Also the mixture fraction f is linearly related to ? , so it is also a passive scalar and obeys the scalar transport equation.
32.
Assuming the phonon transport is diffusive and Boltzmann transport equation ( BTE ) is valid, nanowire thermal conductance " G ( T ) " can be defined as:
33.
Complex transport equations must be solved to determine the time and spatial response of charges, for example, the Boltzmann equation or the Fokker Planck equation or the Navier Stokes equations.
34.
At yet larger length scales ( mesoscale, involving many mean free paths ), the Boltzmann transport equation ( BTE ) which is based on the classical Hamiltonian-statistical mechanics is applied.
35.
He developed the projection operator formalism, which made it possible to derive irreversible transport equations ( such as the Boltzmann equation and other master equations ) from reversible microscopic quantum mechanical dynamic equations.
36.
The Boltzmann transport equation has been found to be very useful in simulations of electron transport in lightly doped semiconductors ( in transistors ), where the electrons are indeed analogous to a rarefied gas.
37.
For instance, in the transport equation, which describes a number of different transport phenomena, terms are separated into " convective " and " diffusive " effects, with " convective " meaning purely advective in context.
38.
For example, in real materials, complex transport equations must be solved to determine the time and spatial response of charges, for example, the Boltzmann equation or the Fokker Planck equation or the Navier-Stokes equations.
39.
The evolution of the m-th fluid in a system on n fluids is governed by the transport equation ( actually the same equation that has to be fulfilled by the level set method distance function \ phi ):
40.
The transport equation can be applied to a given part of phase space ( time t, energy E, location \ mathbf { r }, and direction of travel \ mathbf { \ hat { \ Omega } } ).
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