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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Zeitschrift für angewandte Mathematik und Physik 44 (1993), S. 707-721 
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The possibility of initiating reaction-diffusion waves in an autocatalytic system represented schematically byA→B, ratekab p (p 〉- 1, witha, b being the concentrations ofA andB respectively) is considered through the local input ofB, measured by the parameter β0, into an otherwise uniform expanse ofA. It is shown that for 1 〈-p 〈 1 + (2/N) (whereN is the space dimension) waves develop no matter how small the value of β0, while forp 〉 1 + (2/N) there is some threshold value of β0 below which waves are not formed, with diffusion playing the dominant role throughout. A lower bound for this threshold value is found. The permanent-form travelling wave equations are then discussed and the behaviour of the solution asp → 1 is considered in detail. It is shown that a three-region structure develops with the asymptotic wave speedv being singular (of the formv ∼ 2−2.3381 (p- 1)2/3) asp → 1.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Zeitschrift für angewandte Mathematik und Physik 43 (1992), S. 471-480 
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract In this paper we consider the question of the existence of solutions to an initial-boundary value problem for a singular, semilinear, parabolic equation arising from the study of autocatalytic chemical kinetics of the typeA →B at ratek[A][B] P , whereA is a reactant,B is the autocatalyst,k〉0 the rate constant and 0〈p〈1 the order of the reaction, King and Needham [1]. A monotone iteration method is adopted in the spirit of Sattinger [2], However the general theory due to Sattinger [2] cannot be applied directly because of the singular nature of the source term in the equation.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Zeitschrift für angewandte Mathematik und Physik 42 (1991), S. 455-459 
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract In this note we consider a reaction-diffusion problem which describes a simple model chemical reaction scheme for quadratic autocatalysis with linear decay. We show that withk〉1 (wherek is a parameter measuring the relative strength of the decay step to the autocatalytic step) the dimensionless unreacting state α≡1, β≡0 is globally asymptotically stable, with α∼1+0(t −1/2) and β∼ 0(t −1/2 e −(k−1)t) ast→-∞. Here α and β are the concentrations of the reactant and the autocatalyst respectively, andt is time. The casek〈1 has been considered in detail by Merkin et al. [1].
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Journal of engineering mathematics 27 (1993), S. 113-145 
    ISSN: 1573-2703
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Abstract A clock reaction is a chemical reaction which gives rise to an initial induction period before a significant concentration of one of the chemical species involved is produced. We study four closely related isothermal model reactions schemes which can exhibit clock reaction behaviour in a well-stirred situation. These reaction schemes represent a combination of quadratic or cubic autocatalysis with linear or quadratic inhibition.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Biotechnology and Bioengineering 38 (1991), S. 838-852 
    ISSN: 0006-3592
    Keywords: hybridoma cells ; cell cycle ; morphology ; geometry ; mechanical properties ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Morphological, geometrical, and rheological properties of the GAP A3 hybridoma cell line have been evaluated as a function of the cell cycle. Interference contrast video microscopy and scanning electron microscopy (SEM) showed that a sample of cells taken from the middle of the exponential growht phase displayed a range of cell morphologies, consistent with a heterogeneous growing culture. Micropipet manipulation was used to measure the geometrical (cell volume) and mechanical (cortical tension and apparent cell viscosity) properties of single cells selected at random from a sample in the middle of the exponential growth phase. Consistent with the range of morphologies, cell volumes (1400 to 5700 μm3) and apparent viscosities (430 to 1.2 × 104 P) showed a wide range of values at 37°C, demonstrating that a hybridoma cell line cannot be characterized by a single value for any one property, and that properties must be related to their cycle dependence when considering proliferating cells. Direct, video-microscopic observation of synchronized cells, and of individual cells that were followed throughout their cell cycle, allowed us to correlated distinct morphologies with phases of the cell cycle. As the cell cycle progresses, an increase in cell volume by a factor of 3 to 4is accompanied by an overall increase in apparent cell viscosity by approximately the same ratio, consistent with an accumulation of more cytoplasmic material in the older cells. Also, a decrease in average apparent viscosity by a factor of 10. These results are important in order to evaluate the possible role of certain structural, cell-cycle dependent features in shear and abrasion sensitivity. This is a problem of current concern in the bioreactor culture of mammalian cells.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
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