The notion of a volume element is not limited to three dimensions : in two dimensions it is often known as the "'area element "', and in this setting it is useful for doing surface integrals.
42.
The scattering is best described by an emission coefficient which is defined as ? where ? dt dV d? d? is the energy scattered by a volume element dV in time dt into solid angle d? between wavelengths ? and ? + d?.
43.
This model means that macro-fracture initiation from one material element, or more precisely one representative volume element ( RVE ), causes the whole structure to fail, like the failure of one link in a chain ( Fig . 1a ).
44.
This leads to tensor random fields in which the key role is played here a Statistical Volume Element ( SVE ); when the SVE becomes sufficiently large, its properties become deterministic and one recovers the Representative volume element ( RVE ) of deterministic continuum physics.
45.
This leads to tensor random fields in which the key role is played here a Statistical Volume Element ( SVE ); when the SVE becomes sufficiently large, its properties become deterministic and one recovers the Representative volume element ( RVE ) of deterministic continuum physics.
46.
Some of the applications of the Bures metric include that given a target error, it allows the calculation of the minimum number of measurements to distinguish two different states and the use of the volume element as a candidate for the Jeffreys prior probability density for mixed quantum states.
47.
Where \ theta is the angle between the liquid-crystal molecular axis and the " local director " ( which is the'preferred direction'in a volume element of a liquid crystal sample, also representing its " EPR can be used to determine S.
48.
Note that we have used the fact that the phase space volume element d ^ 3 \ bf { r } d ^ 3 \ bf { p } is constant, which can be shown using Hamilton's equations ( see the discussion under Liouville's theorem ).
49.
The emission of atomic line radiation at frequency may be described by an emission coefficient \ epsilon with units of energy / time / volume / solid angle . " ? dt dV d? " is then the energy emitted by a volume element dV in time dt into solid angle d \ Omega.
50.
When the separation of scales does not hold, or when one wants to establish a continuum of a finer resolution than that of the representative volume element ( RVE ) size, one employs a " statistical volume element " ( SVE ), which, in turn, leads to random continuum fields.
