Sources of Multiplicity

Catalytic and biocatalytic reactors are exceptionally rich in bifurcation and instability problems. These can come from many sources, of which we outline a few below. 

---

Fig. 16.1 Homestead - a source of multiple products (trees, vegetables, cows, chicken)... 

Chitnis V, Chitnis D, Patil S, Kant R (2000) Hospital effluent as a source of multiple drug-resistant bacteria. Curr Sci India 79 989-991... 

The multiplicity of steady states and associated bifurcation phenomena are associated with open systems which allow more than one stationary nonequilibrium state for the same set of parameters. This multiplicity of a steady state may result from many causes. The most important sources of multiplicity in chemical/biological engineering processes are ... 

Figure 2.5 shows a distributed system with recycle which is a source of multiplicity. 3. Countercurrent operation as shown below. 

These sources of multiplicity are very frequent in actual chemical/biological processes. Chapter 7 highlights examples of multiplicity, bifurcation, and chaotic behavior for a number of experimental and industrial chemical/biochemical processes. We also include Appendix 2 on multiplicity and bifurcation at the end of the book. 

This source of multiplicity is probably the most intrinsic one in catalytic and biocatalytic reactors, for it occurs due to the nonmonotonic dependence of the intrinsic rate of reaction upon the concentration of reactants and products. Although a decade ago, nonmonotonic kinetics of catalytic reactions were considered the exceptional case, today it is clear that nonmonotonic kinetics in catalytic reactions are much more widespread than previously thought. The reader can learn more about various examples from the long list of catalytic reactions exhibiting nonmonotonic kinetics [71-76]. 

Therefore, the main source of multiplicity in fixed-bed catalytic reactors is through the coupling between the exothermic reaction and the catalyst pellet mass- and heat-transfer resistances. 

Glial cells are a source of multiple cytokines, including interleukin-1 /3 (IL-1 /3), IL-6, and tumor necrosis factor-a (Hanisch, 2002). These cytokines can contribute to different features of pathological pain, although their role within the spinal cord has not been completely understood (DeLeo and Yezierski, 2001 Watkins... 

The example clearly demonstrates the scale of difficulty involved in speciation analysis, and the fact that it requires a case-by-case approach. A helpful tool in the process is a list of typical errors (Table 12.3). Each time, however, one should be aware that the procedures are extremely complex, the stability of compounds is a source of multiple problems, and the quality of separation and assaying depends to a... 

Damm KL, Carlson HA (2007) Exploring experimental sources of multiple protein conformations in structure-based drug design. J Am Chem Soc 129 8225-8235... 

Every second protein domain in PDB is represented by more than one PDB entry 20% of proteins have two structures, and the remaining 30% more than two structures. Some of them are mutants (e.g., 400 of T4 lysozyme structures from Brian Matthews s laboratory) but in most cases, these multiple structures represent snapshots of the pocket conformational diversity. Furthermore, many entries contain more than one chain in an asymmetric unit. These protein structures related by noncrystallographic symmetry can also be used as a source of multiple pocket conformations. The noncrystallographic symmetry-related subunits increase the number of domains already represented by multiple experimental conformations from 50% to the overall level of 75% (Fig. 2). About 5% of the domains are represented by more than 30 copies. 

The sources of nitrogen for worldwide crop production are given in Table 19.2 [4]. Soils are the source of multiple nutrients however, resources of nutrients in the soil are always limited and must be supplemented. The atmosphere supplies some nitrogen, sulfur dioxide, and chlorides near ocean shores. Water supplies some quantities of calcium, magnesium, and potassium. AH of ftese sources should be considered in the selection of soil man- age.m.e.rifJ3.ractice.s.- ... 

FIGURE 4.3.2 Typical setup for the optical (laser) readout system. VCSEL is usually used as a source of multiple laser light. Each laser light reflected on the surface of each cantilever is measured by a PSD. Reproduced from Ref. [10], with permission from the Royai Society of Chemistry. 

---