Adaptive FEM

Ferrigno et al. [239] describe the use of FEM for steady state simulations of recessed, flush and protruding ultramicrodisk electrodes, giving a good description of FEM. The method was made adaptive by Nann (and Heinze) [407,408], and Harriman et al. later published an extensive series of papers on adaptive FEM [287,288,289,290,291]. 

It was soon realised that at least unequal intervals, crowded closely around the UMDE edge, might help with accuracy, and Heinze was the first to use these in 1986 [300], as well as Bard and coworkers [71] in the same year. Taylor followed in 1990 [545]. Real Crank-Nicolson was used in 1996 [138], in a brute force manner, meaning that the linear system was simply solved by LU decomposition, ignoring the sparse nature of the system. More on this below. The ultimate unequal intervals technique is adaptive FEM, and this too has been tried, beginning with Nann [407] and Nann and Heinze [408,409], and followed more recently by a series of papers by Harriman et al. [287,288,289, 290,291,292,293], some of which studies concern microband electrodes and recessed UMDEs. One might think that FEM would make possible the use of very few sample points in the simulation space however, as an example, Harriman et al. [292] used up to about 2000 nodes in their work. This is similar to the number of points one needs to use with conformal mapping and multi-point approximations in finite difference methods, for similar accuracy. 

The ways to simulate our chosen example, the UMDE, are described here. The integral equation approach, taken by Coen and coworkers over a number of years [167,176,177,178, 179, 180, 219] for microband electrodes, can be used on the UMDE as well [179], The reader is referred to these papers for the method. Also, although the adaptive FEM approach might be thought to be about the most efficient, and has been developed by a few workers (see above, references to Nann and Heinze, and Harriman et al), it does not seem the most popular it is not trivial to program, and as Harriman et al. found, it appears that a rather large number of nodes were required. The reason is probably that this is a kind of discretisation in the original cylindrical (A, Z)... 

Several hybrid simulations on crystal growth can be found in recent literature. Examples include dendritic solidification by coupling finite-different discretization of a phase field model to a MC simulation (Plapp and Karma, 2000), coupling a finite difference for the melt with a cellular automata for the solidification (Grujicic et al., 2001), a DSMC model for the fluid phase with a Metropolis-based MC for the surface to address cluster deposition onto substrates (Hongo et al., 2002 Mizuseki et al., 2002), a step model for the surface processes coupled with a CFD simulation of flow (Kwon and Derby, 2001) (two continuum but different feature scale models), an adaptive FEM CVD model coupled with a feature scale model (Merchant et al., 2000), and one-way coupled growth models in plasma systems (Hoekstra et al., 1997). Some specific applications are discussed in more detail below. 

Strano M, Jirathearanat S, Allan T (2001) Adaptive FEM simulation for tube hydroforming a geometry-based approach for wrinkle detection. CIRP Ann Manuf Technol 50(1) 185-190... 

Figure 23. Electronic spectra of [FenI(LBuMet)] [FenI(LBuMet )]+, and [Fem(LB"Met )]2+. [Adapted from (142).]...

Figure 24. Resonance Raman spectra of [Fem(LBuMet )]+. (a) At 418-nm, (b) at 571-nm excitation, and (c) of [Fe(LBuMet)l at 571-nm excitation (LOMe = LBuMet). [Adapted from (147).]...

Hallet, B. Sherratt, D.J. (1997) Transposition and site-specific recombination adapting DNA cut-and-paste mechanisms to a variety of genetic rearrangements. FEMS Microbiol. Rev. 21,... 

Budroni, M., Zara, S., Zara, G., Pirino, G., and Mannazzu, I. (2005). Peculiarities of flor strains adapted to Sardinian sherry-like wine aging conditions. FEMS Yeast Res. 5, 951-958. 

Erasmus, D. J., van der Merwe, G. K., and van Vuuren, H. J. (2003). Genome-wide expression analyses Metabolic adaptation of Saccharomyces cerevisiae to high sugar stress. FEMS Yeast Res. 3, 375-399. 

FEM and the like Chap. 9, Sect. 9.5. These are possibly the most efficient methods, can be made adaptive to changing conditions, but are not trivial to program. Usually packages are used. 

Saluzzi, L., Flint, H. J., and Stewart, C. S., Adaptation of Ruminococcus flavefaciens resulting in increased degradation of ryegrass cell walls. FEMS Microbiol Ecol 2001, 36 (2-3), 131-137. 

Beagley, K. W., and Gockel, C. M. (2003), Regulation of innate and adaptive immunity by the female sex hormones oestradiol and progesterone, FEMS Immunol. Med. Microbiol., 38,13-22. 

The benzene molecule contains a ring of six carbon atoms around which six delocalized jt-electrons can circulate. An adaptation of the free-electron model (FEM) for a cyclic molecule predicts a ground-state electron configuration which we can write as Itt as shown in Fig. 6.1. 

As for pure TAG or binary mixtures (13,14), a numerical model called FEM-TTT and previously developed for phase transformations in steel (16) was adapted in the case of crystallization of cocoa butter during any cooling cycle. A finite ele-... 

Alenquer, M., Tenreiro, S., and Sa-Correia, I. (2006) Adaptive response to the antimalarial drug artesunate in yeast involves PdiTp/Pdr3p-mediated transcriptional activation of the resistance determinants TPOl and PDR5. FEMS Yeast Research. 6. 1130-1139. 

The application modules can be subdivided, according to their area of employment, into genertil and specialty modules. General application modules for widespread tasks, such as FEM modules or interfaces to widely used program systems, are commercially marketed by the supplier of the CAD system or by a system supplier of complementary software. Specially adapted extensions, on the other hand, are usually either created by the user or outsourced. 

Frank, S., Schmidt, F., Klockgether, J., Davenport, C.F., Gesell Salazar, M., Volker, U., and Tummler, B. (2011) Functional genomics of the initial phase of cold adaptation of Pseudomonas putida KT2440. FEMS Microbiol Lett., 318 (1), 47-54. 

Kim, W. S., Ren, 1., Dunn, N. W. (1999). Differentiation of Lactococcus lactis subspecies lactis and subspecies cremoris strains by their adaptive response to stresses. FEMS Microbiology Letters, 171(1), 57-65. 

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