Birge model

Fora recent survey of reactive and stochastic chemical batch scheduling approaches, the reader is referred to Floudas and Lin [2], For a survey of the different types of probabilistic mathematical models that explicitly take uncertainties into account, see Sahinidis [12]. For detailed information about stochastic programming and its applications, the reader is referred to the books of Birge and Louveaux [9], Ruszczynski and Shapiro [10], or Wallace and Ziemba [26]. 

Birge, J.R. (1995) Models and model value in stochastic programming. Annals of Operations Research, 59, 1. 

The problem might also entail multiple stages if it is intended to model multiple design decision periods. See Birge and Louveaux (1997, pp. 59-60) for a discussion of the issue. 

Photoisomerization.—Birge and Hubbard analyse the molecular dynamics of cis-trans isomerization in the visual pigment rhodopsin using INDO-CISD molecular orbital theory and semiempirical molecular dynamic theory. The analysis predicts that the excited-state species is trapped during isomerization in an activated complex that has a lifetime of 0.5ps. This activated species oscillates between two components which preferentially decay to form isomerized product (bathorhodopsin) or unisomerized 11-cw-chromophore (rhodopsin) within 1.9—2.3ps. The authors further conclude that the chromophore in bathorhodopsin has a distorted all-rraw-geometry and is the most realistic model for the first intermediate in the bleaching cycle of rhodopsin. 

The various methods to calculate the vibrational frequencies and force constants from ab-initio data on diatomic molecules is represented in Sections 5 A to K. It is seen that the various approximations yield results which fluctuate from molecule to molecule, although the order of magnitude is mostly correct. It is clear, however, that it is not at the present moment possible to calculate co and ke of molecules to such a d ee of accuracy that the factors which contribute to the intemudear forces in molecules can be pinpointed and compared. This is perhaps the reason why semi-empirical models continue to be exploited, e.g. the simple bond-charge model (electrostatic) model for P.E.-curves of homonudear diatomic molecules of Parr and Borckmann (114) based upon the Fues potential from which the famous Birge-Mecke relation is derived ... 

The general extensive form of a two-stage mixed-integer linear stochastic problem for a finite number of scenarios can be written as follows (Birge and Louveaux, 1997) Model SP ... 

De Araujo and Y. Kawano used curve fitting calculations and local mode theory to assign overtone and combination frequencies in the NIR spectra of polyamide 6 (PA 6), poly(vinyl chloride) (PVC), and polychlorotrifluoroethylene (PCTFE). Anharmonicity correction and mechanical frequency were determined from a Birge-Sponer plot. Anharmonicity corrections of 55, 61, and 20 cm were obtained for CH2 NH, and CO stretch modes of PA 6, respectively, and of 60 and 66 cm for CH2 and CH stretch modes of PVC, respectively. The local mode model seemed to be adequate to interpret the origin of the bands of PA 6 and PVC. Anharmonicity corrections of 33, 19, and 16 cm were... 

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