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Mathematical Air Pollution Models: Eulerian Models
Published in Davidson Moreira, Marco Vilhena, Air Pollution and Turbulence, 2009
The literature proposes several expressions for Kz, which is generally a function of height z (for instance, Pleim and Chang, 1992). For instance, an approach for estimating the eddy diffusivity K and dispersion parameters as functions of eddy scale size in the PBL and relative amount of turbulent energy has been recently proposed by Degrazia and Moraes (1992) and Degrazia et al. (1997, 2000). Making use of Taylor’s statistical theory (Taylor, 1921), the Hay and Pasquill working approximation of the relationship between Lagrangian and Eulerian turbulence spectra (Hay and Pasquill, 1959), and a model for Eulerian spectra, such approach relates plume dispersion in a boundary layer mainly to the turbulent eddies acting in the different stability regimes of the boundary layer (Pasquill and Smith, 1983). Bearing the K-theory limitations in mind, the main idea of the said approach is to obtain an eddy diffusivity scheme for practical applications in air pollution modeling, which reveals the essential features of turbulent diffusion, but which as far as possible preserves the simplicity and flexibility of the K-theory formulation. Degrazia et al. (1997, 2000) propose the vertical profiles of diffusion coefficients obtained by means of spectral techniques.
The history of Tutte–Whitney polynomials
Published in Joanna A. Ellis-Monaghan, Iain Moffatt, Handbook of the Tutte Polynomial and Related Topics, 2022
Brylawski [251, 252] discerns in Tutte's “ring in graph theory” [T47] a relative of the Grothendieck ring of K-theory.29 To express this idea, he develops in [252] a theory of the Tutte bidecomposition, under which a matroid M may be decomposed into the formal sum M\e+M/e (where e∈E(M)), and if M is a disjoint union (i.e., direct sum) of M1 and M2, it may also be decomposed into the formal product M1M2. In so doing, he generalizes the core of [T47] to matroids (geometrically viewed), expanding on the algebraic aspects (and without Tutte's topological language). Instead of Tutte's notion of V-functions, we now have Tutte(–Grothendieck) invariants, which are like V-functions except (i) they apply to matroids, not just graphs; (ii) the deletion–contraction relation need not hold for bridges; and (iii) they must be multiplicative over blocks, not just over components. In [251], Brylawski gives a “reaxiomatization” of the Grothendieck ring, calling it the Tutte–Grothendieck ring and noting that Tutte's work was earlier. The theory covers other settings with their own Tutte–Grothendieck rings, including some involving vector spaces, matrices, and groups. These papers report some of the work of Brylawski's PhD (Dartmouth College, 1970), also supervised by Rota. Kung [728, Section IV.1] gives an excellent discussion of the connection with K-theory.
Sensitivity assessment of PM2.5 simulation to the below-cloud washout schemes in an atmospheric chemical transport model
Published in Tellus B: Chemical and Physical Meteorology, 2018
XINGCHENG LU, JIMMY C. H. FUNG
The CAMx model domain coverage is represented by the solid line in Fig. 1. In CAMx, CB05 (Carbon Bond Mechanism 05) and RADM (Regional Acid Deposition Model) were selected for gas-phase chemistry and aqueous-phase chemistry schemes. The inorganic aerosol and secondary organic aerosol modules are ISORROPIA 1.7 (Nenes et al., 1998) and SOAP, respectively. We selected the coarse/fine aerosol chemistry scheme (CF) and used the K-theory for the vertical diffusion simulation, and the Euler Backward Iterative (EBI) served as the chemical solver. The base model was CAMx v6.00 and we changed the source code of the wet deposition module based on different schemes (including CAMx v6.40) and size distribution for the comparison. We used INTEX-B (Zhang et al., 2009) emission inventory (including SO2, NOx, CO, VOC, PM, BC and OC) for the 27-km and 9-km domains. A resolved local emission inventory (Zheng et al., 2009) is used for the simulation in the 3-km domain. We used the Model of Gases and Aerosols from Nature (MEGAN v2.04) (Guenther et al., 2006) for biogenic emission generation. The spatial map of the emissions used in this study can be found in Lu et al. (2015).