In molecular replacement, a model, described as a list of orthogonal coordinates, is to be moved into a new position and orientation. The orthogonal coordinate system also has to be related to the crystallographic system, which may not be orthogonal, and crystallographic symmetry must be considered, which applies to coordinates expressed as fractions of the unit cell. Elementary properties of r...

a fundamental topic in computational fluid dynamics is the role of coordinate particularly for searching optimized coordinates. the objective of this study is the numerical modeling of supersonic flows using a new coordinate system i.e. unified coordinate system (ucs) uses moving mesh with motionless viewing window technique. ucs has an advantage over traditional coordinate systems (eulerian an...

An orthogonal terrain-following coordinate (OS coordinate) was proposed by Li et al. (2013) to reduce the advection errors in the classic σ-coordinate. The OS coordinate can smooth the vertical layers above the steep terrain as well as create the orthogonal terrain-following grids in the vertical. The idealized advection experiments in Li et al. (2013) validated that the OS coordinate can signi...

The Proper Orthogonal Decomposition (POD) is a method that may be applied to linear and nonlinear structures for extracting important information from a measured structural response. Previous methods of using the POD for system identification typically use the POD for model reduction only and system identification is accomplished via standard methods. A method for using the POD-based identifica...

Nanopositioning and nanomeasuring machines are 3D coordinate measuring systems with nanometer precision at measurement volumes in the cubic centimeter range. The base is formed by an interferometer system a common mirror corner. orthogonality deviations of corner require transformation axes. uncertainty must be taken into account overall budget. Starting from complete model, result model simpli...

Local Coordinate Coding (LCC) [18] is a method for modeling functions of data lying on non-linear manifolds. It provides a set of anchor points which form a local coordinate system, such that each data point on the manifold can be approximated by a linear combination of its anchor points, and the linear weights become the local coordinate coding. In this paper we propose encoding data using ort...

Local normal-mode analysis for a collinear potential energy surface g?nrratss a system of curvilinear coordinaieh. which ;\re orthogonal in the mass-skewed system. The motion is locally separable in these coordinatrs. We compars the utility ai one of the normal modes as a transversal-vihralion coordinate. with the convcnrional choicr of the dire&on perpendicular w the reaction coordinate in the...

The differential operator of the monochromatic polarized radiative transfer equation is studied in case of statistically homogeneous turbid medium in Euclidean three-dimensional space, with arbitrary curvilinear coordinate system defined in it. An apparent rotation of the polarization plane along the light ray with respect to the chosen polarization reference plane generally takes place, due to...