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The construction of spectrally accurate tangential basis functions allows a one-third reduction in the number of unknowns required compared with algorithms using non-tangential basis functions.
A key feature of our method is spectrally accurate approximation of the tangential surface current using a new set of tangential basis functions.
If R is the position vector in spherical coordinates then the covariant (tangential) basis vectors, v i, are defined by (2 while the contravariant (cotangent, reciprocal, dual, normal or gradient) basis vectors, v i, are (3).
The tangential velocity in Eq. (26) is obtained from the decomposition (32) v ˆ T = I - ν ˆ ⊗ ν ˆ v ˆ Hence, no assumptions on the smoothness of the contact surface are required for the computation of the tangential basis.
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Previously, we studied several specific features of tangential discontinuities on the basis of Cluster measurements in February April 2003.
We note that instead of defining the "radial" and "tangential" orientations on the basis of a sphere fit on the local curvature of the inner surface of skull near the source location (Haueisen et al. 1995), the SVD automatically provides the source orientation of lowest and highest signal power in the sensor array.
This paper provides the theoretical basis for modeling tangential injection into ideal tubular flames.
A method of predicting the tangential velocity profile on the basis of equivalent settling area without performing velocity measurement is detailed and examined for an experimental velocity profile.
Define a (contravariant) coordinate set (u1, u2, u3) that is a function of the spherical coordinates, (R,θ, ϕ) and then define two sets of basis vectors, one tangential to the geomagnetic field with the other set orthogonal to the ionosphere current sheet.
This shows that d t ′ / Δ ˜ x and d s ′ / Δ ˜ x are the components of the Δ-tangential vector with respect to basis { ∂ φ / Δ 1 ′ t ′, ∂ φ / Δ 2 ′ s ′ }.
Previous studies demonstrated an extensive connectivity between different tangential cells, providing, in principle, the structural basis for their large and complex receptive fields.
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