Differentiability Properties of an Abstract Autonomous Composition Operator

The autonomous composition operator is the nonlinear map whichtakes a pair of functions into its composite function. The compositionoperator often appears in problems of nonlinear analysis andto analyse such problems it is often important to know whetherthe composition operator is continuous or differentiable. Afairly large number of papers in the literature have been devotedto the study of composition operators. For fullscale references,we refer the reader to the extensive monographs of Appell andZabrejko [1] and Runst and Sickel [8]. To exemplify a typicalsituation, we consider the semilinear Dirichlet boundary valueproblem where denotes a sufficiently regular bounded open subset ofR^N, and h₀ a map of R to R, and where u is the unknown of theproblem. We assume that we know that a certain function u₀ belongingto a certain function space X solves (1.1). Then if we wishto know whether by perturbing h₀ in a certain function space,say Y, the solutions u depend on h continuously, with differentiability,with analyticity or bifurcate, we could set G[h, u] u+h u,recast problem (1.1) into the abstract form G[h, u] (1.2) and study the solution set of equation (1.2) around the pair(h₀, u₀) by means of the implicit function theorem or by localbifurcation theorems in a Banach space setting.     

Extended defects in shallow implants

Extended defects are often found after ion implantation and annealing of silicon and they are known to affect dopant diffusion. The article reviews the structure and energetics of the most often found extended defects and describes the mechanisms by which all these defects grow in size and transform during annealing. Defects grow by interchanging the Si atoms they are composed of and thus maintain large supersaturations of free Si interstitials in the region. A model has been developped to describe such an evolution in presence of a free surface. It is shown that after low energy implantation, the surface of the wafer may recombine large amounts of these free Si interstitials, driving defects into dissolution before transformation into more stable forms. Received: 21 August 2002 / Accepted: 21 August 2002 / Published online: 12 February 2003 RID="*" ID="*"Corresponding author. Fax: +33-56/2257-999, E-mail: claverie@cemes.fr     

Delayed crossing in the \pi h_{9/2} 1/2-[541] band of 173 Lu

High-spin states in the odd-proton nucleus ¹⁷³Lu have been populated in a ¹⁷⁰Er(⁷Li,4n) reaction and the emitted -radiation was detected with the GASP array. The favoured and unfavoured sequences of the band have been considerably extended. The favoured sequence does not show any indication of a band crossing up to a rotational frequency of 0.45 MeV. This is the largest crossing frequency ever observed for 1/2^- [541] bands of odd-proton nuclei with and . Previous Cranked Shell Model (CSM) calculations underestimate the crossing frequency by 100 keV.Received: 19 May 2003, Published online: 11 November 2003PACS: 21.10.-k Properties of nuclei; nuclear energy levels - 21.10.Re Collective levels - 23.20.Lv transitions and level energies - 27.70. + q      

Fourth-order perturbation theory for the half-filled Hubbard model in infinite dimensions

We calculate the zero-temperature self-energy to fourth-order perturbation theory in the Hubbard interaction U for the half-filled Hubbard model in infinite dimensions. For the Bethe lattice with bare bandwidth W, we compare our perturbative results for the self-energy, the single-particle density of states, and the momentum distribution to those from approximate analytical and numerical studies of the model. Results for the density of states from perturbation theory at U/W = 0.4 agree very well with those from the Dynamical Mean-Field Theory treated with the Fixed-Energy Exact Diagonalization and with the Dynamical Density-Matrix Renormalization Group. In contrast, our results reveal the limited resolution of the Numerical Renormalization Group approach in treating the Hubbard bands. The momentum distributions from all approximate studies of the model are very similar in the regime where perturbation theory is applicable, . Iterated Perturbation Theory overestimates the quasiparticle weight above such moderate interaction strengths.Received: 9 September 2003, Published online: 30 January 2004PACS: 71.10.Fd Lattice fermion models (Hubbard model, etc.) - 71.27. + a Strongly correlated electron systems; heavy fermions - 71.30. + h Metal-insulator transitions and other electronic transitions     

Growth atomic mechanisms of pulsed laser deposited La modified- $\mathsf{PbTiO_3}$ perovskites

The microstructure and morphology of 100/001-oriented La modified-PbTiO₃ (PLT) films grown by pulsed laser deposition have been analyzed and elucidated within the framework of morphology evolution models, such as the Dynamic Scaling Theory and Structure Zone Model. The experimental results were obtained from X-ray diffraction, atomic force microscopy and cross-section scanning electron microscopy. PLT grows with a compact columnar microstructure. The columns are formed by coherently grouped grains and show oblique walls and rounded tops. Connecting the experimental results with the morphology evolution models, the growth mechanisms involved in the deposition process were identified. While inside each column, the existing Pb vacancies govern the coarsening and coalescence of the grains, a non-local effect of geometric shadowing of the incident particle flux during growth controls competition between columns and their coarsening.Received: 18 June 2003, Published online: 22 September 2003PACS: 68.55.-a Thin film structure and morphology - 81.15.Fg Laser deposition - 77.84.Dy Niobates, titanates, tantalates, PZT ceramics, etc.E. Vasco: Current address: Institut für Festkörperforschung, Forschungszentrum Jülich, 52425 Jülich, GermanyC. Polop: Current address: I. Physikalisches Institut, RWTH-Aachen, 52056 Aachen, Germany     

Using OR to support the development of an integrated musculo-skeletal service

This paper discusses the question of how operational research in general, and discrete event simulation in particular, can help to meet management challenges in hospital-based orthopaedics medicine. It focuses on the reduction of waiting times for elective patients, both for a first outpatient appointment and for the subsequent commencement of in-patient treatment. The research is based on a series of projects carried out by students from the Department of Management Science, University Strathclyde in Stobhill Hospital and the Glasgow Royal Infirmary between 1999 and 2003. An increasingly detailed and complex simulation model was developed for the musculo-skeletal service provided by these hospitals. The paper discusses the application of a modelling methodology—based on the idea of requisite models evolving over time—that is participatory, iterative and focused on enhancing the clients' understanding of the main performance drivers of the service. It concludes that this methodology fits well with successful strategies to sustain reductions in waiting times.     

Millisecond pulsars with r-modes as steady gravitational radiators

Millisecond pulsars (MSPs) probably achieve their fast rotation by mass transfer from their companion stars in low-mass x-ray binaries (LMXBs). The lack of MSPs and LMXBs rotating near breakup has been attributed to the accretion torque being balanced, at fast rotation, by gravitational radiation, perhaps caused by an unstable oscillation mode. It has been argued that internal dissipation involving hyperons may cause LMXBs to evolve into a quasisteady state, with nearly constant rotation rate, temperature, and mode amplitude. We show that MSPs descending from these LMXBs spend a long time in a similar state, as extremely steady sources of gravitational waves and thermal x rays, while they spin down due to gravitational radiation and the standard magnetic torque. Observed MSP braking torques already place meaningful constraints on this scenario.     

Glassy dynamics of polymers confined to nanoporous glasses revealed by relaxational and scattering experiments

The glassy dynamics of poly(propylene glycol) (PPG) and poly(dimethyl siloxane) (PDMS) confined to a nanoporous host system revealed by dielectric spectroscopy, temperature-modulated DSC and neutron scattering is compared. For both systems the relaxation rates estimated from dielectric spectroscopy and temperature-modulated DSC agree quantitatively indicating that both experiments sense the glass transition. For PPG the segmental dynamics is determined by a counterbalance of adsorption and confinement effect. The former results form an interaction of the confined macromolecules with the internal surfaces. A confinement effect originates from an inherent length scale on which the underlying molecular motions take place. The increment of the specific-heat capacity at the glass transition vanishes at a finite length scale of 1.8 nm. Both results support the conception that a characteristic length scale is relevant for glassy dynamics. For PDMS only a confinement effect is observed which is much stronger than that for PPG. Down to a pore size of 7.5 nm, the temperature dependence of the relaxation times follows the Vogel-Fulcher-Tammann dependence. At a pore size of 5 nm this changes to an Arrhenius-like behaviour with a low activation energy. At the same pore size vanishes for PDMS. Quasielastic neutron scattering experiments reveal that also the diffusive character of the relevant molecular motions --found to be characteristic above the glass transition-- seems to disappear at this length scale. These results gives further strong support that the glass transition has to be characterised by an inherent length scale of the relevant molecular motions.Received: 1 January 2003, Published online: 14 October 2003PACS: 64.70.Pf Glass transitions - 77.22.Gm Dielectric loss and relaxation - 61.25.Hq Macromolecular and polymer solutions; polymer melts; swelling     

Superscaling predictions for neutrino-induced charged-current charged pion production at MiniBooNE

Superscaling approximation (SuSA) predictions to neutrino-induced charged-current charged pion production in the Δ-resonance region are explored under MiniBooNE experimental conditions. The results obtained within SuSA for the flux-averaged double-differential cross sections of the π⁺${\pi }^{+}$ production for the _νμ+_CH2${\nu }_{\mu }+{\mathrm{CH}}_2$ reaction as a function of the muon kinetic energy and of the scattering angle, the cross sections averaged over the angle, the total cross section for the π⁺${\pi }^{+}$ production, as well as CC1π⁺$\mathrm{CC}1{\pi }^{+}$ to CCQE cross section ratio are compared with the corresponding MiniBooNE experimental data. The SuSA predictions are in good agreement with data on neutrino flux average cross sections, but a somewhat different dependence on the neutrino energy is predicted than the one resulting from the experimental analysis.