Ultrasonic detection of the pinning of dislocations by point defects in lead—II. Model for dislocation defect interaction

Experiments are presented to establish that irradiation produced defects in lead not only pin dislocations but also can be trapped at the ends of dislocation lines in agreement with the model proposed by Thompson, Buck, Huntington and Barnes. This model indicates that there is a temperature T^* at which there is a maximum pinning of dislocations. T^* is found to be near 140 K. The data of Part I are analyzed according to this model using reasonable values of the dislocation density and the binding energy of the defect in the trap. The resulting activation energy for the region A process in the reaction kinetics model is found to be 0.15 eV which is consistent with the value found from an eigenvalue expansion model.     

Photophysics and Electrochemistry of some Thione Far-Red/Near-IR Triplet Emitters

The photophysics and cyclic voltammetry of two novel phosphorescent thiones, 2,2-dimethyl-indan-1-one-3-thione (DMIKT) and 2,2-dimethyl-indan-1,3-dithione (DMIDT), and three known phosphorescent thiones, 4H-pyran-4-thione (PT), 4H-1-benzopyran-4-thione (BPT) and 2,2-dimethylindan-1-thione (DMIT), have been characterised and compared. The phosphorescence emission of DMIT, DMIKT and DMIDT extends from the red into the near-IR spectral region. The additional carbonyl or thione group of DMIKT and DMIDT causes a significant shift in the emission maxima to 680 nm compared to that of DMIT, at 637 nm, in perfluorinated hydrocarbons. In acetonitrile the emission maxima of DMIKT and DMIDT are at 696 and 706 nm, respectively, and the spectra show vibronic bands which extend out beyond 850 nm. There is a significant reduction in triplet lifetime along this series (from 44 (±2) μs (DMIT) to 10 ((±0.8) μs (DMIKT) in perfluorinated solvents, and 8.6 (±0.5) (DMIT), 1.3 (±0.5) (DMIKT) and 0.35 (±0.07) μs (DMIDT) in acetonitrile), as well as a reduction in the rate constant for ground-state quenching of the triplet, (from 9.8 ((±0.9) to 3.5 ((±0.6) and 1.3 ((±0.2) × 10⁹ mol⁻¹ dm³ s⁻¹ for the same compounds). The addition of the C=O or C=S groups also causes a decrease in phosphorescence quantum yield with the highest emission quantum yield obtained for DMIT (Φ _P = 0.149 (±0.015)). Electrochemical studies show that while PT and BPT exhibit irreversible redox behaviour, DMIT, DMIKT and DMIDT all show at least one reversible reduction wave attributed to a one-electron process centred on the C=S moiety. The suitability of these lumophores for use in OLEDs is discussed.     

Hybrid chirped-pulse amplification

Conversion efficiency in optical parametric chirped-pulse amplification is limited by spatiotemporal characteristics of the pump pulse. We have demonstrated a novel hybrid chirped-pulse amplification scheme that uses a single pump pulse and combines optical parametric amplification and laser amplification to achieve high gain, high conversion efficiency, and high prepulse contrast without utilization of electro-optic modulators. We achieved an overall conversion efficiency of 37% from the hybrid amplification system at a center wavelength of 820nm. Generation of multiterawatt pulses is possible by use of this simple method and commercial Q -switched pump lasers.     

Almost global existence for quasilinear wave equations in three space dimensions

We prove almost global existence for multiple speed quasilinear wave equations with quadratic nonlinearities in three spatial dimensions. We prove new results both for Minkowski space and also for nonlinear Dirichlet-wave equations outside of star shaped obstacles. The results for Minkowski space generalize a classical theorem of John and Klainerman. Our techniques only use the classical invariance of the wave operator under translations, spatial rotations, and scaling. We exploit the decay of solutions of the wave equation as much as the decay. Accordingly, a key step in our approach is to prove a pointwise estimate of solutions of the wave equation that gives decay of solutions of the inhomogeneous linear wave equation in terms of a -weighted norm on the forcing term. A weighted space-time estimate for inhomogeneous wave equations is also important in making the spatial decay useful for the long-term existence argument.

     

6 j symbols for $U_q (\mathfrak{s}\mathfrak{l}_2 )$U_q (\mathfrak{s}\mathfrak{l}_2 ) and non-Euclidean tetrahedra

We relate the semiclassical asymptotics of the 6j symbols for the quantized enveloping algebra at q a root of unity (resp. q real positive) to the geometry of spherical (resp. hyperbolic) tetrahedra.     

An improved Mordell type bound for exponential sums

For a sparse polynomial , with and , we show that

thus improving upon a bound of Mordell. Analogous results are obtained for Laurent polynomials and for mixed exponential sums.

     

Note on Monte Carlo methods without necessary detailed balance

Simple criteria for convergence of Monte Carlo algorithms not necessarily requiring detailed balance for any specified transition probability are derived and it is shown that it is possible to view the algorithm as a superimposition of a Brownian motion on configurational space coupled to the transition probabilities. As such, the error contributions due to a particular Monte Carlo algorithm and the integration limits in configuration space must be distinguished from those due to the nonuniform sampling of the Brownian motion, and criteria related to the number of steps required to distinguish these errors are provided for the simplest cases involving one dimension and symmetrical probability distributions.     

Kodaira dimension of irregular varieties

Let f:X→Y be an algebraic fiber space with general fiber F. If Y is of maximal Albanese dimension, we show that κ(X)≥κ(Y)+κ(F).     

Minimal polynomials of Young permutation modules and idempotents

Applying an epimorphism of the Solomon descent algebra onto the subring of the Green ring spanned by the isomorphism classes of Young permutation modules, we determine a basis of primitive orthogonal idempotents which diagonalise the multiplication maps of Young permutation modules. We determine direct sum decompositions of tensor products of hook Young permutation modules, the minimal polynomials of all Young permutation modules, and of the Young module Y^(r?1,1).