Determining the temperature from Cauchy data in corner domains

We consider the problem of reconstruction of the temperature from knowledge of the temperature and heat flux on a part of the boundary of a bounded planar domain containing corner points. An iterative method is proposed involving the solution of mixed boundary value problems for the heat equation (with time-dependent conductivity). These mixed problems are shown to be well-posed in a weighted Sobolev space.

Bandpass switching based on a nonlinear optical loop mirror and an in-fibre grating reflector

Nonlinear optical loop mirror (NOLM) requires breaking the loop symmetry to enable the counter propagating pulses to acquire a differential π phase shift. This is achieved with either an asymmetric fused fibre coupler at the input or by the inclusion of an asymmetrically located gain or loss element within the loop. By introducing a frequency selective loss element, nonlinear switching may be confined to a narrow band of wavelengths or multiple wavelengths. This configuration may have applications in time-wavelength demultiplexing. We demonstrate this technique of bandpass switching in the soliton regime using a fibre-Bragg grating reflector as the wavelength dependent loss.

A procedure for the temperature reconstruction in corner domains from Cauchy data

An iterative procedure is proposed for the reconstruction of a stationary temperature field from Cauchy data given on a part of the boundary of a bounded plane domain where the boundary is smooth except for a finite number of corner points. In each step, a series of mixed well-posed boundary value problems are solved for the heat operator and its adjoint. Convergence is proved in a weighted L2-space. Numerical results are included which show that the procedure gives accurate and stable approximations in relatively few iterations.

Numerical solution of parabolic Cauchy problems in planar corner domains

An iterative method for the parabolic Cauchy problem in planar domains having a finite number of corners is implemented based on boundary integral equations. At each iteration, mixed well-posed problems are solved for the same parabolic operator. The presence of corner points renders singularities of the solutions to these mixed problems, and this is handled with the use of weight functions together with, in the numerical implementation, mesh grading near the corners. The mixed problems are reformulated in terms of boundary integrals obtained via discretization of the time-derivative to obtain an elliptic system of partial differential equations. To numerically solve these integral equations a Nyström method with super-algebraic convergence order is employed. Numerical results are presented showing the feasibility of the proposed approach. © 2014 IMACS.

Construction and experimental study of an elevation linear Fresnel reflector

This paper outlines a novel elevation linear Fresnel reflector (ELFR) and presents and validates theoretical models defining its thermal performance. To validate the models, a series of experiments were carried out for receiver temperatures in the range of 30-100 °C to measure the heat loss coefficient, gain in heat transfer fluid (HTF) temperature, thermal efficiency, and stagnation temperature. The heat loss coefficient was underestimated due to the model exclusion of collector end heat losses. The measured HTF temperature gains were found to have a good correlation to the model predictions - less than a 5% difference. In comparison to model predictions for the thermal efficiency and stagnation temperature, measured values had a difference of -39% to +31% and 22-38%, respectively. The difference between the measured and predicted values was attributed to the low-temperature region for the experiments. It was concluded that the theoretical models are suitable for examining linear Fresnel reflector (LFR) systems and can be adopted by other researchers.