Two Dimensional ◽  
Curvilinear Coordinate System ◽  
Recirculating Flow ◽  
Model Based ◽  
Curvilinear Coordinate

A model for two-dimensional flows over a cylinder at a plane boundary is developed. The model, based upon a (k-ε) turbulence closure, is formulated in a curvilinear coordinate system based upon frictionless flow. A length scale modification in areas of adverse pressure gradient and recirculating flow appears to be more realistic than the standard (k-ε) model. The main features of the predicted flow do not depend critically upon the details of the grid or model, which means that a well defined solution is obtained. The solution appears to be reasonable and validated to the extent that the data permits.

scholarly journals The partial banana mapping: a robust linear method for impact probability estimation

2019 ◽  
Vol 492 (3) ◽  
pp. 4546-4552
Author(s):  
Dmitrii E Vavilov
Keyword(s):  
Coordinate System ◽  
Confidence Region ◽  
Linear Method ◽  
Probability Estimation ◽  
Curvilinear Coordinate System ◽  
The Earth ◽  
Curvilinear Coordinate ◽  
Near Earth Asteroids ◽  
The Impact ◽  
Confidence Ellipsoid

ABSTRACT This paper presents a robust linear method for impact probability estimation of near-Earth asteroids with the Earth. This method is a significantly modified and improved method, which uses a special curvilinear coordinate system associated with the nominal orbit of an asteroid. One of the coordinates of this system is the mean anomaly in the osculating orbit of an asteroid. A normal distribution of errors of coordinates and velocities of this system is assumed. Because of the usage of the curvilinear coordinate system, the fact that the confidence region is curved and stretched mainly along the nominal asteroid orbit is taken into account. On the main axis of the curvilinear confidence ellipsoid the virtual asteroid, which is the closest to the Earth, is found. The part of the curvilinear confidence ellipsoid, around the found virtual asteroid, is obtained and mapped on to its target plane. The impact probability is calculated as the probability of the asteroid being in the region of the found virtual asteroid multiplied by the probability of a collision of the found virtual asteroid with the Earth. This approach is shown to give more accurate and trustworthy results than the target plane method.

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