A procedure for the reconstruction of a stochastic stationary temperature field

An iterative procedure is proposed for the reconstruction of a temperature field from a linear stationary heat equation with stochastic coefficients, and stochastic Cauchy data given on a part of the boundary of a bounded domain. In each step, a series of mixed well-posed boundary-value problems are solved for the stochastic heat operator and its adjoint. Well-posedness of these problems is shown to hold and convergence in the mean of the procedure is proved. A discretized version of this procedure, based on a Monte Carlo Galerkin finite-element method, suitable for numerical implementation is discussed. It is demonstrated that the solution to the discretized problem converges to the continuous as the mesh size tends to zero.

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.

An iterative method for reconstruction of temperature

An iterative method for the reconstruction of a stationary three-dimensional temperature field, 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 L 2-space is include

Flow patterns and performance of distillation trays

It is known that distillation tray efficiency depends on the liquid flow pattern, particularly for large diameter trays. Scale·up failures due to liquid channelling have occurred, and it is known that fitting flow control devices to trays sometirr.es improves tray efficiency. Several theoretical models which explain these observations have been published. Further progress in understanding is at present blocked by lack of experimental measurements of the pattern of liquid concentration over the tray. Flow pattern effects are expected to be significant only on commercial size trays of a large diameter and the lack of data is a result of the costs, risks and difficulty of making these measurements on full scale production columns. This work presents a new experiment which simulates distillation by water cooling. and provides a means of testing commercial size trays in the laboratory. Hot water is fed on to the tray and cooled by air forced through the perforations. The analogy between heat and mass transfer shows that the water temperature at any point is analogous to liquid concentration and the enthalpy of the air is analogous to vapour concentration. The effect of the liquid flow pattern on mass transfer is revealed by the temperature field on the tray. The experiment was implemented and evaluated in a column of 1.2 m. dia. The water temperatures were measured by thennocouples interfaced to an electronic computerised data logging system. The "best surface" through the experimental temperature measurements was obtained by the mathematical technique of B. splines, and presented in tenos of lines of constant temperature. The results revealed that in general liquid channelling is more imponant in the bubbly "mixed" regime than in the spray regime. However, it was observed that severe channelling also occurred for intense spray at incipient flood conditions. This is an unexpected result. A computer program was written to calculate point efficiency as well as tray efficiency, and the results were compared with distillation efficiencies for similar loadings. The theoretical model of Porter and Lockett for predicting distillation was modified to predict water cooling and the theoretical predictions were shown to be similar to the experimental temperature profiles. A comparison of the repeatability of the experiments with an errors analysis revealed that accurate tray efficiency measurements require temperature measurements to better than ± 0.1 °c which is achievable with conventional techniques. This was not achieved in this work, and resulted in considerable scatter in the efficiency results. Nevertheless it is concluded that the new experiment is a valuable tool for investigating the effect of the liquid flow pattern on tray mass transfer.

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.

An iterative method based on boundary integrals for elliptic Cauchy problems in semi-infinite domains

In this study, we investigate the problem of reconstruction of a stationary temperature field from given temperature and heat flux on a part of the boundary of a semi-infinite region containing an inclusion. This situation can be modelled as a Cauchy problem for the Laplace operator and it is an ill-posed problem in the sense of Hadamard. We propose and investigate a Landweber-Fridman type iterative method, which preserve the (stationary) heat operator, for the stable reconstruction of the temperature field on the boundary of the inclusion. In each iteration step, mixed boundary value problems for the Laplace operator are solved in the semi-infinite region. Well-posedness of these problems is investigated and convergence of the procedures is discussed. For the numerical implementation of these mixed problems an efficient boundary integral method is proposed which is based on the indirect variant of the boundary integral approach. Using this approach the mixed problems are reduced to integral equations over the (bounded) boundary of the inclusion. Numerical examples are included showing that stable and accurate reconstructions of the temperature field on the boundary of the inclusion can be obtained also in the case of noisy data. These results are compared with those obtained with the alternating iterative method.

Recovering boundary data in planar heat conduction using boundary integral equation method

We consider a Cauchy problem for the heat equation, where the temperature field is to be reconstructed from the temperature and heat flux given on a part of the boundary of the solution domain. We employ a Landweber type method proposed in [2], where a sequence of mixed well-posed problems are solved at each iteration step to obtain a stable approximation to the original Cauchy problem. We develop an efficient boundary integral equation method for the numerical solution of these mixed problems, based on the method of Rothe. Numerical examples are presented both with exact and noisy data, showing the efficiency and stability of the proposed procedure and approximations.

Ultrasonic field and temperature sensor based on short in-fibre Bragg gratings

The authors demonstrate that in-fibre Bragg gratings may be successfully used to measure megahertz acoustic fields if the grating length is sufficiently short and the optical fibre is appropriately desensitised. A noise-limited pressure resolution of 4.5 × 10 –3 atm vHz was found. The capability to simultaneously act as a temperature sensor is also demonstrated.

Ultrasonic field and temperature sensor based on short in-fibre Bragg gratings

The authors demonstrate that in-fibre Bragg gratings may be successfully used to measure megahertz acoustic fields if the grating length is sufficiently short and the optical fibre is appropriately desensitised. A noise-limited pressure resolution of 4.5 × 10 –3 atm vHz was found. The capability to simultaneously act as a temperature sensor is also demonstrated.

Exploitation of fibre characteristics in temperature sensing and radio-over-fibre applications

The development of sensing devices is one of the instrumentation fields that has grown rapidly in the last decade. Corresponding to the swift advance in the development of microelectronic sensors, optical fibre sensors are widely investigated because of their advantageous properties over the electronics sensors such as their wavelength multiplexing capability and high sensitivity to temperature, pressure, strain, vibration and acoustic emission. Moreover, optical fibre sensors are more attractive than the electronics sensors as they can perform distributed sensing, in terms of covering a reasonably large area using a single piece of fibre. Apart from being a responsive element in the sensing field, optical fibre possesses good assets in generating, distributing, processing and transmitting signals in the future broadband information network. These assets include wide bandwidth, high capacity and low loss that grant mobility and flexibility for wireless access systems. Among these core technologies, the fibre optic signal processing and transmission of optical and radio frequency signals have been the subjects of study in this thesis. Based on the intrinsic properties of single-mode optical fibre, this thesis aims to exploit the fibre characteristics such as thermal sensitivity, birefringence, dispersion and nonlinearity, in the applications of temperature sensing and radio-over-fibre systems. By exploiting the fibre thermal sensitivity, a fully distributed temperature sensing system consisting of an apodised chirped fibre Bragg grating has been implemented. The proposed system has proven to be efficient in characterising grating and providing the information of temperature variation, location and width of the heat source applied in the area under test.To exploit the fibre birefringence, a fibre delay line filter using a single high-birefringence optical fibre structure has been presented. The proposed filter can be reconfigured and programmed by adjusting the input azimuth of launched light, as well as the strength and direction of the applied coupling, to meet the requirements of signal processing for different purposes in microwave photonic and optical filtering applications. To exploit the fibre dispersion and nonlinearity, experimental investigations have been carried out to study their joint effect in high power double-sideband and single-sideband modulated links with the presence of fibre loss. The experimental results have been theoretically verified based on the in-house implementation of the split-step Fourier method applied to the generalised nonlinear Schrödinger equation. Further simulation study on the inter-modulation distortion in two-tone signal transmission has also been presented so as to show the effect of nonlinearity of one channel on the other. In addition to the experimental work, numerical simulations have also been carried out in all the proposed systems, to ensure that all the aspects concerned are comprehensively investigated.

Spectroscopic studies of field-induced electron emission from isolated microstructures

A detailed investigation has been undertaken into the field induced electron emission (FIEE) mechanism that occurs at microscopically localised `sites' on uncoated and dielectric coated metallic electrodes. These processes have been investigated using two dedicated experimental systems that were developed for this study. The first is a novel combined photo/field emission microscope, which employs a UV source to stimulate photo-electrons from the sample surface in order to generate a topographical image. This system utilises an electrostatic lens column to provide identical optical properties under the different operating conditions required for purely topographical and combined photo/field imaging. The system has been demonstrated to have a resolution approaching 1m. Emission images have been obtained from carbon emission sites using this system to reveal that emission may occur from the edge triple junction or from the bulk of the carbon particle. An existing UHV electron spectrometer has been extensively rebuilt to incorporate a computer control and data acquisition system, improved sample handling and manipulation and a specimen heating stage. Details are given of a comprehensive study into the effects of sample heating on the emission process under conditions of both bulk and transient heating. Similar studies were also performed under conditions of both zero and high applied field. These show that the properties of emission sites are strongly temperature and field dependent thus indicating that the emission process is `non-metallic' in nature. The results have been shown to be consistent with an existing hot electron emission model.

Study of neutral Fe(III) complexes of pyridoxal-N-substituted thiosemicarbazone with desolvation induced spin-state transformation above room temperature

The preparation and characterization of two new neutral ferric complexes with desolvation-induced discontinuous spin-state transformation above room temperature are reported. The compounds, Fe(Hthpy)(thpy).CH3OH.3H2O (1) and Fe(Hmthpy)(mthpy).2H2O (2), are low-spin (LS) at room temperature and below, whereas their nonsolvated forms are high-spin (HS), exhibiting zero-field splitting. In these complexes, Hthpy, Hmthpy, and thpy, mthpy are the deprotonated forms of pyridoxal thiosemicarbazone and pyridoxal methylthiosemicarbazone, respectively; each is an O,N,S-tridentate ligand. The molecular structures have been determined at 100(1) K using single-crystal X-ray diffraction techniques and resulted in a triclinic system (space group P1) and monoclinic unit cell (space group P21/c) for 1 and 2, respectively. Structures were refined to the final error indices, where RF = 0.0560 for 1 and RF = 0.0522 for 2. The chemical inequivalence of the ligands was clearly established, for the "extra" hydrogen atom on the monodeprotonated ligands (Hthpy, Hmthpy) was found to be bound to the nitrogen of the pyridine ring. The ligands are all of the thiol form; the doubly deprotonated chelates (thpy, mthpy) have C-S bond lengths slightly longer than those of the singly deprotonated forms. There is a three-dimensional network of hydrogen bonds in both compounds. The discontinuous spin-state transformation is accompanied with liberation of solvate molecules. This is evidenced also from DSC analysis. Heat capacity data for the LS and HS phases are tabulated at selected temperatures, the values of the enthalpy and entropy changes connected with the change of spin state were reckoned at DeltaH = 12.5 0.3 kJ mol-1 and DeltaS = 33.3 0.8 J mol-1 K-1, respectively, for 1 and DeltaH = 6.5 0.3 kJ mol-1 and DeltaS = 17.6 0.8 J mol-1 K-1, respectively, for 2

Combined ultrasound and temperature sensor using a fibre Bragg grating

The feasibility of in-fiber Bragg gratings for simultaneous acoustic field and temperature sensing was demonstrated. A noise-limited pressure resolution of about 4.5×10-4 Atm/√Hz and a temperature resolution of 0.2 °C was achieved.