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  • 1
    Electronic Resource
    Electronic Resource
    What can be stated by the Glansdorff–Prigogine criterion concerning the stability of mass-action kinetic systems? (1999)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 110 (1999), S. 6128-6134 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We investigate which general results concerning the local stability of steady states of arbitrary chemical reaction networks can be deduced with the Glansdorff–Prigogine stability criterion. Especially, it is proven that the presence of an autocatalytic reaction is not a necessary condition for a violation of the thermodynamic stability condition. It turns out that every reaction with at least one variable reactant at each side of the reaction equation can potentially destabilize the steady states. An explicit example of a simple reaction system without autocatalytic reactions where the stability of the steady state changes via a supercritical Hopf bifurcation is discussed. Furthermore, in expanding the original concept for proving local stability to global stability analyses, a general way for constructing different Lyapunov functions is given. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.478519
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  • 2
    Electronic Resource
    Electronic Resource
    An evolutionary approach to enzyme kinetics: Optimization of ordered mechanisms (1994)
    Springer
    Bulletin of mathematical biology 56 (1994), S. 65-106 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A theoretical investigation is presented which allows the calculation of rate constants and phenomenological parameters in states of maximal reaction rates for unbranched enzymic reactions. The analysis is based on the assumption that an increase in reaction rates was an important characteristic of the evolution of the kinetic properties of enzymes. The corresponding nonlinear optimization problem is solved taking into account the constraint that the rate constants of the elementary processes do not exceed certain upper limits. One-substrate-one-product reactions with two, three and four steps are treated in detail. Generalizations concern ordered uni-uni-reactions involving an arbitrary number of elementary steps. It could be shown that depending on the substrate and product concentrations different types of solutions can be found which are classified according to the number of rate constants assuming in the optimal state submaximal values. A general rule is derived concerning the number of possible solutions of the given optimization problem. For high values of the equilibrium constant one solution always applies to a very large range of the concentrations of the reactants. This solution is characterized by maximal values of the rate constants of all forward reactions and by non-maximal values of the rate constants of all backward reactions. Optimal kinetic parameters of ordered enzymic mechanisms with two substrates and one product (bi-uni-mechanisms) are calculated for the first time. Depending on the substrate and product concentrations a complete set of solutions is found. In all cases studied the model predicts a matching of the concentrations of the reactants and the corresponding Michaelis constants, which is in good accordance with the experimental data. It is discussed how the model can be applied to the calculation of the optimal kinetic design of real enzymes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458290
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  • 3
    Electronic Resource
    Electronic Resource
    Investigation of ion-bombarded conducting polymer films by scanning electrochemical microscopy (SECM) (2000)
    Springer
    Fresenius' journal of analytical chemistry 367 (2000), S. 346-351 
    Details
    ISSN: 1432-1130
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Scanning electrochemical microscopy (SECM) was used to investigate the effect of ion bombardment on thin films of the conducting polymers poly[3-ethoxy-thiophene] (PEOT) and poly[ethylenedioxy-thiophene] (PEDT). Bombardment with Ar+-ions converts the topmost 30 nm thick layer to an essentially insulating material. SECM approach curves as well as two dimensional scans prove the existence of regions of different conductivity within the irradiated regions that did not show a significant dependence on ion dosage. PEDT layers patterned by ion bombardment through microscopic masks are investigated as prototypes of miniaturized printed circuit boards that can be formed by galvanic copper deposition onto conducting PEDT. Defects in conducting polymer patterns were analyzed by SECM imaging before any deposition of copper. Appropriate representations of SECM images for the evaluation of this technologically important question are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002160000389
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  • 4
    Electronic Resource
    Electronic Resource
    Model reduction by extended quasi-steady-state approximation (2000)
    Springer
    Journal of mathematical biology 40 (2000), S. 443-450 
    Details
    ISSN: 1432-1416
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract. We extend the quasi-steady-state approximation (QSSA) with respect to the class of differential systems as well as with respect to the order of approximation. We illustrate the first extension by an example which cannot be treated in the frame of the classical approach. As an application of the second extension we prove that the trimolecular autocatalator can be approximated by a fast bimolecular reaction system. Finally we describe a class of singularly perturbed systems for which a higher order QSSA can easily be obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002850000026
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  • 5
    Electronic Resource
    Electronic Resource
    Localised Electrochemical Desorption of Gold Alkanethiolate Monolayers by Means of Scanning Electrochemical Microscopy (SECM) (2000)
    Springer
    Microchimica acta 133 (2000), S. 1-9 
    Details
    ISSN: 1436-5073
    Keywords: Key words: Microstructuring; monolayer patterning; self-assembled monolayers; scanning electrochemical microscopy; SECM.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract.  Lateral structures of bare gold within self-assembled monolayers (SAMs) of gold alkanethiolates were created by electrochemical desorption in the direct mode of the scanning electrochemical microscope (SECM). The ultramicroelectrode (UME) of the SECM was positioned 10–20 μm above the surface and used as the auxiliary electrode in a three electrode cell with the SAM-coated Au electrode as working electrode. The microscopic auxiliary electrode causes an inhomogeneous electric field above the macroscopic gold electrode and limits the total current. As a consequence only thiols located directly beneath the UME are affected by the desorption procedure. Sample regions from which the SAM had been removed were imaged in the SECM feedback mode or, after galvanic Cu deposition, by scanning electron microscopy (SEM) and optical microscopy (after sulfidisation of Cu). The influence of hydrocarbon chain length, protection of the SAM by an additional layer of n-octanol and the use of alternating current were investigated in order to decrease the size of the bare surface areas and to enhance their edge definition. In particular the use of alternating current led to feature sizes of 1.2 times the UME diameter which represents an advance with regard to 2–3 UME diameters reported earlier.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s006040050001
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  • 6
    Electronic Resource
    Electronic Resource
    Smallest chemical reaction system with Hopf bifurcation (1995)
    Springer
    Journal of mathematical chemistry 17 (1995), S. 1-14 
    Details
    ISSN: 1572-8897
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract The smallest at most bimolecular chemical reaction system with Hopf bifurcation is presented. First the notion smallest reaction system is explained. Since the lowest number of intermediates has the highest priority in this characterization and since it has already been shown that three-component systems can have a Hopf bifurcation [1], the smallest reaction system must contain three intermediates. On the basis of a sufficient condition for a Hopf bifurcation in three-dimensional systems it is possible to find one reaction system which is according to the given characterization, the smallest one. In the first part of this paper it is shortly pictured and in the second part a more extensive proof that this system is really the searched smallest one is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01165134
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  • 7
    Electronic Resource
    Electronic Resource
    Mathematical analysis of the smallest chemical reaction system with Hopf bifurcation (1996)
    Springer
    Journal of mathematical chemistry 19 (1996), S. 111-130 
    Details
    ISSN: 1572-8897
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract Recently we presented an up to now unstudied three-dimensional dynamical system which is, according to our given definition, the smallest chemical reaction system with Hopf bifurcation. We here study the Hopf bifurcation in detail and prove that near the bifurcation point a stable limit cycle arises. In the analysis we use the methods of local bifurcation theory, especially the center manifold and the normal form theorem. In a similar way we analyse the also occurring transcritical bifurcation. Besides studying local stability, we give the proofs for global stability of the trivial steady state in the whole positive phase space and for the nontrivial steady state in a closed domain containing the steady state point.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01165179
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  • 8
    Electronic Resource
    Electronic Resource
    Chemical systems consisting only of elementary steps – a paradigma for nonlinear behavior (2000)
    Springer
    Journal of mathematical chemistry 27 (2000), S. 71-88 
    Details
    ISSN: 1572-8897
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract We present a new analytic method which allows one to interpret a mass‐action kinetic reaction of arbitrary molecularity as the limit case of a sequence of bimolecular steps. Together with other technics (transformation of an arbitrary ODE into a polynomial ODE [8]; transformation of a polynomial ODE into a form which can be interpreted as a mass‐action kinetic system [10]), it is thus possible to construct an at most bimolecular mass‐action kinetic system with the same dynamic behavior as an arbitrary ODE. Furthermore, we demonstrate necessary improvements of the transformation given in [10]. Is is also shown that an arbitrary single mass‐action kinetic reaction can be understood as a sequence of two reactions with a short‐living intermediate. In particular, it therefore follows that an autocatalytic reaction can always be approximated by two nonautocatalytic ones without changing the dynamics of the whole system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019131221994
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  • 9
    Electronic Resource
    Electronic Resource
    Glass transition temperatures of styrene/4-bromostyrene copolymers (1983)
    Basel : Wiley-Blackwell
    Die Makromolekulare Chemie, Rapid Communications 4 (1983), S. 81-85 
    Details
    ISSN: 0173-2803
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/marc.1983.030040207
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  • 10
    Electronic Resource
    Electronic Resource
    Electrical properties of linear poly(ester-urethane)s, 1. D.C. conductivityDedicated to Prof. Dr. R. Kosfeld on the occasion of his 60th birthday (1986)
    New York : Wiley-Blackwell
    Die Makromolekulare Chemie 187 (1986), S. 1313-1327 
    Details
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The steady-state D.C. currents of linear poly(ester-urethane)s with different hard to soft segment ratios were investigated. With increasing hard to soft segment ratios, the conductivity was found to increase and the field strength, where ohmic currents change to space charge limited currents, is significantly lowered. Five distinct regions of different thermal activation energy were observed as a function of temperature. With increasing temperature, the thermal activation energy is decreased. Stretched poly(ester-urethane)s show lower conductivity due to segregation of hard and soft segments. The results are discussed in terms of polymer structure and are correlated with well-known morphological phenomena in polyurethanes.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/macp.1986.021870527
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