Arcs Of Concentric Circles Research Articles

An adaptable equal-area pseudoconic map projection

ABSTRACTEquivalence (the equal-area property of a map projection) is important to some categories of maps. However, unlike conformal projections, completely general techniques do not exist for creating new, computationally reasonable equal-area projections. The literature describes many specific equal-area projections and a few equal-area projections that are more or less configurable, but flexibility is still sparse. This work describes a new, highly configurable equal-area projection system consisting of arcs of concentric circles, placing it in the pseudoconic class. The system uses a novel technique to hybridize the Bonne pseudoconic projection and the Albers conic projection, subsuming many existing projections as degenerate cases. With the resulting system and the technique used to develop it, map projection designers will have greater choice in tailoring the projection to the need. The system may be particularly suited to maps that dynamically adapt to changing scale and region of interest, such as required for online maps.

Determination of definitive standard parallels of normal aspect conic projections equidistant along meridians on an old map

ABSTRACTIn previous research we proved that meridians are straight lines and parallels are arcs of concentric circles on the map Nuova carta geografica dello Stato Ecclesiastico by J. R. Bošković and Ch. Maire, published in 1755. We also proved that the map was produced in a normal aspect conic projection equidistant along meridians. Knowing the map projection type is not enough. We need to know its parameters, too. In the first part of the paper, we described the procedure of determining standard parallels of the normal aspect conic projection equidistant along meridians. We proposed a procedure for determining projection parameters of an old map, especially its standard parallels, if the radius of the sphere in which the map was produced in is unknown. Constant C is introduced as a ratio of constant K and sphere radius R, both of which are unknown. The procedure is illustrated on the map Nuova carta … . Using the procedure, we obtained standard parallels φ1 = 41°50'N and φ2 = 44°30'N. In addition, we tested whether the obtained standard parallels are actually standard parallels in which the map was produced and determined the definitive standard parallels in which the map Nuova carta … has been produced.

Diffusion in curved capillaries

Diffusion in a flat capillary restricted by the arcs of concentric circles is studied. A flow of a substance in a curvilinear capillary turns out to be larger than in a rectilinear channel of the same length. However, for pore structures met in practice, this difference is negligible.

One of the origins for curved edges of polyethylene single crystals

A new concept of lattice strain was developed to explain the origin of the curved edges of polyethylene (PE) single crystals. In the crystallization of PE from poor solvents, the length of critical nucleus generated is rather short. The thin lamellae are thermodynamically unstable especially at high temperature. Thereby, during the growth of PE single crystals an annealing process is going on simultaneously, which results in a reduction of thickness from the center to growing faces of lamellae. It is known that the thinner the single crystals, the bigger the unit-cell dimensions. Consequently, unit-cells in the central part of single crystals formed are somewhat smaller than those in the outer part of the same crystals. In order to fit in with the gradual enlargement of unit-cell dimensions from the center to the edges of single crystals, the lattice planes of a faster growing dominant {110} deform to be a set of parallel arcs of concentric circles. Accordingly, the edge of a slower growing subordinate {200} becomes a part of an ellipse with obvious curvature while the edge of a {110} sector remains almost straight for it is a small part of a large circumference.

Construction of a function that maps an n-connected circular domain onto a disk with cuts along arcs of concentric circles

Construction of a function that maps an n-connected circular domain onto a disk with cuts along arcs of concentric circles

Visualization of the DNA thread packing within bacteriophage T4 heads

Inside the T4 capsid, negatively stained DNA threads of no larger than 2.5 nm in diameter were observed in arcs of concentric circles or in parallel longitudinal arrays. The images of these regular structures changed with the particular relation of the tilting of the specimen, suggesting the coaxial spool of DNA packing.

On the bending of a plane inhomogenbous curved beam: PMM vol. 43, no. 1, 1979, pp. 182–183

The plane problem of pure bending of a uniformly inhomogeneous curved beam bounded by two arcs of concentric circles and two radii, is considered. It is assumed that the material of the beam is isotropic, has a constant Poisson's ratio and a coordinate-dependent Young's modulus. It is shown that when the Young's modulus is defined in a specified manner, men the problem has an exact, elementary solution, and the solution is given.

Perceptual additions with four 90 degrees arcs as stimuli.

The stimulus, 4 black 90° arcs of concentric circles, was viewed under the following three sets of conditions: (a) stroboscopic lighting of 10.5 cps with an increasing number of flashes from 1 to 95, (b) continuous stroboscopic lighting of 10.5 cps, and (c) constant lighting. Ss reported different kinds of experience apart from the perception of the 4 arcs of 90°. These include forms, mainly elongations of the 4 arcs, and additions between the 4 arcs, plus radii, the three forms of which were perceived both in stroboscopic lighting and in constant lighting. Elongations and arc additions become longer and longer with increasing numbers of stroboscopic flashes, and at a certain number of flashes they often grow into circles of 360°. When the number of stroboscopic flashes is increased Ss usually observe an increasing number of radii which, for instance, around 15 flashes reach maximum number of about 16. Elongations and arc additions of 360° and a great number of radii often appear under continued stroboscopic lighting. This new perceptual situation elicits characteristic results from each S, but most Ss form groups with particular characteristics.

New Kinds of Systematic Designs for Spacing Experiments

1. Systematic designs for spacing experiments are developed having the properties that (i) the grid of plant positions is locally approximately rectangular, (ii) the two sets of curves defining the grid are either straight lines or arcs of concentric circles, and (iii) that the contours of equal area and of equal rectangularity of arrangement (length/breadth) are either straight lines or arcs of concentric circles, and the two sets are not coincident. 2. Five designs, four based on polar co-ordinates and one on a rectangular grid, are described and formulae given to enable plans to be constructed for field use. 3. Possible methods of analysis for the designs are discussed, and also the extent of their possible usefulness.

Flexural problems of circular ring plates and sectorial plates. II

ABSTRACTIn a previous paper solutions have been derived for the deflexion of a circular annular plate under various combinations of boundary conditions and subject to certain line loadings spread along the circumference of a concentric circle. These solutions, which were used in the analysis of circular ring plates and sectorial plates acted upon by a concentrated load or a concentrated couple at any point, are utilized in this paper to obtain solutions appropriate to lateral loadings of the typedistributed over the entire circular ring plate. Solutions corresponding to the case φ(r) =rmare then explicitly found, and the principle of superposition can be applied to get the solution when the load on the annulus can be expanded into a Laurent-Fourierseries in the polar coordinatesr, θ. The method of images is used to deduce solutions for an isotropic plate bounded by two arcs of concentric circles and two radii, and loaded by the normal pressurep=p0rmwhen the plate is simply supported along the straight edges and is subject to various conditions along the circular edges.

Flexural problems of circular ring plates and sectorial plates. I

ABSTRACTIn this paper explicit expressions in closed forms are first obtained for the complex potentials and deflexion at any point of a circular annular plate under various edge conditions when the plate is acted upon by general line loadings distributed along the circumference of a concentric circle. These solutions are then used to discuss the bending of a circular plate with a central hole under a concentrated load or a concentrated couple acting at any point of the plate. Solutions for singularly loaded sectorial plates bounded by two arcs of concentric circles and two radii are also derived when the plate is simply supported along the straight edges. The boundary conditions along the circular edges include the cases of a free boundary as well as the elastically restrained boundary which covers the usual rigidly clamped and simply supported boundaries as special cases. The usual restrictions relating to the small deflexion theory of thin plates of constant thickness are assumed. Limiting forms of the resulting solutions are investigated.

Exact Electrode Systems for the Formation of a Curved Space-Charge Beam †

An analytical method of determining the shape of the (Pierce) electrodes required to maintain a two-dimensional space-charge beam is given, which is valid when the edge of the beam is curved. The method is applied to a solution of the space-charge equations given recently by Meltzer, in which the flow pattern is a family of arcs of concentric circles. It is found that a completely enclosed electrode system results, making it unnecessary to adopt the usual approximation of terminating the electrodes at some arbitrary distance from the beam in order to make them finite.

Course and Distance Correction from an Estimated Position

After taking a latitude at noon and obtaining a position, a course and distance to a position nearer the destination is usually required. A course and distance from an estimated noon position may be worked prior to noon and then corrected at noon by the observed latitude and morning position line, by means of a plotting chart, giving reliable results quickly and accurately.In Fig. 1, BA and CA represent the course and distance from B to A and C to A respectively. BD and EC are arcs of concentric circles with centre A; and AC = AE and AB = AD.If BD and CD are small in comparison with AB, arcs BD and EC may be considered straight lines and the figure BECD a rectangle. If the rectangle can be solved, the distance AC can be deduced from AB, i.e. AC = AB - DC or AC = AB + DC if C lies the other side of BD.