Specifically, the vector of surface points can be computed by left-multiplying the vector of control points by a sparse subdivision matrix.
The orientation of electrolyte ions is the angle between artificially defined axis of ions and the normal vector of surface, and the orientation distribution is the probability distribution of the angles.
Resonance occurs when the wave vector of surface plasmon wave equals to the tangential component of evanescent wave vector (i.e., the phase-matching condition) under appropriate incident conditions (e.g., incident angle and wavelength).
Therefore, the fluid pressure acting on a segment surface is expressed by (10 where S is the area of a segment surface and n, the normal vector of the surface.
A nominal length scale based on the solutions of Laplace's equations with the unit normal vectors of surfaces as the boundary conditions is proposed for the adaptive mesh refinement in the thin regions.
It shows that the 45° incident light has better enhancement in the red light; this could be mainly because the coupling efficiency of light to the surface plasmons is higher due to the wave vector of the surface plasmons as described in Equation 1.
Here, kGCSP is the GCSP wavevector, λ0 the incident wavelength, ɛLC and ɛAL the dielectric constants of the LC and aluminium, respectively, u is the unit vector of the surface plasmon before bragg scattering, i and j are the mode orders, and Pi and Pj are the structure periodicities along the grating vectors i and j.
Hence, applying Fourier transform to correlation vector of pavement surface, commonly known as power spectral density, does serve the purpose of spectrum analysis in theory [30].
The wave vector of the surface plasmon can be described as in the equation below: k sp = k 0 sin θ + n * 2 π d, (1).
where n i is the normal vector of the surface ∂ Ω i pointing outward; δ i and γ i are two arbitrary constants; and r,θ,ϕ are radius, colatitude and longitude, respectively, in the reference frame of the spherical cap.
Furthermore, the vector n is the outward-pointing normal on the interface Γ p, r = x − x p is the position vector of the surface point with respect to the center of mass x p of a particle, F l and T l are the force and torque due to lubrication forces, and F c and T c are the force and torque due to particle collisions.
