Inverse backscattering in two dimensions

We interpretN=2 superconformal field theories (SCFTs) formulated by Kazama and Suzuki via Goddard-Kent-Olive (GKO) construction from a viewpoint of the Lie algebra cohomology theory for the affine Lie algebra. We determine the cohomology group completely in terms of a certain subset of the affine Weyl group. We find that this subset describing the cohomology group can be obtained from its classical counterpart by the action of the Dynkin diagram automorphisms. Some algebra automorphisms of theN=2 superconformal algebra are also formulated. Utilizing the algebra automorphisms, we study the field identification problem for the branching coefficient modules in the GKO-construction. Also the structure of the Poincaré polynomial defined for eachN=2 theory is revealed.Dedicated to Professor Noboru Tanaka on his sixtieth birthday     

Application of the inverse scattering problem method to stimulated Mandelstam-Brillouin backscattering of light

Stimulated Mandelstam-Brillouin backscattering of light is analyzed with the aid of the inverse scattering problem method. An asymptotic solution of this problem is obtained, as well as a solution for weak fields. It is shown that, just in the case of forward stimulated Mandelshtam-Brillouin scattering, the effective-interaction region, in which the intensity of the incident light wave is transferred to the scattered one, shifts towards the entrance face of the sample. It is also established that the asymptotic rate of decrease of the acoustic and scattered waves is independent of the rate of decrease of the initial distribution. The parameters characterizing the initial conditions are contained only in the pre-exponential terms.Translated from Preprint No. 173 of the Lebedev Physics Institute Academy of Sciences of the USSR, Moscow, 1988.     

The inverse problem in magnetopneumography

Summary The inverse problem in the magnetic measurement of the lung was studied with a method using hypothetical distributions of magnetic dust. Both unconstrained and constrained minimizations of an objective function were performed. Simulations and analysis showed the efficacy of the method. Paper presented at the ?IV International Workshop on Biomagnetism?, held in Rome, September 14–16, 1982.     

The inverse PMD problem

When a fiber is characterized by measured polarization mode dispersion (PMD) vector data, inversion of these data is required to determine the frequency dependence of the fibers Jones matrix and, thereby, its pulse response. We briefly review approaches to PMD inversion and discuss three second-order models used for this purpose. We report extension of inversion to fourth-order PMD using higher-order concatenation rules, rotations of higher power designating higher rates of acceleration with frequency, and representation of these rotations by Stokes vectors.     

The inverse problem in classical statistical mechanics

We address the problem of whether there exists an external potential corresponding to a given equilibrium single particle density of a classical system. Results are established for both the canonical and grand canonical distributions. It is shown that for essentially all systems without hard core interactions, there is a unique external potential which produces any given density. The external potential is shown to be a continuous function of the density and, in certain cases, it is shown to be differentiable. As a consequence of the differentiability of the inverse map (which is established without reference to the hard core structure in the grand canonical ensemble), we prove the existence of the Ornstein-Zernike direct correlation function. A set of necessary, but not sufficient conditions for the solution of the inverse problem in systems with hard core interactions is derived.Work partially supported by NSF grant PHY-8117463Work partially supported by NSF grant PHY-8116101 A01     

The inverse source problem in radiative transfer

We consider the problem of determining the intensity and interior sources within a plane-parallel half space if the intensity at the surface of the half space is known. Under the constraint that the intensity and sources in the deep interior are bounded in the proper sense by an exponential function, we show that the problem has at most one solution, which we formulate. The problem is shown to be ill-posed, since the solution involves the analytic continuation of the emerging intensity.     

The lattice Georgi-Glashow model in three dimensions

We find the phase diagram of the 3-DSU(2) lattice gauge-Higgs model with the scalar fields transforming as triplets underSU(2). The model is studied for several values of λ, the Higgs self-coupling. When λ is sufficiently small, the Higgs phase transition continues to new regions of the coupling constant space, due to the radial fluctuations.     

The inverse problem for diffusion equations

In the standard procedure one has to find the concentration from given initial (and boundary) conditions. We investigate here an inverse problem: to find the initial concentration from the known resulting concentration. This problem is of importance particularly for non-linear diffusion equations where the concentration dependenceD D(c) of the diffusion coefficient is analysed in terms of the Boltzmann-like solutionc f(xt^–1/2). This type of solution is, however, closely related to a very special initial condition for the concentration. The disregard of this fact might lead to misleading analysis ofD(c).     

Diffraction in three dimensions

Atmospheric Convection . By K. A. Emanuel. 1994, £47.50 (hbk), pp. x+580. Oxford, ISBN 0 19 506630 8. Scope: text. Level: postgraduate.

Automotive Sensors . By M. H. Westbrook and J. D. Turner. 1994, £75.00, US$149.00 (hbk), pp. xviii + 253. IOP, ISBN 0 7903 0293 3. Scope: monograph. Level: specialist.

Computation in Modem Physics . By W. R. Gibbs. 1994, £38.00 (hbk), pp. xvii + 348. World Scientific, ISBN 981 02 2044 8. Scope: text. Level: undergraduate and postgraduate.

Electron Correlations in Molecules and Solids , 2nd Edn. By P. Fulde. 1993, DM78.00 (pbk), pp. xiv + 422. Springer-Verlag, ISBN 3 540 56376 8. Scope: monograph. Level: postgraduate and specialist.

Field Theory, A Path Integral Approach . By A. Das. 1994, £48.00 (hbk), pp. xv + 399. World Scientific, ISBN 981 02 1396 4. Scope: lecture notes. Level: postgraduate.

Infrared Technology Fundamentals , 2nd Edn, revised and expanded. By M. Schlessinger. 1994, US$125.00 (hbk), pp. xii + 462. Dekker, ISBN 0 8247 9259 9. Scope: monograph. Level: postgraduate and specialist.

Oceanography and Acoustics . Edited by A. R. Robinson and D. Lee. 1994, US$65.00 (hbk), pp. xvii + 257. AIP, ISBN 1 56396 203 9. Scope: multi-author review. Level: postgraduate and specialist.

Optoelectronic Integration: Physics, Technology and Applications . Edited by O. Wada. 1994, Dfl. 275.00, US$130.00, £96.25 (hbk), pp. x + 458. Kluwer, ISBN 0 7923 9453 4. Scope: multi-author review. Level: postgraduate and specialist.

Photonic Devices and Systems . Edited by R. C. Hunsperger. 1994, US$135.00 (hbk), pp. xi + 426. Dekker, ISBN 0 8247 9243 2. Scope: multi-author review. Level: postgraduate and specialist.

Physics and Our View of the World . Edited by J. Hilgevoord. 1994, US$22.95 (pbk), pp. 304. Cambridge, ISBN 0 521 47680 1. Scope: multi-author review. Level: scientists and philosophers of science.

Polymer Physics . By U.W. Gedde. 1995, £49.00 (hbk), £24.99 (pbk), pp. x + 298. Chapman &; Hall, ISBN 0 412 62640. Scope: textbook. Level: undergraduate and postgraduate.

Quantization of Gauge Systems . By M. Henneaux and C. Teitelboim. 1994, US$29.95, £25.00 (pbk) pp. xxii + 520. Princeton, ISBN 0 691 03769 8. Scope: textbook. Level: postgraduate and specialist.

Semiconductor Raman Lasers . By K. Suto and J.-I. Nlshlzawa. 1994, £63.00 (hbk), pp. ix + 226. Artech, ISBN 0 89006 667 1. Scope: monograph. Level: specialist.

Shapes and Shells in Nuclear Structure . By S. G. Nilsson and I. Ragnarsson. 1995, £60.00, US$89.95 (hbk), pp. xiv + 408. Cambridge, ISBN 0 521 37377 8. Scope: textbook. Level: postgraduate.

Supersymmetric Gauge Field Theory and String Theory . By D. Bailin and A. Love. 1994, £80.00, US$160.00 (hbk), £27.50, US$49.00 (pbk), pp. xii + 332. IOP, ISBN 0 7503 0268 2. Scope: textbook. Level: postgraduate.

Short notices Advanced Series in Neuroscience , Vol. 3. Biology and Computation, A Physicist's Choice. Reprint volume. Edited by H. Gutfreund and G. Toulouse. 1994, £94.00 (hbk) pp. xv + 852. World Scientific, ISBN 981 02 1405 7. Scope: reprints. Level: postgraduate and specialist.

Electronic Structure of Refractory Carbides and Nitrides . Edited by V. A. Gubanov, A.L. Ivanovsky and V. P. Zhukov. 1994, $79.95 (hbk) pp. xiv + 256. Cambridge University Press, ISBN 0 521 41885 2. Scope: monograph. Level: postgraduate and specialist.

Fritz London: A Scientific Biography . By K. Gavroglu. 1995, £50.00 (hbk), pp. xxiv + 299. Cambridge University Press, ISBN 0 521 43273 1. Scope: biography. Level: general reader.

Gallium Arsenide and Related Compounds 1993 . Edited by H. S. Rupprecht and G. Weinmann. 1994, £115.00, US$230.00 (hbk), pp. xxiv + 842. IOP, ISBN 0 7503 0295 X. Scope: conference proceedings. Level: postgraduate and specialist.

Matvei Petrovich Bronstein and Soviet Physics in the Thirties . By G. E. Gorelik and V. Y. Frenkel. 1994, £65.00, DM 168.00. sFr. 148.00 (hbk), pp. 208. Birkhauser, ISBN 3 7643 2752 9. Scope: biography. Level: non-specialist.

Physical Chemistry . 5th edn. By P. W. Atkins. 1994, £24.00 (pbk), pp. xix + 1145. Oxford, ISBN 0 19 855730 2. Scope textbook. Level: undergraduate.

Polyominoes. Puzzles, Patterns, Problems, and Packings . Revised and expanded 2nd edn. By S.W. Golomb. 1994, US$24.95, £19.95 (hbk) pp. xii + 181. Princeton University Press, ISBN 0 691 08573 0. Scope: text. Level: non-specialist.

Supercollider 5 . Edited by P. Hale. 1994, US$195.00 (hbk), pp. xxviii + 970. Plenum, ISBN 0 306 44705 3. Scope: conference proceedings. Level: postgraduate and specialist.

World Scientific Series in 20th Century Physics , Vol. 5. Selected Papers of Abdus Salam (With Commentary). Edited by A. Ali, C. Isham, T. Kibble and Riazuddin. 1994, £64.00 (hbk) pp. xiv + 679. World Scientific, ISBN 981 02 1662 9. Scope: reprinted papers. Level: specialist.     

Radar equations in the radio wave backscattering problem

We present a method for finding the relation between the singly scattered signal and the Fourier spectrum of dielectric permittivity fluctuations of a medium with regard to the scattering volume which is controlled by the antenna pattern and is not small. Using this method, we found a radar equation which relates the temporal Fourier spectrum of the scattered signal and the spatio-temporal spectrum of permittivity fluctuations. We also obtained a statistical radar equation to relate the statistically averaged spectral power of the scattered signal and the spectral density of permittivity fluctuations without the conventional assumption that the spatial correlation radius of irregularities is small compared with the Fresnel radius. Institute of Solar-Terrestrial Physics, Siberian Branch of the Russian Academy of Sciences, Irkutsk, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 43, No. 6, pp. 520–544, June, 2000.     

The inverse problem of a laser amplifier

Starting from the recurrence relations of a multipass amplifier, an iterative computing method has been presented to solve the inverse problem of a laser amplifier, i.e., to find the initial fluence and pulse shape for a given output pulse and amplifier parameters. Numerical calculations have been performed to illustrate the results.     

The inverse problem of stationary covariance generation

The paper considers the problem of passing from a stationary covariance, or spectral matrix, associated with the output of a constant linear finite-dimensional system excited by white noise to the set of all possible systems of minimum possible dimension which will generate this covariance. The problem, originally posed by R. E. Kalman in 1965, is solved by identifying each possible system with the solution of a quadratic matrix inequality; an algorithm for the solution of the inequality is also presented.Work supported by the Australian Research Grants Committee. University of New castle Technical Report EE-6816.     

Dirac semimetal in three dimensions

We show that the pseudorelativistic physics of graphene near the Fermi level can be extended to three dimensional (3D) materials. Unlike in phase transitions from inversion symmetric topological to normal insulators, we show that particular space groups also allow 3D Dirac points as symmetry protected degeneracies. We provide criteria necessary to identify these groups and, as an example, present ab initio calculations of β-cristobalite BiO(2) which exhibits three Dirac points at the Fermi level. We find that β-cristobalite BiO(2) is metastable, so it can be physically realized as a 3D analog to graphene.     

Andreev reflection in three dimensions

正When an electron with negative charge-e is incident from a normal metal to an interface with a superconductor,it may be reflected as a hole with positive charge e at the interface.In such a way,a pair of electrons can be transferred to the superconductor and form a Cooper pair.This process of electron-hole conversion is called Andreev reflection(AR)[1].In two dimensions where the normal metal-superconductor junction is assumed to be along the x direction,     

Topological insulators in three dimensions

We study three-dimensional generalizations of the quantum spin Hall (QSH) effect. Unlike two dimensions, where a single Z2 topological invariant governs the effect, in three dimensions there are 4 invariants distinguishing 16 phases with two general classes: weak (WTI) and strong (STI) topological insulators. The WTI are like layered 2D QSH states, but are destroyed by disorder. The STI are robust and lead to novel "topological metal" surface states. We introduce a tight binding model which realizes the WTI and STI phases, and we discuss its relevance to real materials, including bismuth.