A unified description of classical and quantal scattering is presented. This description is unified both in the mathematical language and in the conceptual pictures that are used. Statistical states and observables, represented in phase space, are emphasized while both the time dependent trajectory and stationary state beam pictures are used. Semiclassical-type approximation schemes to the generalized differential cross section are presented for the single and double potential cases. Connection is made with the Born and distorted wave Born approximations, for both quantum and classical mechanics. A similar semiclassical-type approximation scheme for the double potential internal state kinetic cross section is presented. Connection is also made with the 'constant acceleration approximation' of Oppenheim and Bloom. Zwanzig's projection operator method is used to express the kinetic cross sections in terms of memory effects for the interacting observables. / Science, Faculty of / Chemistry, Department of / Graduate

Thesis (Ph.D.) -- University of Adelaide, Dept. of Applied Mathematics, 1983. / Typescript (photocopy).

Thesis (doctoral)--Rheinische Friedrich-Wilhelms-Universität Bonn, 1991. / Includes bibliographical references (p. 67-68).

Deng, Xiaomao. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 98-104). / Chapter 1 --- Introduction to Inverse Scattering Problems --- p.6 / Chapter 1.1 --- Direct Problems --- p.6 / Chapter 1.1.1 --- Far-field Patterns --- p.10 / Chapter 1.2 --- Inverse Problems --- p.16 / Chapter 1.2.1 --- Introduction --- p.16 / Chapter 2 --- Numerical Methods in Inverse Obstacle Scattering --- p.19 / Chapter 2.1 --- Linear Sampling Method --- p.19 / Chapter 2.1.1 --- History Review --- p.19 / Chapter 2.1.2 --- Numerical Scheme of LSM --- p.21 / Chapter 2.1.3 --- Theoretic Justification --- p.25 / Chapter 2.1.4 --- Summarize --- p.38 / Chapter 2.2 --- Point Source Method --- p.38 / Chapter 2.2.1 --- Historical Review --- p.38 / Chapter 2.2.2 --- Superposition of Plane Waves --- p.40 / Chapter 2.2.3 --- Approximation of Domains --- p.42 / Chapter 2.2.4 --- Algorithm --- p.44 / Chapter 2.2.5 --- Summarize --- p.49 / Chapter 2.3 --- Singular Source Method --- p.49 / Chapter 2.3.1 --- Historical Review --- p.49 / Chapter 2.3.2 --- Algorithm --- p.51 / Chapter 2.3.3 --- Far-field Data --- p.54 / Chapter 2.3.4 --- Summarize --- p.55 / Chapter 2.4 --- Probe Method --- p.57 / Chapter 2.4.1 --- Historical Review --- p.57 / Chapter 2.4.2 --- Needle --- p.58 / Chapter 2.4.3 --- Algorithm --- p.59 / Chapter 3 --- Numerical Experiments --- p.61 / Chapter 3.1 --- Discussions on Linear Sampling Method --- p.61 / Chapter 3.1.1 --- Regularization Strategy --- p.61 / Chapter 3.1.2 --- Cut off Value --- p.70 / Chapter 3.1.3 --- Far-field data --- p.76 / Chapter 3.2 --- Numerical Verification of PSM and SSM --- p.80 / Chapter 3.3 --- Inverse Medium Scattering --- p.83 / Bibliography --- p.98

The purpose of this work is to study the initial value problem for coherent pulse propagation (SIT) for zero area pulses. We employ the machinery of the newly developed mathematical technique of the inverse scattering method (ISM) to deduce general rules by which one can predict the kind of output pulses for a given input pulse impinging on a resonant attenuator. This study is relevant since the area theorem cannot provide unambiguous information about zero area pulses. Thus in effect we introduce an equivalent and more general formulation to the theorem in terms of the reflection coefficient, r(ν), of the ISM. The poles of r(ν) correspond to the steady state solitary pulses called solitons. We show that the threshold for soliton generation, including breathers, is for an absolute initial area of about π, a result consistent with the predictions of the area theorem. We solve an example of an input zero area profile. We also show that if the input pulse has an odd profile with respect to time, only breathers can be expected as solitons. We demonstrate that the conservation equations are of limited use when applied to zero area pulses. They give satisfactory results only in a limited region. We compare the predictions of the conservation equations to the predictions of the ISM, and come to the conclusion that for zero area pulses, the ISM is the only known satisfactory approach.

No description available.

In this thesis, we will address two most important topics in inverse acoustic and electromagnetic obstacle scattering problems: uniqueness and reconstruction algorithms. / The first part is devoted to the uniqueness issues. A detailed exposition of the background of this problem and a comprehensive discussion of the existing results are presented. The focus of this part is on our contribution to this field, especially on the unique determination of polygonal or polyhedral scatterers with a single or finitely many far-field measurements. In summary, we have shown the following results when the polyhedral type scatterers are concerned in inverse acoustic obstacle scattering: if the scatterer consists of finitely many solid polyhedral obstacles, which may be either sound-soft, sound-hard or two types mixed together, and it may also contain some crack-type obstacles but only sound-soft ones, then one can uniquely determine the scatterer by a single incident plane wave at some fixed k0 > 0 and d0 ∈ SN-1 . This statement is affirmatively verified in any dimensions whenever there is no any sound-hard obstacle present; when there is any sound-hard obstacle, the uniqueness is validated in the R2 case, but still incomplete in the RN case with N ≥ 3, which is proved to be true only by N different incident plane waves. Whenever the scatterer contains some sound-hard crack-type obstacles, we have constructed some examples to show that one cannot uniquely determine the scatterer by any less than N incident waves. So in the case with the additional presence of sound-hard crack-type obstacles, another result we have established that one can uniquely determine such a scatterer by N incident waves at any fixed wave number and arbitrary N linearly independent incident directions is optimal. We also consider more general polyhedral type scatterers with partially coated components, and some uniqueness results are established to determine the underlying physical properties. Besides, we have also collected a global uniqueness result for balls or discs. It is shown that in the resonance region, the shape of a sound-soft/sound-hard ball in R3 or a soundhard/sound-soft disc in R2 is uniquely determined by a single far-field datum measured at some fixed spot corresponding to a single incident plane wave. This seems to be an important result in the uniqueness study field as it is the first to establish the unique determination by a single far-field datum measured at one fixed spot. While all the other existing uniqueness results require far-field data observed at least in one open subset on the unit sphere with non-zero measure. To pave the way for the uniqueness study with such simple balls or discs, we also present a systematic and rather complete study of the interlacing character of the zeros for Bessel and spherical Bessel functions and their respective derivatives. Finally, all the uniqueness results for inverse acoustic obstacle scattering associated with general polyhedral scatterers have been extended to the inverse electromagnetic scattering. / The second part of this thesis is concerned with the reconstruction algorithms. We will present a novel multilevel linear sampling method (MLSM) which is developed in our recent work. The new method resembles the popular multi-level techniques in scientific computing and is shown to possess the asymptotically optimal computational complexity. For an n x n sampling mesh-grid in R2 or an n x n x n sampling mesh-grid in R3 , the proposed algorithm only requires to solve O (nN-1)( N = 2,3) far-field equations for a RN problem, and this is in sharp contrast to the original version of the linear sampling method which needs to solve n N far-field equations instead. Numerical experiments have illustrated the promising feature of the new algorithm in significantly reducing the computational costs. / Liu, Hongyu. / "June 2007." / Adviser: Jun Zou. / Source: Dissertation Abstracts International, Volume: 69-01, Section: B, page: 0354. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 161-168). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

Liu, Keji. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (p. 97-98). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Background and models of inverse scattering --- p.1 / Chapter 1.1 --- Model I --- p.1 / Chapter 1.2 --- Model II --- p.3 / Chapter 1.3 --- Model III --- p.3 / Chapter 2 --- Direct and Inverse Problems of Three Models --- p.6 / Chapter 2.1 --- First Model: Direct Problem --- p.6 / Chapter 2.2 --- First Model: Inverse Problem --- p.10 / Chapter 2.2.1 --- Linear Sampling Method --- p.10 / Chapter 2.2.2 --- Strengthened Linear Sampling Method --- p.12 / Chapter 2.2.3 --- Multilevel Linear Sampling Method --- p.15 / Chapter 2.3 --- Second Model: Direct Problem --- p.19 / Chapter 2.4 --- Second Model: Inverse Problem --- p.21 / Chapter 2.4.1 --- Contrast Source Inversion Method --- p.21 / Chapter 2.4.2 --- Subspace-based Optimization Method --- p.25 / Chapter 2.4.3 --- Multiple Signal Classification Method --- p.31 / Chapter 2.5 --- Third Model: Direct Problem --- p.33 / Chapter 2.6 --- Third Model: Inverse Problem --- p.41 / Chapter 2.6.1 --- Generalized Dual Space Indicator Method --- p.41 / Chapter 3 --- Numerical Simulations --- p.44 / Chapter 3.1 --- Numerical Simulations of First Model --- p.44 / Chapter 3.1.1 --- Linear Sampling Method --- p.44 / Chapter 3.1.2 --- Strengthened Linear Sampling Method --- p.51 / Chapter 3.1.3 --- Multilevel Linear Sampling Method --- p.58 / Chapter 3.2 --- Numerical Simulations of Second Model --- p.68 / Chapter 3.2.1 --- Contrast Source Inversion Method --- p.68 / Chapter 3.2.2 --- Subspace-based Optimization Method --- p.74 / Chapter 3.2.3 --- Twofold Subspace-based Optimization Method --- p.79 / Chapter 3.2.4 --- Multiple Signal Classification Method --- p.85 / Chapter 3.3 --- Numerical Simulations of Third Model --- p.85 / Chapter 3.3.1 --- Boundary Integral Method --- p.86 / Chapter 3.3.2 --- Generalized Dual Space Indicator Method --- p.89 / Chapter 4 --- Conclusion

Dai, Lipeng. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (p. 73-75). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.iv / Chapter 1 --- Introduction --- p.1 / Chapter 1.0.1 --- Linear sampling method --- p.2 / Chapter 1.0.2 --- choice of cut-off values --- p.5 / Chapter 1.0.3 --- Underwater image problem --- p.7 / Chapter 2 --- Mathematical justification of LSM --- p.10 / Chapter 2.1 --- Some mathematical preparations --- p.11 / Chapter 2.2 --- Well-posedness of an interior transmission problem --- p.13 / Chapter 2.3 --- Linear sampling method: full aperture --- p.20 / Chapter 2.4 --- Linear sampling method: limited aperture --- p.23 / Chapter 3 --- Strengthened linear sampling method --- p.28 / Chapter 3.1 --- Proof of theorem 1.0.3 --- p.28 / Chapter 3.2 --- Several estimates in theory for strengthened LSM --- p.33 / Chapter 4 --- Underwater imaging problem --- p.38 / Chapter 4.1 --- Boundary integral method --- p.38 / Chapter 4.2 --- Approximation of the Integral Kernel in (4.12) --- p.40 / Chapter 4.3 --- Numerical solution of (4.12) --- p.44 / Chapter 4.4 --- Underwater image problem --- p.45 / Chapter 4.5 --- Imaging scheme without a reference object --- p.48 / Chapter 4.6 --- Numerical examples without a reference object --- p.49 / Chapter 4.7 --- Imaging scheme with a reference object --- p.59 / Chapter 4.8 --- Numerical examples with a reference object --- p.61

Typescript (photocopy) / vii, 192 leaves : ill. ; 30 cm / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Applied Mathematics, 1983