Finite Element Approximation of the Levi-Civita Connection and Its Curvature in Two DimensionsCURVATURERIEMANNIAN metricTENSOR fieldsDIFFERENTIAL operatorsTRIANGULATIONWe construct finite element approximations of the Levi-Civita connection and its curvature on triangulations of oriented t...
In general, there are two important types of curvature: extrinsic curvature and intrinsic curvature. The extrinsic curvature of curves in two- and three-space was the first type of curvature to be studied historically, culminating in the Frenet formulas,
In addition, the proposed discrete gravity avoids the problem of failure of the Liebnitz rule, which is usually a main obstacle to the development of the theory of discretized manifolds [6]. In this paper, we study numerically the scalar curvature tensor in two dimensions in the discrete ...
In two dimensions, magnetization M (magnetic dipole moment per unit area) is given in units of current (A), which—for the case of a uniformly magnetized domain—describes the equilibrium current that circulates along the edges of the domain. Thus, mz(x, y) and Ja.c.(x, y) ...
A class of mathematical models that treat cells as individual objects, represented by polygons in two dimensions and polyhedra in three dimensions. Epithelial tissues are modelled as a connected mesh of these polygons or polyhedral elements, and mechanical forces are applied to the vertices of these...
This chapter introduces curvature in the following orders: Euclidean Plane --> plane curve --> space curve --> curve in higher dimensions. 1 The Euclidean Plane Congruence: Two plane figures are congruent if one can be transformed into the other by a rigid motion of the plane, which is a...
On uniform Cartesian grids, in two dimensions, the approach proposed in this paper yields the exact same formulas for the second-order estimation of Hx and Hxx as those commonly used in the literature [10]. In the three-dimensional case, however, the coefficients resulting from the proposed ...
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For a very small transverse curvature parameter, the problem can be solved in two dimensions, but for a thin cylinder, the radius order can be the same as the order of the boundary-layer thickness. As a result, the problem can be assumed axisymmetric. In the latter case, the surface ...
Curvature and concentration of Hamiltonian Monte Carlo in high dimensions. arXiv preprint arXiv:1407.1114, 2014.S. Holmes, S. Rubinstein-Salzedo, C. Seiler, "Curvature and concentration of Hamiltonian Monte Carlo in high dimensions", arXiv:1407.1114, May. 2015....