A procedure for determining a spacewise dependent heat source and the initial temperature

The inverse problem of determining a spacewise dependent heat source, together with the initial temperature for the parabolic heat equation, using the usual conditions of the direct problem and information from two supplementary temperature measurements at different instants of time is studied. These spacewise dependent temperature measurements ensure that this inverse problem has a unique solution, despite the solution being unstable, hence the problem is ill-posed. We propose an iterative algorithm for the stable reconstruction of both the initial data and the source based on a sequence of well-posed direct problems for the parabolic heat equation, which are solved at each iteration step using the boundary element method. The instability is overcome by stopping the iterations at the first iteration for which the discrepancy principle is satisfied. Numerical results are presented for a typical benchmark test example, which has the input measured data perturbed by increasing amounts of random noise. The numerical results show that the proposed procedure gives accurate numerical approximations in relatively few iterations.

By writers for writers: developing a writer-centred model of the writing process

This thesis, set within an Action Research framework, details the development and validation of a writer-centred model of the writing process. The model was synthesised within the boundaries of a writers’ group for MA students. The initial data collected, and analysed using the principles of grounded theory, were retrospective descriptions of group members’ writing processes. After initial analysis, additional data, from group members’ writing, and from audio recordings, were used for further analysis, and to form a model of the writing process. To ascertain whether the model had value outside the specific context in which it was made, it was validated from three different perspectives. Firstly, the retrospective descriptions of other writers were collected and analysed, using the model as a framework. Secondly, the model was presented at academic conferences; comments about the model, made by members of the audience, were collected and analysed. Finally, the model was used in writing courses for PhD students. Comments from these students, along with questionnaire responses, were collected and the content analysed. Upon examination of all data sources, the model was updated to reflect additional insights arising from the analysis. Analysis of the data also indicated that the model is useable outside its original context. Potential uses for the model are 1) raising awareness of the process of writing, 2) putting writers at ease, 3) serving as a starting point for individuals or groups to design their own models of the writing process, and 4) as a tool to help writers take control of their writing processes.

Efficacy of memantine on behavioral and psychological symptoms related to dementia:a systematic meta-analysis

BACKGROUND: The behavioral and psychological symptoms related to dementia (BPSD) are difficult to manage and are associated with adverse patient outcomes. OBJECTIVE: To systematically analyze the data on memantine in the treatment of BPSD. METHODS: We searched MEDLINE, EMBASE, Pharm-line, the Cochrane Centre Collaboration, www.clinicaltrials.gov, www.controlled-trials.com, and PsycINFO (1966-July 2007). We contacted manufacturers and scrutinized the reference sections of articles identified in our search for further references, including conference proceedings. Two researchers (IM and CF) independently reviewed all studies identified by the search strategy. We included 6 randomized, parallel-group, double-blind studies that rated BPSD with the Neuropsychiatric Inventory (NPI) in our meta-analysis. Patients had probable Alzheimer's disease and received treatment with memantine for at least one month. Overall efficacy of memantine on the NPI was established with a t-test for the average difference between means across studies, using a random effects model. RESULTS: Five of the 6 studies identified had NPI outcome data. In these 5 studies, 868 patients were treated with memantine and 882 patients were treated with placebo. Patients on memantine improved by 1.99 on the NPI scale (95% Cl -0.08 to -3.91; p = 0.041) compared with the placebo group. CONCLUSIONS: Initial data appear to indicate that memantine decreases NPI scores and may have a role in managing BPSD. However, there are a number of limitations with the current data; the effect size was relatively small, and whether memantine produces significant clinical benefit is not clear.

The use of antidepressants to treat attention deficit hyperactivity disorder in adults

There is increasing evidence that children continue to experience attention deficit hyperactivity disorder (ADHD) symptoms into adult life. The two main treatments for ADHD are antidepressants and stimulants. Here, the effectiveness data relating to the use of antidepressants in adults with ADHD are reviewed. Four controlled and six open studies were identified. Although, there is only limited data currently available, antidepressants may offer an effective therapy for adult ADHD. Controlled trials have studied desipramine, atomoxetine and bupropion, with most evidence supporting the efficacy of desipramine. The initial data indicate that atomoxetine is less effective than desipramine. The efficacy of bupropion is unclear. Initial published open data suggest a response rate of 50-78% with venlafaxine. Controlled studies are required to confirm this efficacy. Most of the present data are short-term, therefore long-term effectiveness data are required.

An aspect oriented performance analysis environment

AOSD'03 Practitioner Report Performance analysis is motivated as an ideal domain for benefiting from the application of Aspect Oriented (AO) technology. The experience of a ten week project to apply AO to the performance analysis domain is described. We show how all phases of a performance analysts’ activities – initial profiling, problem identification, problem analysis and solution exploration – were candidates for AO technology assistance – some being addressed with more success than others. A Profiling Workbench is described that leverages the capabilities of AspectJ, and delivers unique capabilities into the hands of developers exploring caching opportunities.

Quantitative analysis of solid-state processes studied with isothermal microcalorimetry

Quantitative analysis of solid-state processes from isothermal microcalorimetric data is straightforward if data for the total process have been recorded and problematic (in the more likely case) when they have not. Data are usually plotted as a function of fraction reacted (α); for calorimetric data, this requires knowledge of the total heat change (Q) upon completion of the process. Determination of Q is difficult in cases where the process is fast (initial data missing) or slow (final data missing). Here we introduce several mathematical methods that allow the direct calculation of Q by selection of data points when only partial data are present, based on analysis with the Pérez-Maqueda model. All methods in addition allow direct determination of the reaction mechanism descriptors m and n and from this the rate constant, k. The validity of the methods is tested with the use of simulated calorimetric data, and we introduce a graphical method for generating solid-state power-time data. The methods are then applied to the crystallization of indomethacin from a glass. All methods correctly recovered the total reaction enthalpy (16.6 J) and suggested that the crystallization followed an Avrami model. The rate constants for crystallization were determined to be 3.98 × 10-6, 4.13 × 10-6, and 3.98 × 10 -6 s-1 with methods 1, 2, and 3, respectively. © 2010 American Chemical Society.

Numerical approximation of the one-dimensional inverse Cauchy–Stefan problem using a method of fundamental solutions

We investigate an application of the method of fundamental solutions (MFS) to the one-dimensional parabolic inverse Cauchy–Stefan problem, where boundary data and the initial condition are to be determined from the Cauchy data prescribed on a given moving interface. In [B.T. Johansson, D. Lesnic, and T. Reeve, A method of fundamental solutions for the one-dimensional inverse Stefan Problem, Appl. Math Model. 35 (2011), pp. 4367–4378], the inverse Stefan problem was considered, where only the boundary data is to be reconstructed on the fixed boundary. We extend the MFS proposed in Johansson et al. (2011) and show that the initial condition can also be simultaneously recovered, i.e. the MFS is appropriate for the inverse Cauchy-Stefan problem. Theoretical properties of the method, as well as numerical investigations, are included, showing that accurate results can be efficiently obtained with small computational cost.

An integral equation method for a mixed initial boundary value problem for unsteady Stokes system in a doubly-connected domain

We present a novel numerical method for a mixed initial boundary value problem for the unsteady Stokes system in a planar doubly-connected domain. Using a Laguerre transformation the unsteady problem is reduced to a system of boundary value problems for the Stokes resolvent equations. Employing a modied potential approach we obtain a system of boundary integral equations with various singularities and we use a trigonometric quadrature method for their numerical solution. Numerical examples are presented showing that accurate approximations can be obtained with low computational cost.

Determining the temperature from incomplete boundary data

An iterative procedure for determining temperature fields from Cauchy data given on a part of the boundary is presented. At each iteration step, a series of mixed well-posed boundary value problems are solved for the heat operator and its adjoint. A convergence proof of this method in a weighted L2-space is included, as well as a stopping criteria for the case of noisy data. Moreover, a solvability result in a weighted Sobolev space for a parabolic initial boundary value problem of second order with mixed boundary conditions is presented. Regularity of the solution is proved. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

An iterative method for a Cauchy problem for the heat equation

An iterative method for reconstruction of the solution to a parabolic initial boundary value problem of second order from Cauchy data is presented. The data are given on a part of the boundary. At each iteration step, a series of well-posed mixed boundary value problems are solved for the parabolic operator and its adjoint. The convergence proof of this method in a weighted L2-space is included.

Numerical solution of the Dirichlet initial boundary value problem for the heat equation in exterior 3-dimensional domains using integral equations

A numerical method for the Dirichlet initial boundary value problem for the heat equation in the exterior and unbounded region of a smooth closed simply connected 3-dimensional domain is proposed and investigated. This method is based on a combination of a Laguerre transformation with respect to the time variable and an integral equation approach in the spatial variables. Using the Laguerre transformation in time reduces the parabolic problem to a sequence of stationary elliptic problems which are solved by a boundary layer approach giving a sequence of boundary integral equations of the first kind to solve. Under the assumption that the boundary surface of the solution domain has a one-to-one mapping onto the unit sphere, these integral equations are transformed and rewritten over this sphere. The numerical discretisation and solution are obtained by a discrete projection method involving spherical harmonic functions. Numerical results are included.