Zeroth-order point processes

In order to systematically remedy the previous drawbacks, we recently proposed to perform a perturbation treatment, not on a wavefunction built iteratively, but on a wavefunction that already contains every components needed to properly account for the the chemistry of the problem under investigation [34], In that point of view, we mean that this zeroth-order wavefunction has to be at least qualitatively correct the quantitative aspects of the problem are expected to be recovered at the perturbation level that will include the remaining correlation effects that were not taken into account in the variational process any unbalanced error compensations or non-compensations between the correlation recovered for different states is thus avoided contrary to what might happen when using any truncated CIs. In this contribution, we will report the strategy developed along these lines for the determination of accurate electronic spectra and illustrate this process on the formaldehyde molecule H2CO taken as a benchmark. 

Attempts are also known to relate the type of time dependence of viscosity in the curing process to the kinetics of the reaction. Thus, upon curing of diglycidyl ester of Bisphenol A by triethanolamine, the viscosity curve Tj (t) was approximated by two linear segments [40]. The appearance of an inflection point is explained by the authors on the basis of the formation of a meshing network an the linearity of the tj (t) dependence in the first party by the fact that a curing reaction is of a zeroth order. 

Below, we will discuss two important examples of zeroth-order point processes as seen from the perspective of the particle-phase NDF. However, some zeroth-order point processes such as the formation of the disperse phase from the fluid phase are accompanied by a change of state in the fluid phase (i.e. the total mass and momentum of the two phases are conserved). Thus, seen in the perspective of the particle and fluid phase, the overall process requires a decrease in the mass of the fluid phase equal to the mass of the formed particle, which is represented by the term 5m in Eq. (4.68) on page 119. In other words, the term 5m in Eq. (4.77) representing the rate of addition of mass to the particle phase from the fluid phase must follow from the source term for the zeroth-order point process for formation of the disperse phase. Using the properties of delta functions, we can formally write the source term in Eq. (5.1) for a zeroth-order point process as... 

Let us consider as an example nucleation, which is a zeroth-order point process, since it introduces new particles into the system at a rate independent of the NDF. Zeroth-order point processes are usually treated in a very simple way by calculating the contribution to each class. For example, if just nucleation is occurring, the PBE becomes... 

This PBE is written in a general form and contains the terms representing accumulation, real-space advection, phase-space advection, phase-space diffusion, and second-, first-, and zeroth-order point processes. (See Chapter 5 for more details on these processes.) Let us... 

There are, however, three very important implicit assumptions in this model, apart from those of an ideal interface. Firstly, since desorption is only allowed to occur from a constant precursor state population (dn/dt = 0), it is effectively always a zeroth-order process. If a different order is observed, desorption is not the rate-limiting step. The second point is that this treatment is only appropriate for cases where the metal-metal bond energy (around the peripheries of the islands) is less than that for the metal- semiconductor, since for the opposite case the weaker adsorbate—surface bond will not prevent an atom desorbing once it has acquired sufficient energy to break the (stronger) metal—metal bond. Thirdly, no provision is made for possible diffusion of the adsorbate into the substrate during desorption. 

---