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1Author    Gerold Baier, Peter Urban, Klaus WegmannRequires cookie*
 Abstract    N e w M o d e l S y s te m fo r th e S tu d y o f C o m p le x D y n a m ic a l E n z y m e R e a c tio n s . I. A N o n lin e a r E n z y m e R e a c tio n in a C h e m ic a l G r a d ie n t An experimental system for the study of biochemical reaction dynamics is introduced and de­ scribed. A one-enzyme reaction is extended by an artificial feedback loop in an electrochemical device. Cyclic voltammetry is used to show that the reaction rate depends nonlinearly on the amount of cosubstrate offered. For some sets of fixed parameter values a damped oscillatory approach of the steady state was observed. The usefulness of the systems theoretical concepts is discussed. 
  Reference    Z. Naturforsch. 43a, 987—994 (1988); Received August 22 1988 
  Published    1988 
  Keywords    Reaction-diffusion Systems, Peroxidase, Feedback, Nonlinearity, Damped Oscillations 
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 TEI-XML for    default:Reihe_A/43/ZNA-1988-43a-0987.pdf 
 Identifier    ZNA-1988-43a-0987 
 Volume    43 
2Author    M. F. El-Sayed, D. K. CallebautRequires cookie*
 Title    Nonlinear Electrohydrodynamic Stability of Two Superposed Bounded Fluids in the Presence of Interfacial Surface Charges  
 Abstract    The method of multiple scales is used to analyse the nonlinear propagation of waves on the interface between two superposed dielectric fluids with uniform depths in the presence of a normal electric field, taking into account the interfacial surface charges. The evolution of the amplitude for travelling waves is governed by a nonlinear Schrödinger equation which gives the criterion for modulational instability. Numerical results are given in graphical form, and some limiting cases are recovered. Three cases, in the pure hydrodynamical case, depending on whether the depth of the lower fluid is equal to or greater than or smaller than the one of the upper fluid are considered, and the effect of the electric field on the stability regions is determined. It is found that the effect of the electric field is the same in all the cases for small values of the field, and there is a value of the electric field after which the effect differs from case to case. It is also found that the effect of the electric field is stronger in the case where the depth of the lower fluid is larger than the one of the upper fluid. On the other hand, the evolution of the am-plitude for standing waves near the cut-off wavenumber is governed by another type of nonlinear Schrödinger equation with the roles of time and space are interchanged. This equation makes it possible to determine the nonlinear dispersion relation, and the nonlinear effect on the cut-off wavenumber. 
  Reference    Z. Naturforsch. 53a, 217—232 (1998); received January 23 1998 
  Published    1998 
  Keywords    Hydrodynamic Stability, Electrohydrodynamics, Nonlinearity, Interfacial Instability, Dielectric Fluids, Surface Charges 
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 TEI-XML for    default:Reihe_A/53/ZNA-1998-53a-0217.pdf 
 Identifier    ZNA-1998-53a-0217 
 Volume    53 
3Author    Christoph Bauer3, Thomas Burger3, Martin Stetterb, ElmarW. Lang3Requires cookie*
 Title    A Neural Network Model for the Self-Organization of Cortical Grating Cells  
 Abstract    A neural network model with incremental Hebbian learning of afferent and lateral synap­ tic couplings is proposed,which simulates the activity-dependent self-organization o f grating cells in upper layers of striate cortex. These cells, found in areas VI and V2 of the visual cortex of monkeys, respond vigorously and exclusively to bar gratings of a preferred orienta­ tion and periodicity. R esponse behavior to varying contrast and to an increasing number of bars in the grating show threshold and saturation effects. Their location with respect to the underlying orientation map and their nonlinear response behavior are investigated. The number of emerging grating cells is controlled in the model by the range and strength of the lateral coupling structure. 
  Reference    Z. Naturforsch. 55c, 282 (2000); received July 5/Decem ber 10 1999 
  Published    2000 
  Keywords    Self-Organization, Nonlinearities, Visual Cortex, (Anti-)H ebbian Learning, Lateral Plasticity 
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 TEI-XML for    default:Reihe_C/55/ZNC-2000-55c-0282.pdf 
 Identifier    ZNC-2000-55c-0282 
 Volume    55