Axial Nodes Research Articles

Nodal positioning analysis (NPA)—A numerical method for determining flow behavior of thermoplastic materials

AbstractA finite difference method is presented for the solution of two dimensional flow problems in polymer processing. The method is applicable to narrow gaps of any shape and variable thickness. NPA was developed for analyzing the filling stage of the injection molding cycle, but it could be used in extrusion, blown film, and other polymer processing operations. In NPA the position of the flow front is calculated at the end of each time increment, and an axial node is placed at the newest location of the flow front. Each axial node is then divided into a determined number of radial nodes. The velocity and temperature profiles are obtained from the simultaneous solution of the momentum and energy equations. The use of finite differences transforms the continuity, momentum, and energy equations into a system of linear equations which can be solved by any direct or iterative technique. The procedure is repeated until axial nodes have been placed throughout the whole flow channel or until the flow front stops due to polymer solidification. The main advantage of this technique, when compared to the use of a fixed finite difference grid, is that computation time is saved by considering only nodes filled with the fluid. Empty nodes are not considered and corrections for partially filled nodes are not needed. No complications due to the parabolic‐shape of the flow front profile are introduced because the axial nodes are placed at average front locations determined by the average velocity at the particular time interval under consideration.

COMPARATIVE ANATOMY OF CHAROPHYTA: II. THE AXIAL NODAL COMPLEX—AN APPROACH TO THE TAXONOMY OF LAMPROTHAMNIUM12

SUMMARYThe present investigation on the axial nodes of 32 taxa belonging to the genera Chara, Lamprothamnium, Nitellopsis, Nitella and Tolypella confirms previous reports that within a given taxonomic group the structure of the main axial nodal complex is highly consistent. Besides the genera Nitella and Tolypella of the tribe Nitelleae, Lamprothamnium of the tribe Chareae is the only genus in which the central cells of the main axial nodal complex subdivide. This anatomical feature of the main axial nodal complex thus clearly separates the genus Lamprothamnium from the other genera of the tribe chareae. In 2 controversial species of the genus Chara, C. hornemannii and C. buckellii, the present study reveals that the central cells of their main axial nodal complexes do not subdivide. The transfer of these two species to the genus Lamprothamnium by Daily (1) may not be appropriate.

Inheritance of a Completely Branched Mutant in Safflower1

AbstractInheritance of a completely branched (branches arise from 100% of the axial nodes) mutant was studied in safflower (Carthamus tinctorit L.). Data from F2 and F3 progeny of a cross between a mutant and a tall‐branching cultivar (branches arise from 5 to 25% of the nodes) support the hypothesis that one completely dominant gene determines the incompletely branched habit; this gene is designated Cb. The double recessive cbcb determines the completely branched mutant. For the incompletely branched progeny, results suggest the presence of additional genetic variation for distribution of percentage of branching.

The Flexural Vibrations of Thin Laminated Cylinders

A method is developed for calculating the natural frequencies of vibration of a thin right circular cylinder. The vibration pattern may contain any number of peripheral or axial nodes. The cylinder is assumed to consist of a large number of thin laminations of two dissimilar materials, arranged alternately, and with the plane of a lamination normal to the axis of the cylinder. Built-in and simply supported end conditions are considered.

Phase Distribution near Focus in an Aberration-free Diffraction Image

A satisfactory picture of the three-dimensional intensity distribution near focus in the aberration-free diffraction image of a monochromatic point object was first given by Zernike and Nijboer in 1949. No corresponding general picture of the phase relations between different parts of the image seems to have been worked out, although Gouy's discovery in 1890 of the so-called phase anomaly at focus aroused an interest in this topic which, as a succession of publications shows, has not decreased in the intervening 66 years. In the present paper a sharpened version of Lommel's classical analysis is applied to obtain a general picture of the phase distribution near focus and to examine in detail, in the special case of an F/3.5 pencil, its peculiarities near the geometrical focal point, the Airy dark rings and the axial nodes (points of zero intensity) of the diffraction image. The `phase anomaly' near focus and the singular behaviour of the phase along the axis of the pencil become more readily intelligible when they are considered against the background of this general picture.

The Flexural Vibrations of Thin Cylinders

The flexural vibrations of the walls of thin cylinders are considered. In this type of vibration many forms of nodal pattern may exist owing to the combination of circumferential and axial nodes. Theoretical expressions are developed for the natural frequencies of cylinders with freely-supported and fixed ends and a comparison is made with the frequencies obtained experimentally. In practice, the ends of cylinders are subjected to a certain degree of fixing by end-plates, flanges, etc., and the natural frequencies thus lie between the corresponding values for freely-supported and fixed ends. To make possible the estimation of such frequencies, a method is devised in which an equivalent wavelength factor is used. This factor represents the wavelength of the freely-supported cylinder that would have the same frequency as the cylinder under consideration when vibrating in the same mode. The results of experimental investigations with various end thicknesses and flange dimensions are recorded, and from these the equivalent factors are derived. Sets of curves calculated for cylinders with freely-supported ends and covering a range of cylinder thicknesses are given. From these it is possible to obtain close approximation to the frequencies of cylinders under other end conditions by the use of an appropriate factor. An example is given of frequency calculations for a large air-receiver for which two frequencies were identified by experiment.