The multi-instanton solutions by ’tHooft and Jackiw, Nohl & Rebbi are generalized to curvilinear coordinates. Expressions can be notably simplified by the appropriate gauge transformation. This generates the compensating addition to the gauge potential of pseudoparticles. Singularities of the compensating connection are irrelevant for physics but affect gauge dependent quantities. The third con...

Recently Shukurov et al [Phys Rev E 72, 025302 (2008)], made use of nonorthogonal curvilinear coordinate system on a dynamo Moebius strip flow, to investigate the effect of stretching by a turbulent liquid sodium flow. In plasma physics, Chui and Moffatt [Proc Roy Soc A 451,609,(1995)] (CM), considered non-orthogonal coordinates to investigate knotted magnetic flux tube Riemann metric. Here it ...

A vectorial modal method is presented based on transverse magnetic and electric mode expansion, which significantly simplifies the evaluation of operator matrix. The method, features a true open boundary condition, introduced for an orthogonal curvilinear coordinate system with specific examples circular elliptical geometries presented. We validate by considering challenging problems, such as c...

It is shown how orthogonal compact-support multiwavelets may be used for the solution of quantum mechanical eigenvalue problems subject to specific boundary conditions. Special scaling functions and wavelets with convenient limiting behaviors at the edges of an interval are constructed in analogy to earlier work on single wavelet families. All of the integrals required for Hamiltonian matrix el...