Study on Microstructure and Properties of Aeronautical Nickel-Based Superalloy in Laser Directional Solidification

FFor the directional solidification repair of blade damage in an aviation turbine, a directional-growth repair layer on the surface of a nickel-based superalloy was prepared using an Nd:YAG laser. The microstructure of the directional-growth repair layer was investigated using scanning electron microscopy and transmission electron microscopy. Its phase composition and corrosion resistance were also analyzed and tested. The results indicate that the grains in the repair zone solidified in the same direction as the substrate and formed continuous columnar crystals, which were arranged in an orderly manner. A small number of secondary dendritic cells were dispersed in the transverse direction of the columnar crystals. The phase composition was mainly composed of the α′-based phase, β-precipitated strengthening phase, MC carbide, and interdendritic α′/β eutectic phase. The corrosion kinetic curve of the repair zone changed linearly. The oxide film was uniform and dense, and was mainly composed of continuous granular oxide. The corrosion kinetic curve of the substrate conformed to the parabolic law. The oxide film was composed of loose and bulky granular grains, which were stacked in the shape of regular polyhedra and distributed in the form of an island.

High-dimensional Private Quantum Channels and Regular Polytopes

As the quantum analog of the classical one-time pad, the private quantum channel (PQC) plays a fundamental role in the construction of the maximally mixed state (from any input quantum state), which is very useful for studying secure quantum communications and quantum channel capacity problems. However, the undoubted existence of a relation between the geometric shape of regular polytopes and private quantum channels in the higher dimension has not yet been reported. Recently, it was shown that a one-to-one correspondence exists between single-qubit PQCs and three-dimensional regular polytopes (i.e., regular polyhedra). In this paper, we highlight these connections by exploiting two strategies known as a generalized Gell-Mann matrix and modified quantum Fourier transform. More precisely, we explore the explicit relationship between PQCs over a qutrit system (i.e., a three-level quantum state) and regular 4-polytopes. Finally, we attempt to devise a formula for such connections on higher dimensional cases.

Planetary Systems and the Hidden Symmetries of the Kepler Problem

The question of whether the solar distances of the planetary system follow a regular sequence was raised by Kepler more than 400 years ago. He could not prove his expectation, inasmuch as the planetary orbits are not transformed into each other by the regular polyhedra. In 1989, Barut proposed another relation, which was inspired by the hidden symmetry of the Kepler problem. It was found to be approximately valid for our Solar System. Here, we investigate if exoplanet systems follow this rule. We find that the symmetry-governed sequence is valid in several systems. It is very unlikely that the observed regularity is by chance; therefore, our findings give support to Kepler’s guess, although with a different transformation rule.

Visualizing surface formation of semi-regular polyhedra of Archimedes

The most common method of forming semi-control polyhedra consists in cutting off angles and ribs of regular polyhedra by planes. The aim of the work - to consider the automated formation of a number of surfaces of semi-regular Archimedean polyhedra based on the dodecahedron. These include the truncated dodecahedron, the icosododecahedron, the romboicosododecahedron and the truncated icosododecahedron. The formation of surfaces is carried out by the kinematic method in AutoCAD using programs compiled in the AutoLISP language. Methods. The methodology for the formation of these polyhedra provides for truncation of the angles and edges of the dodecahedron. This requires the calculation of a number of geometric parameters of these polyhedra and dodecahedron, such as the value of the truncation of the dodecahedron edges, the size of the edges of truncated polyhedra, the centers of faces, dihedral angles, etc. In order to generate these surfaces, a frame is constructed because the frame lines are used as guides to form surfaces in a kinematic way. The electronic model of each polyhedron is constructed as a set of compartments of surfaces of all its faces, and each compartment is assigned to a certain layer of the drawing. The frame and electronic model of the polyhedra under study are formed by means of user programs composed in the functional language AutoLISP. The process of forming surfaces of selected polyhedra in the AutoCAD environment is provided by special programs that are also compiled in the AutoLISP language. Results. Software was created to demonstrate the process of formation of a number of Archimedes polyhedra on the monitor screen.