Some theorems of the eddy-current theory

Contents In the paper, theorems for the electric vector potentialT and magnetic scalar potentialU are discussed, which occur in the boundary-value problems for eddy currents induced in a conducting block by an external magnetic field. Uniqueness of the solution is examined. An integral representation of the scalar potentialU is derived for a nonmagnetic conductor. It is shown that for a thin metallic shell the integrodifferential equation results from general formulas related to the block.

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Einige Theoreme der Wirbelstromtheorie

Übersicht In der Arbeit werden drei Theoreme für das elektrische VektorpotentialT und das magnetische SkalarpotentialU beschrieben, die in den Randwertaufgaben für in einem metallischen Block durch das äußere magnetische Feld induzierte Wirbelströme auftreten. Es wird bewiesen, daß eine solche Randwertaufgabe eine eindeutige Lösung hat, wenn das Vektorpotential auf dem Rand gleich Null ist. Eine Integralrepräsentation des Skalarpotentials wird abgeleitet. Es wird gezeigt, daß die Integrodifferentialgleichung für eine dünne metallische Hülle aus allgemeinen, den Block betreffenden Formeln hervorgeht.

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List of principal symbols e coordinate unit vector - H magnetic intensity - J current density - T electric vector potential - U magnetic scalar potential - permeability - conductivity - V boundary of regionV     

Residual encoder-decoder up-sampling for structural preservation in noise removal

Multimedia Tools and Applications - While denoising 3D MRI, structural preservation is a very critical process in the medical region. However, Rician noise in MRI has affected the image quality...     

Analysis and simulation of the grinding process. Part II: Mechanics of grinding

This paper is the second of three parts which describe the analysis and simulation of the grinding process. Generation of the workpiece surface depends on the interactions between the grains of the wheel and the workpiece. The grinding wheel surface generated by dressing was simulated by the method described in Part I. This part describes a method to investigate the process of grinding by simulating the cutting action of every grain which engages with the workpiece. Grinding forces are analysed by simulating the force on each grain which passes a section of the workpiece. The simulated workpiece surface shows features which are similar in nature to the experimental results. A more extensive comparison of simulated and experimental grinding behaviour is presented in Part III.     

Korrosion von ölgefeuerten Zentralheizungskesseln

Corrosion of oil-fired domestic boilers Depending on the surface temperature of the flue gas side the corrosion of oil fired domestic boilers proceeds either mainly by acid corrosion or by oxygen corrosion:

• – At surface temperatures of 60°C and higher the corrosion mechanism of acid corrosion prevails and the corrosion rates amount to 0.1–0.3 mm/year (values referred to continuous burner operation). The corrosion products consist of soluble iron(II)- and iron(III)sulfates. Higher corrosion rates can be attributed to an appreciable catalytic formation of sulfur trioxide on the corrosion products formed on the convective heating surfaces.
• – At surface temperatures of 40°C the mechanism of oxygen corrosion already dominates and the corrosion rates are about ten times higher (1.5–3 mm/year, referred to continous burner operation). The high portion of ioron oxide hydrates, especially goethit (α-FeOOH), makes the corrosion products difficult to remove.
• – Distinctly reduced service lives are also expected for the so called reduced temperature boilers (“Niedertemperaturkessel”) and low temperature boiers (“Tieftemperaturkessel”): According to the manufacturers these boilers may be operated at boiler water temperatures well below 60°C, as they are equipped with constructive measures to enhance the surface temperature on the flue gas side. However, these measures are only fully effective under stationary conditions.

Some of the results were obtained from weight loss measurements on test specimen made from St 35.8 and gray cast iron, that were exposed to the flue gases of an oil fired experimental boiler. Other important results come from field measurements of the sulfuric acid content of about 30 boilers that are in practical use.     

A prototype scanning stylus profilometer for rapid measurement of small surface areas

A novel stylus based profiling instrument has been developed for rapid measurement of small surface areas. Outlined in the following paper are some of the key features of the prototype system including the wideband stylus pick-up and the dedicated scanning traverse mechanism. In addition, some preliminary results obtained by scanning the instrument over several different surfaces are presented.     

Two computational regimes of a single-compartment neuron separated by a planar boundary in conductance space

Recent in vitro data show that neurons respond to input variance with varying sensitivities. Here we demonstrate that Hodgkin-Huxley (HH) neurons can operate in two computational regimes: one that is more sensitive to input variance (differentiating) and one that is less sensitive (integrating). A boundary plane in the 3D conductance space separates these two regimes. For a reduced HH model, this plane can be derived analytically from the V nullcline, thus suggesting a means of relating biophysical parameters to neural computation by analyzing the neuron's dynamical system.     

Addressing agent loss in vehicle formations and sensor networks

In this paper, we address the problem of agent loss in vehicle formations and sensor networks via two separate approaches: (1) perform a ‘self‐repair’ operation in the event of agent loss to recover desirable information architecture properties or (2) introduce robustness into the information architecture a priori such that agent loss does not destroy desirable properties. We model the information architecture as a graph G(V, E), where V is a set of vertices representing the agents and E is a set of edges representing information flow amongst the agents. We focus on two properties of the graph called rigidity and global rigidity, which are required for formation shape maintenance and sensor network self‐localization, respectively. For the self‐repair approach, we show that while previous results permit local repair involving only neighbours of the lost agent, the repair cannot always be implemented using only local information. We present new results that can be applied to make the local repair using only local information. We describe implementation and illustrate with algorithms and examples. For the robustness approach, we investigate the structure of graphs with the property that rigidity or global rigidity is preserved after removing any single vertex (we call the property as 2‐vertex‐rigidity or 2‐vertex‐global‐rigidity, respectively). Information architectures with such properties would allow formation shape maintenance or self‐localization to be performed even in the event of agent failure. We review a characterization of a class of 2‐vertex‐rigidity and develop a separate class, making significant strides towards a complete characterization. We also present a characterization of a class of 2‐vertex‐global‐rigidity. Copyright © 2008 John Wiley & Sons, Ltd.     

On finite dynamic equations for fluid-saturated porous media

Summary The paper concerns the relations between two principally different approaches to the formulation of momentum balance equations in porous media theories, namely, the dynamic approach similar to Biot's theory and the modern approach as a result of mixture theories extended by the concept of volume fractions. In particular, it is shown that both approaches necessarily lead to the same type of momentum balance equations and furthermore contain, in a certain sense, within the geometrically linear case, the well-known classical equations of Biot's theory.     

Electromagnetic field diffusion, θ-functions,and image solutions

Contents We discuss some initial and boundary value problems of one-dimensional electromagnetic field diffusion. The solutions can be given by infinite series in two essentially different (however equivalent) forms, one being the usual Fourier-expansion and the other one being an infinite series of Gaussian exponentials or related functions (as for instance error-functions). The second form can be obtained by using infinitely many images to fulfill initial and boundary conditions. Finally the mathematical relations between the two equivalent types of solutions are discussed in terms of -functions and their transformation properties. The existence of the solutions in these two different forms is very interesting from a numerical point of view also.

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Die Diffusion elektromagnetischer Felder, -Funktionen und Spiegelungsmethoden

Übersicht Es werden einige Anfangs- und Randwertprobleme eindimensionaler elektromagnetischer Felddiffusion erörtert. Die Lösungen können in zwei wesentlich verschiedenen (jedoch gleichwertigen) Formen angegeben werden, erstens in Form üblicher Fourier-Reihen und zweitens in Form unendlicher Reihen von Gaußschen Exponentialfunktionen oder damit verwandter Funktionen (z.B. Fehlerfunktionen). Diese zweite Form der Lösungen läßt sich durch die Anwendung unendlich oft wiederholter Spiegelung zur Erfüllung der Rand- und Anfangsbedingung anschaulich interpretieren. Abschließend werden die beiden Lösungstypen mit Hilfe von -Funktionen und deren Transformationseigenschaften erläutert. Die Verfügbarkeit der Lösungen in beiden Formen ist auch numerisch sehr interessant.

     

An Automated Brain Image Analysis System for Brain Cancer using Shearlets

In this paper, an Automated Brain Image Analysis (ABIA) system that classifies the Magnetic Resonance Imaging (MRI) of human brain is presented. The classification of MRI images into normal or low grade or high grade plays a vital role for the early diagnosis. The Non-Subsampled Shearlet Transform (NSST) that captures more visual information than conventional wavelet transforms is employed for feature extraction. As the feature space of NSST is very high, a statistical t-test is applied to select the dominant directional sub-bands at each level of NSST decomposition based on sub-band energies. A combination of features that includes Gray Level Co-occurrence Matrix (GLCM) based features, Histograms of Positive Shearlet Coefficients (HPSC), and Histograms of Negative Shearlet Coefficients (HNSC) are estimated. The combined feature set is utilized in the classification phase where a hybrid approach is designed with three classifiers; k-Nearest Neighbor (kNN), Naive Bayes (NB) and Support Vector Machine (SVM) classifiers. The output of individual trained classifiers for a testing input is hybridized to take a final decision. The quantitative results of ABIA system on Repository of Molecular Brain Neoplasia Data (REMBRANDT) database show the overall improved performance in comparison with a single classifier model with accuracy of 99% for normal/abnormal classification and 98% for low and high risk classification.