Sonar acoustics

The problem of producing a model to determine the beam pattern produced by a sonar set in the form of a circular cylinder with hemispherical end caps is studied. The beam width and the position of the beam centre are also considered and the results of the models are compared with experimental findings. Possible reasons for the discrepancies between these theoretical and experimental results are examined, providing insight into developing more sophisticated mathematical models. The beam patterns were produced using a combination of Matlab and Fortran 77 programs incorporating subroutines from the NAG library. Experimental results and data are included with the kind permission of Thomson Marconi Sonar Systems Ltd

A chemical survey of standing waters in south-east England, with reference to acidification and eutrophication

This study looks at the distribution and magnitude of acidification and eutrophication in south-east England where there are no natural lakes but a large number of shallow artificial ponds. The study area is defined as the region lying within a 100 km radius of central London but excluding the area within the M25 motorway. Water samples were taken from 120 sites between mid-January and the end of February 1990, with a subsequent monthly survey of a subset of 31 of these waters. Twelve chemical variables were measured in the laboratory using standard techniques. PH values for the full dataset ranged from 3.2 to 8.4, although the majority of sites had pH values in the range 7.0 to 8.5; only five sites had a pH of less than 6.0. The five low pH sites expectedly had low alkalinities and are the only sites with values below 0.1 meq per litre. Concentrations of calcium, sodium, potassium, magnesium, chloride, sulphate and nitrate had normal distributions. The majority of sites had total phosphorus concentrations in the range 25 to 200 mu g per litre, although 10 sites had concentrations above 400 mu g per litre. The low number of acid sites suggests that surface water acidity is not a widespread regional problem in south-east England. However the survey shows that a large number of standing waters in the region have high total phosphorus and nitrate concentrations, and 89% may be considered moderately to considerably eutrophic

Approximation of linear functionals using an hp-adaptive discontinuous Galerkin finite element method

We consider the problem of computing a linear functional of the solution of an elliptic partial differential equation to within a given tolerance. We drive an a posteriori error bound for the linear functional and use this as the basis of an hp-adaptive discontinuous Galerkin finite element algorithm to deliver the functional to within a prescribed error tolerance

Application of hpDGFEM to mechanisms at channel microband electrodes

We extend our earlier work (Harriman et al., Oxford University Computing Laboratory Technical Report NA04/19) on hp-DGFEM for disc electrodes to the case of reaction mechanisms to the increasingly popular channel microband electrode configuration. We present results for the simple E reaction mechanism (convection-diffusion equation), for the ECE and EC2E reaction mechanisms (linear and nonlinear systems of reaction-convection- diffusion equations, respectively) and for the DISP1 and DISP2 reaction mechanisms (linear and nonlinear coupled systems of reaction-convection-diffusion equations, respectively). In all cases we demonstrate excellent agreement with previous results using relatively coarse meshes and without the need for streamline-diffusion stabilisation, even at high flow rates

hp-Version discontinuous Galerkin methods with interior penalty for partial differential equations with nonnegative characteristic form.

In this paper we consider the a posteriori and a priori analysis of hp-discontinuous Galerkin interior penalty methods for second-order partial differential equations with nonnegative characteristic form. In particular, we discuss the question of error estimation for linear target functionals, such as the outflow flux and the local average of the solution. Based on our a posteriori error bound we design and implement the corresponding adaptive algorithm to ensure reliable and efficient control of the error in the prescribed functional to within a given tolerance. This involves exploiting both local polynomial-degree variation and local mesh subdivision. The theoretical results are illustrated by a series of numerical experiments

Separability and the stella octangula

A geometrical picture of separability of 2 x 2 composite quantum systems, showing the region of separable density matrices in the space of hermitian matrices, is given. It rests on the criterion of separability given by Peres, and it is an extension of the ``Horodecki diagram'' and the ``stella octangula'' described by Aravind.Comment: 4 pages, 1 figur

Adaptive Finite Element Simulation of Steady State Currents at Microdisc Electrodes to a Guaranteed Accuracy

We consider the general problem of numerical simulation of the currents at microelectrodes using an adaptive finite element approach. Microelectrodes typically consist of an electrode embedded (or recessed) in an insulating material. For all such electrodes, numerical simulation is made difficult by the presence of a boundary singularity at the electrode edge (where the electrode meets the insulator), manifested by the large increase in the current density at this point, often referred to as the "edge-effect". Our approach to overcoming this problem involves the derivation of an a posteriori bound on the error in the numerical approximation for the current which can be used to drive an adaptive mesh-generation algorithm. This allows us to calculate the current to within a prescribed tolerance. Here we demonstrate the power of the method for a simple model problem -- an E reaction mechanism at a microdisc electrode -- for which the analytical solution is known, then we extend the work to the case of a (pseudo) first order EC' reaction mechanism at both an inlaid and a recessed disc

Saving the Substratum: Interpreting Kant’s First Analogy

Kant’s transcendental idealism requires that experience be both spatial and temporal. In the First Analogy of Experience, he argues that in order for experience in time to be possible, there must be something permanent in our experience. This something permanent is substance: a bearer of properties that persists and conserves its quantity throughout any empirical change. The trajectory of Kant’s argument in the First Analogy is not entirely clear and this has left room for multiple interpretations. In this paper, I introduce the First Analogy and three suggested interpretations of its argument. I defend the so-called substratum interpretation, associated with Henry Allison and Andrew Ward, from philosophical objections raised by Paul Guyer. In order to unify all of experience within a singular time-frame, we must presuppose a persistent substratum through which all experiences can be related to one another

Letter from Mary Harriman to John Muir, [1911] Apr 25.

Telephone no 580 Plaza[1]Tuesday April 25th[letterhead]Dear Mr Muir,From Mr. Herrin\u27s telegram yesterday I understand you are to arrive this afternoon at the St Regis Hotel. It is a great pleasure to have05006 [3]see some interesting paintings being done by Mr Fleming the Indian life artist for our Arden House. To-morrow I am going out of town to Arden for the day--would it amuse you to go too? If so I will stop at the Hotel for you at a quarter before nine o\u27clock & return you in time for dinner.Hoping soon to see you & to see much of you while hereWith loveMary W. Harrima