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Über dieses Buch

This research monograph presents a systematic treatment of the theory of the propagation of transient electromagnetic fields (such as optical pulses) through dielectric media which exhibit both dispersion a.nd absorption. The work divides naturally into two parts. Part I presents a summary of the fundamental theory of the radiation and propagation of rather general electromagnetic waves in causal, linear media which are homogeneous and isotropic but which otherwise have rather general dispersive and absorbing properties. In Part II, we specialize to the propagation of a plane, transient electromagnetic field in a homogeneous dielectric. Although we have made some contributions to the fundamental theory given in Part I, most of the results of our own research appear in Part II. The purpose of the theory presented in Part II is to predict and to explain in explicit detail the dynamics of the field after it has propagated far enough through the medium to be in the mature-dispersion regime. It is the subject of a classic theory, based on the research conducted by A. Sommerfeld and L.

Inhaltsverzeichnis

Frontmatter

Introduction

Abstract
Recently a new direction of investigation has developed in the theory and practice of studying heat exchange processes as well as in the thermal design and simulation of thermal conditions of engineering systems. It is based on principles of inverse heat transfer problems. These methods have received special attention in the experimental study of nonstationary heat transfer processes, associated with reentry of space vehicles, rocket launchers, different heat engines, the determination of thermophysical properties of materials, construction and correction of mathematical heat models of engineering systems and in a number of other cases.
Oleg M. Alifanov

Chapter 1. Statements and Use of Inverse Problems in Studying Heat Transfer Processes and Designing Engineering Units

Abstract
Many structures employed in various branches of engineering operate under conditions of strong, often extreme, thermal effects. The general tendency has been the extensive use of heat-loaded engineering objects and the high intensity of heat regimes. At the same time it has been necessary to increase the reliability and service life of goods, whilst reducing the specific consumption of materials. Investigating the processes of heat transfer and providing acceptable heat conditions also occupy an important place in the design and development of production methods related to the heating and cooling of materials as, for example, in continuous steel casting or the different techniques of metal thermal treatment, in glassmaking, foundry work, high-temperature crystal growing out of melt, etc. The non-stationary state and non-linearity (considerable, at times) of heat transfer phenomena can be referred to as the special features of heat conditions of modern heat-loaded structures and production methods. These considerably reduce the possibility of using many traditional design-and-theoretical and experimental methods. So it became necessary to develop new approaches to thermophysical and heat engineering studies. Amongst them are methods based on a solution of inverse problems, in which it is required, by measurements of the system or process state, to specify one or several characteristics causing this state (in other words, to find not causal-sequential, as in direct problems, but rather sequential-causal quantitative relations).
Oleg M. Alifanov

Chapter 2. Analysis of Statements and Solution Methods for Inverse Heat Transfer Problems

Abstract
The effective application of methods based on solving the inverse problems in thermal simulation and in processing the results of thermal tests is determined by the depth of the mathematics required connected with the statement and algorithmic presentation of the problems, by clarifying the specific difficulties in their solution. Misunderstanding of the nature of problems that are poorly based can lead to errors in problem solving. Even in cases when a proper method is used its effective application and specific features of the problem may not be fully realized. Such negligence of the formulation of problems of a given class as well as the methods of their solving can lead to doubt as to the suitability of the very concept of inverse problems for practical research. Experience shows that it is only through understanding the physical, technical and mathematical principles of a given problem that one finds it possible to use inverse problem methods effectively and creatively in thermal research.
Oleg M. Alifanov

Chapter 3. Analytical Forms of Boundary Inverse Heat Conduction Problems

Abstract
This chapter treats the problem statements on specification of transient heat loads, the concept of which involves integral representations of inverse heat conduction problems. To stabilize solutions obtained later in integral forms, one can employ different principles. A method of step regularization is suggested for this purpose in Chap. 4. Some other methods of stability damping are outlined in Chaps. 6 and 7, the integral statements described herein being suitable for them as well.
Oleg M. Alifanov

Chapter 4. Direct Algebraic Method of Determining Transient Heat Loads

Abstract
Data processing methods for transient heat experiments, based on solution of integral forms of IHCPs in the boundary-value statement, are the most widely used techniques at present [1,2, 3, 6,12, 70, 72,150,151,158,159,162,175,192,200,203]. A number of algorithms for solving virtually one and the same inverse problems have been developed. In this connection, it is necessary to formulate some general criteria for a comparative analysis of algorithms of the given type, especially, as in most cases they are created on approximately equal principles of numerical solution using a step regularization principle.
Oleg M. Alifanov

Chapter 5. Solution of Boundary Inverse Heat Conduction Problems by Direct Numerical Methods

Abstract
In studying high-temperature processes of special interest are boundary IHCP in non-linear statements, when thermophysical properties of the body are dependent upon temperature. In particular, for many metals the effects of temperature-dependent thermal conductivity and specific heat must be allowed for at T ≥ 600 ÷ 800°C. The general approach to the solution of non-linear inverse problems uses numerical methods.
Oleg M. Alifanov

Chapter 6. The Extremal Formulations and Methods of Solving Inverse Heat Conduction Problems

Abstract
One of the more promising directions in solving inverse heat conduction problems is to reduce them to extremal formulations and apply numerical methods of the optimization theory. Two cases are thereby possible:
1.
a solution is scragftt-iirthe~~space of parameters;
 
2.
the task is solved in the functional space.
 
Oleg M. Alifanov

Chapter 7. Regularization of Variational Forms of Inverse Heat Conduction Problems

Abstract
As was pointed out in Chap. 2, one of the most general methods used in ill-posed problem solving is the Tikhonov regularization method. At present it has been developed into a broad mathematical direction. This has resulted in a rigorous branched theory which covers a whole number of regular methods within general Tikhonov concept of regularization. The most complete results have been obtained for the major form of this method which is known as variational principle of regularization. This principle with its subsequent algorithms has been quite widely applied in practice for solving various inverse problems, including IHCP. The first study in this field was made by Tikhonov and Glasko (see Ref. * on p. 7), where the authors considered a solution of boundary IHCP on determination of the surface temperature of a semi-infinite body. Next followed the studies of Alifanov [4, 7,17], in which the author elaborated and investigated regularizing algorithms for solving various linear IHCP, mainly for one-dimensional formulations. The expansion of a regularization method onto a solution of non-linear boundary IHCP has been attempted by Alifanov [10,12] and Alifanov and Artyukhin [21,22].
Oleg M. Alifanov

Chapter 8. Iterative Regularization of Inverse Problems

Abstract
The algorithms constructed in Chaps. 4–7 are used for the solution of boundary IHCPs. Lately, the area of practical applications of methodology, based on inverse heat-transfer problems, has expanded considerably, which necessitated solving other types of inverse problems as well. As conducted investigations show, iterative regularization (Chap. 6) appears to be one of the most efficient and universal approaches for the construction of stable algorithms for solving ill-posed problems. With this method algorithms convenient for practical utilization can be obtained for the solution of inverse heat-transfer problems in various formulations (linear and non-linear, one-dimensional and multi-dimensional), in domains with fixed and travelling boundaries, with minimal necessary composition of initial data and overdefinition. Also, the rigorous mathematical proof of this method for a wide class of inverse problems and modernizations of iterative algorithm to account for qualitative and quantitative a priori information about an unknown solution are found.
Oleg M. Alifanov

Conclusions

Abstract
The methods based on solving inverse heat transfer problems provide an opportunity to devise general and universal approaches for identification of thermal processes in various fields of science and technology, to make thermophysical investigations more reliable and informative while designing and testing technical objects and to carr out efficient heat diagnostics on the machinery and on the equipment in operation.
Oleg M. Alifanov

Backmatter

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