The non-uniform transformation strain problem for an anisotropic ellipsoidal inclusion

The problem of an anisotropic ellipsoidal inclusion which undergoes a stress-free transformation strain (in the sense of J.D. Eshelby) is considered, and the following theorem is proved: If an ellipsoidal region in an infinite anisotropic linear elastic medium undergoes, in the absence of its surroundings, a stress-free transformation strain which is a polynomial of degree M in the position coordinates x_t, then the final stress and strain state in the transformed inclusion, when constrained by its surroundings, is also a polynomial of degree M in x_t.     

The importance of chain length for the polyphosphate enhancement of acidic potassium permanganate chemiluminescence

Sodium polyphosphate is commonly used to enhance chemiluminescence reactions with acidic potassium permanganate through a dual enhancement mechanism, but commercially available polyphosphates vary greatly in composition. We have examined the influence of polyphosphate composition and concentration on both the dual enhancement mechanism of chemiluminescence intensity and the stability of the reagent under analytically useful conditions. The average chain length (n) provides a convenient characterisation, but materials with similar values can exhibit markedly different distributions of phosphate oligomers. There is a minimum polyphosphate chain length (∼6) required for a large enhancement of the emission intensity, but no further advantage was obtained using polyphosphate materials with much longer average chain lengths. Providing there is a sufficient average chain length, the optimum concentration of polyphosphate is dependent on the analyte and in some cases, may be lower than the quantities previously used in routine detection. However, the concentration of polyphosphate should not be lowered in permanganate reagents that have been partially reduced to form high concentrations of the key manganese(III) co-reactant, as this intermediate needs to be stabilised to prevent formation of insoluble manganese(IV).     

Simultaneous control of spectroscopic and electrochemical properties in functionalised electrochemiluminescent tris(2,2'-bipyridine)ruthenium(II) complexes

Using a combination of electrochemical, spectroscopic and computational techniques, we have explored the fundamental properties of a series of ruthenium diimine complexes designed for coupling with other molecules or surfaces for electrochemiluminescence (ECL) sensing applications. With appropriate choice of ligand functionality, it is possible to manipulate emission wavelengths while keeping the redox ability of the complex relatively constant. DFT calculations show that in the case of electron withdrawing substituents such as ester or amide, the excited state is located on the substituted bipyridine ligand whereas in the case of alkyl functionality it is localised on a bipyridine. The factors that dictate annihilation ECL efficiency are interrelated. For example, the same factors that determine ΔG for the annihilation reaction (i.e. the relative energies of the HOMO and LUMO) have a corresponding effect on the energy of the excited state product. As a result, most of the complexes populate the excited state with an efficiency (Φ(ex)) of close to 80% despite the relatively wide range of emission maxima. The quantum yield of emission (Φ(p)) and the possibility of competing side reactions are found to be the main determinants of ECL intensity.     

Hydrogen bonding in the hexagonal ice surface

A recently developed technique in sum frequency generation spectroscopy, polarization angle null (or PAN-SFG), is applied to two orientations of the prism face of hexagonal ice. It is found that the vibrational modes of the surface are similar in different faces. As in the basal face, the prism face of ice contains five dominant resonances: 3096, 3146, 3205, 3253, and 3386 cm(-1). On the basal face, the reddest resonance occurs at 3098 cm(-1); within the bandwidth, the same as the prism face. On both the prism and basal faces, this mode contains a significant quadrupole component and is assigned to the bilayer stitching hydrogen bonds. The bluest of the resonances, 3386 cm(-1), occurs slightly blue-shifted at 3393 cm(-1) in the basal face. The prism face has two orientations: one with the optic or c axis in the input plane (the plane formed by the surface normal and the interrogating beam propagation) and one with the c axis perpendicular to the input plane. The 3386 cm(-1) mode has significant intensity only with the c axis in the input plane. On the basis of these orientation characteristics, the 3386 cm(-1) mode is assigned to double-donor molecules in either the top half bilayer or in the lower half bilayer. On the basis of frequency considerations, it is assigned to double-donor molecules in the top half bilayer. These are water molecules containing a nonbonded lone pair. In addition to identification of the components of the broad hydrogen-bonded region, PAN-SFG measures the tangential vs longitudinal content of the vibrational modes. In accord with previous suggestions, the lower frequency modes are predominantly tangential, whereas the higher frequency modes are mainly longitudinal. On the prism face, the 3386 cm(-1) mode is entirely longitudinal.     

Oxygen transfer processes in (La,Sr)MnO3/Y2O3-stabilized ZrO2 cathodes: an impedance spectroscopy study

Impedance spectroscopy was used to study the oxygen reaction kinetics of La_0.8Sr_0.2MnO₃ (LSM)-based electrodes on Y₂O₃-stabilized ZrO₂ (YSZ) electrolytes. Three types of electrodes were studied: pure LSM, LSM–YSZ composites, and LSM/LSM–YSZ bilayers. The electrodes were formed by spin coating and sintering on single-crystal YSZ substrates. Measurements were taken at temperatures ranging from 550 to 850°C and oxygen partial pressures from 1×10⁻³ to 1 atm. An arc whose resistance R_el had a high activation energy, E_a=1.61±0.05 eV, and a weak oxygen partial pressure dependence, (P_O2)^−1/6, was observed for the LSM electrodes. A similar arc was observed for LSM–YSZ electrodes, where R_el(P_O2)^−0.29 and the activation energy was 1.49±0.02 eV. The combination of a high activation energy and a weak P_O2 dependence was attributed to oxygen dissociation and adsorption rate-limiting steps for both types of electrodes. LSM–YSZ composite cathodes showed substantially lower overall interfacial resistance values than LSM, but exhibited an additional arc attributed to the resistance of YSZ grain boundaries within the LSM–YSZ. At 850°C and low P_O2, an additional arc was observed with size varying as (P_O2)^−0.80 for LSM and (P_O2)^−0.57 for LSM–YSZ, suggesting that diffusion had become an additional rate limiting step. Bilayer LSM/LSM–YSZ electrodes yielded results intermediate between LSM and LSM–YSZ. The results showed that most of the improvement in electrode performance was achieved for a LSM–YSZ layer only ≈2 μm thick. However, a decrease in the grain-boundary resistance would produce much better performance in thicker LSM–YSZ electrodes.     

MICROSTRUCTURE AND FRACTAL FORMATION OF ANNEALED Ge-Au FILM AND Ge-Au/Au BILAYER FILMS

The as-deposited and annealed Ge-Au film and Ge-Au/Au bilayer films have been observed by transmission electron microscopy. The bilayer with a composition of Ge-5at%Au film is amorphous, while the Ge-22at%Au film is polycrystalline. Higher concentration of Au raises the structural heterogeneity and instability. Fractals can be observed in the Ge-5at%Au/Au bilayer samples annealed at 60-100℃. The difference of the fractal patterns generated from Ge-Au/An and a-Ge/Au films call be attributed to the higher heterogeneity and instability in Ge-Au/An bilayers.     

Non-Markovian thermalisation of a two-level atom

We consider thermalisation and spontaneous decay of a two-level atom beyond the Markovian approximation. While the standard elimination of the continuum of radiation modes results in exponential decay represented by a Lindblad equation of motion, we use a simple toy model that takes into account the finite relaxation rate of the environment and present an exact non-Markovian master equation of the Nakajima-Zwanzig form. Because the exact derivation of non-Markovian equations has proved very difficult for all more realistic (and hence much more complicated) models, we analyze the master equation obtained and also discuss difficulties that are likely to arise with non-Markovian evolution operators.     

Ultimate quantum limits for resolution of beam displacements

We compare two high sensitivity techniques which are used to measure very small displacements of physical objects by optical techniques: the interferometric devices, measuring longitudinal phase shifts, and the devices used to monitor transverse displacement of light beams. We detail the differences and the similarities for the quantum limits on the resolution of both systems. In both cases squeezed light can be used to resolve beyond the standard quantum limit and number correlated states allow us to reach the “Heisenberg” limit. Received 12 September 2002 Published online 21 January 2003     

Gyrotron travelling wave amplifier: I. Analysis of oscillations

The operation of the gyrotron travelling wave amplifier is based on the convective cyclotron maser instability. It is found that this convective instability may become absolute (nonconvective) at a sufficiently high current level, resulting in oscillation instead of amplification. This threshold current for the transition depends sensitively on the applied magnetic field. The axial wavelength and the characteristic frequency of oscillation at the onset of absolute instability are given. It is found that momentum spread has virtually no effect on the threshold current. A small amount of resistive wall loss, however, raises the threshold current significantly. Oscillations due to partial reflection at the ends of the system are also examined. Preliminary experimental results on both types of oscillations are reported and are found to be in good agreement with the theory.