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  • 1
    Digitale Medien
    Digitale Medien
    INTERACTING OSCILLATORY CHEMICAL REACTORS (1979)
    Oxford, UK : Blackwell Publishing Ltd
    Annals of the New York Academy of Sciences 316 (1979), S. 0 
    Details
    ISSN: 1749-6632
    Quelle: Blackwell Publishing Journal Backfiles 1879-2005
    Thema: Allgemeine Naturwissenschaft
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1111/j.1749-6632.1979.tb29478.x
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  • 2
    Digitale Medien
    Digitale Medien
    Multi-species interactions with hereditary effects and spatial diffusion (1979)
    Springer
    Journal of mathematical biology 7 (1979), S. 231-241 
    Details
    ISSN: 1432-1416
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Summary We study the effect of spatial diffusion on oscillatory states in arbitrary multi-species growth models having hereditary terms. We show that it is a general principle that the addition of spatial diffusion to a stable oscillatory ecological community induces a periodic diffusion wave in which the original wavenumber (or phase) evolves according to a nonlinear evolution equation of generalized Burgers' type.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00275726
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  • 3
    Digitale Medien
    Digitale Medien
    Transport effects on surface–volume biological reactions (1999)
    Springer
    Journal of mathematical biology 39 (1999), S. 533-561 
    Details
    ISSN: 1432-1416
    Schlagwort(e): Key words: Biomolecular reactions ; Rate constants ; Singular perturbations ; Asymptotics ; Integral equations
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract.  Many cellular reactions involve a reactant in solution binding to or dissociating from a reactant confined to a surface. This is true as well for a BIAcoreTM, an optical biosensor that is widely used to study the interaction of biomolecules. In the flow cell of this instrument, one of the reactants is immobilized on a flat sensor surface while the other reactant flows past the surface. Both diffusion and convection play important roles in bringing the reactants into contact. Usually BIAcoreTM binding data are analyzed using well known expressions that are valid only in the reaction-limited case when the Damköhler number Da is small. Asymptotic and singular perturbation techniques are used to analyze dissociation of the bound state when Da is small and O(1). Linear and nonlinear integral equations result from the analysis; explicit and asymptotic solutions are constructed for physically realizable cases. In addition, effective rate constants are derived that illustrate the effects of transport on the measured rate constants. All these expressions provide a direct way to estimate the rate constants from BIAcoreTM binding data.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/s002850050177
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  • 4
    Digitale Medien
    Digitale Medien
    A generalized diffusion model for growth and dispersal in a population (1981)
    Springer
    Journal of mathematical biology 12 (1981), S. 237-249 
    Details
    ISSN: 1432-1416
    Schlagwort(e): Diffusion model ; Populations ; Ginzburg-Landau model
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A reaction-diffusion model is presented in which spatial structure is maintained by means of a diffusive mechanism more general than classical Fickian diffusion. This generalized diffusion takes into account the diffusive gradient (or gradient energy) necessary to maintain a pattern even in a single diffusing species. The approach is based on a Landau-Ginzburg free energy model. A problem involving simple logistic kinetics is fully analyzed, and a nonlinear stability analysis based on a multi-scale perturbation method shows bifurcation to non-uniform states.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00276132
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  • 5
    Digitale Medien
    Digitale Medien
    Positive solutions of nonlinear eigenvalue problems: applications to nonlinear reactor dynamics (1967)
    Springer
    Archive for rational mechanics and analysis 26 (1967), S. 305-315 
    Details
    ISSN: 1432-0673
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00281661
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  • 6
    Digitale Medien
    Digitale Medien
    Correction to the paper (1968)
    Springer
    Archive for rational mechanics and analysis 30 (1968), S. 401-401 
    Details
    ISSN: 1432-0673
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00253671
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  • 7
    Digitale Medien
    Digitale Medien
    An eigenvalue problem arising in guided wave propagation through gyromagnetic media (1965)
    Springer
    Flow, turbulence and combustion 11 (1965), S. 401-411 
    Details
    ISSN: 1573-1987
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Maschinenbau
    Notizen: Summary A study is made of a non-self-adjoint eigenvalue problem which arises in guided wave propagation through gyromagnetic media. Specific information is given concerning the distribution of the eigenvalues, asymptotic formulas for the eigenvalues, and the eigenfunction expansion theorem. Furthermore, for the eigenfunction expansion it is shown that the orthogonality relation commonly used by several authors is not the correct one, and the correct one is given here.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00384040
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  • 8
    Digitale Medien
    Digitale Medien
    A mathematical model for a dissolving polymer (1995)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 41 (1995), S. 2345-2355 
    Details
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: In certain polymer-penetrant systems, nonlinear viscoelastic effects dominate those of Fickian diffusion. This behavior is often embodied in a memory integral incorporating nonlocal time effects into the dynamics; this integral can be derived from an augmented chemical potential. The mathematical framework presented is a moving boundary-value problem. The boundary separates the polymer into two distinct states: glassy and rubbery, where different physical processes dominate. The moving boundary condition that results is not solvable by similarity solutions, but can be solved by perturbation and integral equation techniques. Asymptotic solutions are obtained where sharp fronts move with constant speed. The resultant profiles are quite similar to experimental results in a dissolving polymer. It is then demonstrated that such a model has a limit on the allowable front speed and a self-regulating mass uptake.
    Zusätzliches Material: 6 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/aic.690411102
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  • 9
    Digitale Medien
    Digitale Medien
    Sorption of a finite amount of swelling solvent in a glassy polymerThis work was supported in part by the U.S. Army Research office (Durham) under Contract DAAG29-85-K-0092, by the national Science Foundation under Grant DMS84-00885, and by the Department of Energy under Grant 7405/ENG-36 at the Center for Nonlinear Studies at Los Alamos. (1987)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 25 (1987), S. 611-617 
    Details
    ISSN: 0887-6266
    Schlagwort(e): Chemistry ; Polymer and Materials Science
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Physik
    Notizen: We study the time history of a diffusing front when a polymer is exposed to a finite amount of penetrant which becomes used up. A class of polymers is considered for which slow molecular relaxation occurs only at or near the glass-gel interface with instantaneous relaxation both ahead of and behind the progressing front. We show that the position of the penetrant front versus time undergoes a long smooth transition from standard Fickian t1/2 behavior to exponential time decay onto a final equilibrium position attained when all the penetrant is used up.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/polb.1987.090250312
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  • 10
    Digitale Medien
    Digitale Medien
    The evolution of steep fronts in non-fickian polymer-penetrant systems (1992)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 30 (1992), S. 145-161 
    Details
    ISSN: 0887-6266
    Schlagwort(e): diffusion, non-Fickian, in polymer-penetrant systems ; transport of penetrants in polymers, model involving flux and relaxation in ; penetrant diffusion in polymers, evolution of steep fronts in ; Chemistry ; Polymer and Materials Science
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Physik
    Notizen: We adapt a recently proposed model for non-Fickian diffusion of penetrants into polymers and use it to study a drug-delivery problem. The model modified Fick's diffusion equation by the addition of stress-induced flux. A stress evolution equation incorporating aspects of the Maxwell and Kelvin-Voigt viscoelastic stress models completes the model. The relaxation time in the polymer is taken as a function of the penetrant concentration. The system is studied under the assumption that the diffusivity is large. Singular perturbation techniques are used to show that the concentration and stress evolve diffusively for small time, but exhibit steep fronts in a narrow region within the domain for larger time. These predictions are verified numerically for specified parameter values. Finally, the equations are studied in the steady state and are found to predict the evolution of shocks.
    Zusätzliches Material: 13 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/polb.1992.090300204
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