Summary: | Heat kernel is the fundamental solution of the diffusion equation.
The heat equation is constructed to explain types of physical phenomena (physical
quantity, vector or scalar) that propagates in the medium due to the concentration
gradient. Medium involved in our case here such as Riemannian manifold, that are
the surface of a compact and uniform spherical. Therefore, the heat kernel
formulated is related with metric space. If there are any innitial accumulation in
the surface points of the spherical, then at the same is known the profile
distribution of heat at any other point or in the entire region of the surface
spherical. Different from the space �2 where heat decays and disappears with
time, the distribution of heat on the surface of spherical is showing feedback
process to achieved a state of nature equally. Reversal phenomenon influenced by
medium compact topology. Sharpness of the heat distribution affected by the
value of the diffusion constant of physical quantities (properties) associated,
obtained through an experimentaly investigation. Initial accumulation can be
either contents or discrete quantities on the surface of spherical or the geodesic
circle on the surface of spherical.
|