Download or read book Invariant Imbedding and Wave Propagation in Inhomogeneous Media written by Crawford J. MacCallum and published by . This book was released on 1961 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Wave Propagation written by N.D. Bellman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The SCQlldIII of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gu!ik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with . physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They· draw upon widely different sections of mathematics.
Download or read book Invariant Imbedding and Wave Propagation in Inhomgeneous Media written by Crawford J. MacCallum and published by . This book was released on 1961 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Application of Invariant Imbedding Techniques to Wave Propagation Through Turbulent Media written by and published by . This book was released on 1991 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On the Principle of Invariant Imbedding and Propagation Through Inhomogeneous Media written by Richard Bellman and published by . This book was released on 1956 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of the paper is to present a new technique for the study of propagation through inhomogeneous and random media, based upon an invariance principle which is called the 'principle of invariant imbedding.' As an application, consideration is given to the problem of the scattering of light by an inhomogeneous medium of finite depth. The corresponding problem for homogeneous media was treated by Ambarzumian and Chandrasekhar. (Author).
Download or read book Invariant Imbedding Techniques Used to Solve Wave Propagation in a Horizontally Stratified Plasma Media written by Hugh Alfred Davies and published by . This book was released on 1969 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Invariant Imbedding and Inverse Problems written by James P. Corones and published by SIAM. This book was released on 1992-01-01 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume on invariant imbedding and inverse problems is based on a conference held in Alberquerque, New Mexico, in April 1990.
Download or read book A Generalized Invariant Imbedding for Wave Propagation written by Isam Salim Ayoubi and published by . This book was released on 1983 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Wave Propagation and Turbulent Media written by Roy N. Adams and published by . This book was released on 1966 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Invariant Imbedding and Radiative Transfer in Slabs of Finite Thickness written by Richard Bellman and published by . This book was released on 1963 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book NBS Technical Note written by and published by . This book was released on 1965-04 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Wave Propagation in Complex Media written by George Papanicolaou and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: This IMA Volume in Mathematics and its Applications WAVE PROPAGATION IN COMPLEX MEDIA is based on the proceedings of two workshops: • Wavelets, multigrid and other fast algorithms (multipole, FFT) and their use in wave propagation and • Waves in random and other complex media. Both workshops were integral parts of the 1994-1995 IMA program on "Waves and Scattering." We would like to thank Gregory Beylkin, Robert Burridge, Ingrid Daubechies, Leonid Pastur, and George Papanicolaou for their excellent work as organizers of these meetings. We also take this opportunity to thank the National Science Foun dation (NSF), the Army Research Office (ARO, and the Office of Naval Research (ONR), whose financial support made these workshops possible. A vner Friedman Robert Gulliver v PREFACE During the last few years the numerical techniques for the solution of elliptic problems, in potential theory for example, have been drastically improved. Several so-called fast methods have been developed which re duce the required computing time many orders of magnitude over that of classical algorithms. The new methods include multigrid, fast Fourier transforms, multi pole methods and wavelet techniques. Wavelets have re cently been developed into a very useful tool in signal processing, the solu tion of integral equation, etc. Wavelet techniques should be quite useful in many wave propagation problems, especially in inhomogeneous and nonlin ear media where special features of the solution such as singularities might be tracked efficiently.
Download or read book Methods of Nonlinear Analysis written by Bellman and published by Academic Press. This book was released on 1973-05-25 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: Methods of Nonlinear Analysis
Download or read book Progress in Optics written by and published by Elsevier. This book was released on 1994-11-16 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains six review articles dealing with topics of current research interest in optics and in related fields. The first article deals with the so-called embedding method, which has found useful applications in the study of wave propagation in random media. The second article presents a review of an interesting class of non-linear optical phenomena which have their origin in the dependence of the complex dielectric constant of some media on the light intensity. These phenomena which include self-focusing, self-trapping and self-modulation have found many applications, for example in fibre optics devices, signal processing and computer technology. The next article is concerned with gap solitons which are electromagnetic field structures which can exist in nonlinear media that have periodic variation in their linear optical properties, with periodicities of the order of the wavelength of light. Both qualitative and quantitative descriptions of gap solitons are presented and some experimental schemes for their detection in the laboratory are discussed. The fourth article describes methods for the determination of optical phase from phase-modulated images. These methods have found applications in plasma diagnostics, in connection with flow characterisation and in the design of new optical instruments. The final article reviews developments relating to imaging, through turbulence in the atmosphere. It looks at the state-of-the-art of our understanding of this subject and discusses the most important methods that are presently employed to compensate for image distortion caused by atmospheric turbulence.
Download or read book Invariant Imbedding Wave Propagation and the Wkb Approximation written by Richard Bellman and published by . This book was released on 1957 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: In previous papers, some applications of the principle of invariant imbedding to radiative transfer and neutron diffusion processes were presented. This use of invariance principles was stimulated by the fundamental work of Ambarzumian and Chandrasekhar, and strongly influenced by the point of regeneration technique of Bellman and Harris, and the theory of dynamic programming. Fundamental for the success of these techniques as applied to the above processes is the ability to consider the overall physical process as a sequence of local processes. For the case of particles, this is easily done. This paper indicates how wave propagation may be considered in these terms. It is rather remarkable that the results are based upon an algorithm that, in general, can yield divergent series. Following a provocative paper by Bremmer, the air is to show that wave propagation can be discussed in terms of reflection and refraction at infinitesimally separated interfaces. It was proven that the convergence of the Bremmer series can be established under a simple assumption concerning the slowly varying nature of the local wave number.
Download or read book Invariant Imbedding written by R.E. Bellman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: Imbedding is a powerful and versatile tool for problem solving. Rather than treat a question in isolation, we view it as a member of a family of related problems. Each member then becomes a stepping stone in a path to a simultaneous solution of the entire set of problems. As might be expected, there are many ways of accomplishing this imbedding. Time and space variables have been widely employed in the past, while modern approaches combine these structural features with others less immediate. Why should one search for alternate imbeddings when elegant classical formalisms already exist? There are many reasons. To begin with, different imbeddings are useful for different purposes. Some are well suited to the derivation of existence and uniqueness theorems, some to the derivation of conservation relations, some to perturbation techniques and sensitivity analysis, some to computa tional studies. The digital computer is designed for initial value problems; the analog computer for boundary-value problems. It is essential then to be flexible and possess the ability to use one device or the other, or both. In economics, engineering, biology and physics, some pro cesses lend themselves more easily to one type of imbedding rather than another. Thus, for example, stochastic decision processes are well adapted to dynamic programming. In any case, to go hunting in the wilds of the scientific world armed with only one arrow in one's quiver is quite foolhardy.
Download or read book Wave Propagation in Random Media written by Joseph Bishop Keller and published by . This book was released on 1960 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt:
