Model-Independent Sum Rule Analysis Based on Limited-Range Spectral Data

Partial sum rules are widely used in physics to separate low- and high-energy degrees of freedom of complex dynamical systems. Their application, though, is challenged in practice by the always finite spectrometer bandwidth and is often performed using risky model-dependent extrapolations. We show that, given spectra of the real and imaginary parts of any causal frequency-dependent response function (for example, optical conductivity, magnetic susceptibility, acoustical impedance etc.) in a limited range, the sum-rule integral from zero to a certain cutoff frequency inside this range can be safely derived using only the Kramers-Kronig dispersion relations without any extra model assumptions. This implies that experimental techniques providing both active and reactive response components independently, such as spectroscopic ellipsometry in optics, allow an extrapolation-independent determination of spectral weight 'hidden' below the lowest accessible frequency.Comment: 5 pages, 3 figure

Renormalized Vacuum Polarization and Stress Tensor on the Horizon of a Schwarzschild Black Hole Threaded by a Cosmic String

We calculate the renormalized vacuum polarization and stress tensor for a massless, arbitrarily coupled scalar field in the Hartle-Hawking vacuum state on the horizon of a Schwarzschild black hole threaded by an infinte straight cosmic string. This calculation relies on a generalized Heine identity for non-integer Legendre functions which we derive without using specific properties of the Legendre functions themselves.Comment: This is an expanded version of a previous submission, we have added the calculation of the stress tensor. 28 pages, 7 figure

The self-force on a static scalar test-charge outside a Schwarzschild black hole

The finite part of the self-force on a static scalar test-charge outside a Schwarzschild black hole is zero. By direct construction of Hadamard's elementary solution, we obtain a closed-form expression for the minimally coupled scalar field produced by a test-charge held fixed in Schwarzschild spacetime. Using the closed-form expression, we compute the necessary external force required to hold the charge stationary. Although the energy associated with the scalar field contributes to the renormalized mass of the particle (and thereby its weight), we find there is no additional self-force acting on the charge. This result is unlike the analogous electrostatic result, where, after a similar mass renormalization, there remains a finite repulsive self-force acting on a static electric test-charge outside a Schwarzschild black hole. We confirm our force calculation using Carter's mass-variation theorem for black holes. The primary motivation for this calculation is to develop techniques and formalism for computing all forces - dissipative and non-dissipative - acting on charges and masses moving in a black-hole spacetime. In the Appendix we recap the derivation of the closed-form electrostatic potential. We also show how the closed-form expressions for the fields are related to the infinite series solutions.Comment: RevTeX, To Appear in Phys. Rev.

The hybrid spectral problem and Robin boundary conditions

The hybrid spectral problem where the field satisfies Dirichlet conditions (D) on part of the boundary of the relevant domain and Neumann (N) on the remainder is discussed in simple terms. A conjecture for the C_1 coefficient is presented and the conformal determinant on a 2-disc, where the D and N regions are semi-circles, is derived. Comments on higher coefficients are made. A hemisphere hybrid problem is introduced that involves Robin boundary conditions and leads to logarithmic terms in the heat--kernel expansion which are evaluated explicitly.Comment: 24 pages. Typos and a few factors corrected. Minor comments added. Substantial Robin additions. Substantial revisio

Photodynamic therapy on the normal rabbit larynx with phthalocyanine and 5-aminolaevulinic acid induced protoporphyrin IX photosensitisation.

Photodynamic therapy (PDT) is a promising technique for the treatment of small tumours in organs where it is essential to minimise damage to immediately adjacent normal tissue as PDT damage to many tissues heals by regeneration rather than scarring. As preservation of function is one of the main aims of treating laryngeal tumours, this project studied the effects of PDT on the normal rabbit larynx with two photosensitisers, endogenous protoporphyrin IX (PPIX) induced by the administration of 5-aminolaevulinic acid (ALA) and disulphonated aluminium phthalocyanine (AIS2Pc). The main aims of the study were to examine the distribution of protoporphyrin IX and AIS2Pc by fluorescence microscopy in the different regions of the larnyx and to assess the nature and subsequent healing of PDT damage. Peak levels of PPIX were found 0.5-4 h after administration of ALA (depending on dose) with highest levels in the epithelium of the mucosa. With 100 mg kg-1, PDT necrosis was limited to the mucosa, whereas with 200 mg kg-1 necrosis extended to the muscle. With 1 mg kg-1 AIS2Pc, 1 h after administration, the drug was mainly in the submucosa and muscle, whereas after 24 h, it was predominantly in the mucosa. PDT at 1 h caused deep necrosis whereas at 24 h it was limited to the mucosa. All mucosal necrosis healed by regeneration whereas deeper effects left some fibrosis. No damage to cartilage was seen in any of the animals studied. The results of this study have shown that both photosensitisers are suitable for treating mucosal lesions of the larynx, but that for both it is important to optimise the drug dose and time interval between drug and light to avoid unacceptable changes in normal areas

Analytical solutions for two atoms in a harmonic trap: p-wave interactions

We derive analytical solutions for the system of two ultracold spin-polarized fermions interacting in p wave and confined in an axially symmetric harmonic trap. To this end we utilize p-wave pseudopotential with an energy-dependent scattering volume. This allows to describe the scattering in tight trapping potentials in the presence of scattering resonances. We verify predictions of the pseudopotential treatment for some model interaction potential, obtaining an excellent agreement with exact energy levels. Then we turn to the experimentally relevant case of neutral atom interactions in the vicinity of a p-wave Feshbach resonance. In the framework of the multichannel quantum-defect theory we derive relatively simple formula for an energy-dependent scattering volume, and later we apply it to investigate the energy spectrum of trapped atoms close to the p-wave Feshbach resonance.Comment: 13 pages, 5 figure

Current warming will reduce yields unless maize breeding and seed systems adapt immediately

The development of crop varieties that are better suited to new climatic conditions is vital for future food production1, 2. Increases in mean temperature accelerate crop development, resulting in shorter crop durations and reduced time to accumulate biomass and yield3, 4. The process of breeding, delivery and adoption (BDA) of new maize varieties can take up to 30 years. Here, we assess for the first time the implications of warming during the BDA process by using five bias-corrected global climate models and four representative concentration pathways with realistic scenarios of maize BDA times in Africa. The results show that the projected difference in temperature between the start and end of the maize BDA cycle results in shorter crop durations that are outside current variability. Both adaptation and mitigation can reduce duration loss. In particular, climate projections have the potential to provide target elevated temperatures for breeding. Whilst options for reducing BDA time are highly context dependent, common threads include improved recording and sharing of data across regions for the whole BDA cycle, streamlining of regulation, and capacity building. Finally, we show that the results have implications for maize across the tropics, where similar shortening of duration is projected

High temperature thermodynamics of strongly interacting s-wave and p-wave Fermi gases in a harmonic trap

We theoretically investigate the high-temperature thermodynamics of a strongly interacting trapped Fermi gas near either s-wave or p-wave Feshbach resonances, using a second order quantum virial expansion. The second virial coefficient is calculated based on the energy spectrum of two interacting fermions in a harmonic trap. We consider both isotropic and anisotropic harmonic potentials. For the two-fermion interaction, either s-wave or p-wave, we use a pseudopotential parametrized by a scattering length and an effective range. This turns out to be the simplest way of encoding the energy dependence of the low-energy scattering amplitude or phase shift. This treatment of the pseudopotential can be easily generalized to higher partial-wave interactions. We discuss how the second virial coefficient and thermodynamics are affected by the existence of these finite-range interaction effects. The virial expansion result for a strongly interacting s -wave Fermi gas has already been proved very useful. In the case of p-wave interactions, our results for the high-temperature equation of state are applicable to future high-precision thermodynamic measurements for a spin-polarized Fermi gas near a p-wave Feshbach resonance.Comment: 12 pages,10 figure

The future of medical diagnostics: Review paper

While histopathology of excised tissue remains the gold standard for diagnosis, several new, non-invasive diagnostic techniques are being developed. They rely on physical and biochemical changes that precede and mirror malignant change within tissue. The basic principle involves simple optical techniques of tissue interrogation. Their accuracy, expressed as sensitivity and specificity, are reported in a number of studies suggests that they have a potential for cost effective, real-time, in situ diagnosis. We review the Third Scientific Meeting of the Head and Neck Optical Diagnostics Society held in Congress Innsbruck, Innsbruck, Austria on the 11th May 2011. For the first time the HNODS Annual Scientific Meeting was held in association with the International Photodynamic Association (IPA) and the European Platform for Photodynamic Medicine (EPPM). The aim was to enhance the interdisciplinary aspects of optical diagnostics and other photodynamic applications. The meeting included 2 sections: oral communication sessions running in parallel to the IPA programme and poster presentation sessions combined with the IPA and EPPM posters sessions. © 2011 Jerjes et al; licensee BioMed Central Ltd

Monitoring collagen gelling by elastic scattering spectroscopy (ESS)

Collagen is being used extensively in tissue engineering and on a larger scale in the field of cosmetic surgery. It is either used as a gel or plastically compressed sheet. The fundamental science behind collagen gelling has been studied but little is known about the precise timing of gelling and the variables that affect gelling in the first 30 minutes. Critically, before collagen can be engineered as a predictable functional material we must be able to control fibril aggregation and gel formation. Here we report on the use of elastic scattering spectroscopy (ESS) to detect changes in scattering in rat tail and GMP bovine skin collagen during gelling. Effect of cell seeding on gelling is also reported