A novel multiple scales method is formulated that can be applied to problems which have an almost periodic microstructure not in Cartesian coordinates but in a general curvilinear coordinate system. The method is applied to a model of the electrical activity of cardiac myocytes and used to derive a version of the bidomain equations describing the macroscopic electrical activity of cardiac tissu...

The CH overtone spectra for UCH= 1, 2, and 3 for an intermediate sized molecule, benzene, and the related intramolecular vibrational dynamics are treated theoretically. For this purpose, an artificial intelligence (AI) search technique is employed, using the evaluation function developed in Part II. The curvilinear local-normal mode coordinate system discussed in Part I is also used. The main f...

The Burgers vector b with components (1.1) is teated as a vector of a special space, it is called the Burgers space. The Burgers space is an imaginary space, it is assumed to be filled with the infinite ideal (non-distorted) crystalline grid. The tensor T̂ in (1.1) is a double space tensor : its upper index i is associated with some Cartesian coordinate system in the Burgers space, its lower ind...

A set S of vertices of a connected graph G is convex, if for any pair of vertices u, v ∈ S , every shortest path joining u and v is contained in S . The convex hull CH(S ) of a set of vertices S is defined as the smallest convex set in G containing S . The set S is geodetic, if every vertex of G lies on some shortest path joining two vertices in S, and it is said to be a hull set if its convex ...

Abstract The gyrokinetic Poisson equation arises as a subproblem of Tokamak fusion reactor simulations. It is often posed on disk-like cross sections the that are represented in generalized polar coordinates. On resulting curvilinear anisotropic meshes, we discretize differential by finite differences or low order elements. Using an implicit extrapolation technique similar to multigrid $$\tau $...

The energy functional of ideal magnetohydrodynamics (MHD) is extended to the regime finite resistivity and transformed into an intuitive form, which separates pressure-gradient, current-density drive stabilising phenomena, analogously version derived by Greene Johnson ( Plasma Phys. , vol. 10, issue 8, 1968, pp. 729–745). resulting resistive not in form a solvable eigenvalue problem but intende...

By considering a cigar-shaped trapping potential elongated in proper curvilinear coordinate, we discover new form of wave localization that arises from the interplay geometry and topological protection. The is undulated its shape such local curvature introduces geometrical potential. varying along trap axis encodes Harper modulation. maps our system one-dimensional Andre-Aubry-Harper grating. W...

We discuss the interpretation of the perfectly matched layer (PML) absorbing boundary condition (ABC) as an analytic continuation of the coordinate space to a complex variables spatial domain (complex space). The generalization of the PML to curvilinear coordinates and to general linear media using this rationale is reviewed and summarized. The analytic continuation is shown to be equivalent to...

The reaction path is an important concept of theoretical chemistry. We discuss the definition with the help of the following of the reduced gradient (RGF) [see Quapp et al., Theoret. Chem. Acc. 100 (1998) 285], also named the Newton trajectory. All the important features of the potential energy surface are definable independently of the coordinate system. We demonstrate it for the Newton trajec...

[1] A thermomechanical ice flow model is formulated using the finite volume method. Separate submodels solve the full, two-dimensional momentum equations, the advective-diffusive heat equation, and evolution of the free surface. A unique aspect of the method is the use of a boundary-fitted, orthogonal, curvilinear coordinate system, which simplifies the implementation of boundary conditions, le...