The explicit multi-instanton solutions by ’tHooft and Jackiw, Nohl & Rebbi are generalized to curvilinear coordinates. The idea is that a gauge transformation can notably simplify the expressions obtained after the change of variables. The gauge transform generates a compensating addition to the gauge potential of pseudoparticles. Singularities of the compensating field are irrelevant for physi...

In the scientific literature, field theory is most fully covered in cylindrical and spherical coordinate systems. This explained by fact that mathematical apparatus of these systems well studied. When source has a more complex structure than point or straight line, there need for new approaches to their study. The goal this research adapt related curvilinear coordinates order represent it norma...

The direct coordinate transformation method, which only transforms independent variables and retains Cartesian dependent variables, may not be an appropriate method for the purpose of simplifying the curvilinear parabolic approximation of the vector form of the wave–current equation given by Kirby [Higher-order approximations in the parabolic equation method for water waves, J. Geophys. Res. 91...

Results obtained for a class of degenerated shell elements formulated in convected (curvilinear) coordinates are presented. Each node has five degrees of freedom, with displacements expressed directly in global coordinates. Rotations o'f directors are treated in an efficient manner that preserves continuity across interelement boundaries, and allows treatment of general boundary conditions. A c...

You want to find a linear combination of the x coordinates that correlates well over the data with an (in general, different) linear combination of the y coordinates. In fact, you want to find the best such matched pair of linear combinations on the x and y sides, that is, the one yielding the largest coefficient of correlation. But why stop there? Once you have the best pair, you can ask for t...

A visualization of three-dimensional incompressible flows by divergence-free quasi-twodimensional projections of the velocity field onto three coordinate planes is revisited. An alternative and more general way to compute the projections is proposed. The approach is based on the Chorin projection combined with a SIMPLE-like iteration. Compared to the previous methodology based on divergence-fre...

An Explicit Fourth-Order Orthogonal Curvilinear Staggered-Grid FDTD Method for Maxwell’s Equations Zhongqiang Xie,∗ Chi-Hou Chan,† and Bo Zhang∗,† ∗School of Mathematical and Information Sciences, Coventry University, Coventry CV1 5FB, United Kingdom; and †Department of Electronic Engineering, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong E-mail: [email protected], eechic@c...

Quantum-dynamical full-dimensional (15D) calculations are reported for the protonated water dimer (H5O2+) using the multiconfiguration time-dependent Hartree (MCTDH) method. The dynamics is described by curvilinear coordinates. The expression of the kinetic energy operator in this set of coordinates is given and its derivation, following the polyspherical method, is discussed. The potential-ene...

A numerical high order difference method is developed for solution of the incom-pressible Navier–Stokes equations. The solution is determined on a staggered curvilinear grid in two dimensions and by a Fourier expansion in the third dimension. The description in curvilinear body-fitted coordinates is obtained by an orthogonal mapping of the equations to a rectangular grid where space derivatives...

Parametric cubic spline curves are commonly used to model the geometry of road surfaces in real-time driving simulators. Roads are represented by space curves that define a curvilinear frame of reference in which three-dimensional points are expressed in coordinates of distance along the curve, offset from the central axis, and loft from the road surface. Simulators must map from global Cartesi...