Table of Contents

## 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?**

1 Answer

- θ=arctan(yx)
- x=rcos(θ)
- y=rsin(θ)

### 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.