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Closed orbits and semiclassical wavefunctions in two-dimensional Hamiltonian systems (1992)

Mao, J. -M. ; Shaw, J. ; Delos, J. B.

Springer

Journal of statistical physics 68 (1992), S. 51-96

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ISSN: 1572-9613

Keywords: Semiclassical approximation ; Green's function ; closed-orbit theory ; Maslov index ; atomic absorption spectra

Source: Springer Online Journal Archives 1860-2000

Topics: Physics

Notes: Abstract The periodic-orbit theory of the density-of-states and the closed-orbit theory of atomic absorption spectra relate properties of a quantum system to properties of periodic or of closed orbits of a system. In these theories, every return of an orbit to the initial point makes a contribution, so in general for each orbit an infinite number of terms must be computed and summed. We show that the term asising from thenth return of an orbit can be calculated from properties of the orbit on its first return.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01048837

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Changes of lipase-catalyzed lipolytic rates in a batch reactor (1992)

Wang, Y. J. ; Wang, F. F. ; Sheu, J. Y. ; [et al.]

New York, NY [u.a.] : Wiley-Blackwell

Biotechnology and Bioengineering 39 (1992), S. 1128-1132

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ISSN: 0006-3592

Keywords: lipolytic rates ; hydrolysis ; tributyrin ; Candida rugosa ; Chemistry ; Biochemistry and Biotechnology

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology

Notes: A dramatic change of the reaction rate was observed for the lipase-catalyzed hyrolysis of tributyrin in a batch reactor. Immediately after the addition of the enzyme, the lipolysis rate increased continuously until a maximal reaction rate was reached. The duration of the induction was mainly controlled by the bulk enzyme concentration and the reactor stirring speed. The reaction rate dropped sharply after reaching its maximal value. The lipolysis decayed at a rate of about 0.012 min-1, and was not affected by changes of the stirring speed. This decay was attributed to the fast deactivation of the surface-adsorbed lipase, and possibly to the extremely slow desorption of the inactivated species. For reaction time longer than 120 minutes, the lipolysis decreased at a much slower rate. Several mechanisms for the decay of the lipolysis rate were discussed.

Additional Material: 10 Ill.