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     

Ring expansion of 5- to 6-member zirconacycles by carbenoid insertion

A wide range of carbenoids (1-lithio-1-halo species), including those with α-SiR₃, OEt, SPh, SO₂Ph, P(O)(OEt)₂, and CN substituents, insert into 5-member zirconacycles (saturated and unsaturated, mono- and bi-cyclic) to afford functionalized 6-member zirconacycles. 1-Lithio-1-haloalkenes insert to afford 6-member zirconacycles with an alkylidene substituent next to the metal. Unexpected double insertion of some carbenoids, and evidence for endocylic β-hydride transfer processes provide additional mechanistic interest.     

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.     

Nature et stabilité des complexes métalliques de cryptands dinucléants en solution II. Polythiamacrotricycles et monocycles apparentés

Nature and Stability of Some Metallic Complexes of Dinucleating Cryptands in Solution II. Polythiamacrotricycles and Related Monocyclic Subunits The stability constants of the Cu²⁺ and Ag⁺ complexes of the cylindrical macrotricycle 1a (1,7,13,19-tetraaza 4,16-dioxa 10,22,27,32-tetrathiatricyclo[17.5.5.5]tetratriacontane) have been determined by pH-metry, as well as those of the Cu²⁺, Co²⁺, Zn²⁺, Cd²⁺, Pb²⁺, and Ag⁺ complexes of the monocyclic subunit 2a (1,7-dimethyl-1,7-diaza 4,10-dithiacyclododecane), in aqueous solutions (NaClO₄) at 25°. In the Cu(II) systems, equilibria were reached slowly, and the results established by pH-metry were confirmed by UV/VIS spectrophotometric studies. The tricycle 1a forms dinuclear cryptates with copper and silver, with overall stability constants log β₂₁₀ (Cu₂- 1a )⁴⁺ = 18.5, log β_21-2 (Cu₂- 1a (OH)₂)²⁺ = 4.8, log β₂₁₀(Ag₂- 1a )²⁺ = 23.0. Ag⁺ also forms a mononuclear (Ag- 1a )⁺ complex, with log β₁₁₀ = 13.1, but no mononuclear species were detected in the Cu- 1a system. The absorption spectra of the bis-Cu(II) complexes of 1a and 2a in aqueous medium, MeOH and propylene carbonate (PC) are given, as well as those, in MeOH and PC, of the bis-copper complexes of the related monocycles 3 and 4 (1,7-diaza-4,10,13-trithiacyclopentadecane and 1.10-diaza 4,7,13,16-tetrathiacyclooctadecane, respectively), and tricycle 5 with two benzyl groups in the lateral chains. The complexing properties of the polyoxa- and polythia macrotricycles (Parts I and II of this series) are compared to those of other bis-chelating ligands, the bicyclic bis-tren and the monocyclic bis-dien.