Recent developments in value distribution theory for Schrödinger operators on the half line

The measurement of quality in auditorium acoustics by subjective scaling methods—A review of developments in theory and practice

In this paper a review of the recent developments in the theory of a slowly oscillating low aspect ratio, pointed wing at sonic speed is presented, using the concepts of the parabolic method, the equivalence rule and a iteration method to approximately incorporate the thickness effect in the analysis.

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTComments upon Recent Developments in Theory of FiltrationB. F. Ruth, R. E. Montonna, and G. H. MontillonCite this: Ind. Eng. Chem. 1931, 23, 7, 850–851Publication Date (Print):July 1, 1931Publication History Published online1 May 2002Published inissue 1 July 1931https://doi.org/10.1021/ie50259a036RIGHTS & PERMISSIONSArticle Views57Altmetric-Citations3LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (326 KB) Get e-Alerts

Theories of generation of acoustic and magnetohydrodynamic waves are briefly reviewed with a special emphasis on their applicability to stellar convection zones. Recent developments in these theories and possible directions for future studies are discussed. A new approach allowing to extend the Lighthill-Proudman theory of sound generation to a non-isothermal medium is also presented.

We solve the focusing and defocusing nonlinear Schrödinger (NLS) equations numerically by implementing the inverse scattering transform. The computation of the scattering data and of the NLS solution are both spectrally convergent. Initial conditions in a suitable space are treated. Using the approach of Biondini & Bui, we numerically solve homogeneous Robin boundary-value problems on the half line. Finally, using recent theoretical developments in the numerical approximation of Riemann–Hilbert problems, we prove that, under mild assumptions, our method of approximating solutions to the NLS equations is uniformly accurate in their domain of definition.

Reviews - Selected papers of Abraham Robinson. Volume 1. Model theory and algebra. Edited and with an introduction by H. J. Keisler. Yale University Press, New Haven and London1979, xxxvii + 694 pp. - George B. Selioman. Biography of Abraham Robinson, pp. xiii–xxxii. - H. J. Keisler. Introduction, pp. xxxiii–xxxvii. - Abraham Robinson. On the application of symbolic logic to algebra, pp. 3–11. A reprint of XVIII 182. - Abraham Robinson. Recent developments in model theory, pp. 12–31. A reprint of XL 269. - Abraham Robinson. On the construction of models, pp. 32–42. A reprint of XL 506. - Abraham Robinson, Metamathematical problems, pp. 43–59. (Reprinted from The journal of symbolic logic, vol. 38 (1973), pp. 500–516.) - Abraham Robinson. Model theory as a framework for algebra, pp. 60–83. (Reprinted from Studies in model theory, edited by M. D. Morley, Studies in mathematics, vol. 8, The Mathematical Association of America, Washington, D.C., 1973, pp. 134–157.) - Abraham Robinson. A result on consistency and its application to the theory of definition, pp. 87–98. A reprint of XXV 174. - Abraham Robinson. Ordered structures and related concepts, pp. 99–104. A reprint of XXV 170. - Volume 47 Issue 1

Density functional theory (DFT) and multiple scattering theory (MST) have been used extensively for calculations in condensed matter physics of the electronic structure of materials built from atomic species throughout the periodic table. As originally formulated for the muffin-tin model, MST in general gave disappointing results in applications to molecules, which discouraged use of this methodology. Recent developments in so-called ‘full-potential’ MST have removed these muffin-tin constraints while retaining the computational efficiency associated with these methods. Full-potential MST is reviewed here, with emphasis on the theoretical basis of computational methods that are viable for molecules. Several recent developments in the formalism of DFT are reviewed, in particular reference-state DFT, which frees the theory from the constraint that the electronic density in the variational model state must be identical to that of the true ground state, and places DFT in the context of the Fermi liquid theory of Landau. The theory of self-interaction corrections is reexamined from this point of view.

3R29. Theory of Porous Media: Highlights in Historical Development and Current State. - R de Boer (Inst fur Mechanik, Univ Essen, Fachbereich 10 Bauwesen, Essen, D-45117, Germany). Springer-Verlag, Berlin. 2000. 618 pp. ISBN 3-540-65982-X. $95.00. Reviewed by N Katsube (Dept of Mech Eng, Ohio State Univ, 206 W 18th Ave, Columbus, OH 43210).This book consists of historical and recent development of porous material theory, can be used as a reference book in this area. In the early and classical era, general development of continuum mechanics such as Cauchy's formulation of the stress concept, the development of linear elasticity theory, and the foundation of thermodynamics are summarized. At the end of each chapter, biographical notes of the important contributors are outlined. There the readers could learn about the lives of these prominent researchers, including their characters, and the nature of scholarly debates. The readers can also learn about how the lives of these researchers were influenced by the historical events, and how failure in one event had led to success in another. In the modern era, the emphasis is placed on the porous materials. The historical review includes the controversy between Fillunger and von Terzaghi and the subsequent development of the theory by Biot and others. Further development of elasticity and plasticity theories and a more modern framework of continuum mechanics and mixture theory are also discussed. The current state of porous material theory reflects the author's work as well as the related work developed mostly in Europe. It is based on the assumption that the deformation gradient of the constituent can be separated into the part due to the real material and the part due to the change of the pores in size and shape through a multiplicative decomposition process. In developing constitutive theories, the principle of material objectivity as well as entropy inequality is employed. An extensive development of a porous material theory is presented based on these theoretical frameworks.Theory of Porous Media: Highlights in Historical Development and Current State is a great book to have if you would like to know about the historical development of porous material theory since many of the letters and articles written by the researchers in early days are not available in English. In addition, if you would like to follow the recent development of porous material theory, which is consistent with the above stated assumptions, this book will provide an extensive review. However, the reader should be aware that this is not the only approach available in the area of porous materials. There are a number of different approaches available for the development of constitutive behavior of porous materials. These other approaches are more phenomenologically based and often motivated by experimental observations. The developed models are verified by experimental data and used to solve important practical problems.

<p><span>We experimentally investigated the internal dynamics of stationary mono- and bidisperse granular avalanches in an inclined conveyor belt flume. We used the refractive index matching technique to visualize and obtain information from within the granular bulk. In combination with particle tracking velocimetry and coarse-graining techniques, we were able to calculate continuum particle distributions and velocity fields. The experimental avalanches had distinct flow regions: (i) a convective-bulged front, (ii) a compact-layered tail, and (iii) a breaking size segregation wave structure, serving as a transition between the former two. To describe the dynamics of these regions, we computed local strain rates in the form of its tensor invariants. The invariants varied notably between regions; while the largest values and non-linear distributions were found at the front, linear distributions were observed in the tail. In general, and although that slip was considerable at the base of the flow, time-averaged velocity profiles were found to be well captured by a Bagnold model. Based on recent developments in particle-size segregation theory, we calculated the segregation flux within the bidisperse avalanches. In those experiments, we found that segregation flux was higher at the front than at the back, a fact that was confirmed by the observed recirculation of large particles at the front. All our experimental data show a strong link between rheology and segregation, a result that will provide grounding for new developments in segregation theory.</span></p>

A report of recent events in both theoretical and experimental aspects of double beta decay is given. General theoretical considerations, recent developments in nuclear structure theory, geochronological determinations of half lives and ratios as well as laboratory experiments are discussed with emphasis on the past three years. Some projections are given.KeywordsMatrix ElementMajorana NeutrinoNeutrino Mass MatrixHeavy NeutrinoShell Model CalculationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The public and researchers in psychology and the social sciences are largely unaware of the huge resources invested in metrology and standards in science and commerce, for understandable reasons, but with unfortunate consequences. Measurement quality varies widely in fields lacking uniform standards, making it impossible to coordinate local behaviours and decisions in tune with individually observed instrument readings. However, recent developments in reading measurement have effectively instituted metrological traceability methods within elementary and secondary English and Spanish language reading education in the U.S., Canada, Mexico, and Australia. Given established patterns in the history of science, it may be reasonable to expect that widespread routine reproduction of controlled effects expressed in uniform units in the social sciences may lead to significant developments in theory and practice.

Over the last decades, the development of algorithms and tools for the safety verification of hybrid systems has been content of intensive research. Numerous novel ideas have been presented and implemented in different tools. Whereas the majority of these tools offer fixed implementations, only few general libraries have been provided for the development of new verification tools.HyPro is such an example, providing a C++ programming library for the implementation of certain types of reachability analysis algorithms for linear hybrid systems. These algorithms, based on flowpipe construction, need geometric or symbolic representation for state sets of hybrid systems. HyPro offers datatypes for different representations, conversions between them, and efficient algorithms based on these datatypes.Since its release in 2017, HyPro's functionalities have been extended by several implementations. In this paper we give a general introduction to flowpipe-construction-based methods and report on HyPro's functional advances as well as on applications of the library.

Rapid progress is continuing to be made in the field of ferro-electric polymers. The last few years have seen detailed structural determinations of PVF2 and its copolymers, convincing evidence for Curie transitions, and development of theories that successfully predict the observed ferroelectric behavior. In the field of processing, manufacture of mm-thick polarized PVF2 sheet has been achieved, and a continuous method for simultaneous orientation and poling of PVF2 film and tube has been developed. New piezoelectric polymers have been under study, some of these showing ferroelectric hysteresis. Among applications, ultrasonic transducers in the form of hydrophones, sonar arrays, and focussed medical sensors are attracting wide current attention, while imaginative new uses for these polymers are under continuing investigation.

The present review concerns the relevance of collisionless reconnection in the astrophysical context. Emphasis is put on recent developments in theory obtained from collisionless numerical simulations in two and three dimensions. It is stressed that magnetic reconnection is a universal process of particular importance under collisionless conditions, when both collisional and anomalous dissipation are irrelevant. While collisional (resistive) reconnection is a slow, diffusive process, collisionless reconnection is spontaneous. On any astrophysical time scale, it is explosive. It sets on when electric current widths become comparable to the leptonic inertial length in the so-called lepton (electron/positron) “diffusion region”, where leptons de-magnetise. Here, the magnetic field contacts its oppositely directed partner and annihilates. Spontaneous reconnection breaks the original magnetic symmetry, violently releases the stored free energy of the electric current, and causes plasma heating and particle acceleration. Ultimately, the released energy is provided by mechanical motion of either the two colliding magnetised plasmas that generate the current sheet or the internal turbulence cascading down to lepton-scale current filaments. Spontaneous reconnection in such extended current sheets that separate two colliding plasmas results in the generation of many reconnection sites (tearing modes) distributed over the current surface, each consisting of lepton exhausts and jets which are separated by plasmoids. Volume-filling factors of reconnection sites are estimated to be as large as $${<}10^{-5}$$ per current sheet. Lepton currents inside exhausts may be strong enough to excite Buneman and, for large thermal pressure anisotropy, also Weibel instabilities. They bifurcate and break off into many small-scale current filaments and magnetic flux ropes exhibiting turbulent magnetic power spectra of very flat power-law shape $$W_b\propto k^{-\alpha }$$ in wavenumber k with power becoming as low as $$\alpha \approx 2$$ . Spontaneous reconnection generates small-scale turbulence. Imposed external turbulence tends to temporarily increase the reconnection rate. Reconnecting ultra-relativistic current sheets decay into large numbers of magnetic flux ropes composed of chains of plasmoids and lepton exhausts. They form highly structured current surfaces, “current carpets”. By including synchrotron radiation losses, one favours tearing-mode reconnection over the drift-kink deformation of the current sheet. Lepton acceleration occurs in the reconnection-electric field in multiple encounters with the exhausts and plasmoids. This is a Fermi-like process. It results in power-law tails on the lepton energy distribution. This effect becomes pronounced in ultra-relativistic reconnection where it yields extremely hard lepton power-law energy spectra approaching $$F(\gamma )\propto \gamma ^{-1}$$ , with $$\gamma $$ the lepton energy. The synchrotron radiation limit becomes substantially exceeded. Relativistic reconnection is a probable generator of current and magnetic turbulence, and a mechanism that produces high-energy radiation. It is also identified as the ultimate dissipation mechanism of the mechanical energy in collisionless magnetohydrodynamic turbulent cascades via lepton-inertial-scale turbulent current filaments. In this case, the volume-filling factor is large. Magnetic turbulence causes strong plasma heating of the entire turbulent volume and violent acceleration via spontaneous lepton-scale reconnection. This may lead to high-energy particle populations filling the whole volume. In this case, it causes non-thermal radiation spectra that span the entire interval from radio waves to gamma rays.

Numerical implementation of the reconstruction formulae of Nakamura and Tanuma [Recent Development in Theories and Numerics, International Conference on Inverse Problems 2003] is presented. With the formulae, the conductivity and its normal derivative can be recovered on the boundary of a planar domain from the localized Dirichlet to Neumann map. Such reconstruction method is needed as a preliminary step before full reconstruction of conductivity inside the domain from boundary measurements, as done in electrical impedance tomography. Properties of the method are illustrated with reconstructions from simulated data.