Weak Slice Conditions and Holder Imbeddings

Weak slice conditions are introduced and imbeddings of Sobolevspaces in various Lipschitz-type spaces are investigated.     

The photodegradation of cadmium yellow paints in Henri Matisse’s Le Bonheur de vivre (1905–1906)

Evidence for the alteration of the yellow paints in Henri Matisse’s Le Bonheur de vivre (1905–1906, The Barnes Foundation) has been observed since the 1990s. The changes in this iconic work of Matisse’s Fauvist period include lightening, darkening, and flaking of the yellow paints. Handheld X-ray fluorescence (XRF) and multispectral imaging surveys reveal that the degradation is confined to cadmium yellow (CdS) paints. The discoloration of cadmium yellow paints in Impressionist, Post-Impressionist and early modernist work from the 1880s through the 1920s has been ascribed to the photo-oxidative degradation of CdS. Preliminary investigations of the degraded yellow paints in this work involved Cd L_III-edge X-ray Absorption Near Edge Spectroscopy (XANES) at the Stanford Synchrotron Radiation Light Source (SSRL Menlo Park, California) and Scanning Electron Microscopy-energy dispersive X-ray analysis (SEM-EDS) at the Winterthur Museum Scientific Research and Analysis Laboratory. To determine if the visual changes in the paints did in fact indicate photo-oxidative degradation and if different chemistries could be observed for the lightened versus darkened regions, synchrotron radiation-micro Fourier Transform InfraRed (SR-μFTIR) spectroscopy, X-ray Fluorescence (SR-μXRF) mapping and micro X-ray Absorption Near Edge Spectroscopy (μXANES) mapping at the Cd L_III-edge of the altered paint cross-sections were carried out at the European synchrotron radiation facility (ESRF, Grenoble, France) beamline ID-21. The goal is to elucidate the discoloration mechanisms observed in the paint using elemental and speciation mapping. The μXANES mapping and SR-FTIR imaging showed a substantial enrichment of CdCO₃ in the off-white surface crust of the faded/discolored CdS paint. This suggests that the CdCO₃ is present as an insoluble photodegradation product rather than solely a paint filler or starting reagent. Additionally, oxalates and sulfates were found to be concentrated at the alteration surface.     

Long vectors for quasi-Newton updates

This work concerns the derivation of formulae for updating quasi-Newton matrices used in algorithms for computing approximate minima of smooth unconstrained functions. The paper concentrates strictly on the techniques used to derive update formulae. It demonstrates a technique in which problems of finding matrices in ℝ ^{n ×n} of minimum Frobenius norm are converted to equivalent problems, using vector representations in ℝ ⁿ² and ℝ ^n(n+1)/2 of these matrices, and then solvingl ₂-minimization problems. These problems are more directly dealt with, and indeed, the paper demonstrates how this technique may be used to handle weighted sparse updates.     

Persistence in financial markets

Persistence is studied in a financial context by mapping the time evolution of the values of the shares quoted on the London Financial Times Stock Exchange 100 index (FTSE 100) onto Ising spins. By following the time dependence of the spins, we find evidence for power law decay of the proportion of shares that remain either above or below their 'starting' values. As a result, we estimate a persistence exponent for the underlying financial market to be θ_f∼0.5.     

Electrical tuning of single nitrogen-vacancy center optical transitions enhanced by photoinduced fields

We demonstrate precise control over the zero-phonon optical transition energies of individual nitrogen-vacancy (NV) centers in diamond by applying multiaxis electric fields, via the dc Stark effect. The Stark shifts display surprising asymmetries that we attribute to an enhancement and rectification of the local electric field by photoionized charge traps in the diamond. Using this effect, we tune the excited-state orbitals of strained NV centers to degeneracy and vary the resulting degenerate optical transition frequency by >10 GHz, a scale comparable to the inhomogeneous frequency distribution. This technique will facilitate the integration of NV-center spins within photonic networks.     

Time-stretch oscilloscope with dual-channel differential detection front end for monitoring of 100 Gb/s return-to-zero differential quadrature phase-shift keying data

Optical performance monitoring of high-capacity networks is one of the enabling technologies of future reconfigurable optical switch networks. In such networks, rapid performance evaluation of data streams becomes challenging due to the use of advanced modulation formats and high data rates. The time-stretch enhanced recording oscilloscope offers a potential solution to monitoring high-rate data in a practical time scale. Here we demonstrate an architecture with a differential detection front end for simultaneous I/Q data monitoring of a 100 gigabits/s return-to-zero differential quadrature phase-shift keying signal. This demonstration shows the potential of this technology for rapid performance monitoring of high-rate optical data streams that employ advanced modulation formats.     

An intermediate model method for obtaining a discrete relaxation spectrum from creep data

A convenient method is described for obtaining a discrete stress relaxation spectrum from linear viscoelastic creep data by means of a three-stage process. In stage one, a discrete retardation spectrum is fitted to the creep data using a least squares procedure, subject to the constraint that the discrete spectrum must be a specified order of polynomial function of the retardation time. In stage two, the resulting generalised Voigt model is solved numerically for an imposed step in strain, to determine the stress relaxation modulus function of time. In stage three, a discrete relaxation spectrum is fitted to the calculated stress relaxation modulus function. Although three stages are involved instead of the usual two, the procedure has been found to have certain practical advantages. These advantages make it suitable for the generation of relaxation spectra needed in viscoelastic stress analyses of solids, for example by the finite element method. In order to illustrate the proposed procedure it is applied to both artificial data and experimental creep data for poly(methyl methacrylate) at 70°C and at the glass transition.     

Deformation of thermosetting resins at impact rates of strain. Part 2: constitutive model with rejuvenation

The constitutive responses of three glassy thermoset polymers at impact rates of strain and slower, together with measurements of adiabatic heating, were reported earlier by the authors. The results are interpreted here in the context of a constitutive model proposed previously for amorphous polymers, expanded to incorporate strain-softening and the adiabatic heating deficit. In terms of the model, both features are a natural consequence of strain-induced evolution of the glass structure, as represented by Tool's “fictive temperature”—the phenomenon of structural rejuvenation. A representation is proposed for the evolution of fictive temperature with plastic strain, motivated by an approximate treatment of the kinetics of physical ageing/rejuvenation. Formulated in this manner, the model agrees reasonably well with experimental results across the wide range of strain rates of the previous experiments, 10⁻³ to , and across most of the range of strain to failure in compression. At the highest strains, however, an additional adiabatic heating deficit appears that is not predicted by the model, either suggesting the onset of structural breakdown possibly associated with the appearance of cracks or reflecting a need for better physical understanding of large deformations in glassy polymers.     

Highly efficient visible-light driven photochromism: developments towards a solid-state molecular switch operating through a triplet-sensitised pathway

We introduce a new highly efficient photochromic organometallic dithienylethene (DTE) complex, the first instance of a DTE core symmetrically modified by two Pt(II) chromophores [Pt(PEt(3))(2)(C≡C)(DTE)(C≡C)Pt(PEt(3))(2)Ph] (1), which undergoes ring-closure when activated by visible light in solvents of different polarity, in thin films and even in the solid state. Complex 1 has been synthesised and fully photophysically characterised by (resonance) Raman and transient absorption spectroscopy complemented by calculations. The ring-closing photoconversion in a single crystal of 1 has been followed by X-ray crystallography. This process occurs with the extremely high yield of 80%--considerably outperforming the other DTE derivatives. Remarkably, the photocyclisation of 1 occurs even under visible light (>400 nm), which is not absorbed by the non-metallated DTE core HC≡C(DTE)C≡CH (2) itself. This unusual behaviour and the high photocyclisation yields in solution are attributed to the presence of a heavy atom in 1 that enables a triplet-sensitised photocyclisation pathway, elucidated by transient absorption spectroscopy and DFT calculations. The results of resonance Raman investigation confirm the involvement of the alkynyl unit in the frontier orbitals of both closed and open forms of 1 in the photocyclisation process. The changes in the Raman spectra upon cyclisation have permitted the identification of Raman marker bands, which include the acetylide stretching vibration. Importantly, these bands occur in the spectral region unobstructed by other vibrations and can be used for non-destructive monitoring of photocyclisation/photoreversion processes and for optical readout in this type of efficiently photochromic thermally stable systems. This study indicates a strategy for generating efficient solid-state photoswitches in which modification of the Pt(II) units has the potential to tune absorption properties and hence operational wavelength across the visible range.     

Electrosynthesis of cyclic carbonates from epoxides and atmospheric pressure carbon dioxide

The use of CO(2) for the preparation of value-added compounds has dramatically increased due to increased global warming concerns. We herein report an electrochemical cell containing a copper cathode and a magnesium anode that effectively converts epoxides and carbon dioxide to cyclic carbonates under mild electrochemical conditions at atmospheric pressure.