How do you find a spherical equation?
To convert a point from Cartesian coordinates to spherical coordinates, use equations ρ2=x2+y2+z2,tanθ=yx, and φ=arccos(z√x2+y2+z2). To convert a point from spherical coordinates to cylindrical coordinates, use equations r=ρsinφ,θ=θ, and z=ρcosφ.
What is diffusion wave equation?
The fractional-order diffusion-wave equation is an evolution equation of order α ε (0, 2] which continues to the diffusion equation when α → 1 and to the wave equation when α → 2. We prove some properties of its solution and give some examples.
How do you calculate dV in spherical coordinates?
What is dV is Spherical Coordinates? Consider the following diagram: We can see that the small volume ∆V is approximated by ∆V ≈ ρ2 sinφ∆ρ∆φ∆θ. This brings us to the conclusion about the volume element dV in spherical coordinates: Page 5 5 When computing integrals in spherical coordinates, put dV = ρ2 sinφ dρ dφ dθ.
How do you convert YX to polar form?
How can I use spherical diffusion as an initial condition?
spherical diffusion with any given function f E L’ (5′) as initial condition of the diffusion process by convolving f with the Green’s function (23). Since G is a superposition of zonal spherical harmonics, i.e. spherical harmonics with m 0, G is rotationally symmetric. We can use this by
How do you solve the diffusion equation?
To solve the diffusion equation, we have to replace the Laplacian with its spherical form: We can replace the 3D Laplacian with its one-dimensional spherical form because there is no dependence on an angle (whether polar or azimuthal). The source term is assumed to be isotropic (there is the spherical symmetry).
How do you solve the diffusion equation in a spherical reactor?
The spherical reactor is situated in spherical geometry at the origin of coordinates. To solve the diffusion equation, we have to replace the Laplacian with its spherical form: We can replace the 3D Laplacian with its one-dimensional spherical form because there is no dependence on an angle (whether polar or azimuthal).
What is Green’s function of the spherical diffusion process?
tion as the Green’s function of the spherical diffusion process. This allows to introduce a linear scale space on the sphere. We apply this new filter to the smoothing of 3D object surfaces.