Gravitational quantum states of neutrons in a rough waveguide

A theory of gravitational quantum states of ultracold neutrons in waveguides with absorbing/scattering walls is presented. The theory covers recent experiments in which the ultracold neutrons were beamed between a mirror and a rough scatterer/absorber. The analysis is based on a recently developed theory of quantum transport along random rough walls which is modified in order to include leaky (absorbing) interfaces and, more importantly, the low-amplitude high-aperture roughness. The calculations are focused on a regime when the direct transitions into the continuous spectrum above the absorption threshold dominate the depletion of neutrons from the gravitational states and are more efficient than the processes involving the intermediate states. The theoretical results for the neutron count are sensitive to the correlation radius (lateral size) of surface inhomogeneities and to the ratio of the particle energy to the absorption threshold in a weak roughness limit. The main impediment for observation of the higher gravitational states is the "overhang" of the particle wave functions which can be overcome only by use scatterers with strong roughness. In general, the strong roughness with high amplitude is preferable if one wants just to detect the individual gravitational states, while the strong roughness experiments with small amplitude and high aperture are preferable for the quantitative analysis of the data. We also discuss the ways to further improve the accuracy of calculations and to optimize the experimental regime.Comment: 48 pages, 14 figure

Characterising sand and gravel deposits using electrical resistivity tomography (ERT) : case histories from England and Wales

Electrical Resistivity Tomography (ERT) is a rapidly developing geophysical imaging technique that is now widely used to visualise subsurface geological structure, groundwater and lithological variations. It is being increasingly used in environmental and engineering site investigations, but despite its suitability and potential benefits, ERT has yet to be routinely applied by the minerals industry to sand and gravel deposit assessment and quarry planning. The principal advantages of ERT for this application are that it is a cost-effective non-invasive method, which can provide 2D or 3D spatial models of the subsurface throughout the full region of interest. This complements intrusive sampling methods, which typically provide information only at discrete locations. Provided that suitable resistivity contrasts are present, ERT has the potential to reveal mineral and overburden thickness and quality variations within the body of the deposit. Here we present a number of case studies from the UK illustrating the use of 2D and 3D ERT for sand and gravel deposit investigation in a variety of geological settings. We use these case studies to evaluate the performance of ERT, and to illustrate good practice in the application of ERT to deposit investigation. We propose an integrated approach to site investigation and quarry planning incorporating both conventional intrusive methods and ERT

Curves with rational chord-length parametrization

It has been recently proved that rational quadratic circles in standard Bezier form are parameterized by chord-length. If we consider that standard circles coincide with the isoparametric curves in a system of bipolar coordinates, this property comes as a straightforward consequence. General curves with chord-length parametrization are simply the analogue in bipolar coordinates of nonparametric curves. This interpretation furnishes a compact explicit expression for all planar curves with rational chord-length parametrization. In addition to straight lines and circles in standard form, they include remarkable curves, such as the equilateral hyperbola, Lemniscate of Bernoulli and Limacon of Pascal. The extension to 3D rational curves is also tackled

Seismic topographic scattering in the context of GW detector site selection

In this paper, we present a calculation of seismic scattering from irregular surface topography in the Born approximation. Based on US-wide topographic data, we investigate topographic scattering at specific sites to demonstrate its impact on Newtonian-noise estimation and subtraction for future gravitational-wave detectors. We find that topographic scattering at a comparatively flat site in Oregon would not pose any problems, whereas scattering at a second site in Montana leads to significant broadening of wave amplitudes in wavenumber space that would make Newtonian-noise subtraction very challenging. Therefore, it is shown that topographic scattering should be included as criterion in the site-selection process of future low-frequency gravitational-wave detectors.Comment: 16 pages, 7 figure

An Unruptured Anterior Communicating Artery Aneurysm with Bilateral Infraoptic Anterior Cerebral Arteries. Case Report and Review of the Literature

Variations of the anterior cerebral artery-anterior communicating artery complex are commonly identified in aneurysm surgery. An infraoptic course of the anterior cerebral artery is exceedingly rare. Robison first described this anomaly from an anatomic dissection in 1959. A unilateral anomalous infraoptic anterior cerebral artery is more common than anomalies of bilateral infraoptic anterior cerebral arteries. We present the case of an unruptured aneurysm at the anterior communicating artery in a patient with bilateral infraoptic anterior cerebral arteries, identified by computed tomography angiography and verified during surgery. Implications for aneurysm formation and surgical treatment are discussed

The Effect of Random Surface Inhomogeneities on Microresonator Spectral Properties: Theory and Modeling at Millimeter Wave Range

The influence of random surface inhomogeneities on spectral properties of open microresonators is studied both theoretically and experimentally. To solve the equations governing the dynamics of electromagnetic fields the method of eigen-mode separation is applied previously developed with reference to inhomogeneous systems subject to arbitrary external static potential. We prove theoretically that it is the gradient mechanism of wave-surface scattering which is the highly responsible for non-dissipative loss in the resonator. The influence of side-boundary inhomogeneities on the resonator spectrum is shown to be described in terms of effective renormalization of mode wave numbers jointly with azimuth indices in the characteristic equation. To study experimentally the effect of inhomogeneities on the resonator spectrum, the method of modeling in the millimeter wave range is applied. As a model object we use dielectric disc resonator (DDR) fitted with external inhomogeneities randomly arranged at its side boundary. Experimental results show good agreement with theoretical predictions as regards the predominance of the gradient scattering mechanism. It is shown theoretically and confirmed in the experiment that TM oscillations in the DDR are less affected by surface inhomogeneities than TE oscillations with the same azimuth indices. The DDR model chosen for our study as well as characteristic equations obtained thereupon enable one to calculate both the eigen-frequencies and the Q-factors of resonance spectral lines to fairly good accuracy. The results of calculations agree well with obtained experimental data.Comment: 17+ pages, 5 figure

Mode Coupling in Quantized High Quality Films

The effect of coupling of quantized modes on transport and localization in ultrathin films with quantum size effect (QSE) is discussed. The emphasis is on comparison of films with Gaussian, exponential, and power-law long-range behavior of the correlation function of surface, thickness, or bulk fluctuations. For small-size inhomogeneities, the mode coupling is the same for inhomogeneities of all types and the transport coefficients behave in the same way. The mode coupling becomes extremely sensitive to the correlators for large-size inhomogeneities leading to the drastically distinct behavior of the transport coefficients. In high-quality films there is a noticeable difference between the QSE patterns for films with bulk and surface inhomogeneities which explains why the recently predicted new type of QSE with large oscillations of the transport coefficients can be observed mostly in films with surface-driven relaxation. In such films with surface-dominated scattering the higher modes contribute to the transport only as a result of opening of the corresponding mode coupling channels and appear one by one. Mode coupling also explains a much higher transport contribution from the higher modes than it is commonly believed. Possible correlations between the inhomogeneities from the opposite walls provide, because of their oscillating response to the mode quantum numbers, a unique insight into the mode coupling. The presence of inhomogeneities of several sizes leads not to a mechanical mixture of QSE patterns, but to the overall shifting and smoothing of the oscillations. The results can lead to new, non-destructive ways of analysis of the buried interfaces and to study of inhomogeneities on the scales which are inaccessible for scanning techniques

Fourier, Gauss, Fraunhofer, Porod and the Shape from Moments Problem

We show how the Fourier transform of a shape in any number of dimensions can be simplified using Gauss's law and evaluated explicitly for polygons in two dimensions, polyhedra three dimensions, etc. We also show how this combination of Fourier and Gauss can be related to numerous classical problems in physics and mathematics. Examples include Fraunhofer diffraction patterns, Porods law, Hopfs Umlaufsatz, the isoperimetric inequality and Didos problem. We also use this approach to provide an alternative derivation of Davis's extension of the Motzkin-Schoenberg formula to polygons in the complex plane.Comment: 21 pages, no figure

A model of the reflection distribution in the vacuum ultra violet region

A reflection model with three components, a specular spike, a specular lobe and a diffuse lobe is discussed. This model was successfully applied to describe reflection of xenon scintillation light (175 nm) by PTFE and other fluoropolymers and can be used for Monte Carlo simulation and analysis of scintillation detectors. The measured data favors a Trowbridge-Reitz distribution function of ellipsoidal micro-surfaces. The intensity of the coherent reflection increases with increasing angle of incidence, as expected, since the surface appears smoother at grazing angles. The total reflectance obtained for PTFE is about 70% for VUV light at normal incidence in vacuum and estimated to be up to 100% in contact with liquid xenon

Intra-arterial Onyx Embolization of Vertebral Body Lesions

While Onyx embolization of cerebrospinal arteriovenous shunts is well-established, clinical researchers continue to broaden applications to other vascular lesions of the neuraxis. This report illustrates the application of Onyx (eV3, Plymouth, MN) embolization to vertebral body lesions, specifically, a vertebral hemangioma and renal cell carcinoma vertebral body metastatic lesion