It is shown that if a capillary surface satisfies conditions relating to the eigenvalues of a certain differential operator, then the surface is a constrained strict local minimum for the relevant energy functional. The space of perturbations of the surface is first defined in terms of graphs of functions in curvilinear coordinates and then related to perturbations of capillary surfaces which a...

In this paper a non-relativistic particle moving on a hypersurface in a curved space and the multidimensional rotator are investigated using the Hamilton-Jacobi formalism. The equivalence with the Dirac Hamiltonian formalism is demonstrated in both Cartesian and curvilinear coordinates. The energy spectrum of the multi-dimensional rotator is equal to that of a pure Laplace-Beltrami operator wit...

A set of reduced magnetohydrodynamic equations is described that is appropriate for the simulation of auroral Alfvén waves using curvilinear coordinates. These equations include the parallel electric field, ponderomotive force, diamagnetic drift effects, and gravity and rotation, but do not include the fast mode dynamics. The equations are formulated for multiple species, but quasineutrality is...

The quasi-independent curvilinear coordinate approximation (QUICCA) method [K. Nemeth and M. Challacombe, J. Chem. Phys. 121, 2877 (2004)] is extended to the optimization of crystal structures. We demonstrate that QUICCA is valid under periodic boundary conditions, enabling simultaneous relaxation of the lattice and atomic coordinates, as illustrated by tight optimization of polyethylene, hexag...

We consider the propagation speed of thin premixed flames disturbed by the fluid flow and suggest a new approach based on using the generalized curvilinear system of coordinates and tensor calculus. The suggested technique is shown to be more simple than the traditional technique used by Sivashinsky (1976), Matalon and Matkowsky (1982a) and also in other publications. The result of Matalon and ...

The cubed-sphere grid of gnomonic type [ 7, 8] is used in this study. The grid is generated by mapping the six faces of an inscribed cube to the sphere surface using gnomonic projection. The six expanded patches are continuously attached together with proper boundary conditions. On each patch, the expressions of the SWEs in local curvilinear coordinates (x, y) ∈ [−π/4, π/4] are identical. When ...

The present paper is devoted to the construction and investigation of algorithms of spectral approximation of three-dimensional problems for nonhomogeneous anisotropic elastic multistructures in curvilinear coordinates, which are junctions of three-dimensional body, shell clamped in it and curvilinear rod clamped in shell. Sequences of boundary and initial-boundary value problems defined on the...

The concept of “curved perspective” has been used by artists such as M.C. Escher in order effectively convey a sense of three dimensional space while being restricted to a two dimensional canvas. We present an interactive system to create and manipulate projections with a curvilinear perspective. Our system presents the user with a set of intuitive screen-space perspective primitives that contr...