A monoidal algebraic model for rational SO(2)-spectra

The category of rational SO(2)--equivariant spectra admits an algebraic model. That is, there is an abelian category A(SO(2)) whose derived category is equivalent to the homotopy category of rational$SO(2)--equivariant spectra. An important question is: does this algebraic model capture the smash product of spectra? The category A(SO(2)) is known as Greenlees' standard model, it is an abelian category that has no projective objects and is constructed from modules over a non--Noetherian ring. As a consequence, the standard techniques for constructing a monoidal model structure cannot be applied. In this paper a monoidal model structure on A(SO(2)) is constructed and the derived tensor product on the homotopy category is shown to be compatible with the smash product of spectra. The method used is related to techniques developed by the author in earlier joint work with Roitzheim. That work constructed a monoidal model structure on Franke's exotic model for the K_(p)--local stable homotopy category. A monoidal Quillen equivalence to a simpler monoidal model category that has explicit generating sets is also given. Having monoidal model structures on the two categories removes a serious obstruction to constructing a series of monoidal Quillen equivalences between the algebraic model and rational SO(2)--equivariant spectra.

Searching for swept-up hydrogen and helium in the late-time spectra of 11 nearby Type Ia supernovae

The direct detection of a stellar system that explodes as a Type Ia supernova (SN Ia) has not yet been successful. Various indirect methods have been used to investigate SN Ia progenitor systems but none have produced conclusive results. A prediction of single-degenerate models is that H- (or He-) rich material from the envelope of the companion star should be swept up by the SN ejecta in the explosion. Seven SNe Ia have been analysed to date looking for signs of H-rich material in their late-time spectra and none were detected. We present results from new late-time spectra of 11 SNe Ia obtained at the Very Large Telescope using XShooter and FORS2. We present the tentative detection of Hα emission for SN 2013ct, corresponding to ∼0.007 M_⊙ of stripped/ablated companion star material (under the assumptions of the spectral modelling). This mass is significantly lower than expected for single-degenerate scenarios, suggesting that >0.1 M_⊙ of H-rich is present but not observed. We do not detect Hα emission in the other 10 SNe Ia. This brings the total sample of normal SNe Ia with non-detections (<0.001–0.058 M_⊙) of H-rich material to 17 events. The simplest explanation for these non-detections is that these objects did not result from the explosion of a CO white dwarf accreting matter from a H-rich companion star via Roche lobe overflow or symbiotic channels. However, further spectral modelling is needed to confirm this. We also find no evidence of He-emission features, but models with He-rich companion stars are not available to place mass limits.

Rational O(2)–Equivariant Spectra

The category of rational O(2)-equivariant cohomology theories has an algebraic model A(O(2)), as established by work of Greenlees. That is, there is an equivalence of categories between the homotopy category of rational O(2)-equivariant spectra and the derived category of the abelian model DA(O(2)). In this paper we lift this equivalence of homotopy categories to the level of Quillen equivalences of model categories. This Quillen equivalence is also compatible with the Adams short exact sequence of the algebraic model.

Investigation of the chemical origin and evidential value of differences in the SERS spectra of blue gel inks

Highly swellable polymer films doped with Ag nanoparticle aggregates (poly-SERS films) have been used to record very high signal:noise ratio, reproducible surface-enhanced (resonance) Raman (SER(R)S) spectra of in situ dried ink lines and their constituent dyes using both 633 and 785 nm excitation. These allowed the chemical origins of differences in the SERRS spectra of different inks to be determined. Initial investigation of pure samples of the 10 most common blue dyes showed that the dyes which had very similar chemical structures such as Patent Blue V and Patent Blue VF (which differ only by a single OH group) gave SERRS spectra in which the only indications that the dye structure had been changed were small differences in peak positions or relative intensities of the bands. SERRS studies of 13 gel pen inks were consistent with this observation. In some cases inks from different types of pens could be distinguished even though they were dominated by a single dye such as Victoria Blue B (Zebra Surari) or Victoria Blue BO (Pilot Acroball) because their predominant dye did not appear in other inks. Conversely, identical spectra were also recorded from different types of pens (Pilot G7, Zebra Z-grip) because they all had the same dominant Brilliant Blue G dye. Finally, some of the inks contained mixtures of dyes which could be separated by TLC and removed from the plate before being analysed with the same poly-SERS films. For example, the Pentel EnerGel ink pen was found to give TLC spots corresponding to Erioglaucine and Brilliant Blue G. Overall, this study has shown that the spectral differences between different inks which are based on chemically similar, but nonetheless distinct dyes, are extremely small, so very close matches between SERRS spectra are required for confident identification. Poly-SERS substrates can routinely provide the very stringent reproducibility and sensitivity levels required. This, coupled with the awareness of the reasons underlying the observed differences between similarly coloured inks allows a more confident assessment of the evidential value of inks SERS and should underpin adoption of this approach as a routine method for the forensic examination of inks.

EXCITON ENGINEERING THROUGH TUNALBLE FLUORESCENT QUANTUM DEFECTS

This thesis demonstrates exciton engineering in semiconducting single-walled carbon nanotubes through tunable fluorescent quantum defects. By introducing different functional moieties on the sp2 lattice of carbon nanotubes, the nanotube photoluminescence is systematically tuned over 68 meV in the second near-infrared window. This new class of quantum emitters is enabled by a new chemistry that allows covalent attachment of alkyl/aryl functional groups from their iodide precursors in aqueous solution. Using aminoaryl quantum defects, we show that the pH and temperature of complex fluids can be optically measured through defect photoluminescence that encodes the local environment information. Furthermore, defect-bound trions, which are electron-hole-electron tri-carrier quasi-particles, are observed in alkylated single-walled carbon nanotubes at room temperature with surprisingly high photoluminescence brightness. Collectively, the emission from defect-bound excitons and trions in (6,5)-single walled carbon nanotubes is 18-fold brighter than that of the native exciton. These findings pave the way to chemical tailoring of the electronic and optical properties of carbon nanostructures with fluorescent quantum defects and may find applications in optoelectronics and bioimaging.

The D(D-3)-anyon chain: integrable boundary conditions and excitation spectra

Chains of interacting non-Abelian anyons with local interactions invariant under the action of the Drinfeld double of the dihedral group D-3 are constructed. Formulated as a spin chain the Hamiltonians are generated from commuting transfer matrices of an integrable vertex model for periodic and braided as well as open boundaries. A different anyonic model with the same local Hamiltonian is obtained within the fusion path formulation. This model is shown to be related to an integrable fusion interaction round the face model. Bulk and surface properties of the anyon chain are computed from the Bethe equations for the spin chain. The low-energy effective theories and operator content of the models (in both the spin chain and fusion path formulation) are identified from analytical and numerical studies of the finite-size spectra. For all boundary conditions considered the continuum theory is found to be a product of two conformal field theories. Depending on the coupling constants the factors can be a Z(4) parafermion or a M-(5,M-6) minimal model.

Exciton-mediated photothermal cooling in GaAs membranes

Cooling of the mechanical motion of a GaAs nano-membrane using the photothermal effect mediated by excitons was recently demonstrated by some of the authors (Usami et al 2012 Nature Phys. 8 168) and provides a clear example of the use of thermal forces to cool down mechanical motion. Here, we report on a single-free-parameter theoretical model to explain the results of this experiment which matches the experimental data remarkably well.

Absorption and luminescent excitation spectra of F and M centers in Kcl and NaF

Luminescent excitation spectra were measured for the F and M centers in KCl; in particular, for the F band, M band, and the M2 transition. In all 3 cases, the spectra were nearly double-Gaussian in shape, and the efficiency for luminescence was nearly independent of the wavelength of the exciting light. A comparison of the absorption spectrum with the excitation spectrum of the F-band region of crystals with M centers present and oriented provided further evidence for the existence of the M2 transition of van Doorn and Haven and of Okamoto, and against the energy transfer theory of Lambe and Compton. The efficiency for luminescence of the M center upon M-band excitation was equal to the efficiency for F centers in pulse-annealed crystals of low F-center concentrations. The ratio of the efficiencies of the Ml to M2 transitions was 1.2 ± .25. The oscillator strengths of 3 of the M-center transitions in KCl relative to the oscillator strength for the F center were found to be in better agreement with the results reported by Okamoto, than with the results reported by Delbecq. The polarization of luminescence of M centers in KCl was measured at right angles to the exciting light, and was found to agree with the predictions of the van Doorn-Haven model of the M center. In NaF crystals having no absorption bands to the red side of the M band, the absorption and excitation spectra of the M band were accurately double-Gaussian over a wide range of wavelengths; the efficiency of luminescence of the M center was independent of the wavelength of the exciting light in that range; and the polarization of luminescence upon M-band excitation agreed well with the calculations based on the van DoornHaven model of the M center, In crystals in which the F band was bleached sufficiently to make it smaller in absorption height than the M band, several new color centers appeared on the red side of the M band, in contrast to the results reported by Blum; in these crystals, the polarization of luminescence of the M center upon M-band excitation disagreed strongly with theory, even though the absorptions for the new color centers were small compared to the M-band absorption.

Airborne remote sensing of ocean wave directional wavenumber spectra in the marginal ice zone

Interactions between surface waves and sea ice are thought to be an important, but poorly understood, physical process in the atmosphere-ice-ocean system. In this work, airborne scanning lidar was used to observe ocean waves propagating into the marginal ice zone (MIZ). These represent the first direct spatial measurements of the surface wave field in the polar MIZ. Data were compared against two attenuation models, one based on viscous dissipation and one based on scattering. Both models were capable of reproducing the measured wave energy. The observed wavenumber dependence of attenuation was found to be consistent with viscous processes, while the spectral spreading of higher wavenumbers suggested a scattering mechanism. Both models reproduced a change in peak direction due to preferential directional filtering. Floe sizes were recorded using co-located visible imagery, and their distribution was found to be consistent with ice breakup by the wave field.

Spectra and Laplacian spectra of arbitrary powers of lexicographic products of graphs

Consider two graphs G and H. Let H^k[G] be the lexicographic product of H^k and G, where H^k is the lexicographic product of the graph H by itself k times. In this paper, we determine the spectrum of H^k[G]H and H^k when G and H are regular and the Laplacian spectrum of H^k[G] and H^k for G and H arbitrary. Particular emphasis is given to the least eigenvalue of the adjacency matrix in the case of lexicographic powers of regular graphs, and to the algebraic connectivity and the largest Laplacian eigenvalues in the case of lexicographic powers of arbitrary graphs. This approach allows the determination of the spectrum (in case of regular graphs) and Laplacian spectrum (for arbitrary graphs) of huge graphs. As an example, the spectrum of the lexicographic power of the Petersen graph with the googol number (that is, 10^100 ) of vertices is determined. The paper finishes with the extension of some well known spectral and combinatorial invariant properties of graphs to its lexicographic powers.

Excitonic behaviour in polymeric semiconductors : the effect of morphology and composition in heterostructures

La compréhension des interrelations entre la microstructure et les processus électroniques dans les polymères semi-conducteurs est d’une importance primordiale pour leur utilisation dans des hétérostructures volumiques. Dans cette thèse de doctorat, deux systémes diffèrents sont étudiés ; chacun de ces systèmes représente une approche diffèrente pour optimiser les matériaux en termes de leur microstructure et de leur capacité à se mettre en ordre au niveau moléculaire. Dans le premier système, j’ai effectué une analyse complète des principes de fonctionnement d’une cellule photovoltaïque hybride à base des nanocristaux d’oxyde de zinc (ZnO) et du poly (3-hexylthiophène) (P3HT) par absorption photoinduite en régime quasi-stationnaire (PIA) et la spectroscopie PIA en pompage modulé dépendant de la fréquence. L’interface entre le donneur (le polymère P3HT) et l’accepteur (les nanoparticules de ZnO), où la génération de charges se produit, joue un rôle important dans la performance des cellules photovoltaïques hybrides. Pour améliorer le mécanisme de génération de charges du P3H: ZnO, il est indispensable de modifier l’interface entre ses constituants. Nous avons démontré que la modification d’interface moléculaire avec cis-bis (4, 40 - dicarboxy-2, 20bipyridine) ruthénium (II) (N3-dye) et a-Sexithiophen-2 yl-phosphonique (6TP) a améliorée le photocourant et la performance dans les cellules P3HT: ZnO. Le 6TP et le N3 s’attachent à l’interface du ZnO, en augmentant ainsi l’aire effective de la surface donneur :accepteur, ce qui contribue à une séparation de charge accrue. De plus, le 6TP et le N3 réduisent la densité de pièges dans le ZnO, ce qui réduit le taux de recombinaison des paires de charges. Dans la deuxième partie, jai introduit une matrice hôte polymérique de polystyréne à masse molaire ulra-élevée, qui se comporte comme un solide pour piéger et protéger une solution de poly [2-méthoxy, 5- (2´-éthyl-hexoxy) -1,4-phénylènevinylène- PPV] (MEHPPV) pour utilisation dans des dispositifs optoèlectroniques quantiques. Des travaux antérieurs ont montré que MEH-PPV en solution subit une transition de conformation, d’une conformation enroulé à haute température (phase bleue) à une conformation de chaîne étendue à basse température (phase rouge). La conformation de la chaîne étendue de la solution MEH-PPV favorise les caractéristiques nécessaires à l’amélioration des dispositifs optoélectroniques quantiques, mais la solution ne peut pas être incorporées dans le dispositif. J’ai démontré que la caractéristique de la phase rouge du MEH-PPV en solution se maintient dans une matrice hôte polymérique de polystyrène transformé de masse molaire très élevée, qui se comporte comme un solide (gel de MEH-PPV/UHMW PS), par le biais de la spectroscopie de photoluminescence (PL) dépendant de la température (de 290K à 80 K). La phase rouge du gel MEH-PPV/UHMW PS se manifeste par des largeurs de raie étroites et une intensité augmentée de la transition 0-0 de la progression vibronique dans le spectre de PL ainsi qu’un petit décalage de Stokes entre la PL et le spectre d’absorption à basse température. Ces approches démontrent que la manipulation de la microstructure et des propriétés électroniques des polymères semi-conducteurs ont un impact direct sur la performance de dispositifs pour leurs développements technologiques continus.