Iterated Binomial Sums and their Associated Iterated Integrals

We consider finite iterated generalized harmonic sums weighted by the binomial $\binom{2k}{k}$ in numerators and denominators. A large class of these functions emerges in the calculation of massive Feynman diagrams with local operator insertions starting at 3-loop order in the coupling constant and extends the classes of the nested harmonic, generalized harmonic and cyclotomic sums. The binomially weighted sums are associated by the Mellin transform to iterated integrals over square-root valued alphabets. The values of the sums for $N \rightarrow \infty$ and the iterated integrals at $x=1$ lead to new constants, extending the set of special numbers given by the multiple zeta values, the cyclotomic zeta values and special constants which emerge in the limit $N \rightarrow \infty$ of generalized harmonic sums. We develop algorithms to obtain the Mellin representations of these sums in a systematic way. They are of importance for the derivation of the asymptotic expansion of these sums and their analytic continuation to $N \in \mathbb{C}$. The associated convolution relations are derived for real parameters and can therefore be used in a wider context, as e.g. for multi-scale processes. We also derive algorithms to transform iterated integrals over root-valued alphabets into binomial sums. Using generating functions we study a few aspects of infinite (inverse) binomial sums.Comment: 62 pages Latex, 1 style fil

Modelling and parametric study of the re-anchorage of ruptured tendons in bonded post-tensioned concrete

The contribution of ruptured tendons to the residual strength of bonded post-tensioned concrete structures is currently assessed based on pre-tensioned concrete bond models. However, this approach is inaccurate due to the inherent differences between pre-tensioned and post-tensioned concrete. In this paper, a non-linear 3D finite element model is developed for the re-anchoring of a ruptured tendon in post-tensioned concrete. The model is validated using full-field displacement measurement from 33 post-tensioned concrete prisms and previous experimental data on beams from the literature. The influence of different parameters was investigated, including tendon properties (i.e. diameter, roughness), duct properties (i.e. diameter, thickness, material), initial prestress, concrete strength, grout strength, grout voids, stirrups, and strands, on the tendon re-anchorage. The most influential parameters are found to be tendon and duct properties

Polarisation Patterns and Vectorial Defects in Type II Optical Parametric Oscillators

Previous studies of lasers and nonlinear resonators have revealed that the polarisation degree of freedom allows for the formation of polarisation patterns and novel localized structures, such as vectorial defects. Type II optical parametric oscillators are characterised by the fact that the down-converted beams are emitted in orthogonal polarisations. In this paper we show the results of the study of pattern and defect formation and dynamics in a Type II degenerate optical parametric oscillator for which the pump field is not resonated in the cavity. We find that traveling waves are the predominant solutions and that the defects are vectorial dislocations which appear at the boundaries of the regions where traveling waves of different phase or wave-vector orientation are formed. A dislocation is defined by two topological charges, one associated with the phase and another with the wave-vector orientation. We also show how to stabilize a single defect in a realistic experimental situation. The effects of phase mismatch of nonlinear interaction are finally considered.Comment: 38 pages, including 15 figures, LATeX. Related material, including movies, can be obtained from http://www.imedea.uib.es/Nonlinear/research_topics/OPO

Compassionate pedagogy: the ethics of care in early childhood professionalism

This paper builds upon an earlier attempt (Taggart, 2011) to articulate a rationale for professional training in early childhood education and care (ECEC) which is ethical as opposed to one which is purely instrumental or rooted in a patriarchal notion of women’s supposed unique suitability. The argument proposes that a feminist approach to ethics, as both socially critical and psychologically affective or flexible, has a particular relevance to professional identity in ECEC. In particular, compassion, as a concept which has both sociological and psychological connotations, foregrounds the ethical dimension of the work whilst overcoming false dichotomies between discourses of ‘children’s rights’ and ‘care’. The implications for the training and professional identity of practitioners are discussed

Multidimensional cosmological models: cosmological and astrophysical implications and constraints

We investigate four-dimensional effective theories which are obtained by dimensional reduction of multidimensional cosmological models with factorizable geometry and consider the interaction between conformal excitations of the internal space (geometrical moduli excitations) and Abelian gauge fields. It is assumed that the internal space background can be stabilized by minima of an effective potential. The conformal excitations over such a background have the form of massive scalar fields (gravitational excitons) propagating in the external spacetime. We discuss cosmological and astrophysical implications of the interaction between gravexcitons and four-dimensional photons as well as constraints arising on multidimensional models of the type considered in our paper. In particular, we show that due to the experimental bounds on the variation of the fine structure constant, gravexcitons should decay before nucleosynthesis starts. For a successful nucleosynthesis the masses of the decaying gravexcitons should be m>10^4 GeV. Furthermore, we discuss the possible contribution of gravexcitons to UHECR. It is shown that, at energies of about 10^{20}eV, the decay length of gravexcitons with masses m>10^4 GeV is very small, but that for m <10^2 GeV it becomes much larger than the Greisen-Zatsepin-Kuzmin cut-off distance. Finally, we investigate the possibility for gravexciton-photon oscillations in strong magnetic fields of astrophysical objects. The corresponding estimates indicate that even the high magnetic field strengths of magnetars are not sufficient for an efficient and copious production of gravexcitons.Comment: 16 pages, LaTeX2e, minor changes, improved references, to appear in PR

Measurement of the Branching Fraction for B- --> D0 K*-

We present a measurement of the branching fraction for the decay B- --> D0 K*- using a sample of approximately 86 million BBbar pairs collected by the BaBar detector from e+e- collisions near the Y(4S) resonance. The D0 is detected through its decays to K- pi+, K- pi+ pi0 and K- pi+ pi- pi+, and the K*- through its decay to K0S pi-. We measure the branching fraction to be B.F.(B- --> D0 K*-)= (6.3 +/- 0.7(stat.) +/- 0.5(syst.)) x 10^{-4}.Comment: 7 pages, 1 postscript figure, submitted to Phys. Rev. D (Rapid Communications

Nanoscale control of Ag nanostructures for plasmonic fluorescence enhancement of near-infrared dyes

Potential utilization of proteins for early detection and diagnosis of various diseases has drawn considerable interest in the development of protein-based detection techniques. Metal induced fluorescence enhancement offers the possibility of increasing the sensitivity of protein detection in clinical applications. We report the use of tunable plasmonic silver nanostructures for the fluorescence enhancement of a near-infrared (NIR) dye (Alexa Fluor 790). Extensive fluorescence enhancement of ∼2 orders of magnitude is obtained by the nanoscale control of the Ag nanostructure dimensions and interparticle distance. These Ag nanostructures also enhanced fluorescence from a dye with very high quantum yield (7.8 fold for Alexa Fluor 488, quantum efficiency (Qy) = 0.92). A combination of greatly enhanced excitation and an increased radiative decay rate, leading to an associated enhancement of the quantum efficiency leads to the large enhancement. These results show the potential of Ag nanostructures as metal induced fluorescence enhancement (MIFE) substrates for dyes in the NIR “biological window” as well as the visible region. Ag nanostructured arrays fabricated by colloidal lithography thus show great potential for NIR dye-based biosensing applications

Measurement of Branching Fraction and Dalitz Distribution for B0->D(*)+/- K0 pi-/+ Decays

We present measurements of the branching fractions for the three-body decays B0 -> D(*)-/+ K0 pi^+/-$and their resonant submodes$B0 -> D(*)-/+ K*+/- using a sample of approximately 88 million BBbar pairs collected by the BABAR detector at the PEP-II asymmetric energy storage ring. We measure: B(B0->D-/+ K0 pi+/-)=(4.9 +/- 0.7(stat) +/- 0.5 (syst)) 10^{-4} B(B0->D*-/+ K0 pi+/-)=(3.0 +/- 0.7(stat) +/- 0.3 (syst)) 10^{-4} B(B0->D-/+ K*+/-)=(4.6 +/- 0.6(stat) +/- 0.5 (syst)) 10^{-4} B(B0->D*-/+ K*+/-)=(3.2 +/- 0.6(stat) +/- 0.3 (syst)) 10^{-4} From these measurements we determine the fractions of resonant events to be : f(B0-> D-/+ K*+/-) = 0.63 +/- 0.08(stat) +/- 0.04(syst) f(B0-> D*-/+ K*+/-) = 0.72 +/- 0.14(stat) +/- 0.05(syst)Comment: 7 pages, 3 figures submitted to Phys. Rev. Let