The geodesic approximation for lump dynamics and coercivity of the Hessian for harmonic maps

The most fruitful approach to studying low energy soliton dynamics in field theories of Bogomol'nyi type is the geodesic approximation of Manton. In the case of vortices and monopoles, Stuart has obtained rigorous estimates of the errors in this approximation, and hence proved that it is valid in the low speed regime. His method employs energy estimates which rely on a key coercivity property of the Hessian of the energy functional of the theory under consideration. In this paper we prove an analogous coercivity property for the Hessian of the energy functional of a general sigma model with compact K\"ahler domain and target. We go on to prove a continuity property for our result, and show that, for the CP^1 model on S^2, the Hessian fails to be globally coercive in the degree 1 sector. We present numerical evidence which suggests that the Hessian is globally coercive in a certain equivariance class of the degree n sector for n>1. We also prove that, within the geodesic approximation, a single CP^1 lump moving on S^2 does not generically travel on a great circle.Comment: 29 pages, 1 figure; typos corrected, references added, expanded discussion of the main function spac

Electron accumulation and doping in InN and InGaN alloys

InN and group III nitride materials have attracted great interest due to their potential applications for optoelectronic devices, as the range of band gaps cover the ultra-violet to the near infrared. InN and all In-rich InxGa1−xN alloys exhibit a surface electron accumulation layer. This is due to the unusually low conduction band minimum (CBM) at the Brouillon zone centre (Γ-point) with respect to the charge- neutrality level. Electron accumulation has been observed at the surface of almost all n-type and p-type InN, making proof of p-type doping of this material very difficult. Routine characterization of p-type conductivity of Mg-doped samples using single-field Hall effect is prevented by the presence of a surface inversion space-charge layer, and hence the surface electron-rich region dominates the measurements. In this thesis, the results of investigations on non-polar InN surfaces, Mg-doped InN surfaces and a range of InxGa1−xN alloys across the composition entire range are presented. Considerable improvement of the quality of a- and m-plane InN thin films has been achieved using free standing GaN substrates in conjunction with a GaN buffer layer and grown by PAMBE. Using a combination of infrared reflectivity (FTIR), x-ray photoemission spectroscopy (XPS) and electrochemical capacitance voltage (ECV) measurements, the surface space charge properties of these samples have been investigated. The surface Fermi level has been determined to be lower than previously observed on non- cleaved InN samples. Additionally a high carrier concentration has been found on the non-polar InN, close to the interface with the GaN buffer layer, associated with unintentionally incorporated oxygen impurities. The increased concentration of oxygen impurities near the InN/GaN interface, confirmed by secondary ion mass spectrometry (SIMS), is due to the relatively low growth temperature (380 - 450 ◦C) used to produce the non-polar InN films. XPS has been also used in the investigations of Mg-doped InN. A significant lowering of the surface Fermi level has been observed with increasing Mg-doping for the highest Mg concentration (> 1 × 1019 cm−3) indicating a highly desirable reduction in the degree of surface electron accumulation. While for moderate Mg concentrations the surface Fermi level is at the previously determined ‘universal’ value of ~ 1.4 eV above the valence band maximum, for [Mg]=1.2×1020 cm−3, a value of 0.83 eV is found. As a consequence, for [Mg]> 1 × 1019 cm−3 the donor surface state density increases while the surface electron density decreases enormously, resulting in a transition from electron accumulation to almost just hole depletion layer. This reduction of electron accumulation in high Mg-doped InN can be improved by additional surface treatment, therefore results of a series of sulfur treated Mg-doped InN sample are also reported in this thesis. Finally, the electronic properties of InxGa1−xN alloys with a composition range of 0.20 >= x >= 1.00 have been investigated, using XPS and FTIR. The transition from electron accumulation to electron depletion has been observed at a composition of x = 0.20, while for x >= 0.20 an increasing electron accumulation with decreasing Ga fraction has been observed

Growth and properties of GaSbBi alloys

Molecular-beam epitaxy has been used to grow GaSb 1− x Bi x alloys with x up to 0.05. The Bi content, lattice expansion, and film thickness were determined by Rutherford backscattering and x-ray diffraction, which also indicate high crystallinity and that >98% of the Bi atoms are substitutional. The observed Bi-induced lattice dilation is consistent with density functional theory calculations. Optical absorption measurements and valence band anticrossing modeling indicate that the room temperature band gap varies from 720 meV for GaSb to 540 meV for GaSb 0.95Bi0.05, corresponding to a reduction of 36 meV/%Bi or 210 meV per 0.01 Å change in lattice constant

High Bi content GaSbBi alloys

The epitaxial growth, structural, and optical properties of GaSb 1– x Bi x alloys have been investigated. The Bi incorporation into GaSb is varied in the range 0 < x ≤ 9.6% by varying the growth rate (0.31–1.33 μm h−1) at two growth temperatures (250 and 275 °C). The Bi content is inversely proportional to the growth rate, but with higher Bi contents achieved at 250 than at 275 °C. A maximum Bi content of x = 9.6% is achieved with the Bi greater than 99% substitutional. Extrapolating the linear variation of lattice parameter with Bi content in the GaSbBi films enabled a zinc blende GaBi lattice parameter to be estimated of 6.272 Å. The band gap at 300 K of the GaSbBi epitaxial layers decreases linearly with increasing Bi content down to 410 ± 40 meV (3 μm) for x = 9.6%, corresponding to a reduction of ∼35 meV/%Bi. Photoluminescence indicates a band gap of 490 ± 5 meV at 15 K for x = 9.6%

Band gap reduction in InNxSb1-x alloys: Optical absorption, k . P modeling, and density functional theory

Using infrared absorption, the room temperature band gap of InSb is found to reduce from 174 (7.1 μm) to 85 meV (14.6 μm) upon incorporation of up to 1.13% N, a reduction of ∼79 meV/%N. The experimentally observed band gap reduction in molecular-beam epitaxial InNSb thin films is reproduced by a five band k ⋅· P band anticrossing model incorporating a nitrogen level, EN, 0.75 eV above the valence band maximum of the host InSb and an interaction coupling matrix element between the host conduction band and the N level of β = 1.80 eV. This observation is consistent with the presented results from hybrid density functional theory

Bi-induced band gap reduction in epitaxial InSbBi alloys

The properties of molecular beam epitaxy-grown InSb1−xBix alloys are investigated. Rutherford backscattering spectrometry shows that the Bi content increases from 0.6% for growth at 350 °C to 2.4% at 200 °C. X-ray diffraction indicates Bi-induced lattice dilation and suggests a zinc-blende InBi lattice parameter of 6.626 Å. Scanning electron microscopy reveals surface InSbBi nanostructures on the InSbBi films for the lowest growth temperatures, Bi droplets at intermediate temperatures, and smooth surfaces for the highest temperature. The room temperature optical absorption edge was found to change from 172 meV (7.2 μm) for InSb to ∼88 meV (14.1 μm) for InSb0.976Bi0.024, a reduction of ∼35 meV/%Bi. The work at Liverpool and Warwick was supported by the University of Liverpool and the Engineering and Physical Sciences Research Council (EPSRC) under Grant Nos. EP/G004447/2 and EP/H021388/1. RBS measurements performed at Lawrence Berkeley National Lab were supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division. Barry Karlin and Joe Woicik are thanked for use of the X24a HAXPES end station at the National Institute of Standards and Technology bending magnet beamline X24 at the National Synchrotron Light Source at Brookhaven National Laboratory. The National Synchrotron Light Source is supported by the U.S. Department of Energy, Contract No. DE-AC02-98CH10886. The work at Binghamton was supported by a Grant from State University of New York Research Foundation Collaboration Fund

Application of pharmacogenomics and bioinformatics to exemplify the utility of human <i>ex vivo</i> organoculture models in the field of precision medicine

Here we describe a collaboration between industry, the National Health Service (NHS) and academia that sought to demonstrate how early understanding of both pharmacology and genomics can improve strategies for the development of precision medicines. Diseased tissue ethically acquired from patients suffering from chronic obstructive pulmonary disease (COPD), was used to investigate inter-patient variability in drug efficacy using ex vivo organocultures of fresh lung tissue as the test system. The reduction in inflammatory cytokines in the presence of various test drugs was used as the measure of drug efficacy and the individual patient responses were then matched against genotype and microRNA profiles in an attempt to identify unique predictors of drug responsiveness. Our findings suggest that genetic variation in CYP2E1 and SMAD3 genes may partly explain the observed variation in drug response

Diamond Detectors for the TOTEM Timing Upgrade

This paper describes the design and the performance of the timing detector developed by the TOTEM Collaboration for the Roman Pots (RPs) to measure the Time-Of-Flight (TOF) of the protons produced in central diffractive interactions at the LHC. The measurement of the TOF of the protons allows the determination of the longitudinal position of the proton interaction vertex and its association with one of the vertices reconstructed by the CMS detectors. The TOF detector is based on single crystal Chemical Vapor Deposition (scCVD) diamond plates and is designed to measure the protons TOF with about 50 ps time precision. This upgrade to the TOTEM apparatus will be used in the LHC run 2 and will tag the central diffractive events up to an interaction pileup of about 1. A dedicated fast and low noise electronics for the signal amplification has been developed. The digitization of the diamond signal is performed by sampling the waveform. After introducing the physics studies that will most profit from the addition of these new detectors, we discuss in detail the optimization and the performance of the first TOF detector installed in the LHC in November 2015.Comment: 26 pages, 18 figures, 2 tables, submitted for publication to JINS

A new hammer to crack an old nut : interspecific competitive resource capture by plants is regulated by nutrient supply, not climate

Peer reviewedPublisher PD