Single exposure wavefront curvature estimation of high harmonic radiation by diffraction from a regular array

We present a novel technique for estimating the radius of curvature from a single exposure of EUV light from a high harmonic source diffracted by a grating of square apertures

Superficial geology and hydrogeological domains between Durham and Darlington. Phase 2, (Durham North)

The North East Region’s Groundwater Modelling Strategy has identified the need for the development of a conceptual model for the Magnesian Limestone aquifer. In line with the Environment Agency R&D Technical Report W214 (Environment Agency Framework for Groundwater Resources Conceptual and Numerical Modelling), a scoping study was produced, that identified areas of uncertainty and work required for the development of the conceptual model. The purpose of this project is to give the Environment Agency (EA) a regional understanding of the geology and hydrogeology of the Magnesian Limestone and overlying superficial deposits in the North East Region, using information held by the British Geological Survey (BGS). This report contributes to the conceptual model and understanding of the Magnesian Limestone aquifer. There is uncertainty in the amount of recharge that the Magnesian Limestone receives from rainfall. The project is designed to gain a greater understanding of the geology of the superficial deposits and their hydrogeological properties. These are the key factors for the calculation of recharge to the Magnesian Limestone aquifer from rainfall. This element of the conceptual model is essential in understanding the potential water resource available within this aquifer

Fluctuation Theorems for Entropy Production and Heat Dissipation in Periodically Driven Markov Chains

Asymptotic fluctuation theorems are statements of a Gallavotti-Cohen symmetry in the rate function of either the time-averaged entropy production or heat dissipation of a process. Such theorems have been proved for various general classes of continuous-time deterministic and stochastic processes, but always under the assumption that the forces driving the system are time independent, and often relying on the existence of a limiting ergodic distribution. In this paper we extend the asymptotic fluctuation theorem for the first time to inhomogeneous continuous-time processes without a stationary distribution, considering specifically a finite state Markov chain driven by periodic transition rates. We find that for both entropy production and heat dissipation, the usual Gallavotti-Cohen symmetry of the rate function is generalized to an analogous relation between the rate functions of the original process and its corresponding backward process, in which the trajectory and the driving protocol have been time-reversed. The effect is that spontaneous positive fluctuations in the long time average of each quantity in the forward process are exponentially more likely than spontaneous negative fluctuations in the backward process, and vice-versa, revealing that the distributions of fluctuations in universes in which time moves forward and backward are related. As an additional result, the asymptotic time-averaged entropy production is obtained as the integral of a periodic entropy production rate that generalizes the constant rate pertaining to homogeneous dynamics

Vale of York 3-D borehole interpretation and cross-sections study

The Vale of York between Doncaster and Scunthorpe in the south and York and Bugthorpe in the north is largely underlain by bedrock of the Sherwood Sandstone Group – one of the regions principal aquifers. Significant superficial deposits of Quaternary age overlie the Sherwood Sandstone. This study aims to investigate the nature of these superficial deposits with respect to their relationship with the underlying aquifer. The Vale of York project area represents a varied glaciated terrain, consisting of pro-glacial finegrained sediments, coarser glaciofluvilal sediments and extensive glacial tills. These diverse superficial units vary in thickness throughout the project area. The hydrogeological nature of the natural superficial sequence is consequently highly variable. Units may be considered as aquitards, while others may act as aquifers, providing a potential pathway to the underlying sandstone. The classification of lithologies as aquifer or aquitard is described in detail in this report. To investigate the hydrogeological nature of the superficial sequence, six east-west and three north-south lithostratigraphical cross-sections were constructed. A range of geoscientific information was considered, including existing geological mapping and over 3000 fully attributed and coded boreholes. The cross-sections show a subdivision of the superficial sequence into lithostratigraphical units. Each unit is described in detail in this report. In addition, a series of thematic maps were generated from the lithological component of the digital borehole data. Total superficial aquifer and superficial aquitard maps show how the lithological nature of the superficial sequence varies across the area. Rockhead elevation and superficial thickness maps indicate where the sandstone aquifer outcrops at the ground surface. In summary, four main lithostratigraphical units overlie the Sherwood Sandstone Group aquifer in the project area: a basal sequence of glaciofluvial sand and gravel (interpreted as a superficial aquifer), glaciolacustrine laminated silt & clay (aquitard), glacial till comprising sandy gravelly clay (aquitard), and a cover sequence of fluvial and aeolian sand, clay and peat (aquifer / aquitard). The correlations illustrate that in certain areas, superficial deposits are thin or absent and that in these areas the Sherwood Sandstone aquifer comes directly to ground surface

Simulating Turbulence Using the Astrophysical Discontinuous Galerkin Code TENET

In astrophysics, the two main methods traditionally in use for solving the Euler equations of ideal fluid dynamics are smoothed particle hydrodynamics and finite volume discretization on a stationary mesh. However, the goal to efficiently make use of future exascale machines with their ever higher degree of parallel concurrency motivates the search for more efficient and more accurate techniques for computing hydrodynamics. Discontinuous Galerkin (DG) methods represent a promising class of methods in this regard, as they can be straightforwardly extended to arbitrarily high order while requiring only small stencils. Especially for applications involving comparatively smooth problems, higher-order approaches promise significant gains in computational speed for reaching a desired target accuracy. Here, we introduce our new astrophysical DG code TENET designed for applications in cosmology, and discuss our first results for 3D simulations of subsonic turbulence. We show that our new DG implementation provides accurate results for subsonic turbulence, at considerably reduced computational cost compared with traditional finite volume methods. In particular, we find that DG needs about 1.8 times fewer degrees of freedom to achieve the same accuracy and at the same time is more than 1.5 times faster, confirming its substantial promise for astrophysical applications.Comment: 21 pages, 7 figures, to appear in Proceedings of the SPPEXA symposium, Lecture Notes in Computational Science and Engineering (LNCSE), Springe

Strichartz estimates on Schwarzschild black hole backgrounds

We study dispersive properties for the wave equation in the Schwarzschild space-time. The first result we obtain is a local energy estimate. This is then used, following the spirit of earlier work of Metcalfe-Tataru, in order to establish global-in-time Strichartz estimates. A considerable part of the paper is devoted to a precise analysis of solutions near the trapping region, namely the photon sphere.Comment: 44 pages; typos fixed, minor modifications in several place

Cold Plasma Wave Analysis in Magneto-Rotational Fluids

This paper is devoted to investigate the cold plasma wave properties. The analysis has been restricted to the neighborhood of the pair production region of the Kerr magnetosphere. The Fourier analyzed general relativistic magnetohydrodynamical equations are dealt under special circumstances and dispersion relations are obtained. We find the $x$-component of the complex wave vector numerically. The corresponding components of the propagation vector, attenuation vector, phase and group velocities are shown in graphs. The direction and dispersion of waves are investigated.Comment: 22 pages, 18 figures, accepted for publication in Astrophys. Space Sc

Optimal low-thrust trajectories to asteroids through an algorithm based on differential dynamic programming

In this paper an optimisation algorithm based on Differential Dynamic Programming is applied to the design of rendezvous and fly-by trajectories to near Earth objects. Differential dynamic programming is a successive approximation technique that computes a feedback control law in correspondence of a fixed number of decision times. In this way the high dimensional problem characteristic of low-thrust optimisation is reduced into a series of small dimensional problems. The proposed method exploits the stage-wise approach to incorporate an adaptive refinement of the discretisation mesh within the optimisation process. A particular interpolation technique was used to preserve the feedback nature of the control law, thus improving robustness against some approximation errors introduced during the adaptation process. The algorithm implements global variations of the control law, which ensure a further increase in robustness. The results presented show how the proposed approach is capable of fully exploiting the multi-body dynamics of the problem; in fact, in one of the study cases, a fly-by of the Earth is scheduled, which was not included in the first guess solution

Testing the disturbed zone around a rigid inclusion in salt

Deformational processes within a zone of rock surrounding excavations in salt result in alteration of the geophysical and hydrologic properties as compared to the undisturbed condition. The disturbed rock zone offers little resistance to fluid flow. It is hypothesized that rigid inclusions such as concrete seals will arrest and subsequently reverse the disturbance process and induce healing in the disturbed This experiment gathered in situ data that substantiates this hypothesis. A series of tests was conducted in a volume of rock surrounding concrete seals that were placed in a 1-m borehole approximately eight years ago. Fluid flow measurements, measurements of geophysical parameters of the surrounding rock and petrographic analyses on core samples were performed to characterize the rock. This paper presents the testing methodology and summarizes the data gathered from the field test program