The Downs-Thomson Paradox: Existence, Uniqueness and Stability of User Equilibria

Consider a network where two routes are available for users wishing to travel from a source to a destination. On one route (which could be viewed as private transport) service slows as traffic increases. On the other (which could be viewed as public transport) the service frequency increases with demand. The Downs-Thomson paradox occurs when improvements in service produce an overall decline in performance as user equilibria adjust. Using the model proposed by Calvert [10], with a ⋅|M|1 queue corresponding to the private transport route, and a bulk-service infinite server queue modelling the public transport route, we give a complete analysis of this system in the setting of probabilistic routing. We obtain the user equilibria (which are not always unique), and determine their stability.AMS subject classification: 60K30, 90B15, 90B20, 91A10, 91A13This revised version was published online in June 2005 with corrected coverdate     

Model-dependent nature of blowtorch effect on the escape and equilibration rates

We analyze the relaxation behavior of a bistable system when the background temperature profile is inhomogeneous due to the presence of a localized hot region (blowtorch) on one side of the potential barrier. Since the diffusion equation for inhomogeneous medium is model-dependent, we consider two physical models to study the kinetics of such system. Using a conventional stochastic method, we obtain the escape and equilibration rates of the system for the two physical models. For both models, we find that the hot region enhances the escape rate from the well where it is placed while it retards the escape rate from the other well. However, the value of the escape rate from the well where the hot region is placed differs for the two models while that of the escape rate from the other well is identical for both. This work, for the first time, gives a detailed report of the similarities and differences of the escape rates and, hence, exposes the common and distinct features of the two known physical models in determining the way the bistable system relaxes. Received 25 September 2001     

Cyclopolymerisation. 3. Mitt. ESR-Untersuchungen von Diallylaminen mit Redox-Systemen

Ohne Zusammenfassung     

Covalent bonding of alkene and alkyne reagents to graphitic carbon surfaces

Various aromatic and aliphatic alkynes and one alkene were covalently bonded to sp(2)-hybridized carbon surfaces by heat treatment in an argon atmosphere. X-ray photoelectron spectroscopy, Raman, and FTIR spectra of the modified surfaces showed that the molecules were intact after the 400 degrees C heat treatment but that the alkyne group had reacted with the surface to form a covalent bond. Alkynes with ferrocene and porphyrin centers exhibited chemically reversible voltammetric waves that could be cycled many times. Atomic force microscopy of the modified surfaces indicated a thickness of the molecular layer consistent with monolayer coverage, and surface coverage determined by voltammetry was also in the monolayer range. Raman spectroscopy of the porphyrin monolayers formed from a porphyrin alkyne showed no evidence for dimer formation, although multilayer formation may occur at undetected levels. FTIR spectra of the porphyrin-modified carbon surfaces were well-defined, similar to the parent molecule, and indicative of an average tilt angle between the porphyrin plane and the surface normal of 37 degrees . The bond between the molecular monolayer and the carbon surface was quite stable, withstanding sonication in tetrahydrofuran, mild aqueous acid and base, and repeated voltammetric cycling in propylene carbonate electrolyte. Heat treatment of alkynes and alkenes appears to be a generally useful method for modifying carbon surfaces, which can be applied to both aromatic and aliphatic molecules.     

Physically based molecular device model in a transient circuit simulator

Two efficient, physically based models for the real-time simulation of molecular device characteristics of single molecules are developed. These models assume that through-molecule tunnelling creates a steady-state Lorentzian distribution of excess electron density on the molecule and provides for smooth transitions for the electronic degrees of freedom between the tunnelling, molecular-excitation, and charge-hopping transport regimes. They are implemented in the fREEDA™ transient circuit simulator to allow for the full integration of nanoscopic molecular devices in standard packages that simulate entire devices including CMOS circuitry. Methods are presented to estimate the parameters used in the models via either direct experimental measurement or density-functional calculations. The models require 6–8 orders of magnitude less computer time than do full a priori simulations of the properties of molecular components. Consequently, molecular components can be efficiently implemented in circuit simulators. The molecular-component models are tested by comparison with experimental results reported for 1,4-benzenedithiol.     

Anisotropic membranes with carboxypeptidase G1

Anisotropic polysulfone membranes were prepared with carboxypeptidase G₁ embedded in the polymer structure. The enzymatically active flat and hollow-fiber membranes were obtained by precipitating the polymer from solution in an organic mixture in which an aqueous solution of the enzyme had been dispersed. The process has been found to be particularly suitable for the immobilization of enzymes in anisotropic hollow fibers that exhibited no detectable enzyme leakage upon perfusion. The pH profiles measured with the enzyme in free solution and in the embedded form were similar. Kinetic parameters of multitubular enzyme reactors were investigated by measuring the rate of hydrolysis of glutamate from folic acid or methotrexate at different flow rates and substrate concentrations. The relatively slow mass transfer in such reactors was found to affect strongly the observed kinetics. The results of in vitro experiments with 5000 fiber reactors suggest that hollow fiber cartridges prepared with such membranes have clinical potential for the extracorporeal removal of methotrexate from blood.