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In vector calculus, divergence is a vector operator that operates on a vector field, producing a scalar field giving the quantity of the vector field's source at each point. More technically, the divergence represents the volume density of the outward flux of a vector field from an infinitesimal volume around a given point.
The divergence theorem can be used to calculate a flux through a closed surface that fully encloses a volume, like any of the surfaces on the left. It can not directly be used to calculate the flux through surfaces with boundaries, like those on the right. (Surfaces are blue, boundaries are red.)
Bottom: Field line through a curved surface, showing the setup of the unit normal and surface element to calculate flux. To calculate the flux of a vector field F (red arrows) through a surface S the surface is divided into small patches dS. The flux through each patch is equal to the normal (perpendicular) component of the field, the dot ...
It can be used to calculate directional derivatives of scalar functions or normal directions. Divergence gives a measure of how much "source" or "sink" near a point there is. It can be used to calculate flux by divergence theorem. Curl measures how much "rotation" a vector field has near a point.
To be able to calculate this time evolution, one needs to know how to calculate the flux. This section explores the simplest hypothesis: flux is linearly related to the concentration difference (just as for molecular diffusion). This also comes as the most intuitive guess from the analysis just made. Flux is in principle a vector.
Since the flux is defined as an integral of the electric field, this expression of Gauss's law is called the integral form. A tiny Gauss's box whose sides are perpendicular to a conductor's surface is used to find the local surface charge once the electric potential and the electric field are calculated by solving Laplace's equation.
Chemical graph theory is the topology branch of mathematical chemistry which applies graph theory to mathematical modelling of chemical phenomena. [1] The pioneers of chemical graph theory are Alexandru Balaban, Ante Graovac, Iván Gutman, Haruo Hosoya, Milan Randić and Nenad Trinajstić [2] (also Harry Wiener and others). In 1988, it was ...
Fick's first law relates the diffusive flux to the gradient of the concentration. It postulates that the flux goes from regions of high concentration to regions of low concentration, with a magnitude that is proportional to the concentration gradient (spatial derivative), or in simplistic terms the concept that a solute will move from a region of high concentration to a region of low ...