This is an example of a regular volumetric grid, with each volume element, or voxel represented by a single value that is obtained by sampling the immediate area surrounding the voxel.
32.
Because most heterogeneous materials show a statistical rather than a deterministic arrangement of the constituents, the methods of micromechanics are typically based on the concept of the representative volume element ( RVE ).
33.
For a certain volume element in the material \ Delta V, which carries a dipole moment \ Delta \ mathbf p, we define the polarization density "'P " ':
34.
The absolute value of a volume form is a volume element, which is also known variously as a " twisted volume form " or " pseudo-volume form ".
35.
The total energy radiated by a volume element dV in time dt between wavelengths ? and ? + d? is found by integrating the sum of the emission coefficients over all directions ( solid angle ):
36.
The 3-current density "'J "'corresponds to the motion of the charge element " dq " in volume element " dV " and varies throughout the continuum.
37.
*The time rate of temperature change at " x " is proportional to the heat flowing into an infinitesimal volume element, where the constant of proportionality is dependent on a constant " ?"
38.
The analogue of the differential element in the continuum concept ( which contains enough atom, or molecular structure to be representative of that material ), is known as the " Representative Volume Element " in homogenization and micromechanics.
39.
If " M " is not oriented, then the above calculation carries through exactly as presented, except that the volume form must instead be replaced by a volume element ( a density rather than a form ).
40.
Where d ^ 3k is a volume element in " k "-space, and which, for electrons, will need to be multiplied by a factor of 2 to account for the two possible spin orientations.
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