A phase space approach to generalized Hamilton–Jacobi theory

Generalizations of H–J theory have been discussed before in the literature. The present approach differs from others in that it employs geometrical ideas on phase space and classical transformation theory to derive the basic equations. The relation between constants of motion and symmetries of the generalized H–J equations is then clarified. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

The kinetics and reactivity of several polyatomic free radicals in reactions with NO2, O2, Cl2, and HCl

In this thesis, the kinetics of several alkyl, halogenated alkyl, and alkenyl free radical reactions with NO2, O2, Cl2, and HCl reactants were studied over a wide temperature range in time resolved conditions. Laser photolysis photoionisation mass spectrometer coupled to a flow reactor was the experimental method employed and this thesis present the first measurements performed with the experimental system constructed. During this thesis a great amount of work was devoted to the designing, building, testing, and improving the experimental apparatus. Carbon-centred free radicals were generated by the pulsed 193 or 248 nm photolysis of suitable precursors along the tubular reactor. The kinetics was studied under pseudo-first-order conditions using either He or N2 buffer gas. The temperature and pressure ranges employed were between 190 and 500 K, and 0.5 45 torr, respectively. The possible role of heterogeneous wall reactions was investigated employing reactor tubes with different sizes, i.e. to significantly vary the surface to volume ratio. In this thesis, significant new contributions to the kinetics of carbon-centred free radical reactions with nitrogen dioxide were obtained. Altogether eight substituted alkyl (CH2Cl, CHCl2, CCl3, CH2I, CH2Br, CHBr2, CHBrCl, and CHBrCH3) and two alkenyl (C2H3, C3H3) free radical reactions with NO2 were investigated as a function of temperature. The bimolecular rate coefficients of all these reactions were observed to possess negative temperature dependencies, while pressure dependencies were not noticed for any of these reactions. Halogen substitution was observed to moderately reduce the reactivity of substituted alkyl radicals in the reaction with NO2, while the resonance stabilisation of the alkenyl radical lowers its reactivity with respect to NO2 only slightly. Two reactions relevant to atmospheric chemistry, CH2Br + O2 and CH2I + O2, were also investigated. It was noticed that while CH2Br + O2 reaction shows pronounced pressure dependence, characteristic of peroxy radical formation, no such dependence was observed for the CH2I + O2 reaction. Observed primary products of the CH2I + O2 reaction were the I-atom and the IO radical. Kinetics of CH3 + HCl, CD3 + HCl, CH3 + DCl, and CD3 + DCl reactions were also studied. While all these reactions possess positive activation energies, in contrast to the other systems investigated in this thesis, the CH3 + HCl and CD3 + HCl reactions show a non-linear temperature dependency on the Arrhenius plot. The reactivity of substituted methyl radicals toward NO2 was observed to increase with decreasing electron affinity of the radical. The same trend was observed for the reactions of substituted methyl radicals with Cl2. It is proposed that interactions of frontier orbitals are responsible to these observations and Frontier Orbital Theory could be used to explain the observed reactivity trends of these highly exothermic reactions having reactant-like transition states.

A note on the effective medium theory of random resistive-reactive medium

The effective medium theory for a system with randomly distributed point conductivity and polarisability is reformulated, with attention to cross-terms involving the two disorder parameters. The treatment reveals a certain inconsistency of the conventional theory owing to the neglect of the Maxwell-Wagner effect. The results are significant for the critical resistivity and dielectric anomalies of a binary liquid mixture at the phase separation point.

The non-planar peptide unit II. Comparison of theory with crystal structure datastar, open

The theoretical results derived in Part I (Ramachandran, G.N., Lakshminarayan, A.V. and Kolaskar, A.S. (1973) Biochim. Biophys. Acta 303, 8–13) that the three bonds of the peptide unit meeting at N can have a pyramidal structure is confirmed by an analysis of 14 published crystal structures of small peptides. It is shown that the dihedral angles θN and Δω are correlated, while θC, is small and is uncorrelated with Δω, showing that the non-planar distortion at C′ is generally small.

A theory of the upper critical field in antiferromagnetic superconductors

A generalized Ginzburg-Landau approach is used to study the nonmonotonic temperature dependence of the upper critical field H c 2(T) in antiferromagnetic superconductors RE(Mo)6S8; RE = Dy, Tb, Gd. It is found that electrodynamic effects incorporated through screening and indirect coupling between the staggered magnetization M Q (T) and superconducting order parameter psgr cannot explain the observed nonmonotonicity. This suggests that the direct coupling between the two order parameters should be considered to understand the experimental results, a finding which is consistent with recent microscopic calculations.

Theory of the non-planar peptide unitstar, open

By means of CNDO/2 calculations on N-methyl acetamide, it is shown that the state of minimum energy of the trans-peptide unit is a non-planar conformation, with the NH and NC2α bonds being significantly out of the plane formed by the atoms C1α, C′, O and N.

Reducing falls in hospital through education to change patient and staff behaviour: A stepped wedge cluster randomised controlled effectiveness trial

Background: Falls remain the most frequent adverse event reported in hospitals, particularly geriatric rehabilitation wards. Randomised trials reducing fall injuries in hospitals have been elusive. Our previous randomised trial (n = 1206) demonstrated that multimedia education with physiotherapist falls educator support reduced falls among patients with higher cognition levels, but this benefit was offset by a potential increase in falls rates among patients with poor cognition. In the previous trial, hospital staff were blinded to the allocation of individual patients, and only delivered usual care.

Einstein relation in n-i-p-i and microstructures of nonlinear optical, optoelectronic and related materials: Simplified theory, relative comparison and suggestions for an experimental determination

We investigate the Einstein relation for the diffusivity-mobility ratio (DMR) for n-i-p-i and the microstructures of nonlinear optical compounds on the basis of a newly formulated electron dispersion law. The corresponding results for III-V, ternary and quaternary materials form a special case of our generalized analysis. The respective DMRs for II-VI, IV-VI and stressed materials have been studied. It has been found that taking CdGeAs2, Cd3As2, InAs, InSb, Hg1−xCdxTe, In1−xGaxAsyP1−y lattices matched to InP, CdS, PbTe, PbSnTe and Pb1−xSnxSe and stressed InSb as examples that the DMR increases with increasing electron concentration in various manners with different numerical magnitudes which reflect the different signatures of the n-i-p-i systems and the corresponding microstructures. We have suggested an experimental method of determining the DMR in this case and the present simplified analysis is in agreement with the suggested relationship. In addition, our results find three applications in the field of quantum effect devices.

Refractory boron compounds for high performance: Theory and experiment

We have shown that novel synthesis methods combined with careful evaluation of DFT phonon calculations provides new insight into boron compounds including a capacity to predict Tc for AlB2-type superconductors.

Conformal Field Theory Methods for Variants of Schramm-Loewner Evolutions

This thesis consists of an introduction, four research articles and an appendix. The thesis studies relations between two different approaches to continuum limit of models of two dimensional statistical mechanics at criticality. The approach of conformal field theory (CFT) could be thought of as the algebraic classification of some basic objects in these models. It has been succesfully used by physicists since 1980's. The other approach, Schramm-Loewner evolutions (SLEs), is a recently introduced set of mathematical methods to study random curves or interfaces occurring in the continuum limit of the models. The first and second included articles argue on basis of statistical mechanics what would be a plausible relation between SLEs and conformal field theory. The first article studies multiple SLEs, several random curves simultaneously in a domain. The proposed definition is compatible with a natural commutation requirement suggested by Dubédat. The curves of multiple SLE may form different topological configurations, ``pure geometries''. We conjecture a relation between the topological configurations and CFT concepts of conformal blocks and operator product expansions. Example applications of multiple SLEs include crossing probabilities for percolation and Ising model. The second article studies SLE variants that represent models with boundary conditions implemented by primary fields. The most well known of these, SLE(kappa, rho), is shown to be simple in terms of the Coulomb gas formalism of CFT. In the third article the space of local martingales for variants of SLE is shown to carry a representation of Virasoro algebra. Finding this structure is guided by the relation of SLEs and CFTs in general, but the result is established in a straightforward fashion. This article, too, emphasizes multiple SLEs and proposes a possible way of treating pure geometries in terms of Coulomb gas. The fourth article states results of applications of the Virasoro structure to the open questions of SLE reversibility and duality. Proofs of the stated results are provided in the appendix. The objective is an indirect computation of certain polynomial expected values. Provided that these expected values exist, in generic cases they are shown to possess the desired properties, thus giving support for both reversibility and duality.

Renormalization methods in KAM theory

It is well known that an integrable (in the sense of Arnold-Jost) Hamiltonian system gives rise to quasi-periodic motion with trajectories running on invariant tori. These tori foliate the whole phase space. If we perturb an integrable system, the Kolmogorow-Arnold-Moser (KAM) theorem states that, provided some non-degeneracy condition and that the perturbation is sufficiently small, most of the invariant tori carrying quasi-periodic motion persist, getting only slightly deformed. The measure of the persisting invariant tori is large together with the inverse of the size of the perturbation. In the first part of the thesis we shall use a Renormalization Group (RG) scheme in order to prove the classical KAM result in the case of a non analytic perturbation (the latter will only be assumed to have continuous derivatives up to a sufficiently large order). We shall proceed by solving a sequence of problems in which theperturbations are analytic approximations of the original one. We will finally show that the approximate solutions will converge to a differentiable solution of our original problem. In the second part we will use an RG scheme using continuous scales, so that instead of solving an iterative equation as in the classical RG KAM, we will end up solving a partial differential equation. This will allow us to reduce the complications of treating a sequence of iterative equations to the use of the Banach fixed point theorem in a suitable Banach space.