A linear theory of straight elastic rods

This paper is based on the work of Green & Laws who have given a general thermodynamical theory of rods which is valid for any material. Here, starting with the general non-linear theory of elastic rods, we derive a linear theory allowing for thermal effects. The resulting free energy as a quadratic function of kinematic variables is restricted by certain symmetry conditions. The basic equations then separate into four groups, two for flexure, one for torsion and one for extension of the rod with temperature effects occurring only in the latter group. Wave propagation along an infinite rod is considered. There are two wave speeds for each type of flexure, two for torsion and three for isothermal extension and all wave speeds depend on the wave length.     

Dynamic routing in open queueing networks: Brownian models,cut constraints and resource pooling

We present an introductory review of recent work on the control of open queueing networks. We assume that customers of different types arrive at a network and pass through the system via one of several possible routes; the set of routes available to a customer depends on its type. A route through the network is an ordered set of service stations: a customer queues for service at each station on its route and then leaves the system. The two methods of control we consider are the routing of customers through the network, and the sequencing of service at the stations, and our aim is to minimize the number of customers in the system. We concentrate especially on the insights which can be obtained from heavy traffic analysis, and in particular from Harrison's Brownian network models. Our main conclusion is that in many respects dynamic routingsimplifies the behaviour of networks, and that under good control policies it may well be possible to model the aggregate behaviour of a network quite straightforwardly.Supported by SERC grant GR/F 94194.     

Metal-specific allosteric activation and deactivation of a diamine

The reaction of a potentially tetradentate bis(pyridyl-thiazole) ligand with acetone is allosterically activated upon complexation with Cd(II) but deactivated by reaction with Cu(I), demonstrating metal-specific allosteric controlled reactivity.     

Cymantrene radical cation family: spectral and structural characterization of the half-sandwich analogues of ferrocenium ion

The anodic one-electron oxidation of three members of the half-sandwich family of piano-stool compounds MnCp (gamma)(CO) 3, where Cp (gamma) is a generic cyclopentadienyl ligand, has been studied in a CH 2Cl 2/[NBu 4][TFAB] electrolyte (TFAB = [B(C6F5) 4] (-)). The long-sought 17 e (-) radical cation of the parent complex MnCp(CO) 3 (cymantrene, 1, E 1/2 = 0.92 V vs ferrocene) has been shown to be persistent in solutions that use weakly coordinating anions in place of more nucleophilic traditional electrolyte anions. Spectroscopically characterized for the first time, 1 (+) was shown to absorb in the visible (530 nm), near-IR (2066 nm), and IR (2118, 1934 cm (-1)) regions. It was ESR-active at low temperatures (g parallel = 2.213, g perpendicular = 2.079, A parallel (Mn) = 79.2 G, A perpendicular (Mn) = 50 G) and NMR active at room temperature (delta = 22.4 vs TMS). The radical cations of the Cp-functionalized analogues, Mn(eta (5)-C5H 4NH2)(CO) 3, 2, E 1/2 = 0.62 V, and MnCp*(CO) 3 (Cp*= eta (5)-C 5Me 5, 3), E 1/2 = 0.64 V, were generated electrochemically as well by the chemical oxidant [ReCp(CO) 3] (+). The structures of 2 (+) and 3 (+) were determined by X-ray crystallographic studies of their TFAB salts. Compared to the structures of the corresponding neutral compounds, the cations showed elongated Mn-C(O) bonds and shortened C-O bonds, displaying the effect of diminished metal-to-CO backbonding. The bond-length changes in the Mn(CO) 3 moiety were much larger in 3 (+) (avg changes, Mn-C(O) = + 0.142 A, C-O = -0.063 A) than in 2 (+) (avg changes, Mn-C(O) = + 0.006 A, C-O = -0.003 A). Although there were only minor changes in the metal-to-center ring distances upon oxidation of either 2 or 3, there was decidedly less bending of the C(N) atom out of the cyclopentadienyl plane in 2 (+) compared to 2. The optical, vibrational, and magnetic resonance spectra of radicals 2 (+) and 3 (+) were also observed. The spectral data argue for the SOMOs of the 17-electron species being largely located on the Mn(CO) 3 moiety, having 40-50% Mn d-orbital character, with the ground states of the radicals, most likely (2)A', lying close in energy (within about 6000 cm (-1)) to excited states that are responsible for their rapid electronic relaxations. The cymantrenyl moiety is proposed as an anodic redox tag (or label) having physical and chemical properties that are significantly different from those of its ferrocenyl analogue.