Adaptive finite element methods for computing band gaps in photonic crystals

In this paper we propose and analyse adaptive finite element methods for computing the band structure of 2D periodic photonic crystals. The problem can be reduced to the computation of the discrete spectra of each member of a family of periodic Hermitian eigenvalue problems on a unit cell, parametrised by a two-dimensional parameter - the quasimomentum. These eigenvalue problems involve non-coercive elliptic operators with generally discontinuous coefficients and are solved by adaptive finite elements. We propose an error estimator of residual type and show it is reliable and efficient for each eigenvalue problem in the family. In particular we prove that if the error estimator converges to zero then the distance of the computed eigenfunction from the true eigenspace also converges to zero and the computed eigenvalue converges to a true eigenvalue with double the rate. We also prove that if the distance of a computed sequence of approximate eigenfunctions from the true eigenspace approaches zero, then so must the error estimator. The results hold for eigenvalues of any multiplicity. We illustrate the benefits of the resulting adaptive method in practice, both for fully periodic structures and also for the computation of eigenvalues in the band gap of structures with defect, using the supercell method

Density fluctuations from warm inflation

Thermal fluctuations provide the main source of large scale density perturbations in warm inflationary models of the early universe. For the first time, general results are obtained for the power spectrum in the case when the friction coefficient in the inflaton equation of motion depends on temperature. A large increase in the amplitude of perturbations occurs when the friction coefficient increases with temperature. This has to be taken into account when constructing models of warm inflation. New results are also given for the thermal fluctuations in the weak regime of warm inflation when the friction coefficient is relatively small.Comment: 14 pages, 4 figures, ReVTe

Experimental Searches for the Axion and Axion-Like Particles

Four decades after its prediction, the axion remains the most compelling solution to the strong-CP problem and a well-motivated dark matter candidate, inspiring a host of elegant and ultrasensitive experiments based on axion-photon mixing. This article reviews the experimental situation on several fronts. The microwave cavity experiment is making excellent progress in the search for dark matter axions in the µeV range and may plausibly be extended up to 100 µeV. Within the past several years, however, researchers have realized that axions are pervasive throughout string theories, but with masses that fall naturally in the neV range, for which an NMR-based search is under development. Both searches for axions emitted from the Sun's burning core and purely laboratory experiments based on photon regeneration have recently made great progress, with ambitious projects proposed for the coming decade. Each of these campaigns has pushed the state of the art in technology, enabling large gains in sensitivity and mass reach. Furthermore, each modality has been exploited in order to search for more generalized axion-like particles, which we also discuss in this review. We are hopeful, even optimistic, that the next review of the subject will concern the discovery of the axion, its properties, and its exploitation as a probe of early universe cosmology and structure formation

Non-gaussianity in the strong regime of warm inflation

The bispectrum of scalar mode density perturbations is analysed for the strong regime of warm inflationary models. This analysis generalises previous results by allowing damping terms in the inflaton equation of motion that are dependent on temperature. A significant amount of non-gaussianity emerges with constant (or local) non-linearity parameter $f_{NL}\sim 20$, in addition to the terms with non-constant $f_{NL}$ which are characteristic of warm inflation.Comment: 15 pages, 3 figures. New plots in v

Constraints on Jupiters from Observations of Galactic bulge microlensing events during 2000

Peer reviewe

Warming up for Planck

The recent Planck results and future releases on the horizon present a key opportunity to address a fundamental question in inflationary cosmology of whether primordial density perturbations have a quantum or thermal origin, i.e. whether particle production may have significant effects during inflation. Warm inflation provides a natural arena to address this issue, with interactions between the scalar inflaton and other degrees of freedom leading to dissipative entropy production and associated thermal fluctuations. In this context, we present relations between CMB observables that can be directly tested against observational data. In particular, we show that the presence of a thermal bath warmer than the Hubble scale during inflation decreases the tensor-to-scalar ratio with respect to the conventional prediction in supercooled inflation, yielding $r< 8|n_t|$, where $n_t$ is the tensor spectral index. Focusing on supersymmetric models at low temperatures, we determine consistency relations between the observables characterizing the spectrum of adiabatic scalar and tensor modes, both for generic potentials and particular canonical examples, and which we compare with the WMAP and Planck results. Finally, we include the possibility of producing the observed baryon asymmetry during inflation through dissipative effects, thereby generating baryon isocurvature modes that can be easily accommodated by the Planck data.Comment: 14 pages, 10 figures. Published in JCA

Compactness properties of operator multipliers

We continue the study of multidimensional operator multipliers initiated in [arXiv:math/0701645]. We introduce the notion of the symbol of an operator multiplier. We characterise completely compact operator multipliers in terms of their symbol as well as in terms of approximation by finite rank multipliers. We give sufficient conditions for the sets of compact and completely compact multipliers to coincide and characterise the cases where an operator multiplier in the minimal tensor product of two C*-algebras is automatically compact. We give a description of multilinear modular completely compact completely bounded maps defined on the direct product of finitely many copies of the C*-algebra of compact operators in terms of tensor products, generalising results of Saar

A multidisciplinary scientific investigation of the 1916 Hawthorn Mine Crater, Beaumont Hamel, Somme, Northern France

Hawthorn Crater is a prominent feature of the former Somme battlefield near Beaumont Hamel, Northern France. It resulted from the detonation of arguably the most famous of nine mines that the British had prepared below German lines on 1 July 1916, as part of the opening day of the Battle of the Somme. However, the crater has not been studied scientifically, as was in private land until recently taken over by the Hawthorn Crater Association. This paper documents three field seasons of multi-disciplinary site investigations. Methods included: remote sensing, drones, ground-based-LiDAR and surface surveys, geophysics and archaeological investigations. Magnetic anomalies were identified as: still-intact German fire pits, barbed wire and equipment, as the crater became the frontline after formation, and Allied shell craters. This study provided a rare opportunity to study a First World War mine crater, and highlighting modern science can assist detection and characterisation of significant archaeological sites

Shear viscous effects on the primordial power spectrum from warm inflation

We compute the primordial curvature spectrum generated during warm inflation, including shear viscous effects. The primordial spectrum is dominated by the thermal fluctuations of the radiation bath, sourced by the dissipative term of the inflaton field. The dissipative coefficient \Upsilon, computed from first principles in the close-to-equilibrium approximation, depends in general on the temperature T, and this dependence renders the system of the linear fluctuations coupled. Whenever the dissipative coefficient is larger than the Hubble expansion rate H, there is a growing mode in the fluctuations before horizon crossing. However, dissipation intrinsically means departures from equilibrium, and therefore the presence of a shear viscous pressure in the radiation fluid. This in turn acts as an extra friction term for the radiation fluctuations that tends to damp the growth of the perturbations. Independently of the T functional dependence of the dissipation and the shear viscosity, we find that when the shear viscous coefficient \zeta_s is larger than 3 \rho_r/H at horizon crossing, \rho_r being the radiation energy density, the shear damping effect wins and there is no growing mode in the spectrum.Comment: 18 pages, 6 figure

Extreme events and predictability of catastrophic failure in composite materials and in the Earth

Despite all attempts to isolate and predict extreme earthquakes, these nearly always occur without obvious warning in real time: fully deterministic earthquake prediction is very much a ‘black swan’. On the other hand engineering-scale samples of rocks and other composite materials often show clear precursors to dynamic failure under controlled conditions in the laboratory, and successful evacuations have occurred before several volcanic eruptions. This may be because extreme earthquakes are not statistically special, being an emergent property of the process of dynamic rupture. Nevertheless, probabilistic forecasting of event rate above a given size, based on the tendency of earthquakes to cluster in space and time, can have significant skill compared to say random failure, even in real-time mode. We address several questions in this debate, using examples from the Earth (earthquakes, volcanoes) and the laboratory, including the following. How can we identify ‘characteristic’ events, i.e. beyond the power law, in model selection (do dragon-kings exist)? How do we discriminate quantitatively between stationary and non-stationary hazard models (is a dragon likely to come soon)? Does the system size (the size of the dragon’s domain) matter? Are there localising signals of imminent catastrophic failure we may not be able to access (is the dragon effectively invisible on approach)? We focus on the effect of sampling effects and statistical uncertainty in the identification of extreme events and their predictability, and highlight the strong influence of scaling in space and time as an outstanding issue to be addressed by quantitative studies, experimentation and models