Internal coordinates such as bond lengths, bond angles, and torsion angles (BAT) are natural coordinates for describing a bonded molecular system. However, the molecular dynamics (MD) simulation methods that are widely used for proteins, DNA, and polymers are based on Cartesian coordinates owing to the mathematical simplicity of the equations of motion. However, constraints are often needed wit...

Correctly propagating waves from overhanging reflectors is crucial for imaging in complex geology. This type of reflections are difficult or impossible to use in imaging using one-way downward continuation, because they violate an intrinsic assumption of this imaging method, i.e. vertical upward propagation of reflection data. Riemannian wavefield extrapolation is one of the techniques develope...

To detect image copy-paste tampering, an improved blind identification was proposed in this study. Firstly, according to gray-level and gray-structure, every couple of doubtful blocks can be located. Secondly, for each located couple of doubtful blocks, use logarithm polar coordinate transformation to translate the rotation and scaling in Cartesian coordinate system into translation in logarith...

Recent studies show that deformations in quantum mechanics are inevitable. In this contribution, we consider a relativistic mechanical differential equation the presence of Dunkl operator-based deformation and investigate solutions for two important problems three-dimensional spatial space. To end, after introducing mechanics, examine Dunkl–Klein–Gordon oscillator with Cartesian spherical coord...

A new kind of parallel mechanism machine called the CGT (Cartesian-Guided Tripod) for three-axis machining, CGP (Cartesian-Guided Pentapod) for five-axis machining, and CGH (Cartesian-Guided Hexapod) for six-axis positioning is presented on this paper. The CGT/CGP/CGH has two kinds of functional independent legs: the driving functional leg and the integrated Cartesian guiding/metrology function...

A Rodrigues vector is a triplet of real numbers used for parameterizing rotations or orientations in three-dimensional space. Because of its properties (e.g. simplicity of fundamental regions for misorientations) this parameterization is frequently applied in analysis of orientation maps of polycrystalline materials. By conventional definition, the Rodrigues parameters are specified in orthonor...

The non-orthogonal boundary-fitted coordinate transformation method is applied to the solution of steady three-dimensional conservation equations of mass, momentum, energy and speciescontinuity to obtain the laminar velocity, temperature and concentration fields for simulation of polymerization of styrene in arbitrary cross-sectional duct reactors. Variable physical properties (except for speci...