In the autocorrelation case, the symmetric and Toeplitz structure of the correlation matrix R s is exploited to obtain numerical and computational benefits as well as an alternative view of the solution that leads to the so-called lattice methods. In this example we ignore the effects of finite propagation speed.
Thus, as previously, ρ, is a constant parameter rather than the state variable. This assumption makes the effects considered more transparent. The macroscopic motion is eliminated by the choice of vanishing barycentric velocity and assumption about the constancy of the system density, ρ, consistent with the mechanical equilibrium assumption. For the alternative ionic description, see Ref. As shown by Sundheim this setting leads to the independent fluxes of mass, energy, and electric current. The components are neutral obeying the phase rule. Again, its basic principle rests on the observation that extremizing of an arbitrary criterion subject to given constraints yields automatically a set of equations for Lagrange multipliers that is adjoint with respect to the set of constraints.Ī multicomponent, nonisothermal system is now considered, which is composed of components undergoing various transport phenomena in the bulk. The procedure may involve nongradient representations for the considered set of fields thus it constitutes a versatile tool to test various evolution functionals.
Here we shall outline a formal procedure applied for a set of vector equations of change that describe fields of temperature and chemical potentials in a coupled process of heat and mass transfer. Stanislaw Sieniutycz, in Variational and Extremum Principles in Macroscopic Systems, 2005 15 Potential representations of vector equations of change
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