On the numerical solution of a Cauchy problem for the Laplace equation via a direct integral equation approach

We investigate the problem of determining the stationary temperature field on an inclusion from given Cauchy data on an accessible exterior boundary. On this accessible part the temperature (or the heat flux) is known, and, additionally, on a portion of this exterior boundary the heat flux (or temperature) is also given. We propose a direct boundary integral approach in combination with Tikhonov regularization for the stable determination of the temperature and flux on the inclusion. To determine these quantities on the inclusion, boundary integral equations are derived using Green’s functions, and properties of these equations are shown in an L2-setting. An effective way of discretizing these boundary integral equations based on the Nystr¨om method and trigonometric approximations, is outlined. Numerical examples are included, both with exact and noisy data, showing that accurate approximations can be obtained with small computational effort, and the accuracy is increasing with the length of the portion of the boundary where the additionally data is given.

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.

On an indirect integral equation approach for stationary heat transfer in semi-infinite layered domains in R3 with cavities

Regions containing internal boundaries such as composite materials arise in many applications.We consider a situation of a layered domain in IR3 containing a nite number of bounded cavities. The model is stationary heat transfer given by the Laplace equation with piecewise constant conductivity. The heat ux (a Neumann condition) is imposed on the bottom of the layered region and various boundary conditions are imposed on the cavities. The usual transmission (interface) conditions are satised at the interface layer, that is continuity of the solution and its normal derivative. To eciently calculate the stationary temperature eld in the semi-innite region, we employ a Green's matrix technique and reduce the problem to boundary integral equations (weakly singular) over the bounded surfaces of the cavities. For the numerical solution of these integral equations, we use Wienert's approach [20]. Assuming that each cavity is homeomorphic with the unit sphere, a fully discrete projection method with super-algebraic convergence order is proposed. A proof of an error estimate for the approximation is given as well. Numerical examples are presented that further highlights the eciency and accuracy of the proposed method.

Binocular fusion, suppression and diplopia for blurred edges

Purpose: (1) To devise a model-based method for estimating the probabilities of binocular fusion, interocular suppression and diplopia from psychophysical judgements, (2) To map out the way fusion, suppression and diplopia vary with binocular disparity and blur of single edges shown to each eye, (3) To compare the binocular interactions found for edges of the same vs opposite contrast polarity. Methods: Test images were single, horizontal, Gaussian-blurred edges, with blur B = 1-32 min arc, and vertical disparity 0-8.B, shown for 200 ms. In the main experiment, observers reported whether they saw one central edge, one offset edge, or two edges. We argue that the relation between these three response categories and the three perceptual states (fusion, suppression, diplopia) is indirect and likely to be distorted by positional noise and criterion effects, and so we developed a descriptive, probabilistic model to estimate both the perceptual states and the noise/criterion parameters from the data. Results: (1) Using simulated data, we validated the model-based method by showing that it recovered fairly accurately the disparity ranges for fusion and suppression, (2) The disparity range for fusion (Panum's limit) increased greatly with blur, in line with previous studies. The disparity range for suppression was similar to the fusion limit at large blurs, but two or three times the fusion limit at small blurs. This meant that diplopia was much more prevalent at larger blurs, (3) Diplopia was much more frequent when the two edges had opposite contrast polarity. A formal comparison of models indicated that fusion occurs for same, but not opposite, polarities. Probability of suppression was greater for unequal contrasts, and it was always the lower-contrast edge that was suppressed. Conclusions: Our model-based data analysis offers a useful tool for probing binocular fusion and suppression psychophysically. The disparity range for fusion increased with edge blur but fell short of complete scale-invariance. The disparity range for suppression also increased with blur but was not close to scale-invariance. Single vision occurs through fusion, but also beyond the fusion range, through suppression. Thus suppression can serve as a mechanism for extending single vision to larger disparities, but mainly for sharper edges where the fusion range is small (5-10 min arc). For large blurs the fusion range is so much larger that no such extension may be needed. © 2014 The College of Optometrists.

Determination of a spacewise dependent heat source

This paper investigates the inverse problem of determining a spacewise dependent heat source in the parabolic heat equation using the usual conditions of the direct problem and information from a supplementary temperature measurement at a given single instant of time. The spacewise dependent temperature measurement ensures that the inverse problem has a unique solution, but this solution is unstable, hence the problem is ill-posed. For this inverse problem, we propose an iterative algorithm based on a sequence of well-posed direct problems which are solved at each iteration step using the boundary element method (BEM). The instability is overcome by stopping the iterations at the first iteration for which the discrepancy principle is satisfied. Numerical results are presented for various typical benchmark test examples which have the input measured data perturbed by increasing amounts of random noise.

Cojumps in stock prices:empirical evidence

We examine contemporaneous jumps (cojumps) among individual stocks and a proxy for the market portfolio. We show, through a Monte Carlo study, that using intraday jump tests and a coexceedance criterion to detect cojumps has a power similar to the cojump test proposed by Bollerslev et al. (2008). However, we also show that we should not expect to detect all common jumps comprising a cojump when using such coexceedance based detection methods. Empirically, we provide evidence of an association between jumps in the market portfolio and cojumps in the underlying stocks. Consistent with our Monte Carlo evidence, moderate numbers of stocks are often detected to be involved in these (systematic) cojumps. Importantly, the results suggest that market-level news is able to generate simultaneous large jumps in individual stocks. We also find evidence of an association between systematic cojumps and Federal Funds Target Rate announcements. © 2013 Elsevier B.V.

Fatigue behaviour of C-Mn-B steels:effects of heat treatment prestrain and residual stress

The fatigue-crack propagation and threshold behaviour of a C-Mn steel containing boron has been investigated at a range of strength levels suitable for mining chain applications. The heat-treatment variables examined include two austenitizing temperatures (900 degree C and 1250 degree C) and a range of tempering treatments from the as-quenched condition to tempering at 400 degree C. In mining applications the haulage chains undergo a 'calibration' process which has the effect of imposing a tensile prestrain on the chain links before they go into service. Prestrain is shown to reduce threshold values in these steels and this behaviour is related to its effects on the residual stress distribution in the test specimens.

Economic efficiency of mobile latent heat storages

In a pilot project an optimized mobile latent heat storage based on a system available on the market has been tested at Fraunhofer Institute for Environmental, Safety and Energy Technology. Initially trials were conducted with the aim of optimizing the process of charging and discharging. A specifically constructed test rig at the incineration trials centre at the institute allowed charging and discharging procedures of the mobile latent heat storage with adjustable parameters. In addition an evaluation model was constructed to further optimize the heat exchanger systems. In conclusion the prototype of the mobile latent heat storage was tested in practical operation. The economic and technical feasibility of heat transportation was shown if not utilized waste heat is available. © 2014 The Authors.

Biomass fast pyrolysis energy balance of a 1kg/h test rig

The present paper offers a methodological approach towards the estimation and definition of enthalpies constituting an energy balance around a fast pyrolysis experiment conducted in a laboratory scale fluid bed with a capacity of 1 kg/ h. Pure N2 was used as fluidization medium at atmospheric pressure and the operating temperature (∼500°C) was adjusted with electrical resistors. The biomass feedstock type that was used was beech wood. An effort was made to achieve a satisfying 92.5% retrieval of products (dry basis mass balance) with the differences mainly attributed to loss of some bio-oil constituents into the quenching medium, ISOPAR™. The chemical enthalpy recovery for bio-oil, char and permanent gases is calculated 64.6%, 14.5% and 7.1%, respectively. All the energy losses from the experimental unit into the environment, namely the pyrolyser, cooling unit etc. are discussed and compared to the heat of fast pyrolysis that was calculated at 1123.5 kJ per kg of beech wood. This only represents 2.4% of the biomass total enthalpy or 6.5% its HHV basis. For the estimation of some important thermo-physical properties such as heat capacity and density, it was found that using data based on the identified compounds from the GC/MS analysis is very close to the reference values despite the small fraction of the bio-oil components detected. The methodology and results can help as a starting point for the proper design of fast pyrolysis experiments, pilot and/or industrial scale plants.