Casimir effect in source theory II

Another derivation is presented, one that emphasizes the physical normalization conditions, and employs a mathematical property of a theta function that originated with S. D. Poisson.     

Electromagnetic mass revisited

Examples of uniformly moving charge distributions that possess conserved electromagnetic stress tensors are exhibited. These constitute stable systems with covariantly characterized electromagnetic mass. This note, on a topic to which Paul Dirac made a significant contribution in 1938, is dedicated to him for his 80th birthday.     

Monotone matrices and monotone Markov processes

A stochastic matrix is “monotone” [4] if its row-vectors are stochastically increasing. Closure properties, characterizations and the availability of a second maximal eigenvalue are developed. Such monotonicity is present in a variety of processes in discrete and continous time. In particular, birth-death processes are monotone. Conditions for the sequential monotonicity of a process are given and related inequalities presented.     

Gas-phase ozonolysis of cis- and trans-dichloroethylene

Dichloroethylene (DCE), either cis or trans, was reacted with O₃ at 23°C in both N₂ and O₂ buffered mixtures. Both reactant consumption and product formation were monitored by infrared spectroscopy and, in some cases, O₃ consumption was monitored by ultraviolet absorption. For thoroughly dried mixtures, the initial products were only HCClO and O₂, but geometrical isomerization also occurred. The stoichiometry of the overall reaction always was The HCClO was unstable and disappeared slowly in a first-order reaction which was, at least in part, heterogeneous. The products were CO and HCl so that the stoichiometric reaction was The rate law was complex. The rate was always faster in N₂ than in O₂. In the N₂ buffered reaction, inhibition occurred as the reaction progressed and O₂ was produced. From the reactant and product decay curves, the following rate behavior was established: where high and low concentrations are relative terms for the initial pressure ranges covered ([DCE]₀ = 0.21?78.4 torr, [O₃]₀ = 0.30?6.76 torr). The rate coefficients k₂, k₃, and k₄ were larger for the trans-DCE than the cis-DCE, and for each isomer they were larger in N₂ than in O₂ buffered reactions. The ozonolysis can be explained in terms of the mechanism where R₂ is DCE, RO is HCClO, and RO₂ is HCClO₂. Rate ceofficients are computed. The isomerization is first order in [O₃] and approximately first order in [DCE] for the limited kinetic data we were able to obtain. The isomerization does not appear to be explained by the reverse reactions of reactions (6), (7), and (9). Presumably isomerization occurs through some other route.     

Diffusion-controlled processes among partially absorbing stationary sinks

A general linear response theory is presented to calculate the zero-wavevector and zero-frequency reaction rate coefficient for particles diffusing into absorbing spheres. Allowance is made for possible incomplete particle absorption. A Faxén-like theorem for chemical reactions is derived. The problem is solved completely for a simple regular array of sinks. Exact analytic expressions for the rate coefficient as a function of sink volume fraction are obtained for the sc and fcc lattices. The case of a disordered array of sinks is also considered and the leading order nonanalytic density dependence of the rate coefficient is calculated. In both cases an increase in the rate coefficient with sink density in a local region of the system is found. The general formalism is extended to examine the modification to the particle diffusion coefficient due to the presence of the spheres. For regular arrays of spheres, the mean field result is reproduced.Research supported in part by a grant from the National Research Council of Canada.     

The mercury-sensitized oxidation of carbon monoxide

The mercury-photosensitized oxidation of CO was studied at 275°C over a wide range of [O₂]/[CO] ratios in the absence and presence of the oxygen atom scavenger 2-trifluoromethylpropene (TMP) and at 25°C at low [O₂]/[CO] ratios in the presence of TMP. By following the quantum yield of CO₂ production, Φ {CO₂}, as a function of the [O₂]/[CO] ratio, the reactions of vibrationally excited CO (v υ 9) and electronically excited O₂, probably in the c¹Σ^?_u state, were studied. At low [O₂]/[CO] ratios the predominant reactions are of vibrationally excited CO (v υ 9). Relative rate constants for chemical reaction versus deactivation of CO (v υ 9) were obtained. At higher [O₂]/[CO] ratios, the principal reactions are of electronically excited O₂. Relative rate constants for chemical reactions and deactivation of this electronically excited O₂ with CO, O₂, and TMP were obtained. From the effect of total pressure on Φ {CO₂}, it is proposed that an intermediate CO₃ is formed in the reaction of electronically excited O₂ with CO.     

The reaction of O(3P) with C2HCl3

The reaction of O(³P), prepared from the Hg photosensitization of N₂O, with C₂HCl₃ was studied at 25°C. The products of the reaction in the absence of O₂ were CO, CHCl₃, and polymer (as well as N₂ from the N₂O). The quantum yields of CO and CHCl₃ were 0.23 ± 0.01 and 0.14 ± 0.05, is respectively independent of reaction conditions. The reaction mechanism is with k_14a/k₁₄ = 0.23, where k_14a + k_14b. Most of the HCl and CCl₂ combine to form CHCl₃, but some other products must also be formed to account for the difference in the CO and CHCl₃ quantum yields. The C₂HCl₃O* adduct polymerizes without involving additional C₂HCl₃ molecules, since the quantum yield of C₂HCl₃ disappearance, ? Φ{C₂HCl₃}, was about 1.0 at high values of [N₂O]/[C₂HCl₃]. The rate coefficient for the reaction of O(³P) with C₂HCl₃ is 0.10 that for the reaction of O(³P) with C₂F₄. In the presence of O₂ the free radical chain oxidation occurs because of the reaction The main product is CHCl₂CCl(O) with smaller amounts of CO and CCl₂O, and some CO₂. The chain lengths were long and values of ? Φ {C₂HCl₃} up to 90 were observed.