Liouville-space R-matrix-Floquet description of atomic radiative processes involving autoionizing states in the presence of intense electromagnetic fields

A reduced-density-operator description is developed for coherent optical phenomena in many-electron atomic systems, utilizing a Liouville-space, multiple-mode Floquet–Fourier representation. The Liouville-space formulation provides a natural generalization of the ordinary Hilbert-space (Hamiltonian) R-matrix-Floquet method, which has been developed for multi-photon transitions and laser-assisted electron–atom collision processes. In these applications, the R-matrix-Floquet method has been demonstrated to be capable of providing an accurate representation of the complex, multi-level structure of many-electron atomic systems in bound, continuum, and autoionizing states. The ordinary Hilbert-space (Hamiltonian) formulation of the R-matrix-Floquet method has been implemented in highly developed computer programs, which can provide a non-perturbative treatment of the interaction of a classical, multiple-mode electromagnetic field with a quantum system. This quantum system may correspond to a many-electron, bound atomic system and a single continuum electron. However, including pseudo-states in the expansion of the many-electron atomic wave function can provide a representation of multiple continuum electrons. The 'dressed' many-electron atomic states thereby obtained can be used in a realistic non-perturbative evaluation of the transition probabilities for an extensive class of atomic collision and radiation processes in the presence of intense electromagnetic fields. In order to incorporate environmental relaxation and decoherence phenomena, we propose to utilize the ordinary Hilbert-space (Hamiltonian) R-matrix-Floquet method as a starting-point for a Liouville-space (reduced-density-operator) formulation. To illustrate how the Liouville-space R-matrix-Floquet formulation can be implemented for coherent atomic radiative processes, we discuss applications to electromagnetically induced transparency, as well as to related pump–probe optical phenomena, and also to the unified description of radiative and dielectronic recombination in electron–ion beam interactions and high-temperature plasmas.

The eigenphase formulation of fine-structure transition cross sections

The eigenphase formulation of Blatt and Biedenharn is applied to fine-structure transitions in *P atoms colliding with ‘S perturbers. Consideration is given to the limit of weak spin-orbit interaction. If the eigenphases are equal to the phaseshifts for elastic scattering by the molecular potentials then the expression for the total cross section reduces to the expression derived in the elastic approximation. However, a numerical comparison for the Li(2p ’P) + He(’S) system shows that the elastic molecular phaseshifts are not good approximations to the eigenphases. Hence the elastic approximation cannot be reliable.

Formulation and characterisation of tetracycline-containing bioadhesive polymer networks designed for the treatment of periodontal disease.

This study described the drug release, rheological (dynamic and flow) and textural/mechanical properties of a series of formulations composed of 15% w/w polymethylvinylether-co-maleic anhydride (PMVE-MA), 0-9% w/w polyvinylpyrrolidone (PVP) and containing 1-5% w/w tetracycline hydrochloride, designed for the treatment of periodontal disease. All formulations exhibited pseudoplastic flow with minimal thixotropy. Increasing the concentration of PVP sequentially increased the zero-rate viscosity (derived from the Cross model) and the hardness and compressibility of the formulations (derived from texture profile analysis). These affects may be accredited to increased polymer entanglement and, in light of the observed synergy between the two polymers with respect to their textural and rheological properties, interaction between PVP and PMVE-MA. Increasing the concentration of PVP increased the storage and loss moduli yet decreased the loss tangent of all formulations, indicative of increased elastic behaviour. Synergy between the two polymers with respect to their viscoelastic properties was observed. Increased adhesiveness, associated with increased concentrations of PVP was ascribed to the increasing bioadhesion and tack of the formulations. The effect of increasing drug concentration on the rheological and textural properties was dependent on PVP concentration. At lower concentrations (0, 3% w/w) no effect was observed whereas, in the presence of 9% w/w PVP, increasing drug concentration increased formulation elasticity, zero rate viscosity, hardness and compressibility. These observations were ascribed to the greater mass of suspended drug in formulations containing the highest concentration of PVP. Drug release from formulations containing 6 and 9% PVP (and 5% w/w drug) was prolonged and swelling/diffusion controlled. Based on the drug release, rheological and textural properties, it is suggested that the formulation containing 15% w/w PMVE-MA, 6% w/w PVP and tetracycline hydrochloride (5% w/w) may be useful for the treatment of periodontal disease.

Design, characterisation and preliminary clinical evaluation of a novel mucoadhesive topical formulation containing tetracycline for the treatment of periodontal disease

This study describes the formulation, characterisation and preliminary clinical evaluation of mucoadhesive, semi-solid formulations containing hydroxyethylcellulose (HEC, 1-5%, w/w), polyvinylpyrrolidine (PVP, 2 or 3%, w/w), poly carbophil (PC, 1 or 3%, w/w) and tetracycline (5%, w/w, as the hydrochloride). Each formulation was characterised in terms of drug release, hardness, compressibility, adhesiveness (using a texture analyser in texture profile analysis mode), syringeability (using a texture analyser in compression mode) and adhesion to a mucin disc (measured as a detachment force using the texture analyser in tensile mode). The release exponent for the formulations ranged from 0.78+/-0.02 to 1.27+/-0.07, indicating that drug release was non-diffusion controlled. Increasing the concentrations of each polymeric component significantly increased the time required for 10 and 30% release of the original mass of tetracycline, due to both increased viscosity and, additionally, the unique swelling properties of the formulations. Increasing concentrations of each polymeric component also increased the hardness, compressibility, adhesiveness, syringeability and mucoadhesion of the formulations. The effects on product hardness, compressibility and syringeability may be due to increased product viscosity and, hence, increased resistance to compression. Similarly, the effects of these polymers on adhesiveness/mucoadhesion highlight their mucoadhesive nature and, importantly, the effects of polymer state (particularly PC) on these properties. Thus, in formulations where the neutralisation of PC was maximally suppressed, adhesiveness and mucoadhesion were also maximal. Interestingly, statistical interactions were primarily observed between the effects of HEC and PC on drug release, mechanical and mucoadhesive properties. These were explained by the effects of HEC on the physical state of PC, namely swollen or unswollen. In the preliminary clinical evaluation, a formulation was selected that offered an appropriate balance of the above physical properties and contained 3% HEC, 3% PVP and 1% PC, in addition to tetracycline 5% (as the hydrochloride). The clinical efficacy of this (test) formulation was compared to an identical tetracycline-devoid (control) formulation in nine periodontal pockets (greater than or equal to 5 mm depth). One week following administration of the test formulation, there was a significant improvement in periodontal health as identified by reduced numbers of sub-gingival microbial pathogens. Therefore, it can be concluded that, when used in combination with mechanical plaque removal, the tetracycline-containing semi-solid systems described in this study would augment such therapy by enhancing the removal of pathogens, thus improving periodontal health. (C) 2000 Elsevier Science B.V. All rights reserved.

Integrating Land Use Planning and Transportation: Policy formulation in the Belfast Metropolitan Area

Much of the interest in sustainable cities relates to the inexorable rise in the demand for car travel and the contribution that certain urban forms and land-use relationships can make to reducing energy consumption. Indeed, this demand is fuelled more by increased spatial separation of homes and workplaces, shops and schools than by any rise in trip making. This paper evaluates recent efforts to integrate land-use planning and transportation policy in the Belfast Metropolitan Area by reviewing the policy formulation process at both a regional and city scale. The paper suggests that considerable progress has been made in integrating these two areas of public policy, both institutionally and conceptually. However, concerns are expressed that the rhetoric of sustainability may prove difficult to translate into implementation, leading to a further dislocation of land-use and transportation.

Coupled consolidation of a solid, infinite cylinder using a Terzaghi formulation

Axisymmetric consolidation is a classical boundary value problem for geotechnical engineers. Under some circumstances an analysis in which the changes in pore pressure, effective stress and displacement can be uncoupled from each other is sufficient, leading to a Terzaghi formulation of the axisymmetric consolidation equation in terms of the pore pressure. However, representation of the Mandel-Cryer effect usually requires more complex, coupled, Biot formulations. A new coupled formulation for the plane strain, axisymmetric consolidation problem is presented for small, linear elastic deformations. A single, easily evaluated parameter couples changes in pore pressure to changes in effective stress, and the resulting differential equation for pore pressure dissipation is very similar to Terzaghi’s classic formulation. The governing equations are then solved using finite differences and the consolidation of a solid infinite cylinder analysed, calculating the variation with time and with radius of the excess pore pressure and the radial displacement. Comparison with a previously published semi-analytical solution indicates that the formulation successfully embodies the Mandel-Cryer effect.