DETERMINATION OF DEFECTS SIZES AND THEIR POSITION DURING ULTRASONIC CONTROL BY METHODS OF MATHEMATICAL AND COMPUTER SIMULATION

The use of sound waves to study the integrity of various metal structures is the most relevant method. The relevance is traced, in particular, in the ease of conducting such experiments, as well as its cheapness. The design of various parts requires the use of modern computer technology, which, using a mathematical apparatus that describes the process, allows you to determine the actual characteristics of the material to determine durability. This approach makes it possible to effectively create design solutions in order to create new parts and upgrade existing materials to extend their service life. The purpose of this work is to build mathematical models of homogeneous wave processes and their analysis in the form of computational experiments to control the passage of sound signals through the surface of the studied materials of objects. This approach is used to determine the influence of geometric parameters of defects in the form of cracks through which the signal passes, on its characteristics, which it describes after passing through these defects to the signal receiver, in particular, is the amplitude and frequency. For computational experiments, a point exciter of harmonic oscillations and a point receiver were chosen, which are located on different sides relative to the defect of a simple geometric shape. It should be noted that even minor defects affect the amplitude of the received signal, which passed through such defects. When a signal passes through defects of a simple geometric shape, the amplitude of such a signal decreases by 5–8 times and the average frequency decreases by 2–3 times.

Collision and Stable Regions around Bodies with Simple Geometric Shape

We show the expressions of the gravitational potential of homogeneous bodies with well-defined simple geometric shapes to study the phase space of trajectories around these bodies. The potentials of the rectangular and triangular plates are presented. With these expressions we study the phase space of trajectories of a point of mass around the plates, using the Poincaré surface of section technique. We determined the location and the size of the stable and collision regions in the phase space, and the identification of some resonances. This work is the first and an important step for others studies, considering 3D bodies. The study of the behavior of a point of mass orbiting around these plates (2D), near their corners, can be used as a parameter to understand the influence of the gravitational potential when the particle is close to an irregular surface, such as large craters and ridges.

Newgrange — Science or Symbolizm

The Newgrange passage tomb is examined for evidence of ‘Neolithic science’. Claims that it incorporated an astronomical alignment, and was constructed using Pythagorean geometry and the megalithic yard are reviewed as are scientific interpretations of its art. A new analysis of the tomb's structure reveals that it was based on a simple geometric shape measurable by a 13.1 m unit of length. The locations of particular motifs and decorated surfaces are shown to conform to the spatial relationships evident in the tomb's form. These are defined in terms of oppositions between left and right, front and back, inside and outside, visible and hidden, as well as making reference to symbols found in the art of the neighbouring passage tomb at Knowth.These features are interpreted, not as evidence of a specificically scientific discourse in the Irish Neolithic, but as the elaboration of elements common to the passage tomb ritual discourse. Competition for political control, in the context of mortuary practices, resulted in the increasing formalization and rigid interpretation of passage tomb symbolizm, and the ritualization of new areas of knowledge.