Related papers: The transformation matrices (distortion, orientati…
In the following short paper we list some useful results concerning determinants and inverses of matrices. First we show, how to calculate determinants of $d \times d$ matrices, if their traces are known. As a next step $4 \times 4$…
The identification of orientation relationships (ORs) plays a crucial r\^ole in the understanding of solid phase transformations. In steels, the most common models of ORs are the ones by Nishiyama-Wassermann (NW) and Kurdjumov-Sachs (KS).…
Finding the inverse of a matrix is an open problem especially when it comes to engineering problems due to their complexity and running time (cost) of matrix inversion algorithms. An optimum strategy to invert a matrix is, first, to reduce…
The orientation of a rigid object can be described by a rotation that transforms it into a standard position. For a symmetrical object the rotation is known only up to multiplication by an element of the symmetry group. Such ambiguous…
Triply periodic minimal surfaces (TPMS) are discovered to conform to surfaces of given charge density distributions embedded in crystals [Z. Kristallogr. \textbf{170}, 138 (1985)]. Based on our previous work [Phys. Rev. Mater. \textbf{9},…
Materials which can undergo slow diffusive transformations as well as fast displacive transformations are studied using the phase-field method. The model captures the essential features of the time-temperature-transformation (TTT) diagrams,…
We derive transformation formulas for the generalized polarization tensors under rigid motions and scaling in three dimensions, and use them to construct an infinite number of invariants under those transformations. These invariants can be…
Orientation mapping is a widely used technique for revealing the microstructure of a polycrystalline sample. The crystalline orientation at each point in the sample is determined by analysis of the diffraction pattern, a process known as…
Using a modified Lennard-Jones model for elliptic particles and spherical impurities, we present results of molecular dynamics simulation in two dimensions. In one-component systems of elliptic particles, we find an orientation phase…
Invariants withstand transformations and, therefore, represent the essence of objects or phenomena. In mathematics, transformations often constitute a group action. Since the 19th century, studying the structure of various types of…
One of basic difficulties of machine learning is handling unknown rotations of objects, for example in image recognition. A related problem is evaluation of similarity of shapes, for example of two chemical molecules, for which direct…
Contrary to canonical expectations we show that lattice translational symmetry breaking often accompanies uniformly ordered flux phases. We demonstrate this phenomena by studying a spinless-fermion model on a square latttice with…
The Jahn-Teller distortive transition of \lmo is described by a modified 3-state Potts model. The interactions between the three possible orbits depends both on the orbits and their relative orientation on the lattice. Values of the two…
The transformation of the vortex lattice in a tetragonal superconductor which consists of its 45 degree reorientation relative to the crystal axes is studied using the nonlocal London model. It is shown that the reorientation occurs as two…
The article presents four identities containing the spatio-temporal differential operator also known as four-divergence. These equations are used to prove the invariance of wave equation under orthogonal paravector transformations.…
The influence of coherent interface on dissipations of mechanical energy of driven dislocations near to a point of martensite type phase transition is considered. The expressions for dynamic braking of dislocations, owing to losses of…
The problem of N interacting spins on a lattice is equivalent to one of N clusters linked in a specific manner. The energy of any configuration of spins can be expressed in terms of the energy levels of this cluster. A new expression is…
The continuum theory of dislocations, as developed predominantly by Kr\"oner and Kosevich, views each dislocation as a source of incompatibility of strains. We show that this concept can be employed efficiently in the Landau free energy…
This paper describes a method of calculating the transforms, currently obtained via Fourier and reverse Fourier transforms. The method allows calculating efficiently the transforms of a signal having an arbitrary dimension of the digital…
Phase separation in a complex fluid with lamellar order has been studied in the case of cold thermal fronts propagating diffusively from external walls. The velocity hydrodynamic modes are taken into account by coupling the…