An analytic solution to the transient diffusion-reaction problem in particles dispersed in a slurry reactor

In this work, we present the solution of the equations that govern the reactant transport in a well mixed system that contains particles where diffusion and first-order reaction occur. The transport equations are coupled by an interfacial boundary condition that includes mass transfer resistance. The statement of the problem allows arbitrary time depending feed functions. The evaluation of the solution obtained by the Laplace method requires the solution of an eigenvalue problem. We discuss the evaluation of the solution, and typical results for three different feed functions: step, pulse and oscillatory functions are presented. The resulting equations are able to show the effect of internal and external mass transfer limitations on the particle and fluid concentrations and on kinetic experimental results.     

An analytical model for freeboard and in-bed limestone sulfation in fluidized-bed coal combustors

A new model, which combines in-bed and freeboard sulfation, significantly improves the ability to predict sulfur capture by limestone sorbents in fluidized-bed coal combustors. In this model, the in-bed hydrodynamics are described in terms of a bubble phase and an emulsion phase while the freeboard region has only a diluted emulsion phase. The solids, which are in the emulsion phases, are considered to be completely back-mixed; the gaseous bubble phase travels in plug-flow but exchanges with the emulsion phase. The sulfation reaction occurs principally in the emulsion phase and the reaction rate is a direct function of the sulfur dioxide concentration, the extent of the calcium oxide conversion (as measured by a thermogravimetric analyzer), and the amount of limestone present in the bed and in the freeboard. The amount present, or holdup, in the free-board is calculated from empirical correlations for elutriation and from particle-time trajectories as predicted from equations of motion.The model indicates that a significant amount of sulfur capture can occur in the freeboard region, especially with high superficial gas velocities and small particle sizes, both of which lead to increased freeboard holdup. For an overall sulfur retention of 90%, approximately 9% of the sulfur is predicted to be captured within the freeboard above a combustor bed 1.8 m by 1.8 m by 1.2 m high of 1200 μm diameter limestone particles that are fluidized at 2.4 m/s. The model also predicts that the sulfur captured by the entrained particles is negligible. These predictions compare favorably with the actual sulfur retentions experienced in similar sized pilot-scale combustors.     

Wave-front recovery from two orthogonal sheared interferograms

We present a new technique for using the information of two orthogonal lateral-shear interferograms to estimate an aspheric wave front. The wave-front estimation from sheared inteferometric data may be considered an ill-posed problem in the sense of Hadamard. We apply Thikonov regularization theory to estimate the wave front that has produced the lateral sheared interferograms as the minimizer of a positive definite-quadratic cost functional. The introduction of the regularization term permits one to find a well-defined and stable solution to the inverse shearing problem over the wave-front aperture as well as to reduce wave-front noise as desired.     

Practical control studies of batch reactors using realistic mathematical models

Most of the optimal control studies of batch chemical reactors have assumed simple, ideal systems where heat removal can be changed instantaneously between zero and some maximum rate. These systems are of low order, usually second, so elegant variational mathematics can be employed to compute optimal time-temperature trajectories.This paper reports results of studies of more realistic systems in which the dynamics of the cooling and heating systems are not neglected, giving systems of much higher order (7th–10th). Reversible and consecutive exothermic reactions are considered. A variety of practical heat removal systems are studied. Reactor performance is found to be reasonably insensitive to some of the practical departures from ideality, but quite sensitive to others.     

An accurate and efficient bayesian method for automatic segmentation of brain MRI

Automatic three-dimensional (3-D) segmentation of the brain from magnetic resonance (MR) scans is a challenging problem that has received an enormous amount of attention lately. Of the techniques reported in the literature, very few are fully automatic. In this paper, we present an efficient and accurate, fully automatic 3-D segmentation procedure for brain MR scans. It has several salient features; namely, the following. 1) Instead of a single multiplicative bias field that affects all tissue intensities, separate parametric smooth models are used for the intensity of each class. 2) A brain atlas is used in conjunction with a robust registration procedure to find a nonrigid transformation that maps the standard brain to the specimen to be segmented. This transformation is then used to: segment the brain from nonbrain tissue; compute prior probabilities for each class at each voxel location and find an appropriate automatic initialization. 3) Finally, a novel algorithm is presented which is a variant of the expectation-maximization procedure, that incorporates a fast and accurate way to find optimal segmentations, given the intensity models along with the spatial coherence assumption. Experimental results with both synthetic and real data are included, as well as comparisons of the performance of our algorithm with that of other published methods.     

Regularization methods for processing fringe-pattern images

A powerful technique for processing fringe-pattern images is based on Bayesian estimation theory with prior Markov random-field models. In this approach the solution of a processing problem is characterized as the minimizer of a cost function with terms that specify that the solution should be compatible with the available observations and terms that impose certain (prior) constraints on the solution. We show that, by the appropriate choice of these terms, one can use this approach in almost every processing step for accurate and robust interferogram demodulation and phase unwrapping.     

Piecewise smooth models for electromagnetic inverse problems

This paper presents a new method for constructing one-dimensional (1D) electrical conductivity models of the Earth from surface electromagnetic measurements. The construction of these models is a nonlinear inverse problem that can be approached by linearization techniques combined with iterative methods and Tikhonov's regularization. The standard application of these techniques usually leads to smooth models that represent a continuous variation of conductivity with depth. In this work, the authors describe how these methods can be modified to incorporate what is known in computer vision as the line process (LP) decoupling technique, which has the ability to include discontinuities in the models. This results in piecewise smooth models that are often more adequate for representing stratified media. They have implemented a relaxation technique to construct these types of models and present numerical experiments as well as an application to field data. These examples illustrate the performance of the combined LP and Tikhonov's regularization method     

The reliability of apical x-ray pictures in the diagnosis of mandibular bone lesions. A review of the literature and in-vitro study

Using 6 macerated human anatomical preparations of mandibular jaw regions with either front teeth or premolars and molars, the radiological detectability of artificial periapical bone lesions was evaluated in relation to the size of the lesions and to the angle of x-ray projection. The artificial lesions were enlarged stepwise until distinct radiological visibility was attained. For each step of enlargement, x-ray pictures were taken with orthoradial as well as with at 25 degrees mesially and distally excentered projections. All x-ray pictures were evaluated by 6 dentists. The following results were obtained: The size of a periapical bone lesion, at which it is becoming radiologically detectable, varies between the different regions of the lower jaw. Isolated spongiosa lesions being larger than 3 mm in diameter are most often detectable at mandibular front teeth and premolars. Isolated spongiosa lesions at mandibular molars are generally non-detectable. Atypical lesions, e.g. discontinuities of bony structures are particularly difficult to detect radiologically. There were no statistically significant differences in lesion detectability between x-rays of different angle projections.     

Demodulation of a single interferogram by use of a two-dimensional regularized phase-tracking technique

We present a two-dimensional regularized phase-tracking technique that is capable of demodulating a single fringe pattern with either open or closed fringes. The proposed regularized phase-tracking system gives the detected phase continuously so that no further unwrapping is needed over the detected phase.     

Piecewise continuous models for resistivity soundings

A robust method is presented for constructing layered Earth models from surface resistivity data. The algorithm automatically accommodates any number of discontinuities without the need to specify a priori its number or location in the vertical profile. It further includes automatic correction factors for the common segmentation of Schlumberger soundings due to static shift effects