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  • 1
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 107 (1997), S. 5929-5944 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A mathematically exact method is presented for sampling conformations of polymer molecules in an external field with fixed energy or energy range in accord with the formulation of statistical mechanics for a microcanonical ensemble. As a consequence, conformations of negligible Boltzmann weight can be selectively eliminated from simulations for efficient calculation of macroscopic polymer properties. The method is applicable for conformations that are described by a stochastic differential equation along the contour length in the field-free situation. It is based on the concept of a stochastic bridge process for which a new stochastic differential equation is derived that has stipulations at both ends of the process. This idea is exploited on a pair of stochastic differential equations in the conformation vector X and an augmented variable Z which represents the running Boltzmann weight in the given field, transforming to a new pair of equations for which the terminal Boltzmann weight can be arbitrarily stipulated. The stochastic equation for the bridge involves solving the Fokker–Planck equation for the original stochastic pair. We demonstrate the method on the conformation of a "Brownian" polymer in a quadratic external field of varying strength. The stochastic differential equations for the bridge process in this case can be derived analytically. Sample conformations are displayed that satisfy exactly energy constraints either at fixed values or within a stipulated range. It is shown that polymer properties can be computed more efficiently and accurately with the bridge process simulations than by unconstrained process simulations. The bridge process approach presented here must be distinguished from other approaches such as umbrella sampling methods because of the former's ability to sample conformations exactly with stipulated energy constraints. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    Biotechnology progress 10 (1994), S. 574-587 
    ISSN: 1520-6033
    Source: ACS Legacy Archives
    Topics: Process Engineering, Biotechnology, Nutrition Technology
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    Biotechnology progress 10 (1994), S. 588-605 
    ISSN: 1520-6033
    Source: ACS Legacy Archives
    Topics: Process Engineering, Biotechnology, Nutrition Technology
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    Macromolecules 27 (1994), S. 5987-5999 
    ISSN: 1520-5835
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    Industrial and engineering chemistry 25 (1986), S. 258-265 
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    Industrial and engineering chemistry 25 (1986), S. 554-560 
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    Industrial & engineering chemistry research 34 (1995), S. 3223-3230 
    ISSN: 1520-5045
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Flow, turbulence and combustion 36 (1980), S. 13-34 
    ISSN: 1573-1987
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The extension of the Graetz problem to include axial conduction has been of interest in view of its application to a number of low Peclet number heat or mass transfer situations. Past efforts in dealing with this problem have been plagued with uncertainties arising from expansion in terms of “eigenfunctions” and “eigenvalues” belonging to a nonselfadjoint operator. The uncertainties spring from a lack of basis for the assumptions that no complex eigenvalues exist and that the calculated eigenvectors originate from a complete set. Other methods have been entirely numerical. The present work produces an entirelyanalytical solution to the Graetz problem for the Dirichlet boundary condition based on a selfadjoint formalism resulting from a decomposition of the convective diffusion equation into a pair of first order partial differential equations. Physically, the decomposition views the convective diffusion process as a pair of stipulations on how the temperature (or concentration) and theaxial energy (or mass) flow through a partial tube cross-section vary with radial and axial distances. The solution obtained is simple, and readily computed.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Biotechnology and Bioengineering 52 (1996), S. 141-151 
    ISSN: 0006-3592
    Keywords: cybernetic modeling ; biosynthetic precursors ; metabolic regulation ; enzyme synthesis ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Growth of microorganisms on substitutable substrate mixtures display diverse growth dynamics characterized by simultaneous or preferential uptake of carbon sources. This article shows that cybernetic modeling concepts which were successful in predicting diauxic growth patterns can be extended to describe simultaneous consumption of substrates. Thus the growth of Escherichia coli on mixtures of glucose and organic acids such as pyruvate, fumarate, and succinate has been described successfully by the cybernetic model presented here showing both diauxic and simultaneous uptake when observed. The model also describes the changes in utilization patterns that occur under changing dilution rates, substrate concentrations, and models of preculturing. The model recognizes the importance of the synthesis of biosynthetic precursors in cell growth through a kinetic structure that is quite general for any mixture of carbon-energy sources. © 1996 John Wiley & Sons, Inc.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Biotechnology and Bioengineering 54 (1997), S. 77-90 
    ISSN: 0006-3592
    Keywords: microbial growth ; consumer-resource relationship ; substrate ; carbon sources ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: In this article, we consider the growth of microorganisms on mixtures of carbon sources and characterize the consumer-resource relationship for this system. The characteristic features observed for the growth of a single microorganism on a pair of carbon sources allow a representation of this relationship based on a general paradigm for resource classification. This representation is verified using a comprehensive model for microbial growth on carbon sources. The results show that for the same pair of carbon sources the qualitative nature of the consumer-resource relationship changes with changing specific growth rate, and therefore a change in the identity of the rate-limiting substrate(s). © 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 54: 77-90, 1997.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
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