Small Disks and Semiclassical Resonances

We study the effect on quantum spectra of the existence of small circular disks in a billiard system. In the limit where the disk radii vanish there is no effect, however this limit is approached very slowly so that even very small radii have comparatively large effects. We include diffractive orbits which scatter off the small disks in the periodic orbit expansion. This situation is formally similar to edge diffraction except that the disk radii introduce a length scale in the problem such that for wave lengths smaller than the order of the disk radius we recover the usual semi-classical approximation; however, for wave lengths larger than the order of the disk radius there is a qualitatively different behaviour. We test the theory by successfully estimating the positions of scattering resonances in geometries consisting of three and four small disks.Comment: Final published version - some changes in the discussion and the labels on one figure are correcte

Wave Chaos in Elastodynamic Cavity Scattering

The exact elastodynamic scattering theory is constructed to describe the spectral properties of two- and more-cylindrical cavity systems, and compared to an elastodynamic generalization of the semi-classical Gutzwiller unstable periodic orbits formulas. In contrast to quantum mechanics, complex periodic orbits associated with the surface Rayleigh waves dominate the low-frequency spectrum, and already the two-cavity system displays chaotic features.Comment: 7 pages, 5 eps figures, latex (with epl.cls

Global Mangrove Watch:Updated 2010 Mangrove Forest Extent (v2.5)

This study presents an updated global mangrove forest baseline for 2010: Global Mangrove Watch (GMW) v2.5. The previous GMW maps (v2.0) of the mangrove extent are currently considered the most comprehensive available global products, however areas were identified as missing or poorly mapped. Therefore, this study has updated the 2010 baseline map to increase the mapping quality and completeness of the mangrove extent. This revision resulted in an additional 2660 km2 of mangroves being mapped yielding a revised global mangrove extent for 2010 of some 140,260 km2. The overall map accuracy was estimated to be 95.1% with a 95th confidence interval of 93.8–96.5%, as assessed using 50,750 reference points located across 60 globally distributed sites. Of these 60 validation sites, 26 were located in areas that were remapped to produce the v2.5 map and the overall accuracy for these was found to have increased from 82.6% (95th confidence interval: 80.1–84.9) for the v2.0 map to 95.0% (95th confidence interval: 93.7–96.4) for the v2.5 map. Overall, the improved GMW v2.5 map provides a more robust product to support the conservation and sustainable use of mangroves globall

Periodic orbit quantization of the Sinai billiard in the small scatterer limit

We consider the semiclassical quantization of the Sinai billiard for disk radii R small compared to the wave length 2 pi/k. Via the application of the periodic orbit theory of diffraction we derive the semiclassical spectral determinant. The limitations of the derived determinant are studied by comparing it to the exact KKR determinant, which we generalize here for the A_1 subspace. With the help of the Ewald resummation method developed for the full KKR determinant we transfer the complex diffractive determinant to a real form. The real zeros of the determinant are the quantum eigenvalues in semiclassical approximation. The essential parameter is the strength of the scatterer c=J_0(kR)/Y_0(kR). Surprisingly, this can take any value between plus and minus infinity within the range of validity of the diffractive approximation kR <<4. We study the statistics exhibited by spectra for fixed values of c. It is Poissonian for |c|=infinity, provided the disk is placed inside a rectangle whose sides obeys some constraints. For c=0 we find a good agreement of the level spacing distribution with GOE, whereas the form factor and two-point correlation function are similar but exhibit larger deviations. By varying the parameter c from 0 to infinity the level statistics interpolates smoothly between these limiting cases.Comment: 17 pages LaTeX, 5 postscript figures, submitted to J. Phys. A: Math. Ge

Geometrical theory of diffraction and spectral statistics

We investigate the influence of diffraction on the statistics of energy levels in quantum systems with a chaotic classical limit. By applying the geometrical theory of diffraction we show that diffraction on singularities of the potential can lead to modifications in semiclassical approximations for spectral statistics that persist in the semiclassical limit $\hbar \to 0$. This result is obtained by deriving a classical sum rule for trajectories that connect two points in coordinate space.Comment: 14 pages, no figure, to appear in J. Phys.

Spectral statistics in chaotic systems with a point interaction

We consider quantum systems with a chaotic classical limit that are perturbed by a point-like scatterer. The spectral form factor K(tau) for these systems is evaluated semiclassically in terms of periodic and diffractive orbits. It is shown for order tau^2 and tau^3 that off-diagonal contributions to the form factor which involve diffractive orbits cancel exactly the diagonal contributions from diffractive orbits, implying that the perturbation by the scatterer does not change the spectral statistic. We further show that parametric spectral statistics for these systems are universal for small changes of the strength of the scatterer.Comment: LaTeX, 21 pages, 7 figures, small corrections, new references adde

Classical, semiclassical, and quantum investigations of the 4-sphere scattering system

A genuinely three-dimensional system, viz. the hyperbolic 4-sphere scattering system, is investigated with classical, semiclassical, and quantum mechanical methods at various center-to-center separations of the spheres. The efficiency and scaling properties of the computations are discussed by comparisons to the two-dimensional 3-disk system. While in systems with few degrees of freedom modern quantum calculations are, in general, numerically more efficient than semiclassical methods, this situation can be reversed with increasing dimension of the problem. For the 4-sphere system with large separations between the spheres, we demonstrate the superiority of semiclassical versus quantum calculations, i.e., semiclassical resonances can easily be obtained even in energy regions which are unattainable with the currently available quantum techniques. The 4-sphere system with touching spheres is a challenging problem for both quantum and semiclassical techniques. Here, semiclassical resonances are obtained via harmonic inversion of a cross-correlated periodic orbit signal.Comment: 12 pages, 5 figures, submitted to Phys. Rev.

Periodic Orbit Quantization beyond Semiclassics

A quantum generalization of the semiclassical theory of Gutzwiller is given. The new formulation leads to systematic orbit-by-orbit inclusion of higher $\hbar$ contributions to the spectral determinant. We apply the theory to billiard systems, and compare the periodic orbit quantization including the first $\hbar$ contribution to the exact quantum mechanical results.Comment: revte

Reservoir properties and reactivity of the Faroe Islands Basalt Group : Investigating the potential for CO2 storage in the North Atlantic Igneous Province

Funding Information: We acknowledge funding from the University of Oslo through the Department of Geosciences, the European Research Council (ERC) through the ERC Advanced Grant Disequilibrium metamorphism of stressed lithosphere (DIME) (ERC-2015-AdG_669972), the Cambridge Arctic Shelf Program (CASP) through the Andrew Whitham CASP Fieldwork Awards 2020, and the Faculty of Mathematics and Natural Sciences at the University of Oslo through the project CO2Basalt. S. Planke acknowledges support from the Norwegian Research Council through center of Excellence funding to CEED (project no. 223272). H. J. Kjøll acknowledges AkerBP for funding through the project 8040 Paleocene. In addition, we thank the University of Iceland for covering the costs of the kinetic experiments. We would like to thank the Faroese Geological Survey (Jarðfeingi), Øyvind Hammer at the Museum of Natural History (Norway), Benjamin Bellwald at Volcanic Basin Energy Research (VBER), John Aiken from the Njord center, and Benoit Cordonnier from the European Synchrotron Radiation Facility (ESRF) in Grenoble, France, for their contributions to the project. Finally, we thank Sigurður Gíslason and the Carbfix team for providing laboratory facilities and assistance during part of this research. Funding Information: We acknowledge funding from the University of Oslo through the Department of Geosciences, the European Research Council (ERC) through the ERC Advanced Grant Disequilibrium metamorphism of stressed lithosphere (DIME) ( ERC-2015-AdG_669972 ), the Cambridge Arctic Shelf Program (CASP) through the Andrew Whitham CASP Fieldwork Awards 2020, and the Faculty of Mathematics and Natural Sciences at the University of Oslo through the project CO2Basalt. S. Planke acknowledges support from the Norwegian Research Council through center of Excellence funding to CEED (project no. 223272 ). H. J. Kjøll acknowledges AkerBP for funding through the project 8040 Paleocene. In addition, we thank the University of Iceland for covering the costs of the kinetic experiments. We would like to thank the Faroese Geological Survey (Jarðfeingi), Øyvind Hammer at the Museum of Natural History (Norway), Benjamin Bellwald at Volcanic Basin Energy Research (VBER), John Aiken from the Njord center, and Benoit Cordonnier from the European Synchrotron Radiation Facility (ESRF) in Grenoble, France, for their contributions to the project. Finally, we thank Sigurður Gíslason and the Carbfix team for providing laboratory facilities and assistance during part of this research.Peer reviewedPublisher PD

A Pilot Study - Comparison between a Novel Combination of Bioactive Glass with Clodronate and Bioactive Glass Alone as a Treatment for Chronic Periodontitis

Bioactive glass (BAG) and clodronate are both used for bone regeneration. In this pilot clinical study, we compared the effect of BAG and a novel BAG+clodronate combination as a topical maintenance phase treatment for chronic periodontitis. Two dental residual pockets were treated in each subject (n=10): one with BAG alone and the other with combination product, by applying the products subgingivally for 10 min once a week for four weeks. We describe the effects of these investigational products to the clinical parameters of periodontitis and two bone metabolism markers (osteoprotegerin and osteocalcin). Additionally, subjective satisfaction for the treatment was evaluated. The results must be considered as directional, understanding that further investigation is needed to confirm the findings. Based on clinical parameters measured both treatments could benefit as maintenance therapy for chronic periodontitis. The positive effect of the combination product on tooth sensitivity may bring additional benefits in comparison to the use of BAG alone. Both treatments were well tolerated and safe.  </p