Sentence examples for parallel transport from inspiring English sources

Then, we solve a first-order ODE of the tangent vector using the fourth-order Runge Kutta method, and parallel transport it along ˆγ.

In the case of a plasma with strongly magnetized electrons, we apply the technique to determine the parallel electric field and parallel transport within the plasma.

The Kato dynamics, W s), tells you how to "parallel transport" a vector (v in {text {ran}}, P gamma (0))) along a curve (gamma (s);,0 le s le 1) in ({mathcal M}).

Accuracy-wise, the approach is free from the numerical pollution introduced by the discrete parallel transport term when the perpendicular to parallel transport coefficient ratio χ⊥/χ∥ becomes arbitrarily small, and is shown to capture the correct limiting solution when ϵ="χ⊥L∥2χ∥L⊥2→0 (with L∥, L⊥ the parallel and perpendicular diffusion length scales, respectively).

The numerical implementation is based on an operator-split formulation, with two straightforward steps: a perpendicular transport step (including sources), and a Lagrangian (field-line integral) parallel transport step.

However, since the two normals (nu _E x)) and (nu _{B_vartheta (p)}(pi _{vartheta,p}(x))) lie in two different tangent spaces in order to measure their distance correctly we have to parallel transport the normal (nu _{B_vartheta (p)}(pi _{vartheta,p}(x))) to the tangent space (T_xmathbb {S}^n).

A straight line in Euclidean space is the only curve that parallel-transports its own tangent vector.

That is, a curve \ \gamma\) in curved space, which parallel-transports its own tangent vector along all of its points, is called a geodesic curve.

A linear connection D ~ Open image in new window on TM ( D ~ Open image in new window on L π E ) Open image in new window is said to be a distinguished connection (d-connection) if it preserves by parallelism (i.e., by parallel transports defined by the corresponding covariant derivative) the vertical and horizontal distributions (Equation 70) on TM (Equation 71 on L π E Open image in new window).

The gradient flow parallel-transports the normal vector to the surface (and to the gradient) from the start to the end of the simulated reach.

A parallel resistance transport model has been developed to describe variations in separation ability (quality) of nanoporous carbon membranes.