A shock capturing scheme for steady, supercritical, free-surface flow

Abstract A finite difference scheme is presented for the solution of the two-dimensional shallow water equations in steady, supercritical flow. The scheme incorporates numerical characteristic decomposition, is shock capturing by design and incorporates space-marching as a result of the assumption that the flow is wholly supercritical in at least one space dimension. Results are shown for problems involving oblique hydraulic jumps and reflection from a wall.

Flux difference splitting for open channel flows

A finite difference scheme based on flux difference splitting is presented for the solution of the one-dimensional shallow-water equations in open channels, together with an extension to two-dimensional flows. A linearized problem, analogous to that of Riemann for gas dynamics, is defined and a scheme, based on numerical characteristic decomposition, is presented for obtaining approximate solutions to the linearized problem. The method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second-order scheme which avoids non-physical, spurious oscillations. The scheme is applied to a one-dimensional dam-break problem, and to a problem of flow in a river whose geometry induces a region of supercritical flow. The scheme is also applied to a two-dimensional dam-break problem. The numerical results are compared with the exact solution, or other numerical results, where available.

The cloud chamber and CTR Wilson’s legacy to atmospheric science

2011 is the centenary year of the short paper (Wilson,1911) first describing the cloud chamber, the device for visualising high-energy charged particles which earned the Scottish physicist Charles Thomas Rees (‘CTR’) Wilson the 1927 Nobel Prize for physics. His many achievements in atmospheric science, some of which have current relevance, are briefly reviewed here. CTR Wilson’s lifetime of scientific research work was principally in atmospheric electricity at the Cavendish Laboratory, Cambridge; he was Reader in Electrical Meteorology from 1918 and Jacksonian Professor from 1925 to 1935. However, he is immortalised in physics for his invention of the cloud chamber, because of its great significance as an early visualisation tool for particles such as cosmic rays1 (Galison, 1997). Sir Lawrence Bragg summarised its importance:

Extracting quantitative structural parameters for disordered polymers from neutron scattering data

The organization of non-crystalline polymeric materials at a local level, namely on a spatial scale between a few and 100 a, is still unclear in many respects. The determination of the local structure in terms of the configuration and conformation of the polymer chain and of the packing characteristics of the chain in the bulk material represents a challenging problem. Data from wide-angle diffraction experiments are very difficult to interpret due to the very large amount of information that they carry, that is the large number of correlations present in the diffraction patterns.We describe new approaches that permit a detailed analysis of the complex neutron diffraction patterns characterizing polymer melts and glasses. The coupling of different computer modelling strategies with neutron scattering data over a wide Q range allows the extraction of detailed quantitative information on the structural arrangements of the materials of interest. Proceeding from modelling routes as diverse as force field calculations, single-chain modelling and reverse Monte Carlo, we show the successes and pitfalls of each approach in describing model systems, which illustrate the need to attack the data analysis problem simultaneously from several fronts.

DE-2 observations of filamentary currents at ionospheric altitudes

Conjunctive measurements made by the Dynamics Explorer 1 and 2 spacecraft on October 22, 1981, under conditions of southward IMF, suggest the existence of a cusp ion injection from a region at the magnetopause with a scale size of ∼ 1/2 to 1 R E . Current signatures observed by the LAPI and MAGB instruments on board DE-2 indicate the existence of a rotation in the magnetic field that is consistent with a filamentary current system. The observed current structure can be interpreted as the ionospheric signature of a flux transfer event (FTE). In addition to this large-scale current structure there exist three small-scale filamentary current pairs. These current pairs close locally and thus, if our interpretation of this event as an FTE is correct, represent the first reported observations of FTE interior structure at low-altitudes.

The response of the magnetosphere-ionosphere system to solar wind dynamic pressure variations

We study the causal chain of events by which variations in the solar wind dynamic pressure cause the magnetopause boundary to move and excite magnetic perturbations at the ground. The observation of large ground magnetic transients is argued to be due to the coupling of the magnetohydrodynamic compressional wave to the field-guided Alfvén wave, which carrying current, can thereby transfer momentum to the ionosphere. The study highlights the similarity of the ionospheric signatures at a single station arising from the response of the coupled magnetosphere-ionosphere system to disparate impulsive processes at the magnetopause.

Evaluating nitrogen utilization efficiency of nonpregnant dry cows offered solely fresh cut grass at maintenance levels

The present study aimed to identify key parameters influencing N utilization and develop prediction equations for manure N output (MN), feces N output (FN), and urine N output (UN). Data were obtained under a series of digestibility trials with nonpregnant dry cows fed fresh grass at maintenance level. Grass was cut from 8 different ryegrass swards measured from early to late maturity in 2007 and 2008 (2 primary growth, 3 first regrowth, and 3 second regrowth) and from 2 primary growth early maturity swards in 2009. Each grass was offered to a group of 4 cows and 2 groups were used in each of the 8 swards in 2007 and 2008 for daily measurements over 6 wk; the first group (first 3 wk) and the second group (last 3 wk) assessed early and late maturity grass, respectively. Average values of continuous 3-d data of N intake (NI) and output for individual cows ( = 464) and grass nutrient contents ( = 116) were used in the statistical analysis. Grass N content was positively related to GE and ME contents but negatively related to grass water-soluble carbohydrates (WSC), NDF, and ADF contents ( < 0.01), indicating that accounting for nutrient interrelations is a crucial aspect of N mitigation. Significantly greater ratios of UN:FN, UN:MN, and UN:NI were found with increased grass WSC contents and ratios of N:WSC, N:digestible OM in total DM (DOMD), and N:ME ( < 0.01). Greater NI, animal BW, and grass N contents and lower grass WSC, NDF, ADF, DOMD, and ME concentrations were significantly associated with greater MN, FN, and UN ( < 0.05). The present study highlighted that using grass lower in N and greater in fermentable energy in animals fed solely fresh grass at maintenance level can improve N utilization, reduce N outputs, and shift part of N excretion toward feces rather than urine. These outcomes are highly desirable in mitigation strategies to reduce nitrous oxide emissions from livestock. Equations predicting N output from BW and grass N content explained a similar amount of variability as using NI and grass chemical composition (excluding DOMD and ME), implying that parameters easily measurable in practice could be used for estimating N outputs. In a research environment, where grass DOMD and ME are likely to be available, their use to predict N outputs is highly recommended because they strongly improved of the equations in the current study.

A priori error analysis of space–time Trefftz discontinuous Galerkin methods for wave problems

We present and analyse a space–time discontinuous Galerkin method for wave propagation problems. The special feature of the scheme is that it is a Trefftz method, namely that trial and test functions are solution of the partial differential equation to be discretised in each element of the (space–time) mesh. The method considered is a modification of the discontinuous Galerkin schemes of Kretzschmar et al. (2014) and of Monk & Richter (2005). For Maxwell’s equations in one space dimension, we prove stability of the method, quasi-optimality, best approximation estimates for polynomial Trefftz spaces and (fully explicit) error bounds with high order in the meshwidth and in the polynomial degree. The analysis framework also applies to scalar wave problems and Maxwell’s equations in higher space dimensions. Some numerical experiments demonstrate the theoretical results proved and the faster convergence compared to the non-Trefftz version of the scheme.

Lower semicontinuity of attractors for non-autonomous dynamical systems

This paper is concerned with the lower semicontinuity of attractors for semilinear non-autonomous differential equations in Banach spaces. We require the unperturbed attractor to be given as the union of unstable manifolds of time-dependent hyperbolic solutions, generalizing previous results valid only for gradient-like systems in which the hyperbolic solutions are equilibria. The tools employed are a study of the continuity of the local unstable manifolds of the hyperbolic solutions and results on the continuity of the exponential dichotomy of the linearization around each of these solutions.

Strongly damped wave problems: Bootstrapping and regularity of solutions

The aim of the article is to present a unified approach to the existence, uniqueness and regularity of solutions to problems belonging to a class of second order in time semilinear partial differential equations in Banach spaces. Our results are applied next to a number of examples appearing in literature, which fall into the class of strongly damped semilinear wave equations. The present work essentially extends the results on the existence and regularity of solutions to such problems. Previously, these problems have been considered mostly within the Hilbert space setting and with the main part operators being selfadjoint. In this article we present a more general approach, involving sectorial operators in reflexive Banach spaces. (C) 2008 Elsevier Inc. All rights reserved.

Gamma transition intensity determination using multidetector coincidence data

This work describes two similar methods for calculating gamma transition intensities from multidetector coincidence measurements. In the first one, applicable to experiments where the angular correlation function is explicitly fitted, the normalization parameter from this fit is used to determine the gamma transition intensities. In the second, that can be used both in angular correlation or DCO measurements, the spectra obtained for all the detector pairs are summed up, in order to get the best detection statistics possible, and the analysis of the resulting bidimensional spectrum is used to calculate the transition intensities; in this method, the summation of data corresponding to different angles minimizes the influence of the angular correlation coefficient. Both methods are then tested in the calculation of intensities for well-known transitions from a (152)Eu standard source, as well as in the calculation of intensities obtained in beta-decay experiments with (193)Os and (155)Sm sources, yielding excellent results in all these cases. (C) 2009 Elsevier B.V. All rights reserved.

Parametric analysis of discrepant sets of data

In this paper a new parametric method to deal with discrepant experimental results is developed. The method is based on the fit of a probability density function to the data. This paper also compares the characteristics of different methods used to deduce recommended values and uncertainties from a discrepant set of experimental data. The methods are applied to the (137)Cs and (90)Sr published half-lives and special emphasis is given to the deduced confidence intervals. The obtained results are analyzed considering two fundamental properties expected from an experimental result: the probability content of confidence intervals and the statistical consistency between different recommended values. The recommended values and uncertainties for the (137)Cs and (90)Sr half-lives are 10,984 (24) days and 10,523 (70) days, respectively. (C) 2009 Elsevier B.V. All rights reserved.

The magnetized steel and scintillator calorimeters of the MINOS experiment

The Main Injector Neutrino Oscillation Search (MINOS) experiment uses an accelerator-produced neutrino beam to perform precision measurements of the neutrino oscillation parameters in the ""atmospheric neutrino"" sector associated with muon neutrino disappearance. This long-baseline experiment measures neutrino interactions in Fermilab`s NuMI neutrino beam with a near detector at Fermilab and again 735 km downstream with a far detector in the Soudan Underground Laboratory in northern Minnesota. The two detectors are magnetized steel-scintillator tracking calorimeters. They are designed to be as similar as possible in order to ensure that differences in detector response have minimal impact on the comparisons of event rates, energy spectra and topologies that are essential to MINOS measurements of oscillation parameters. The design, construction, calibration and performance of the far and near detectors are described in this paper. (C) 2008 Elsevier B.V. All rights reserved.

Challenging measurement of the (16)O+(27)Al elastic and inelastic angular distributions up to large angles

The (16)O+(27)Al elastic and inelastic angular distributions have been measured in a broad angular range (13 degrees < theta(lab) < 52 degrees) at about 100 MeV incident energy. The use of the MAGNEX large acceptance magnetic spectrometer and of the ray-reconstruction analysis technique has been crucial in order to provide, in the same experiment, high-resolution energy spectra and cross-section measurements distributed over more than seven orders of magnitude down to hundreds of nb/sr. (C) 2011 Elsevier B.V. All rights reserved.