Laplace transformation formation

Comparing eqns. (170) and (171) shows that the density distribution for the steady-state formation, recombination and scavenging, pss(r cs r0), is closely related to the Laplace transformed (time-dependent) density distribution for recombination and escape. The partially reflecting boundary condition [eqn. (46)] with p replaced by p or pss... 

D Me-S surface alloy and/or 3D Me-S bulk alloy formation and dissolution (eq. (3.83)) is considered as either a heterogeneous chemical reaction (site exchange) or a mass transport process (solid state mutual diffusion of Me and S). In site exchange models, the usual rate equations for the kinetics of heterogeneous reactions of first order (with respect to the species Me in Meads and Me t-S>>) are applied. In solid state diffusion models, Pick s second law and defined boundary conditions must be solved using Laplace transformation. 

A theoretical estimate of the temperature course at the inner wall surfaces of a 200 1 extraction vessel (solution via Laplace transformation) is shown in Figure 10. The recognisable deviations from the experimentally-measured course are attributed both to the decrease in heat transfer with time and to the lack of consideration of the enthalpy of solidification which is released during the formation of dry ice. It has also proved necessary to record the local temperatures which differ greatly during pressure release. 

Sudicky, E. A., and R.G. McLaren. 1992. The Laplace transform Galerkin technique for large-scale simulation of mass transport in discretely fractured porous formations. Water Resour. Res. 28 499-514. 

The ILT method is based on the fact that the isotopic transient of the product formation rate [r (t)] represents the Laplace transform of Np k f(k). For a pseudo-first order reaction, the transient of the product formation rate can be expressed as... 

This is typical operator format for example, we replace K with we would have the Laplace transform with respect to time, written for an unbounded time... 

Laplace transformation is another useful tool. When used in combination with linearization it can help us to write the model equations in transfer function format. Thus, to apply Laplace transform to non-Unear equations, they should first be linearized. 

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