Nondispersing Bohr Wave Packets
Long-lived, nondispersing circular, or Bohr, wave packets are produced starting from Li Rydberg atoms by exposing them first to a linearly polarized microwave field at the orbital frequency, 17.6 GHz at principal quantum number n=72, which locks the electron's motion into an approximately linear orbit in which the electron oscillates in phase with the microwave field. The microwave polarization is changed to circular polarization slowly compared to the orbital frequency, and the electron's motion follows, resulting in a nondispersing Bohr wave packet
Willden, Jeff
2001-01-01
"Bohr's Atomic Model" is a small interactive multimedia program that introduces the viewer to a simplified model of the atom. This interactive simulation lets students build an atom using an atomic construction set. The underlying design methodology for "Bohr's Atomic Model" is model-centered instruction, which means the central model of the…
This report is organized around the contribution of A. Pais, 'Niels Bohr and the development of physics', presented at CERN on the occasion of a special colloquium in the honour of Niels Bohr. It gives a broad survey of Bohr's life, the revolution in physics created by his quantum theory and his attempts to influence the peaceful development of nuclear energy. (orig.)
Bellac, Michel Le
2014-11-01
The final form of quantum physics, in the particular case of wave mechanics, was established in the years 1925-1927 by Heisenberg, Schrödinger, Born and others, but the synthesis was the work of Bohr who gave an epistemological interpretation of all the technicalities built up over those years; this interpretation will be examined briefly in Chapter 10. Although Einstein acknowledged the success of quantum mechanics in atomic, molecular and solid state physics, he disagreed deeply with Bohr's interpretation. For many years, he tried to find flaws in the formulation of quantum theory as it had been more or less accepted by a large majority of physicists, but his objections were brushed away by Bohr. However, in an article published in 1935 with Podolsky and Rosen, universally known under the acronym EPR, Einstein thought he had identified a difficulty in the by then standard interpretation. Bohr's obscure, and in part beyond the point, answer showed that Einstein had hit a sensitive target. Nevertheless, until 1964, the so-called Bohr-Einstein debate stayed uniquely on a philosophical level, and it was actually forgotten by most physicists, as the few of them aware of it thought it had no practical implication. In 1964, the Northern Irish physicist John Bell realized that the assumptions contained in the EPR article could be tested experimentally. These assumptions led to inequalities, the Bell inequalities, which were in contradiction with quantum mechanical predictions: as we shall see later on, it is extremely likely that the assumptions of the EPR article are not consistent with experiment, which, on the contrary, vindicates the predictions of quantum physics. In Section 3.2, the origin of Bell's inequalities will be explained with an intuitive example, then they will be compared with the predictions of quantum theory in Section 3.3, and finally their experimental status will be reviewed in Section 3.4. The debate between Bohr and Einstein goes much beyond a
Heilbron, J. L.
1981-03-01
Bohr used to introduce his attempts to explain clearly the principles of the quantum theory of the atom with an historical sketch, beginning invariably with the nuclear model proposed by Rutherford. That was sound pedagogy but bad history. The Rutherford-Bohr atom stands in the middle of a line of work initiated by J.J. Thomson and concluded by the invention of quantum mechanics. Thompson's program derived its inspiration from the peculiar emphasis on models characteristic of British physics of the 19th century. Rutherford's atom was a late product of the goals and conceptions of Victorian science. Bohr's modifications, although ultimately fatal to Thomson's program, initially gave further impetus to it. In the early 1920s the most promising approach to an adequate theory of the atom appeared to be the literal and detailed elaboration of the classical mechanics of multiply periodic orbits. The approach succeeded, demonstrating in an unexpected way the force of an argument often advanced by Thomson: because a mechanical model is richer in implications than the considerations for which it was advanced, it can suggest new directions of research that may lead to important discoveries.
Bohr's way to defining complementarity
De Gregorio, Alberto
2012-01-01
We go through Bohr's talk about complementary features of quantum theory at the Volta Conference in September 1927, by collating a manuscript that Bohr wrote in Como with the unpublished stenographic report of his talk. We conclude - also with the help of some unpublished letters - that Bohr gave a very concise speech in September. The formulation of his ideas became fully developed only between the fifth Solvay Conference, in Brussels in October, and early 1928. The unpublished stenographic ...
Reconsidering Bohr's reply to EPR
Halvorson, Hans; Clifton, Rob
2001-01-01
Although Bohr's reply to the EPR argument is supposed to be a watershed moment in the development of his philosophy of quantum theory, it is difficult to find a clear statement of the reply's philosophical point. Moreover, some have claimed that the point is simply that Bohr is a radical positivist. In this paper, we show that such claims are unfounded. In particular, we give a mathematically rigorous reconstruction of Bohr's reply to the \\emph{original} EPR argument that clarifies its logica...
Reconsidering Bohr's reply to EPR
Halvorson, H; Halvorson, Hans; Clifton, Rob
2001-01-01
Although Bohr's reply to the EPR argument is supposed to be a watershed moment in the development of his philosophy of quantum theory, it is difficult to find a clear statement of the reply's philosophical point. Moreover, some have claimed that the point is simply that Bohr is a radical positivist. In this paper, we show that such claims are unfounded. In particular, we give a mathematically rigorous reconstruction of Bohr's reply to the \\emph{original} EPR argument that clarifies its logical structure, and which shows that it does not rest on questionable philosophical assumptions. Rather, Bohr's reply is dictated by his commitment to provide "classical" and "objective" descriptions of experimental phenomena.
This paper combines algebraic and Lagrangian geometry to construct a special basis in every space of conformal blocks, the Bohr-Sommerfeld (BS) basis. We use the method of Borthwick-Paul-Uribe, in which every vector of a BS basis is determined by some half-weight Legendrian distribution coming from a Bohr-Sommerfeld fibre of a real polarization of the underlying symplectic manifold. The advantage of BS bases (compared to the bases of theta functions) is that we can use the powerful methods of asymptotic analysis of quantum states. This shows that Bohr-Sommerfeld bases are quasiclassically unitary. Thus we can apply these bases to compare the Hitchin connection and the KZ connection defined by the monodromy of the Knizhnik-Zamolodchikov equation in the combinatorial theory
A Simple Relativistic Bohr Atom
Terzis, Andreas F.
2008-01-01
A simple concise relativistic modification of the standard Bohr model for hydrogen-like atoms with circular orbits is presented. As the derivation requires basic knowledge of classical and relativistic mechanics, it can be taught in standard courses in modern physics and introductory quantum mechanics. In addition, it can be shown in a class that…
Gravitational Bohr's model with Newton's and Weber's potentials
Tiandho, Yuant; Triyanta
2015-09-01
Similarity between Newtonian gravitational force and Coulomb's force leads one to define gravitational electric and magnetic fields or gravito-electromagnetic fields. Also, one may define a gravitational Bohr's theory in analogy with the electromagnetic Bohr's theory for which the latter is quite successful in explaining some properties of hydrogen atom. Unlike to the Coulomb's force, the Newton`s force is believed to be an approximated theory of gravity as it is unable to explain the Mercury's orbit. This paper discusses the gravitational Bohr's theory by taking into account the Newton's potential and Weber's potential; the later is a modified Newton's gravitational potential that conforms, to some degrees, to the anomaly of the Mercury's orbit.
Solutions of the Bohr hamiltonian, a compendium
Fortunato, L
2004-01-01
The Bohr hamiltonian, also called collective hamiltonian, is one of the cornerstone of nuclear physics and a wealth of solutions (analytic or approximated) of the associated eigenvalue equation have been proposed over more than half a century (confining ourselves to the quadrupole degree of freedom). Each particular solution is associated with a peculiar form for the $V(\\beta,\\gamma)$ potential. The large number and the different details of the mathematical derivation of these solutions, as well as their increased and renewed importance for nuclear structure and spectroscopy, demand a thorough discussion. It is the aim of the present monograph to present in detail all the known solutions in $\\gamma-$unstable and $\\gamma-$stable cases, in a taxonomic and didactical way. In pursuing this task we especially stressed the mathematical side leaving the discussion of the physics to already published comprehensive material. The paper contains also a new approximate solution for the linear potential, and a new solutio...
Bohr's Principle of Complementarity and Beyond
Jones, R.
2004-05-01
All knowledge is of an approximate character and always will be (Russell, Human Knowledge, 1948, pg 497,507). The laws of nature are not unique (Smolin, Three Roads to Quantum Gravity, 2001, pg 195). There may be a number of different sets of equations which describe our data just as well as the present known laws do (Mitchell, Machine Learning, 1997, pg 65-66 and Cooper, Machine Learning, Vol. 9, 1992, pg 319) In the future every field of intellectual study will possess multiple theories of its domain and scientific work and engineering will be performed based on the ensemble predictions of ALL of these. In some cases the theories may be quite divergent, differing greatly one from the other. The idea can be considered an extension of Bohr's notions of complementarity, "...different experimental arrangements.. described by different physical concepts...together and only together exhaust the definable information we can obtain about the object" (Folse, The Philosophy of Niels Bohr, 1985, pg 238). This idea is not postmodernism. Witchdoctor's theories will not form a part of medical science. Objective data, not human opinion, will decide which theories we use and how we weight their predictions.
Corda, Christian [Dipartimento di Fisica e Chimica, Istituto Universitario di Ricerca Scientifica ' Santa Rita' , Centro di Scienze Naturali, Via di Galceti, 74, 59100 Prato (Italy); Institute for Theoretical Physics and Advanced Mathematics (IFM) Einstein-Galilei, Via Santa Gonda 14, 59100 Prato (Italy); International Institute for Applicable Mathematics and Information Sciences (IIAMIS), B.M. Birla Science Centre, Adarsh Nagar, Hyderabad - 500 463 (India)
2015-03-10
The idea that black holes (BHs) result in highly excited states representing both the “hydrogen atom” and the “quasi-thermal emission” in quantum gravity is today an intuitive but general conviction. In this paper it will be shown that such an intuitive picture is more than a picture. In fact, we will discuss a model of quantum BH somewhat similar to the historical semi-classical model of the structure of a hydrogen atom introduced by Bohr in 1913. The model is completely consistent with existing results in the literature, starting from the celebrated result of Bekenstein on the area quantization.
Bohr vs. Einstein: Fortolkning af kvantemekanikken
Andersen, Christian Kraglund; Wade, Andrew Christopher James
2013-01-01
Siden 1913, da Bohr fremlagde sin kvantemekaniske model for atomet, har fysikere diskuteret, hvordan kvan- temekanikken skal fortolkes. Specielt aktive i denne diskussion var Bohr og Einstein, som havde modstridende opfattelser af, hvordan kvantemekanikken skulle forstås. Kan katte være både...... levende og døde på samme tid? Kan vi teleportere partikler mellem Månen og Jorden? Disse spørgsmål, og mange flere, forsøgte Bohr og Einstein at besvare, og det vil vi ligeledes i denne artikel....
Camilleri, Kristian
2015-01-01
Niels Bohr's doctrine of the primacy of "classical concepts" is arguably his most criticized and misunderstood view. We present a new, careful historical analysis that makes clear that Bohr's doctrine was primarily an epistemological thesis, derived from his understanding of the functional role of experiment. A hitherto largely overlooked disagreement between Bohr and Heisenberg about the movability of the "cut" between measuring apparatus and observed quantum system supports the view that, for Bohr, such a cut did not originate in dynamical (ontological) considerations, but rather in functional (epistemological) considerations. As such, both the motivation and the target of Bohr's doctrine of classical concepts are of a fundamentally different nature than what is understood as the dynamical problem of the quantum-to-classical transition. Our analysis suggests that, contrary to claims often found in the literature, Bohr's doctrine is not, and cannot be, at odds with proposed solutions to the dynamical problem...
Bohr's double-slit experiment - once again
In recent years there has been an upsurge in the discussion of so-called ''delayed-choice'' experiments, as exemplified in the interferometer experiment discussed by Wheeler. In commenting on this experiment Bohm et al. claim that their quantum potential ''interpretation gives results entirely compatible while Bohr's view on wholeness and complementarity''. It seems to me, however, that this discussion to a large extent completely misses the fundamental point in Bohr's argumentation as given in his famour answer to Einstein, Podolsky and Rosen as well as in his paper on his discussions with Einstein. Expressing it a bit paradoxically one might say that in the examples discussed the experiments are not ''sufficiently delayed''. I shall therefore here discuss a different thought experiment, much closer to Bohr's own examples, which brings out this point. (orig.)
Considerations on Bohr's, Heisenberg's and Schroedinger's philosophy
In denying that the words 'physical reality' are meaningful without reference to an experimental arrangement, Bohr renounces any knowledge of the 'thing-in-itself'. However, the relation of his epistemology to both idealism and positivism remains obscure. Heisenberg departs from Bohr in enunciating a metaphysical implication of quantum mechanics. Heisenberg asserts that there is an intermediate modality -potentiality- between logical possibility and existence. His attempts to explain the transition from potentiality to existence are not convincing. Schroedinger rejects Bohr's interpretation of quantum mechanics as a positivist exercise and seeks instead a realist interpretation. Nevertheless, the metaphysics of Schroedinger is fundamentally idealistic, maintaining that the material aspect of the world is composed of the same elements as mind, but in a different order
What classicality? Decoherence and Bohr's classical concepts
Schlosshauer, Maximilian
2010-01-01
Niels Bohr famously insisted on the indispensability of what he termed "classical concepts." In the context of the decoherence program, on the other hand, it has become fashionable to talk about the "dynamical emergence of classicality" from the quantum formalism alone. Does this mean that decoherence challenges Bohr's dictum and signifies a break with the Copenhagen interpretation-for example, that classical concepts do not need to be assumed but can be derived? In this paper we'll try to shine some light down the murky waters where formalism and philosophy cohabitate. To begin, we'll clarify the notion of classicality in the decoherence description. We'll then discuss Bohr's and Heisenberg's take on the quantum-classical problem and reflect on different meanings of the terms "classicality" and "classical concepts" in the writings of Bohr and his followers. This analysis will allow us to put forward some tentative suggestions for how we may better understand the relation between decoherence-induced classical...
Niels Bohr - his life and scientific achievements
Niels Bohr, a Nobel laureate and a celebrated scientist of the 20th century is remembered for his lasting contributions to atomic and nuclear physics. His pioneering works on Energy loss by charged particles, the structure of the atom, the compound nucleus model and the mechanism of nuclear fission are indeed remarkable. In this article a brief account of his life and scientific achievements is provided. (author)
Spreading the gospel: The Bohr atom popularised
Kragh, Helge
2011-01-01
The emergence of quantum theory in the early decades of the twentieth century was accompanied by a wide range of popular science books, all of which presented in words and in images new scientific ideas about the structure of the atom. The work of physicists such as Ernest Rutherford and Niels Bohr, among others, was pivotal to the so-called planetary model of the atom, which, still today, is used in popular accounts and in science textbooks. In an attempt to add to our knowledge about the popular trajectory of the new atomic physics, this paper examines one book in particular, coauthored by Danish science writer Helge Holst and Dutch physicist and close collaborator of Niels Bohr, Hendrik A. Kramers. Translated from Danish into four European languages, the book not only presented contemporary ideas about the quantum atom, but also went into rather lengthy discussions about unresolved problems. Moreover, the book was quite explicit in identifying the quantum atom with the atom as described by Bohr's theory. W...
The Bohr-Sommerfeld atom theory. Sommerfeld's extension of Bohr's atomic model 1915/16
In December 6th 1915 and January 8th 1916 Arnold Sommerfeld put the Bavarian Academy of Sciences two treatises in the amount of 75 printed pages before, by which he extended Bohr's atomic model from the year 1913 to the Bohr-Sommerfeld atom theory. In Sommerfeld's collected works only the publication submitted 1916 by Sommerfeld in the Annals of Physics about this is found.''My spectral lines are finally printed in the Academy to the impure. In the Annals they will appear in purer form'', so Sommerfeld has announced in this publication in February 10th 1916 to the editor of the Annals of Physics. From the science-historical view however for the extension of Bohr's atom theory just the Academy-treatises published before the purification process are of special interest. To the reproduction of these Academy-treatises an extensive physics-historical essay is prepended.
Epistemological Dimensions in Niels Bohr's Conceptualization of Complementarity
Derry, Gregory
2008-03-01
Contemporary explications of quantum theory are uniformly ahistorical in their accounts of complementarity. Such accounts typically present complementarity as a physical principle that prohibits simultaneous measurements of certain dynamical quantities or behaviors, attributing this principle to Niels Bohr. This conceptualization of complementarity, however, is virtually devoid of content and is only marginally related to Bohr's actual writing on the topic. Instead, what Bohr presented was a subtle and complex epistemological argument in which complementarity is a shorthand way to refer to an inclusive framework for the logical analysis of ideas. The important point to notice, historically, is that Bohr's work involving complementarity is not intended to be an improvement or addition to a particular physical theory (quantum mechanics), which Bohr regarded as already complete. Bohr's work involving complementarity is actually an argument related to the goals, meaning, and limitations of physical theory itself, grounded in deep epistemological considerations stemming from the fundamental discontinuity of nature on a microscopic scale.
Complementarity: a study of Bohr's philosophy of quantum physics
A comprehensive interpretation is given of Bohr's philosophy of quantum physics based upon a close examination of his writings. Extensive use is made of unpublished documents in the Niels Bohr Archive. The evolution of Bohr's attempts to resolve the paradox of wave-particle duality, which culminated in his thesis of complementarity in 1927, is reconstructed from published and unpublished sources. The meaning and significance of the complementarity thesis is examined in the light of the detailed arguments which Bohr proposed to support it. Two main sorts of complementarity are distinguished: wave-particle complementarity, and position-momentum complementarity. Bohr's theory of measurement is reconstructed and compared with some formal theories, none of which is found to represent Bohr's theory adequately. (author)
Address at the opening session of the Niels Bohr Symposium
In his address at the opening session of the Niels Bohr Symposium organized jointly by UNESCO and the Niels Bohr Institute in Copenhagen in May 1998 in order to examine the latest developments in key fields of physics, the Director General of UNESCO presented the scientific work and the spirit of Niels Bohr, emphasizing the impact of his discoveries for new openings in science and in society in general
Niels Bohr and Complementarity An Introduction
Plotnitsky, Arkady
2012-01-01
This book offers a discussion of Niels Bohr’s conception of “complementarity,” arguably his greatest contribution to physics and philosophy. By tracing Bohr’s work from his 1913 atomic theory to the introduction and then refinement of the idea of complementarity, and by explicating different meanings of “complementarity” in Bohr and the relationships between it and Bohr’s other concepts, the book aims to offer a contained and accessible, and yet sufficiently comprehensive account of Bohr’s work on complementarity and its significance.
Bohr Inequality for Multiple Op erators
LIAN Tie-yan; TANG Wei
2016-01-01
An absolute value equation is established for linear combinations of two operators. When the parameters take special values, the parallelogram law of operator type is given. In addition, the operator equation in literature [3] and its equivalent deformation are obtained. Based on the equivalent deformation of the operator equation and using the properties of conjugate number as well as the operator, an absolute value identity of multiple operators is given by means of mathematical induction. As Corollaries, Bohr inequalities are extended to multiple operators and some related inequalities are reduced to, such as inequalities in [2] and [3].
Bohr's Creation of his Quantum Atom
Heilbron, John
2013-04-01
Fresh letters throw new light on the content and state of Bohr's mind before and during his creation of the quantum atom. His mental furniture then included the atomic models of the English school, the quantum puzzles of Continental theorists, and the results of his own studies of the electron theory of metals. It also included the poetry of Goethe, plays of Ibsen and Shakespeare, novels of Dickens, and rhapsodies of Kierkegaard and Carlyle. The mind that held these diverse ingredients together oscillated between enthusiasm and dejection during the year in which Bohr took up the problem of atomic structure. He spent most of that year in England, which separated him for extended periods from his close-knit family and friends. Correspondence with his fianc'ee, Margrethe Nørlund, soon to be published, reports his ups and downs as he adjusted to J.J. Thomson, Ernest Rutherford, the English language, and the uneven course of his work. In helping to smooth out his moods, Margrethe played an important and perhaps an enabling role in his creative process.
Bohr Hamiltonian with Hulth?en plus Ring shaped potential for triaxial nuclei
Chabab, M; Oulne, M
2015-01-01
In this paper, we solve the eigenvalues and eigenvectors problem with Bohr collective Hamil- tonian for triaxial nuclei. The ? beta part of the collective potential is taken to be equal to Hulth?en potential while the gamma part is de?ned by a new generalized potential obtained from a ring shaped one. Analytical expressions for spectra and wave functions are derived by means of a recent version of the asymptotic iteration method and the usual approximations. The calculated energies and B(E2) transition rates are compared with experimental data and the available theoretical results in the literature.
Comment on breakdown of Bohr's Correspondence Principle by Bo Gao, In
Tannous, C
2001-01-01
Gao applied LeRoy and Bernstein semi-classical analysis for the energy levels in a potential of the form -C/r^n to sequences of scaled energy differences progressing towards low lying states and found a better agreement with the semi-classical prediction. We checked that for the energy levels obtained by Stwalley et al. with the same potential, the agreement with the semi-classical approximation is better for higher vibrational quantum numbers in agreement with Bohr's correspondence principle.
Bohr Hamiltonian with Hulthen plus ring-shaped potential for triaxial nuclei
In this paper, we solve the eigenvalues and eigenvectors problem with the Bohr collective Hamiltonian for triaxial nuclei. The β-part of the collective potential is taken to be equal to the Hulthen potential while the γ-part is defined by a new generalized potential obtained from a ring-shaped one. Analytical expressions for spectra and wave functions are derived by means of a recent version of the asymptotic iteration method and the usual approximations. The calculated energies and B(E2) transition rates are compared with experimental data and the available theoretical results in the literature. (orig.)
When champions meet: Rethinking the Bohr--Einstein debate
Landsman, N P
2005-01-01
Einstein's philosophy of physics (as clarified by Fine and Howard) was predicated on his Trennungsprinzip, a combination of separability and locality, without which he believed "physical thought" and "physical laws" to be impossible. Bohr's philosophy (as elucidated by Hooker, Scheibe, Folse, Howard, and others), on the other hand, was grounded in a seemingly different doctrine about the possibility of objective knowledge, namely the necessity of classical concepts. In fact, it follows from Raggio's Theorem in algebraic quantum theory that within a suitable class of physical theories Einstein's doctrine is mathematically equivalent to Bohr's, so that quantum mechanics accommodates Einstein's Trennungsprinzip if and only if it is interpreted a la Bohr through classical physics. Unfortunately, the protagonists themselves failed to discuss their differences in a constructive way, since in its early phase their debate was blurred by an undue emphasis on the uncertainty relations, whereas in its second stage it wa...
Constitution and model. The quantum theory of Bohr and imagining the atom
Hon, Giora; Goldstein, Bernard R.
2014-01-01
The quantum theory of Bohr has roots in the theories of Rutherford and J. J. Thomson on the one hand, and that of Nicholson on the other. We note that Bohr neither presented the theories of Rutherford and Thomson faithfully, nor did he refer to the theory of Nicholson in its own terms. The contrasting attitudes towards these antecedent theories is telling and reveals the philosophical disposition of Bohr. We argue that Bohr intentionally avoided the concept of model as inappropriate for descr...
Bohr--Sommerfeld Lagrangians of moduli spaces of Higgs bundles
Biswas, Indranil; Gammelgaard, Niels Leth; Logares, Marina
Let $X$ be a compact connected Riemann surface of genus at least two. Let $M_H(r,d)$ denote the moduli space of semistable Higgs bundles on $X$ of rank $r$ and degree $d$. We prove that the compact complex Bohr-Sommerfeld Lagrangians of $M_H(r,d)$ are precisely the irreducible components of the n...
Cranking Bohr Mottelson Hamiltonian applied to rotational bands
Cranking Bohr Mottelson Hamiltonian is applied to rotational bands of well deformed nuclei. The derived formula for the rotational spectrum shows explicitly the coupling between the rotational and vibrational motions. Applications of the formula to the ground state rotational bands of well deformed even-even nuclei are presented with encouraging results
Bohr's Relational Holism and the classical-quantum Interaction
Dorato, Mauro
2016-01-01
In this paper I present and critically discuss the main strategies that Bohr used and could have used to fend off the charge that his interpretation does not provide a clear-cut distinction between the classical and the quantum domain. In particular, in the first part of the paper I reassess the main arguments used by Bohr to advocate the indispensability of a classical framework to refer to quantum phenomena. In this respect, by using a distinction coming from an apparently unrelated philosophical corner, we could say that Bohr is not a revisionist philosopher of physics but rather a descriptivist one in the sense of Strawson. I will then go on discussing the nature of the holistic link between classical measurement apparatuses and observed system that he also advocated. The oft-repeated conclusion that Bohr's interpretation of the quantum formalism is untenable can only be established by giving his arguments as much force as possible, which is what I will try to do in the following by remaining as faithful ...
The Bohr-Heisenberg correspondence principle viewed from phase space
Dahl, Jens Peder
Phase-space representations play an increasingly important role in several branches of physics. Here, we review the author's studies of the Bohr-Heisenberg correspondence principle within the Weyl-Wigner phase-space representation. The analysis leads to refined correspondence rules that can be...
Gjedde, Albert
2004-01-01
-to-back in the 1910 volume of Skandinavisches Archiv für Physiologie. The Devils unjustifiably sealed the fate of Christian Bohr's theory of active cellular participation in the transport of oxygen from the lungs to the pulmonary circulation. The author's renewed examination of the original papers of Bohr...... and the Kroghs reveals that Bohr's concept of active cellular participation in diffusion is entirely compatible with the mechanism of capillary recruitment, for the discovery of which Krogh was later awarded Nobel's Prize, years after Bohr's untimely and unexpected death in 1911. Udgivelsesdato: 2004-null...
Exactly separable version of the Bohr Hamiltonian with the Davidson potential
Bonatsos, Dennis; Minkov, N; Casten, R F; Yotov, P; Lenis, D; Petrellis, D; Yigitoglu, I
2007-01-01
An exactly separable version of the Bohr Hamiltonian is developed using a potential of the form u(beta)+u(gamma)/beta^2, with the Davidson potential u(beta)= beta^2 + beta_0^4/beta^2 (where beta_0 is the position of the minimum) and a stiff harmonic oscillator for u(gamma) centered at gamma=0. In the resulting solution, called exactly separable Davidson (ES-D), the ground state band, gamma band and 0_2^+ band are all treated on an equal footing. The bandheads, energy spacings within bands, and a number of interband and intraband B(E2) transition rates are well reproduced for almost all well-deformed rare earth and actinide nuclei using two parameters (beta_0, gamma stiffness). Insights regarding the recently found correlation between gamma stiffness and the gamma-bandhead energy, as well as the long standing problem of producing a level scheme with Interacting Boson Approximation SU(3) degeneracies from the Bohr Hamiltonian, are also obtained.
QBism, Bohr, and the quantum omelette tossed by de Ronde
Mohrhoff, Ulrich
2016-01-01
In his recent paper "QBism, FAPP and the Quantum Omelette" [1608.00548v1] de Ronde makes a variety of questionable claims concerning QBism, Bohr, and the present author's critical appraisal of QBism [1409.3312v1]. These claims are examined. Subsequently an outline is presented of what one might see if one looks into the quantum domain through the window provided by the quantum-mechanical correlations between outcome-indicating events in the classical domain.
Challenges to the Bohr Wave Particle Complementarity Principle
Rabinowitz, Mario
2012-01-01
Contrary to the Bohr complementarity principle, in 1995 Rabinowitz proposed that by using entangled particles from the source it would be possible to determine which slit a particle goes through while still preserving the interference pattern in the Young two slit experiment. In 2000, Kim et al used spontaneous parametric down conversion to prepare entangled photons as their source, and almost achieved this. In 2012, Menzel et al. experimentally succeeded in doing this. When the source emits ...
Experimental Test of Bohr's Complementarity Principle with Single Neutral Atom
WANG, Zhihui; TIAN, YALI; Yang, Chen; Zhang, Pengfei; Li, Gang; Zhang, Tiancai
2016-01-01
Bohr's complementarity principle (BCP) is one of the cornerstones of quantum mechanics, and the counterintuitive behavior of wave-particle duality lies at its heart.BCP says that the properties of waves and particles for a quantum system cannot be simultaneously observed. Various tests of BCP with single photons have been performed.However, the low detection efficiency associated with fast-moving, massless photons makes the results less persuasive and more untenable. Here we use a well-contro...
Bohr-Weisskopf effect. Experiment with an ion trap
Recent developments of ion-trap and laser-microwave spectroscopy techniques enable us to measure the ground-state hyperfine structure with very high accuracy. The magnetic hyperfine coupling constant A shows a small but finite isotope dependence called hyperfine anomaly, the main part of which stems from the finite size of the magnetization distribution in the nucleus (Bohr-Weisskopf effect). This effect affords unique and interesting probe for the valence neutron distribution in a nucleus, particularly in a so called halo nucleus. (author)
Traffic restrictions on Routes Bloch, Maxwell and Bohr
IT Department
2008-01-01
Excavation and pipework is being carried out in the framework of the transfer of the waste water treatment plant for the effluents from the surface treatment workshops from Building 254 to Building 676, currently under construction. This work may encroach onto Routes Bloch, Maxwell and Bohr and disrupt the flow of traffic. Users are requested to comply with the road signs that will be erected. The work is expected to last until the beginning of December 2008. Thank you for your understanding. TS/CE and TS/FM Groups Tel.7 4188 or 16 4314
El modelo semicuántico de Bohr en los libros de texto The Bohr's quantum model in the textbook
Jorge Eliécer Moreno Ramírez
2010-01-01
Full Text Available La didáctica de las ciencias naturales está cuestionando la transposición de los modelos científicos en modelos didácticos. Otras investigaciones muestran que el conocimiento científico convertido en conocimiento escolar produce deformaciones de la actividad científica y la simplificación de modelos, contribuyendo con la actitud negativa de los estudiantes hacia las ciencias y al fracaso escolar reportado por algunos estudios. Se pregunta si el modelo atómico de Bohr que se muestra en los textos se corresponde histórica y epistemológicamente con las actividades científicas y cuáles son las posibles deformaciones que de ésta se hace cuando se muestra el modelo en los libros. Los resultados de la investigación muestran una clara diferencia entre la propuesta de Bohr (1913 y la transposición del modelo, lo que invita a una reflexión profunda acerca de la confiabilidad que pueden tener los textos utilizados para la enseñanza de la ciencia químicaNatural science teaching is questioning the transposition that is made of scientific models into didactic models, because research has shown that when scientific knowledge is transformed into scholarly knowledge in order to be taught it causes the deformation of the scientific activity and the simplification of the models. This contributes to the negative attitude of students towards science, and student failure shown in some studies. This research inquired if the transposition of Bohr's atomic model that is shown in textbooks corresponds historically and epistemologically to scientific activity and what the possible deformations are that, coming from this model, are made to the scientific activity that comes from the transposition. The research results show differences between what Bohr (1913 proposed and the transposition of the model in textbooks. This information will contribute to the analysis that is being done regarding the dependability of textbooks.
The Bohr-Wheeler spontaneous fission limit: an undergraduate-level derivation
An upper-undergraduate level derivation of the Z2/A ∼ 50 limit against spontaneous fission first published by Bohr and Wheeler (1939 Phys. Rev. 56 426) is provided. The purpose in offering this derivation is that most textbooks give no details of it and sometimes fail to make clear key assumptions and mathematical manipulations underlying the Bohr and Wheeler model
De novo nonsense mutations in ASXL1 cause Bohring-Opitz syndrome
Hoischen, Alexander; van Bon, Bregje W M; Rodríguez-Santiago, Benjamín; Gilissen, Christian; Vissers, Lisenka E L M; de Vries, Petra; Janssen, Irene; van Lier, Bart; Hastings, Rob; Smithson, Sarah F; Newbury-Ecob, Ruth; Kjærgaard, Susanne; Goodship, Judith; McGowan, Ruth; Bartholdi, Deborah; Rauch, Anita; Peippo, Maarit; Cobben, Jan M; Wieczorek, Dagmar; Gillessen-Kaesbach, Gabriele; Veltman, Joris A; Brunner, Han G; de Vries, Bert B B A
2011-01-01
Bohring-Opitz syndrome is characterized by severe intellectual disability, distinctive facial features and multiple congenital malformations. We sequenced the exomes of three individuals with Bohring-Opitz syndrome and in each identified heterozygous de novo nonsense mutations in ASXL1, which is...
Constitution and model. The quantum theory of Bohr and imagining the atom
Hon, Giora
2014-01-01
The quantum theory of Bohr has roots in the theories of Rutherford and J. J. Thomson on the one hand, and that of Nicholson on the other. We note that Bohr neither presented the theories of Rutherford and Thomson faithfully, nor did he refer to the theory of Nicholson in its own terms. The contrasting attitudes towards these antecedent theories is telling and reveals the philosophical disposition of Bohr. We argue that Bohr intentionally avoided the concept of model as inappropriate for describing his proposed theory. Bohr had no problem in referring to the works of others as 'models', thus separating his theory from previous theories. He was interested in uncovering 'a little piece of reality'.
The quest for reality Bohr and Wittgenstein : two complementary views
Stenholm, Stig
2015-01-01
In both science and philosophy, the twentieth century saw a radical breakdown of certainty in the human worldview, as quantum uncertainty and linguistic ambiguity destroyed the comfortable certitudes of the past. As these disciplines form the foundation for a human position in the world, a major epistemological reorganization had to take place. In this book, quantum theorist Stig Stenholm presents Bohr and Wittgenstein, in physics and in philosophy, as central figures representing this revision. Each of them took up the challenge of replacing apparent order and certainty with a provisional understanding based on limited concepts in constant flux. Stenholm concludes that the modern synthesis created by their heirs is far from satisfactory, and the story is so far an unfinished one. The book will appeal to any researcher in either discipline curious about the foundation of modern science, and works to provoke a renewal of discussion, and the eventual emergence of a reformed clarity and understanding.
Systematic Measurements of the Bohr-Weisskopf Effect at ISOLDE
Nojiri, Y; Matsuki, S; Ragnarsson, I; Neugart, R; Redi, O; Stroke, H H; Duong, H T; Marescaux, D; Pinard, J; Juncar, P; Ekstrom, C; Pellarin, M; Vialle, J-L; Inamura, T
2002-01-01
The " Bohr-Weisskopf " effect, or " hyperfine structure (hfs) anomaly ", which results from the effect of the distribution of nuclear magnetization on the electro-nuclear interaction, will be measured systematically at the PS Booster ISOLDE, first for a long chain of radioactive cesium isotopes, analogously to previous isotope shift and hfs studies. In addition to the direct measurement of magnetic moment values, the results are expected to provide independent data for testing nuclear wavefunctions, these will be of importance for interpreting systematic parity non-conservation experiments, complementary to the single isotope study which requires a high precision knowledge of the electron wavefunction. Substantial progress in these calculations has been achieved recently. Precision measurements of the hfs splittings and nuclear magnetic moments are required, with sensitivity adequate for the radioactive isotopes produced. A triple resonance atomic beam magnetic resonance apparatus (Figure 1) with optical pump...
Delayed-choice experiments and Bohr's elementary quantum phenomenon
In today's words, ''No elementary quantum phenomenon is a phenomenon until it is a registered ('observed', 'indelibly recorded') phenomenon, 'brought to a close' by 'an irreversible act of amplification'. ''In a delayed-choice experiment, one decides which of one or another complementary feature of a phenomenon the observing device will register after the development of the phenomenon is already under way. Several proposals for such experiments are reviewed. When a delayed-choice experiment is conducted at the cosmological level (light coming to the telescope from a distant quasar by two different gravitationally-bent routes), ''one-half of the ghost of a photon'' can be delayed by a month or a year compared to the ''other half''. The circumstance raises an interesting technical question, ''How can one keep one-half the ghost of a photon alive for a year.'' Bohr's phenomenon is discussed as a primordial building element for all of physics. (author)
Challenges to the Bohr Wave Particle Complementarity Principle
Rabinowitz, Mario
2012-01-01
Contrary to the Bohr complementarity principle, in 1995 Rabinowitz proposed that by using entangled particles from the source it would be possible to determine which slit a particle goes through while still preserving the interference pattern in the Young two slit experiment. In 2000, Kim et al used spontaneous parametric down conversion to prepare entangled photons as their source, and almost achieved this. In 2012, Menzel et al. experimentally succeeded in doing this. When the source emits entangled particle pairs, the traversed slit is inferred from measurement of the entangled particle location by using triangulation. The violation of complementarity breaches the prevailing probabilistic interpretation of quantum mechanics, and benefits the Bohm pilot wave theory.
Systematic Measurements of the Bohr-Weisskopf Effect at ISOLDE
2002-01-01
Nuclear electric and magnetic structure properties are measurable by high-resolution atomic spectroscopy through isotope shifts and the Bohr-Weisskopf effect (hyperfine structure anomalies). \\\\ \\\\ The greatest value of these measurements is when made systematically over a large number of isotopes. This has been done in the case of isotopes shifts most extensively by the experiment at ISOLDE. To date the magnetic distribution studies are few and isolated. Here we propose to intitiate a program at ISOLDE to measure hfs anomalies systematically. The experiments, requiring high-precision data on magnetic dipole constants as well as on nuclear g-factors, will be done by atomic-beam magnetic resonance with the use of laser excitation for polarization of the beam and a sixpole magnet acting as an analyser. \\\\ \\\\ The heavy alkali elements are the most promising candidates for hfs anomaly studies because of the large effect expected, the high production yields at ISOLDE and most importantly, the interesting variations...
Placing molecules with Bohr radius resolution using DNA origami
Funke, Jonas J.; Dietz, Hendrik
2016-01-01
Molecular self-assembly with nucleic acids can be used to fabricate discrete objects with defined sizes and arbitrary shapes. It relies on building blocks that are commensurate to those of biological macromolecular machines and should therefore be capable of delivering the atomic-scale placement accuracy known today only from natural and designed proteins. However, research in the field has predominantly focused on producing increasingly large and complex, but more coarsely defined, objects and placing them in an orderly manner on solid substrates. So far, few objects afford a design accuracy better than 5 nm, and the subnanometre scale has been reached only within the unit cells of designed DNA crystals. Here, we report a molecular positioning device made from a hinged DNA origami object in which the angle between the two structural units can be controlled with adjuster helices. To test the positioning capabilities of the device, we used photophysical and crosslinking assays that report the coordinate of interest directly with atomic resolution. Using this combination of placement and analysis, we rationally adjusted the average distance between fluorescent molecules and reactive groups from 1.5 to 9 nm in 123 discrete displacement steps. The smallest displacement step possible was 0.04 nm, which is slightly less than the Bohr radius. The fluctuation amplitudes in the distance coordinate were also small (±0.5 nm), and within a factor of two to three of the amplitudes found in protein structures.
Wellington Nardin Favaro; Alejandro López-Castillo
2013-01-01
The atomic shell structure can be observed by inspecting the experimental periodic properties of the Periodic Table. The (quantum) shell structure emerges from these properties and in this way quantum mechanics can be explicitly shown considering the (semi-)quantitative periodic properties. These periodic properties can be obtained with a simple effective Bohr model. An effective Bohr model with an effective quantum defect (u) was considered as a probe in order to show the quantum structure e...
Niels Bohr on the wave function and the classical/quantum divide
Zinkernagel, Henrik
2016-01-01
It is well known that Niels Bohr insisted on the necessity of classical concepts in the account of quantum phenomena. But there is little consensus concerning his reasons, and what he exactly meant by this. In this paper, I re-examine Bohr's interpretation of quantum mechanics, and argue that the necessity of the classical can be seen as part of his response to the measurement problem. More generally, I attempt to clarify Bohr's view on the classical/quantum divide, arguing that the relation between the two theories is that of mutual dependence. An important element in this clarification consists in distinguishing Bohr's idea of the wave function as symbolic from both a purely epistemic and an ontological interpretation. Together with new evidence concerning Bohr's conception of the wave function collapse, this sets his interpretation apart from both standard versions of the Copenhagen interpretation, and from some of the reconstructions of his view found in the literature. I conclude with a few remarks on ho...
Bohr's Electron was Problematic for Einstein: String Theory Solved the Problem
Webb, William
2013-04-01
Neils Bohr's 1913 model of the hydrogen electron was problematic for Albert Einstein. Bohr's electron rotates with positive kinetic energies +K but has addition negative potential energies - 2K. The total net energy is thus always negative with value - K. Einstein's special relativity requires energies to be positive. There's a Bohr negative energy conflict with Einstein's positive energy requirement. The two men debated the problem. Both would have preferred a different electron model having only positive energies. Bohr and Einstein couldn't find such a model. But Murray Gell-Mann did! In the 1960's, Gell-Mann introduced his loop-shaped string-like electron. Now, analysis with string theory shows that the hydrogen electron is a loop of string-like material with a length equal to the circumference of the circular orbit it occupies. It rotates like a lariat around its centered proton. This loop-shape has no negative potential energies: only positive +K relativistic kinetic energies. Waves induced on loop-shaped electrons propagate their energy at a speed matching the tangential speed of rotation. With matching wave speed and only positive kinetic energies, this loop-shaped electron model is uniquely suited to be governed by the Einstein relativistic equation for total mass-energy. Its calculated photon emissions are all in excellent agreement with experimental data and, of course, in agreement with those -K calculations by Neils Bohr 100 years ago. Problem solved!
Love, literature and the quantum atom Niels Bohr's 1913 trilogy revisited
Aaserud, Finn
2013-01-01
Niels Bohr ranks with Einstein among the physicists of the 20th century. He rose to this status through his invention of the quantum theory of the atom and his leadership in its defense and development. He also ranks with Einstein in his humanism and his sense of responsibility to his science and the society that enabled him to create it. Our book presents unpublished excerpts from extensive correspondence between Bohr and his immediate family, and uses it to describe and analyze the psychological and cultural background to his invention. The book also contains a reprinting of the three papers of 1913 - the "Trilogy" - in which Bohr worked out the provisional basis of a quantum theory of the atom.
Probing the (empirical quantum structure embedded in the periodic table with an effective Bohr model
Wellington Nardin Favaro
2013-01-01
Full Text Available The atomic shell structure can be observed by inspecting the experimental periodic properties of the Periodic Table. The (quantum shell structure emerges from these properties and in this way quantum mechanics can be explicitly shown considering the (semi-quantitative periodic properties. These periodic properties can be obtained with a simple effective Bohr model. An effective Bohr model with an effective quantum defect (u was considered as a probe in order to show the quantum structure embedded in the Periodic Table. u(Z shows a quasi-smoothed dependence of Z, i.e., u(Z ≈ Z2/5 - 1.
The theory of the Bohr-Weisskopf effect in the hyperfine structure
Karpeshin, F. F.; Trzhaskovskaya, M. B.
2015-01-01
For twenty years research into the anomalies in the HF spectra was going in a wrong direction by fighting the related Bohr-Weisskopf effect. As a way out, the model-independent way is proposed of estimating the nuclear radii from the hyper-fine splitting. The way is based on analogy of HFS to internal conversion coefficients, and the Bohr-Weisskopf effect - to the anomalies in the internal conversion coefficients. This makes transparent It is shown that the parameters which can be extracted f...
Atomically thin spherical shell-shaped superscatterers based on Bohr model
Li, Rujiang; Lin, Shisheng; Liu, Xu; Chen, Hongsheng
2015-01-01
Graphene monolayers can be used for atomically thin three-dimensional shell-shaped superscatterer designs. Due to the excitation of the first-order resonance of transverse magnetic (TM) graphene plasmons, the scattering cross section of the bare subwavelength dielectric particle is enhanced significantly by five orders of magnitude. The superscattering phenomenon can be intuitively understood and interpreted with Bohr model. Besides, based on the analysis of Bohr model, it is shown that contrary to the TM case, superscattering is hard to occur by exciting the resonance of transverse electric (TE) graphene plasmons due to their poor field confinements.
Relation between energy and mass in Bohr's essay on his debate with Einstein
The famous debate between Einstein and Bohr on the (in)consistency of quantum mechanics was described in detail by Bohr in his essay of 1949. The present article comments not on the main subject of the debate but only on the terminology that is relevant to the notions of the theory of relativity and which was used by the participants. In particular, their statement on the equivalence of mass and energy should not be taken literally. In fact, the rest energy is meant here. The authority of the two great physicists should not be misused to preserve the confusing terminology
Bohr's complementarity relation put to test for CP-violating neutral kaons
Full text: The complementarity principle was phrased by Niels Bohr in an attempt to express the most fundamental difference between classical and quantum physics. According to this principle, and in sharp contrast to classical physics, in quantum physics we cannot capture all aspects of reality simultaneously, the information content is always limited. We try to shed new light on this fundamental complementarity relation by considering a system in high energy physics, namely, the neutral kaon system. In contrast to usually considered quantum systems as e.g. photons, they violate the CP symmetry (C...charge conjugation, P...parity) and this affects Bohr's relation. (author)
Quantum Explorers: Bohr, Jordan, and Delbrück Venturing into Biology
Joaquim, Leyla; Freire, Olival; El-Hani, Charbel N.
2015-09-01
This paper disentangles selected intertwined aspects of two great scientific developments: quantum mechanics and molecular biology. We look at the contributions of three physicists who in the 1930s were protagonists of the quantum revolution and explorers of the field of biology: Niels Bohr, Pascual Jordan, and Max Delbrück. Their common platform was the defense of the Copenhagen interpretation in physics and the adoption of the principle of complementarity as a way of looking at biology. Bohr addressed the problem of how far the results reached in physics might influence our views about life. Jordan and Delbrück were followers of Bohr's ideas in the context of quantum mechanics and also of his tendency to expand the implications of the Copenhagen interpretation to biology. We propose that Bohr's perspective on biology was related to his epistemological views, as Jordan's was to his political positions. Delbrück's propensity to migrate was related to his transformation into a key figure in the history of twentieth-century molecular biology.
EPR before EPR: A 1930 Einstein-Bohr thought Experiment Revisited
Nikolic, Hrvoje
2012-01-01
In 1930, Einstein argued against the consistency of the time-energy uncertainty relation by discussing a thought experiment involving a measurement of the mass of the box which emitted a photon. Bohr seemingly prevailed over Einstein by arguing that Einstein's own general theory of relativity saves the consistency of quantum mechanics. We revisit…
The Bohr Correspondence Principle: Kepler Orbits of the Electron in a Hydrogen Atom
2016-06-01
We consider the quantum-mechanical non-relativistichydrogen atom. We show that for boundstates with size much larger than the Bohr radius,one can construct a wave packet that is localizedin space corresponding to a classical particlemoving in a circular orbit.
Gaussian overlap approximation for the quadrupole collective states
Rohoziński, Stanisław G.
2012-09-01
The generator coordinate method in the Gaussian overlap approximation (GOA) is applied to a description of the nuclear quadrupole collective states. The full five-dimensional quadrupole tensor is used as a set of the generator coordinates. The integral Hill-Wheeler equation is reduced to a differential equation by using the Fourier transforms of the overlap and energy kernels. The differential Bohr Hamiltonian obtained this way is compared with that derived by the usual approach to the collective Hamiltonian in the GOA which does contain an additional approximation. The method of calculating the quantities which determine the Bohr Hamiltonian from the set of deformation-dependent intrinsic states is demonstrated. In particular, it appears that the moments of inertia at the quadrupole rotations are of the Yoccoz type.
Virtual Visit to the ATLAS Control Room by Niels Bohr Institute - Kulturnatten, Copenhagen
ATLAS Experiment
2012-01-01
This ATLAS Virtual Visit will be part of outreach and education programme of the Niels Bohr Institute during a Copenhagen wide night of culture and science, Kulturnatten. Visitors of all ages and background will have the chance to get an introduction to the ATLAS Experiment, the LHC, and basic particle physics. The Virtual Visit will supplement an exhibition and give the opportunity to ask questions about anything related to ATLAS to a Danish physicist at CERN. The Niels Bohr Institute is a long time member of the ATLAS Collaboration and has contributed to Kulturnatten for many years now. http://atlas-live-virtual-visit.web.cern.ch/atlas-live-virtual-visit/2012/Copenhagen-2012.html
Matsuyanagi, Kenichi; Nakatsukasa, Takashi; Yoshida, Kenichi; Hinohara, Nobuo; Sato, Koichi
2016-01-01
We discuss the nature of the low-frequency quadrupole vibrations from small-amplitude to large-amplitude regimes. We consider full five-dimensional quadrupole dynamics including three-dimensional rotations restoring the broken symmetries as well as axially symmetric and asymmetric shape fluctuations. Assuming that the time-evolution of the self-consistent mean field is determined by five pairs of collective coordinates and collective momenta, we microscopically derive the collective Hamiltonian of Bohr and Mottelson, which describes low-frequency quadrupole dynamics. We show that the five-dimensional collective Schr\\"odinger equation is capable of describing large-amplitude quadrupole shape dynamics seen as shape coexistence/mixing phenomena. We summarize the modern concepts of microscopic theory of large-amplitude collective motion, which is underlying the microscopic derivation of the Bohr-Mottelson collective Hamiltonian.
A Bohr-type model with gravity as the attractive force
Vayenas, C G; Fokas, A
2013-01-01
We formulate a Bohr-type rotating particle model for three light particles of the same rest mass, forming a bound rotational state under the influence of their gravitational attraction, in the same way that electrostatic attraction leads to the formation of a bound proton-electron state in the classical Bohr model of the H atom. By using special relativity, the equivalence principle and the de Broglie wavelength equation, we find that when the three rotating particles have the rest masses of neutrinos or antineutrinos then surprisingly the rest mass of the rotating state has the rest mass of the stable baryons, i.e. of the proton and the neutron. This rest mass is due almost exclusively to the kinetic energy of the rotating neutrinos. The results are found to be consistent with the theory of general relativity. Predictions for the properties of these bound rotational states are compared with experimental values.
Conceptual objections to the Bohr atomic theory — do electrons have a "free will" ?
Kragh, Helge
2011-11-01
The atomic model introduced by Bohr in 1913 dominated the development of the old quantum theory. Its main features, such as the radiationless stationary states and the discontinuous quantum jumps between the states, were hard to swallow for contemporary physicists. While acknowledging the empirical power of the theory, many scientists criticized its foundation or looked for ways to reconcile it with classical physics. Among the chief critics were A. Crehore, J.J. Thomson, E. Gehrcke and J. Stark. This paper examines from a historical perspective the conceptual objections to Bohr's atom, in particular the stationary states (where electrodynamics was annulled by fiat) and the mysterious, apparently teleological quantum jumps. Although few of the critics played a constructive role in the development of the old quantum theory, a history neglecting their presence would be incomplete and distorted.
Darwinism in disguise? A comparison between Bohr's view on quantum mechanics and QBism.
Faye, Jan
2016-05-28
The Copenhagen interpretation is first and foremost associated with Niels Bohr's philosophy of quantum mechanics. In this paper, I attempt to lay out what I see as Bohr's pragmatic approach to science in general and to quantum physics in particular. A part of this approach is his claim that the classical concepts are indispensable for our understanding of all physical phenomena, and it seems as if the claim is grounded in his reflection upon how the evolution of language is adapted to experience. Another, recent interpretation, QBism, has also found support in Darwin's theory. It may therefore not be surprising that sometimes QBism is said to be of the same breed as the Copenhagen interpretation. By comparing the two interpretations, I conclude, nevertheless, that there are important differences. PMID:27091172
Gjedde, Albert
2010-01-01
facilitated by a specific cellular activity substitute to secretion. The subjects of the present reevaluation of this controversy are Christian Bohr, Professor and Doctor of Medicine (1855–1911), nominated three times for the Nobel Prize; August Krogh, Doctor of Philosophy (1874–1949), Christian Bohr......'s assistant and later Nobel Prize laureate (1920); and Marie Krogh, née Jørgensen, Doctor of Medicine and wife of August Krogh (1874–1943). The controversy concerned is the transport of oxygen from the lungs into the bloodstream: are passive transport and diffusion capacity together sufficient to secure the...... posterity recognized. Posterity has judged the dispute unilaterally from the Nobel laureate's point of view, but it is evident that August Krogh's Nobel Prize was awarded for the discovery of a cellular activity (Christian Bohr's expression), represented by Krogh's discovery of capillary recruitment...
Sprinzak, D.; Buks, E.; Heiblum, M.; Shtrikman, H.
1999-01-01
Interference results when a quantum particle is free to choose among a few indistinguishable paths. A canonical example of Bohr's complementarity principle [1] is a two-path interferometer with an external detector coupled to one of the paths. Then, interference between the two paths vanishes (i.e. dephasing) if one is able to detect, even in principle, the path taken by the particle. This type of which path (WP) experiment was already executed with photons, cooled atoms, neutrons, solitons, ...
Electric quadrupole transitions of the Bohr Hamiltonian with the Morse potential
Eigenfunctions of the collective Bohr Hamiltonian with the Morse potential have been obtained by using the asymptotic iteration method (AIM) for both γ-unstable and rotational structures. B(E2) transition rates have been calculated and compared to experimental data. Overall good agreement is obtained for transitions within the ground-state band, while some interband transitions appear to be systematically underpredicted in γ-unstable nuclei and overpredicted in rotational nuclei.
Einstein–Bohr recoiling double-slit gedanken experiment performed at the molecular level
Liu, X-J; Miao, Q.; Gel'mukhanov, F.; Patanen, M.; Travnikova, O; C. Nicolas; Ågren, H; Ueda, K.; Miron, C.
2015-01-01
Double-slit experiments illustrate proof for wave–particle complementarity. The essence of Einstein–Bohr's debate about wave–particle duality was whether the momentum transfer between a particle and a recoiling slit could mark the path, thus destroying the interference. We realized this recoiling double-slit gedanken experiment by resonant X-ray photoemission from molecular oxygen for geometries near equilibrium (coupled slits) and in a dissociative state far away from equilibrium (decoupled ...
Complementarity and the Nature of Uncertainty Relations in Einstein–Bohr Recoiling Slit Experiment
Shogo Tanimura
2015-01-01
A model of the Einstein–Bohr recoiling slit experiment is formulated in a fully quantum theoretical setting. In this model, the state and dynamics of a movable wall that has two slits in it, as well as the state of a particle incoming to the two slits, are described by quantum mechanics. Using this model, we analyzed complementarity between exhibiting an interference pattern and distinguishing the particle path. Comparing the Kennard–Robertson type and the Ozawa-type uncertainty relations, we...
Inversion of the Bohr effect upon oxygen binding to 24-meric tarantula hemocyanin.
Sterner, R; Decker, H
1994-01-01
The Bohr effect describes the usually negative coupling between the binding of oxygen and the binding of protons to respiratory proteins. It was first described for hemoglobin and provides for an optimal oxygen supply of the organism under changing physiological conditions. Our measurements of both oxygen and proton binding to the 24-meric tarantula hemocyanin establish the unusual case where a respiratory protein binds protons at low degrees of oxygenation but releases protons at high degree...
Bohr-Sommerfeld quantization condition for Dirac states derived from an Ermakov-type invariant
Thylwe, Karl-Erik [KTH-Mechanics, Royal Institute of Technology, S-10044 Stockholm (Sweden); McCabe, Patrick [CCDC, 12 Union Road, CB2 1EZ Cambridge (United Kingdom)
2013-05-15
It is shown that solutions of the second-order decoupled radial Dirac equations satisfy Ermakov-type invariants. These invariants lead to amplitude-phase-type representations of the radial spinor solutions, with exact relations between their amplitudes and phases. Implications leading to a Bohr-Sommerfeld quantization condition for bound states, and a few particular atomic/ionic and nuclear/hadronic bound-state situations are discussed.
Des images et des paraboles : Niels Bohr et le discours descriptif en physique quantique
Ilias Yocaris
2011-01-01
Full Text Available Cette étude porte sur l’importance accordée aux images verbales dans le discours descriptif utilisé en mécanique quantique, et plus précisément sur la conception de la langue scientifique qui est celle de Niels Bohr (1885-1962 : en raison d’une série de considérations techniques, méthodologiques et épistémologiques que nous nous proposons d’analyser in extenso, Bohr considère effectivement que les phénomènes subatomiques ne peuvent être évoqués directement (sans référence au contexte observationnel, par le biais d’un langage dénotatif non figural, mais uniquement de manière métaphorique, détournée, ce qui réduit à ses yeux le discours descriptif des physiciens à « des images et des paraboles ». En examinant les textes de Bohr à la lumière d’un certain nombre de travaux épistémologiques, de commentaires et d’expérimentations auxquels ils ont donné lieu ultérieurement, nous nous proposons de décrire les implications conceptuelles d’une telle prise de position, qui constitue une vraie révolution sur le plan philosophique.
The theory of the Bohr-Weisskopf effect in the hyperfine structure
Karpeshin, F. F.; Trzhaskovskaya, M. B.
2015-09-01
Description of the Bohr-Wesskopf effect in the hyperfine structure of few-electron heavy ions is a challenging problem, which can be used as a test of both QED and atomic calculations. However, for twenty years the research has actually been going in a wrong direction, aimed at fighting the Bohr-Weisskopf effect through its cancellation in specific differences. Alternatively, we propose the constructive model-independent way, which enables the nuclear radii and their momenta to be retrieved from the hyper-fine splitting (HFS). The way is based on analogy of HFS to internal conversion coefficients, and the Bohr-Weisskopf effect - to the anomalies in the internal conversion coefficients. It is shown that the parameters which can be extracted from the data are the even nuclear momenta of the magnetization distribution. The radii R2 and - for the first time - R4 are obtained in this way by analysis of the experimental HFS values for the H- and Li-like ions of 209Bi. The critical prediction concerning the HFS for the 2p1/2 state is made. The present analysis shows high sensitivity of the method to the QED effects, which offers a way of precision test of QED. Experimental recommendations are given, which are aimed at retrieving data on the HFS values for a set of a few-electron configurations of each atom.
Bohr Hamiltonian with a deformation-dependent mass term: physical meaning of the free parameter
Bonatsos, Dennis; Petrellis, D
2015-01-01
Embedding of the 5-dimensional (5D) space of the Bohr Hamiltonian with a deformation-dependent mass (DDM) into a 6-dimensional (6D) space shows that the free parameter in the dependence of the mass on the deformation is connected to the curvature of the 5D space, with the special case of constant mass corresponding to a flat 5D space. Comparison of the DDM Bohr Hamiltonian to the 5D classical limit of Hamiltonians of the 6D interacting boson model (IBM), shows that the DDM parameter is proportional to the strength of the pairing interaction in the U(5) (vibrational) symmetry limit, while it is proportional to the quadrupole-quadrupole interaction in the SU(3) (rotational) symmetry limit, and to the difference of the pairing interactions among s, d bosons and d bosons alone in the O(6) (gamma-soft) limit. The presence of these interactions leads to a curved 5D space in the classical limit of IBM, in contrast to the flat 5D space of the original Bohr Hamiltonian, which is made curved by the introduction of the ...
Are we living in a quantum world? Bohr and quantum fundamentalism
Zinkernagel, Henrik
2016-01-01
The spectacular successes of quantum physics have made it a commonplace to assert that we live in a quantum world. This idea seems to imply a kind of "quantum fundamentalism" according to which everything in the universe (if not the universe as a whole) is fundamentally of a quantum nature and ultimately describable in quantum-mechanical terms. Bohr's conception of quantum mechanics has traditionally been seen as opposed to such a view, not least because of his insistence on the necessity of the concepts of classical physics in the account of quantum phenomena. Recently, however, a consensus seems to be emerging among careful commentators on Bohr to the effect that he, after all, did subscribe to some version of quantum fundamentalism. Against this consensus, and by re-examining the historical record, I will defend a variant of the traditional reading of Bohr in which (1) the answer to what an object is (quantum or classical) depends on the experimental context; and (2) in principle, any physical system can b...
The unitary convolution approximation for heavy ions
Grande, P L
2002-01-01
The convolution approximation for the impact-parameter dependent energy loss is reviewed with emphasis on the determination of the stopping force for heavy projectiles. In this method, the energy loss in different impact-parameter regions is well determined and interpolated smoothly. The physical inputs of the model are the projectile-screening function (in the case of dressed ions), the electron density and oscillators strengths of the target atoms. Moreover, the convolution approximation, in the perturbative mode (called PCA), yields remarkable agreement with full semi-classical-approximation (SCA) results for bare as well as for screened ions at all impact parameters. In the unitary mode (called UCA), the method contains some higher-order effects (yielding in some cases rather good agreement with full coupled-channel calculations) and approaches the classical regime similar as the Bohr model for large perturbations (Z/v>>1). The results are then used to compare with experimental values of the non-equilibri...
Bohr effect and temperature sensitivity of hemoglobins from highland and lowland deer mice.
Jensen, Birgitte; Storz, Jay F; Fago, Angela
2016-05-01
An important means of physiological adaptation to environmental hypoxia is an increased oxygen (O2) affinity of the hemoglobin (Hb) that can help secure high O2 saturation of arterial blood. However, the trade-off associated with a high Hb-O2 affinity is that it can compromise O2 unloading in the systemic capillaries. High-altitude deer mice (Peromyscus maniculatus) have evolved an increased Hb-O2 affinity relative to lowland conspecifics, but it is not known whether they have also evolved compensatory mechanisms to facilitate O2 unloading to respiring tissues. Here we investigate the effects of pH (Bohr effect) and temperature on the O2-affinity of high- and low-altitude deer mouse Hb variants, as these properties can potentially facilitate O2 unloading to metabolizing tissues. Our experiments revealed that Bohr factors for the high- and low-altitude Hb variants are very similar in spite of the differences in O2-affinity. The Bohr factors of deer mouse Hbs are also comparable to those of other mammalian Hbs. In contrast, the high- and low-altitude variants of deer mouse Hb exhibited similarly low temperature sensitivities that were independent of red blood cell anionic cofactors, suggesting an appreciable endothermic allosteric transition upon oxygenation. In conclusion, high-altitude deer mice have evolved an adaptive increase in Hb-O2 affinity, but this is not associated with compensatory changes in sensitivity to changes in pH or temperature. Instead, it appears that the elevated Hb-O2 affinity in high-altitude deer mice is compensated by an associated increase in the tissue diffusion capacity of O2 (via increased muscle capillarization), which promotes O2 unloading. PMID:26808972
El modelo atómico de Bohr: una aplicación
Raul Garcia Llamas
2013-01-01
Se aplica la teoría atómica de Bohr cuyo centenario se celebra este 2013, utilizando la aproximación electrostática y un algoritmo numérico para resolver las ecuaciones clásicas de movimiento del núcleo y de los electrones en átomos complejos, con el fin de estudiar su dinámica. Se presentan resultados numéricos para el caso del átomo de Hidrogeno y el átomo de Helio.
Exactly separable version of the Bohr Hamiltonian with the Davidson potential
Bonatsos, Dennis; McCutchan, E. A.; Minkov, N.; Casten, R. F.; Yotov, P.; Lenis, D.; Petrellis, D.; Yigitoglu, I.
2008-01-01
An exactly separable version of the Bohr Hamiltonian is developed using a potential of the form u(beta)+u(gamma)/beta^2, with the Davidson potential u(beta)= beta^2 + beta_0^4/beta^2 (where beta_0 is the position of the minimum) and a stiff harmonic oscillator for u(gamma) centered at gamma=0. In the resulting solution, called exactly separable Davidson (ES-D), the ground state band, gamma band and 0_2^+ band are all treated on an equal footing. The bandheads, energy spacings within bands, an...
AMMARI, Zied; Falconi, Marco
2016-01-01
In the mid Sixties Edward Nelson proved the existence of a consistent quantum field theory that describes the Yukawa-like interaction of a non-relativistic nucleon field with a relativistic meson field. Since then it is thought, despite the renormalization procedure involved in the construction, that the quantum dynamics should be governed in the classical limit by a Schr\\"odinger-Klein-Gordon system with Yukawa coupling. In the present paper we prove this fact in the form of a Bohr correspon...
van Dongen, Jeroen
2015-01-01
The Einstein-Rupp experiments have been unduly neglected in the history of quantum mechanics. While this is to be explained by the fact that Emil Rupp was later exposed as a fraud and had fabricated the results, it is not justified, due to the importance attached to the experiments at the time. This paper discusses Rupp's fraud, the relation between Albert Einstein and Rupp, and the Einstein-Rupp experiments, and argues that these experiments were an influence on Niels Bohr's development of c...
Electric quadrupole transitions of the Bohr Hamiltonian with Manning-Rosen potential
Chabab, M; Lahbas, A; Oulne, M
2016-01-01
Analytical expressions of the wave functions are derived for a Bohr Hamiltonian with the Manning{Rosen potential in the cases of {\\gamma}-unstable nuclei and axially symmetric prolate deformed ones with {\\gamma}=0. By exploiting the results we have obtained in a recent work on the same theme Ref. [1], we have calculated the B(E2) transition rates for 34 {\\gamma}-unstable and 38 rotational nuclei and compared to experimental data, revealing a qualitative agreement with the experiment and phase transitions within the ground state band and showing also that the Manning-Rosen potential is more appropriate for such calculations than other potentials.
The language of Orthodox theology & quantum mechanics: St Gregory Palamas and Niels Bohr
Tanev, Stoyan
2013-01-01
The objective of this chapter is to provide an analytical framework that would enable the comparison of the ways of using words and language in the cases of St. Gregory Palamas and Niels Bohr. The main motivation will be to explore Christos Yannaras’ point about the opportunity of using quantum...... mechanics as a source of a new language that could be useful in enhancing the power of theological statements. It is important to point out that the main goal here is to use the insights from existing studies to provide a preliminary comparative analysis. The novelty in such an approach should be sought in...
van Dongen, Jeroen
2015-01-01
The Einstein-Rupp experiments have been unduly neglected in the history of quantum mechanics. While this is to be explained by the fact that Emil Rupp was later exposed as a fraud and had fabricated the results, it is not justified, due to the importance attached to the experiments at the time. This paper discusses Rupp's fraud, the relation between Albert Einstein and Rupp, and the Einstein-Rupp experiments, and argues that these experiments were an influence on Niels Bohr's development of complementarity and Werner Heisenberg's formulation of the uncertainty relations.
El modelo atómico de Bohr: una aplicación
Raul Garcia Llamas
2013-06-01
Full Text Available Se aplica la teoría atómica de Bohr cuyo centenario se celebra este 2013, utilizando la aproximación electrostática y un algoritmo numérico para resolver las ecuaciones clásicas de movimiento del núcleo y de los electrones en átomos complejos, con el fin de estudiar su dinámica. Se presentan resultados numéricos para el caso del átomo de Hidrogeno y el átomo de Helio.
Wave-particle duality and Bohr's complementarity principle in quantum mechanics
Interest on Bohr's complementarity principle has recently been revived particularly because of several thought experiments and some actually performed experiments to test the validity of mutual exclusiveness of wave and particle properties. A critical review of the situation is undertaken and it is pointed out that the problem with mutual exclusiveness arises because of some vagueness in the conventional formulation. An attempt is made to remove this vagueness by connecting the origin of mutual exclusiveness to some principles of quantum mechanics. Accordingly, it becomes obvious that to contradict complementarity principle without contradicting quantum mechanics would be impossible. Some of the recent experiments are critically analysed. (author). 31 refs., 3 ills
Niven, Ivan
2008-01-01
This self-contained treatment originated as a series of lectures delivered to the Mathematical Association of America. It covers basic results on homogeneous approximation of real numbers; the analogue for complex numbers; basic results for nonhomogeneous approximation in the real case; the analogue for complex numbers; and fundamental properties of the multiples of an irrational number, for both the fractional and integral parts.The author refrains from the use of continuous fractions and includes basic results in the complex case, a feature often neglected in favor of the real number discuss
Approximate Representations and Approximate Homomorphisms
Moore, Cristopher; Russell, Alexander
2010-01-01
Approximate algebraic structures play a defining role in arithmetic combinatorics and have found remarkable applications to basic questions in number theory and pseudorandomness. Here we study approximate representations of finite groups: functions f:G -> U_d such that Pr[f(xy) = f(x) f(y)] is large, or more generally Exp_{x,y} ||f(xy) - f(x)f(y)||^2$ is small, where x and y are uniformly random elements of the group G and U_d denotes the unitary group of degree d. We bound these quantities i...
Russell, Bianca; Johnston, Jennifer J; Biesecker, Leslie G; Kramer, Nancy; Pickart, Angela; Rhead, William; Tan, Wen-Hann; Brownstein, Catherine A; Kate Clarkson, L; Dobson, Amy; Rosenberg, Avi Z; Vergano, Samantha A Schrier; Helm, Benjamin M; Harrison, Rachel E; Graham, John M
2015-09-01
Bohring-Opitz syndrome is a rare genetic condition characterized by distinctive facial features, variable microcephaly, hypertrichosis, nevus flammeus, severe myopia, unusual posture (flexion at the elbows with ulnar deviation, and flexion of the wrists and metacarpophalangeal joints), severe intellectual disability, and feeding issues. Nine patients with Bohring-Opitz syndrome have been identified as having a mutation in ASXL1. We report on eight previously unpublished patients with Bohring-Opitz syndrome caused by an apparent or confirmed de novo mutation in ASXL1. Of note, two patients developed bilateral Wilms tumors. Somatic mutations in ASXL1 are associated with myeloid malignancies, and these reports emphasize the need for Wilms tumor screening in patients with ASXL1 mutations. We discuss clinical management with a focus on their feeding issues, cyclic vomiting, respiratory infections, insomnia, and tumor predisposition. Many patients are noted to have distinctive personalities (interactive, happy, and curious) and rapid hair growth; features not previously reported. PMID:25921057
The boundary conditions for Bohr's law: when is reacting faster than acting?
Pinto, Yaïr; Otten, Marte; Cohen, Michael A; Wolfe, Jeremy M; Horowitz, Todd S
2011-02-01
In gunfights in Western movies, the hero typically wins, even though the villain draws first. Niels Bohr (Gamow, The great physicists from Galileo to Einstein. Chapter: The law of quantum, 1988) suggested that this reflected a psychophysical law, rather than a dramatic conceit. He hypothesized that reacting is faster than acting. Welchman, Stanley, Schomers, Miall, and Bülthoff (Proceedings of the Royal Society of London B: Biological Sciences, 277, 1667-1674, 2010) provided empirical evidence supporting "Bohr's law," showing that the time to complete simple manual actions was shorter when reacting than when initiating an action. Here we probe the limits of this effect. In three experiments, participants performed a simple manual action, which could either be self-initiated or executed following an external visual trigger. Inter-button time was reliably faster when the action was externally triggered. However, the effect disappeared for the second step in a two-step action. Furthermore, the effect reversed when a choice between two actions had to be made. Reacting is faster than acting, but only for simple, ballistic actions. PMID:21264708
The theory of the Bohr-Weisskopf effect in the hyperfine structure
Karpeshin, F F
2015-01-01
For twenty years research into the anomalies in the HF spectra was going in a wrong direction by fighting the related Bohr-Weisskopf effect. As a way out, the model-independent way is proposed of estimating the nuclear radii from the hyper-fine splitting. The way is based on analogy of HFS to internal conversion coefficients, and the Bohr-Weisskopf effect - to the anomalies in the internal conversion coefficients. This makes transparent It is shown that the parameters which can be extracted from the data are the even nuclear moments of the magnetization distribution. The radii $R_2$ and (for the first time) $R_4$ are thus obtained by analysis of the experimental HFS for the H- and Li-like ions of $^{209}$Bi. The critical prediction of the HFS for the $2p_{1/2}$ state is discussed. The moments may be determined in this way only if the higher QED effects are properly taken into account. Therefore, this set of the parameters form a basis of a strict QED test. Experimental prospects are discussed, aimed at retrie...
CERN. Geneva
2015-01-01
Most physics results at the LHC end in a likelihood ratio test. This includes discovery and exclusion for searches as well as mass, cross-section, and coupling measurements. The use of Machine Learning (multivariate) algorithms in HEP is mainly restricted to searches, which can be reduced to classification between two fixed distributions: signal vs. background. I will show how we can extend the use of ML classifiers to distributions parameterized by physical quantities like masses and couplings as well as nuisance parameters associated to systematic uncertainties. This allows for one to approximate the likelihood ratio while still using a high dimensional feature vector for the data. Both the MEM and ABC approaches mentioned above aim to provide inference on model parameters (like cross-sections, masses, couplings, etc.). ABC is fundamentally tied Bayesian inference and focuses on the “likelihood free” setting where only a simulator is available and one cannot directly compute the likelihood for the dat...
Schmidt, Wolfgang M
1980-01-01
"In 1970, at the U. of Colorado, the author delivered a course of lectures on his famous generalization, then just established, relating to Roth's theorem on rational approxi- mations to algebraic numbers. The present volume is an ex- panded and up-dated version of the original mimeographed notes on the course. As an introduction to the author's own remarkable achievements relating to the Thue-Siegel-Roth theory, the text can hardly be bettered and the tract can already be regarded as a classic in its field."(Bull.LMS) "Schmidt's work on approximations by algebraic numbers belongs to the deepest and most satisfactory parts of number theory. These notes give the best accessible way to learn the subject. ... this book is highly recommended." (Mededelingen van het Wiskundig Genootschap)
Hastings, Rob; Cobben, Jan-Maarten; Gillessen-Kaesbach, Gabriele; Goodship, Judith; Hove, Hanne Buciek; Kjærgaard, Susanne; Kemp, Helena; Kingston, Helen; Lunt, Peter; Mansour, Sahar; McGowan, Ruth; Metcalfe, Kay; Murdoch-Davis, Catherine; Ray, Mary; Rio, Marlène; Smithson, Sarah; Tolmie, John; Turnpenny, Peter; van Bon, Bregje; Wieczorek, Dagmar; Newbury-Ecob, Ruth
2011-01-01
Bohring-Opitz syndrome (BOS) is a rare congenital disorder of unknown etiology diagnosed on the basis of distinctive clinical features. We suggest diagnostic criteria for this condition, describe ten previously unreported patients, and update the natural history of four previously reported patien...
Annual Congress 2013 of the Swiss Academy of Science : the Quantum atom at 100 - Niels Bohr's Legacy
2013-01-01
This year, the annual congress of SCNAT will be dedicated to the celebration of the hundredth anniversary of the discovery of the quantum atomic model by the Danish physicist Niels Bohr. In 1913, Bohr proposed to apply the quanta discovered in 1900 by Max Planck to elucidate the puzzling problem of the stability of the atom: in the classical description, to keep the atom mechanically stable, the electrostatic attraction exerted by the nucleus on the electron has to be compensated by an accelerated motion of the electron causing emission of electromagnetic radiation and hence leading to an eventual collapse of the atom. Pondering upon the simpliest case of Hydrogen, Bohr boldly postulated the stability of a discrete set of circular electron orbits distinguished by their quantum number. The electron transitions between the allowed orbits were responsible for the spectral lines and Bohr was able to derive the value of the Rydberg constant in the Balmer series in terms of Planck constant, an «enormous achiev...
Inspirations from the theories of Bohr and Mottelson: a Canadian perspective
Ward, D.; Waddington, J. C.; Svensson, C. E.
2016-03-01
The theories developed by Bohr and Mottelson have inspired much of the world-wide experimental investigation into the structure of the atomic nucleus. On the occasion of the 40th anniversary of the awarding of their Nobel prize, we reflect on some of the experimental developments made in understanding the structure of nuclei. We have chosen to focus on experiments performed in Canada, or having strong ties to Canada, and the work included here spans virtually the whole of the second half of the 20th century. The 8π Spectrometer, which figures prominently in this story, was a novel departure for funding science in Canada that involved an intimate collaboration between a Crown Corporation (Atomic Energy of Canada Ltd) and University research, and enabled many of the insights discussed here.
An atomic beam magnetic resonance (ABMR) apparatus has been constructed at Orsay, and has been installed at the CERN PS Booster ISOLDE mass separator facility for 'on-line' work with radioactive isotopes in a program to measure hyperfine structure anomalies (the Bohr-Weisskopf effect) over long isotopic chains. The hfs anomalies result from the effect of the spatial distribution of the nuclear magnetization on the atomic hfs interaction. Constructional details of the system are described: Emphasis is placed on the measurement of nuclear g-factors by a triple resonance, laser state selected, ABMR method. A precision better than 10-4 for gI values has been obtained in stable atomic beam tests, leading to hfs anomaly measurements better than 10%. Two types of detection systems are described: Laser fluorescence and surface ionization coupled with mass spectrometry. (orig.)
Excited collective states of nuclei within Bohr Hamiltonian with Tietz-Hua potential
Chabab, M; Hamzavi, M; Lahbas, A; Oulne, M
2016-01-01
In this paper, we present new analytical solutions of the Bohr Hamiltonian problem that we derived with the Tietz-Hua potential, here used for describing the {\\beta}-part of the nuclear collective potential plus harmonic oscillator one for the {\\gamma}-part. Also, we proceed to a systematic comparison of the numerical results obtained with this kind of {\\beta}-potential with others which are widely used in such a framework as well as with the experiment. The calculations are carried out for energy spectra and electromagnetic transition probabilities for {\\gamma}-unstable and axially symmetric deformed nuclei. In the same frame, we show the effect of the shape flatness of the {\\beta}-potential beyond its minimum on transition rates calculations.
The Compton Radius, the de Broglie Radius, the Planck Constant, and the Bohr Orbits
Daywitt W. C.
2011-04-01
Full Text Available The Bohr orbits of the hydrogen atom and the Planck constant can be derived classically from the Maxwell equations and the assumption that there is a variation in the electron's velocity about its average value. The resonant nature of the circulating electron and its induced magnetic and Faraday fields prevents a radiative collapse of the electron into the nuclear proton. The derived Planck constant is $h=2pi e^2/alpha c$, where $e$, $alpha$, and $c$ are the electronic charge, the fine structure constant, and the speed of light. The fact that the Planck vacuum (PV theory derives the same Planck constant independently of the above implies that the two derivations are related. The following highlights that connection.
The Compton Radius, the de Broglie Radius, the Planck Constant, and the Bohr Orbits
Daywitt W. C.
2011-04-01
Full Text Available The Bohr orbits of the hydrogen atom and the Planck constant can be derived classically from the Maxwell equations and the assumption that there is a variation in the electron’s velocity about its average value [1]. The resonant nature of the circulating electron and its induced magnetic and Faraday fields prevents a radiative collapse of the electron into the nuclear proton. The derived Planck constant is h = 2 e 2 = c , where e , , and c are the electronic charge, the fine structure constant, and the speed of light. The fact that the Planck vacuum (PV theory [2] derives the same Planck constant independently of the above implies that the two derivations are related. The following highlights that connection.
The Holographic Nature of Bohr Atomic Model%波尔原子模型及其全息性
赵丽特; 王喜建; 周党培
2016-01-01
This paper shows the holographic nature of the micro world and the macro world in physics by comparing the Bohr atomic model and the movement of the planets in the solar system.%文章通过波尔原子模型和太阳系中行星运动的对比，展现物理学中微观世界和宏观世界的全息性。
Chababa, M; lahbas, A; Oulne, M
2016-01-01
A prolate {\\gamma}-rigid regime of the Bohr-Mottelson Hamiltonian within the minimal length formalism, involving an infinite square well like potential in {\\beta} collective shape variable, is developed and used to describe the spectra of a variety of vibrational-like nuclei. The effect of the minimal length on the energy spectrum and the wave function is duly investigated. Numerical calculations are performed for some nuclei revealing a qualitative agreement with the available experimental data.
Srinivasan, R
2005-01-01
The Bohr Complementarity Principle (BCP) holds in Afshar's experiment under the newly proposed NAFL (non-Aristotelian finitary logic) interpretation of quantum mechanics. NAFL requires that no `physical' reality can be ascribed to the wave nature of a single photon. The NAFL theory QM, formalizing quantum mechanics, treats the superposed state ($S$) of a single photon taking two or more different paths at the same time as a logical contradiction that is formally unprovable in QM. Nevertheless, in a non-classical NAFL model for QM in which the law of non-contradiction fails, $S$ has a meaningful metamathematical interpretation that the photon has not been measured (or axiomatically declared) to take any particular path available to it. It is argued that even the existence of an interference pattern does not logically amount to a proof that a single photon exhibits self-interference. Since QM does not prove the existence of the state $S$, it follows that one can retroactively infer, from a measurement $Q$ made ...
What is complementarity?: Niels Bohr and the architecture of quantum theory
Plotnitsky, Arkady
2014-12-01
This article explores Bohr’s argument, advanced under the heading of ‘complementarity,’ concerning quantum phenomena and quantum mechanics, and its physical and philosophical implications. In Bohr, the term complementarity designates both a particular concept and an overall interpretation of quantum phenomena and quantum mechanics, in part grounded in this concept. While the argument of this article is primarily philosophical, it will also address, historically, the development and transformations of Bohr’s thinking, under the impact of the development of quantum theory and Bohr’s confrontation with Einstein, especially their exchange concerning the EPR experiment, proposed by Einstein, Podolsky and Rosen in 1935. Bohr’s interpretation was progressively characterized by a more radical epistemology, in its ultimate form, which was developed in the 1930s and with which I shall be especially concerned here, defined by his new concepts of phenomenon and atomicity. According to this epistemology, quantum objects are seen as indescribable and possibly even as inconceivable, and as manifesting their existence only in the effects of their interactions with measuring instruments upon those instruments, effects that define phenomena in Bohr’s sense. The absence of causality is an automatic consequence of this epistemology. I shall also consider how probability and statistics work under these epistemological conditions.
What is complementarity?: Niels Bohr and the architecture of quantum theory
This article explores Bohr’s argument, advanced under the heading of ‘complementarity,’ concerning quantum phenomena and quantum mechanics, and its physical and philosophical implications. In Bohr, the term complementarity designates both a particular concept and an overall interpretation of quantum phenomena and quantum mechanics, in part grounded in this concept. While the argument of this article is primarily philosophical, it will also address, historically, the development and transformations of Bohr’s thinking, under the impact of the development of quantum theory and Bohr’s confrontation with Einstein, especially their exchange concerning the EPR experiment, proposed by Einstein, Podolsky and Rosen in 1935. Bohr’s interpretation was progressively characterized by a more radical epistemology, in its ultimate form, which was developed in the 1930s and with which I shall be especially concerned here, defined by his new concepts of phenomenon and atomicity. According to this epistemology, quantum objects are seen as indescribable and possibly even as inconceivable, and as manifesting their existence only in the effects of their interactions with measuring instruments upon those instruments, effects that define phenomena in Bohr’s sense. The absence of causality is an automatic consequence of this epistemology. I shall also consider how probability and statistics work under these epistemological conditions. (paper)
Niels Bohr, Max Delbruck and the paradox of light and life
This paper features a concise, interdisciplinary history of philosophical issues which were the basis of Delbruck's scientific career. The paradox in living behavior of freedom-to-adapt versus deterministic atomism required complete reassessment with the advent of quantum mechanics. Apparent contradictions implied, for example, by the wave-particle model led Bohr to a belief in the ''complementarity of nature,'' which in 1932 he applied to biology. His claim was that purely physicochemical explanations of purposeful life functions such as ''self-generation and freedom of the will'' were impossible since mutually exclusive situations were involved. Thus Delbruck was challenged to spend his career investigating these vital functions. Beginning with ''fruit-fly photochemistry'' he established the molecular nature of the gene and then collected a world-wide group for a research effort on phage virus, which culminated in discovery of the DNA double helix by Watson and Crick. The second phase of his career featured a study of the total stimulus-response system of the fungus Phycomuces, which is still in progress. The extreme light-sensitivity observed, approaching one-quantum response, has raised the question of the survival value of amplified quantum noise. In critical comments to the author, Delbruck opposed the ''Compton-switch model'' for mind-body interaction; and in his lecture, ''Mind from Matter?'' he revealed his ''a priori concept of truth,'' which embraces a neutral monism and rejects the language of emergent evolution. His views are contrasted with those expressed in Popper's First Darwin Lecture
Complementarity and the Nature of Uncertainty Relations in Einstein–Bohr Recoiling Slit Experiment
Shogo Tanimura
2015-07-01
Full Text Available A model of the Einstein–Bohr recoiling slit experiment is formulated in a fully quantum theoretical setting. In this model, the state and dynamics of a movable wall that has two slits in it, as well as the state of a particle incoming to the two slits, are described by quantum mechanics. Using this model, we analyzed complementarity between exhibiting an interference pattern and distinguishing the particle path. Comparing the Kennard–Robertson type and the Ozawa-type uncertainty relations, we conclude that the uncertainty relation involved in the double-slit experiment is not the Ozawa-type uncertainty relation but the Kennard-type uncertainty relation of the position and the momentum of the double-slit wall. A possible experiment to test the complementarity relation is suggested. It is also argued that various phenomena which occur at the interface of a quantum system and a classical system, including distinguishability, interference, decoherence, quantum eraser, and weak value, can be understood as aspects of entanglement.Quanta 2015; 4: 1–9.
In this paper, the main outlines of the discussions between Niels Bohr with Albert Einstein, Werner Heisenberg, and Erwin Schroedinger during 1920-1927 are treated. From the formulation of quantum mechanics in 1925-1926 and wave mechanics in 1926, there emerged Born's statistical interpretation of the wave function in summer 1926, and on the basis of the quantum mechanical transformation theory - formulated in fall 1926 by Dirac, London, and Jordan - Heisenberg formulated the uncertainty principle in early 1927. At the Volta Conference in Como in September 1927 and at the fifth Solvay Conference in Brussels the following month, Bohr publicly enunciated his complementarity principle, which had been developing in his mind for several years. The Bohr-Einstein discussions about the consistency and completeness of quantum mechanics and of physical theory as such - formally begun in October 1927 at the fifth Solvay Conference and carried on at the sixth Solvay Conference in October 1930 - were continued during the next decades. All these aspects are briefly summarized
Bohr-Weisskopf effect: influence of the distributed nuclear magnetization on hfs
Nuclear magnetic moments provide a sensitive test of nuclear wave functions, in particular those of neutrons, which are not readily obtainable from other nuclear data. These are taking added importance by recent proposals to study parity non-conservation (PNC) effects in alkali atoms in isotopic series. By taking ratios of the PNC effects in pairs of isotopes, uncertainties in the atomic wave functions are largely cancelled out at the cost of knowledge of the change in the neutron wave function. The Bohr-Weisskopf effect (B-W) in the hyperfine structure interaction of atoms measures the influence of the spatial distribution of the nuclear magnetization, and thereby provides an additional constraint on the determination of the neutron wave function. The added great importance of B-W in the determination of QED effects from the hfs in hydrogen-like ions of heavy elements, as measured recently at GSI, is noted. The B-W experiments require precision measurements of the hfs interactions and, independently, of the nuclear magnetic moments. A novel atomic beam magnetic resonance (ABMR) method, combining rf and laser excitation, has been developed for a systematic study and initially applied to stable isotopes. Difficulties in adapting the experiment to the ISOLDE radioactive ion beam, which have now been surmounted, are discussed. A first radioactive beam measurement for this study, the precision hfs of 126Cs, has been obtained recently. The result is 3629.515( 0.001) MHz. The ability of ABMR to determine with high precision nuclear magnetic moments in free atoms is a desideratum for the extraction of QED effects from the hfs of the hydrogen-like ions. We also point out manifestations of B-W in condensed matter and atomic physics
El pabellón Niels Bohr. Tradición Danesa y Modernidad
Carmen García Sánchez
2015-12-01
Full Text Available La casa de invitados de Niels Bohr fue el primer edificio del arquitecto danés Vilhelm Wohlert (1920-2007. Arraigado a la tradición danesa, representa una renovación basada en la absorción de influencias extranjeras: la arquitectura americana y la tradición japonesa. La caja de madera tiene el carácter sensible de un organismo vivo, siempre cambiante según las variaciones de luz del día o temperatura. Puertas plegables y contraventanas generan extensiones de las habitaciones. Cuando se abren, crean una prolongación del espacio interior, que se extiende a la naturaleza circundante, y se expande hacia el espacio exterior, permitiendo su movilización. Se establece una arquitectura de flujos. Protagoniza un ejemplo de la modernidad como refinamiento en la técnica de los límites y la idea de que la arquitectura no es un objeto material, sino el espacio generado en su interior. Podría ser visto como un ikebana; “el arte del espacio”, donde se produce una circulación de aire entre sus componentes; algo vivo que expresa la tercera dimensión, el equilibrio asimétrico, un interés por la materia, su textura y efecto emocional que emana. Hay armonía y equilibrio, que transmiten serenidad y belleza; un encuentro con la naturaleza; un mundo de relaciones amable al ser humano.
Exact numerical diagonalization is carried out for the Bohr Hamiltonian with a β-soft, axially stabilized potential. Wave function and observable properties are found to be dominated by strong β-γ coupling effects. The validity of the approximate separation of variables introduced with the X(5) model, extensively applied in recent analyses of axially stabilized transitional nuclei, is examined, and the reasons for its breakdown are analyzed
Yoshitada Sakai
Full Text Available BACKGROUND: Carbon dioxide (CO(2 therapy refers to the transcutaneous administration of CO(2 for therapeutic purposes. This effect has been explained by an increase in the pressure of O(2 in tissues known as the Bohr effect. However, there have been no reports investigating the oxygen dissociation of haemoglobin (Hb during transcutaneous application of CO(2in vivo. In this study, we investigate whether the Bohr effect is caused by transcutaneous application of CO2 in human living body. METHODS: We used a novel system for transcutaneous application of CO(2 using pure CO(2 gas, hydrogel, and a plastic adaptor. The validity of the CO(2 hydrogel was confirmed in vitro using a measuring device for transcutaneous CO(2 absorption using rat skin. Next, we measured the pH change in the human triceps surae muscle during transcutaneous application of CO(2 using phosphorus-31 magnetic resonance spectroscopy ((31P-MRS in vivo. In addition, oxy- and deoxy-Hb concentrations were measured with near-infrared spectroscopy in the human arm with occulted blood flow to investigate O2 dissociation from Hb caused by transcutaneous application of CO(2. RESULTS: The rat skin experiment showed that CO(2 hydrogel enhanced CO(2 gas permeation through the rat skin. The intracellular pH of the triceps surae muscle decreased significantly 10 min. after transcutaneous application of CO(2. The NIRS data show the oxy-Hb concentration decreased significantly 4 min. after CO(2 application, and deoxy-Hb concentration increased significantly 2 min. after CO(2 application in the CO(2-applied group compared to the control group. Oxy-Hb concentration significantly decreased while deoxy-Hb concentration significantly increased after transcutaneous CO(2 application. CONCLUSIONS: Our novel transcutaneous CO(2 application facilitated an O(2 dissociation from Hb in the human body, thus providing evidence of the Bohr effect in vivo.
ERMAMATOV M J; YÉPEZ-MARTÍNEZ H; SRIVASTAVA P C
2016-05-01
The band structure of the proton-odd nuclei $^{153,155}$Eu, built on Nilsson orbitals, is investigated within the framework of a recently developed extended Bohr Hamiltonian model. The relative distance between spherical orbitals is taken into account by considering single-particle energies as a parameter which changes with increasing neutron number. Energy levels of each band and$B(E2)$ values inside the ground-state band are calculated and compared with the available experimental data. Thus, more comprehensive information on the structure of deformed nuclei can be obtained by studying the rotation–vibration spectra of odd nuclei built on Nilsson single-particle orbitals.
We consider an oscillator subjected to a sudden change in equilibrium position or in effective spring constant, or both-to a squeeze in the language of quantum optics. We analyze the probability of transition from a given initial state to a final state, in its dependence on final-state quantum number. We make use of five sources of insight: Bohr-Sommerfeld quantization via bands in phase space, area of overlap between before-squeeze band and after-squeeze band, interference in phase space, Wigner function as quantum update of B-S band and near-zone Fresnel diffraction as mockup Wigner function
Trivalent hard acids (Ga3+, In3+, Yb3+, Tm3+), which have complete d-shells, were bound to the acid mucopolysaccharide with a molecular mass of about 10.000 Daltons in soft tissue. Tri-, tetra-, and pentavalent hard acids and some borderline acids which have incomplete d-shells were bound to the acid mucopolysaccharides, whose molecular masses exceed 40.000 Daltons in soft tissues. Based on these results and the facts reported previously a very interesting relationship was recognized between the location of elements in the Thomsen-Bohr periodic table and the substances to which they bind. (author) 21 refs.; 2 figs.; 3 tabs
Vayenas, Constantinos G
2012-01-01
This book shows that the strong interaction forces, which keep hadrons and nuclei together, are relativistic gravitational forces exerted between very small particles in the mass range of neutrinos. First, this book considers the problematic motion of two charged particles under the influence of electrostatic and gravitational forces only, which shows that bound states are formed by following the same semi-classical methodology used by Bohr to describe the H atom. This approach is also coupled with Newton's gravitational law and with Einstein's special relativity. The results agree with experi
Schmidt, L Ph H; Lower, J; Jahnke, T; Schößler, S; Schöffler, M S; Menssen, A; Lévêque, C; Sisourat, N; Taïeb, R; Schmidt-Böcking, H; Dörner, R
2013-09-01
We simultaneously measured the momentum transferred to a free-floating molecular double slit and the momentum change of the atom scattering from it. Our experimental results are compared to quantum mechanical and semiclassical models. The results reveal that a classical description of the slits, which was used by Einstein in his debate with Bohr, provides a surprisingly good description of the experimental results, even for a microscopic system, if momentum transfer is not ascribed to a specific pathway but shared coherently and simultaneously between both. PMID:25166663
Diophantine approximation and badly approximable sets
Kristensen, S.; Thorn, R.; Velani, S.
2006-01-01
Let (X,d) be a metric space and (Omega, d) a compact subspace of X which supports a non-atomic finite measure m. We consider `natural' classes of badly approximable subsets of Omega. Loosely speaking, these consist of points in Omega which `stay clear' of some given set of points in X....... The classical set Bad of `badly approximable' numbers in the theory of Diophantine approximation falls within our framework as do the sets Bad(i,j) of simultaneously badly approximable numbers. Under various natural conditions we prove that the badly approximable subsets of Omega have full Hausdorff dimension...
Heyrovska, Raji
2007-01-01
An earlier finding that the van der waals radii are related to their de broglie wavelengths for some non-metallic elements has been extended here to show that in fact, they vary linearly with the ground state bohr radii for all the elements of groups 1a to 8 a. Similarly, the valence shell radii and the covalent radii are shown to be linearly dependent on the bohr radii. One table of data and 5 figures have been provided here showing that all the above radii are sums of two lengths, one of which is a multiple of the bohr radius and the other, a positive or negative constant for each group of elements.
Recent developments and applications of an algebraic version of Bohr's collective model, known as the algebraic collective model (ACM), have shown that fully converged calculations can be performed for a large range of Hamiltonians. Examining the algebraic structure underlying the Bohr model (BM) has also clarified its relationship with the interacting boson model (IBM), with which it has related solvable limits and corresponding dynamical symmetries. In particular, the algebraic structure of the IBM is obtained as a compactification of the BM and conversely the BM is regained in various contraction limits of the IBM. In a previous paper, corresponding contractions were identified and confirmed numerically for axially-symmetric states of relatively small deformation. In this paper, we extend the comparisons to realistic deformations and compare results of the two models in the rotor-vibrator limit. These models describe rotations and vibrations about an axially symmetric prolate or oblate rotor, and rotations and vibrations of a triaxial rotor. It is determined that most of the standard results of the BM can be obtained as contraction limits of the IBM in its U(5)-SO(6) dynamical symmetries.
Heyrovska, R
2005-01-01
Sommerfeld introduced the fine-structure constant into physics, while he was taking into account the relativistic effects in the theory of the hydrogen atom. Ever since, it has puzzled many scientists like Eddington, Dirac, Feynman and others. Here the mysterious fine-structure constant, alpha = (Compton wavelength/de Broglie wavelength) = 1/137.036 = 2.627/360 is interpreted based on the finding that it is close to 2.618/360 = 1/137.508, where the Compton wavelength for hydrogen is a distance equivalent to an arc length on the circumference (given by the de Broglie wavelength) of a circle with the Bohr radius and 2.618 is the square of the Golden ratio, which was recently shown to divide the Bohr radius into two Golden sections at the point of electrical neutrality. From the data for the electron (e) and proton (p) g-factors, it is found that (137.508 - 137.036)= 0.472 = [g(p) - g(e)]/[g(p) + g(e)] (= 2/cube of the Golden ratio), and that (2.627 - 2.618)/360 = (small part of the Compton wavelength correspond...
Heyrovska, Raji
2007-01-01
An earlier finding that the van der waals radii are related to their de broglie wavelengths for some non-metallic elements has been extended here to show that in fact, they vary linearly with the ground state bohr radii for all the elements of groups 1a to 8 a. Similarly, the valence shell radii and the covalent radii are shown to be linearly dependent on the bohr radii. One table of data and 5 figures have been provided here showing that all the above radii are sums of two lengths, one of wh...
Bin Qin
2014-01-01
Relationships between fuzzy relations and fuzzy topologies are deeply researched. The concept of fuzzy approximating spaces is introduced and decision conditions that a fuzzy topological space is a fuzzy approximating space are obtained.
Stochastic approximation: invited paper
Lai, Tze Leung
2003-01-01
Stochastic approximation, introduced by Robbins and Monro in 1951, has become an important and vibrant subject in optimization, control and signal processing. This paper reviews Robbins' contributions to stochastic approximation and gives an overview of several related developments.
Rasin, A
1994-01-01
We discuss the idea of approximate flavor symmetries. Relations between approximate flavor symmetries and natural flavor conservation and democracy models is explored. Implications for neutrino physics are also discussed.
Approximate iterative algorithms
Almudevar, Anthony Louis
2014-01-01
Iterative algorithms often rely on approximate evaluation techniques, which may include statistical estimation, computer simulation or functional approximation. This volume presents methods for the study of approximate iterative algorithms, providing tools for the derivation of error bounds and convergence rates, and for the optimal design of such algorithms. Techniques of functional analysis are used to derive analytical relationships between approximation methods and convergence properties for general classes of algorithms. This work provides the necessary background in functional analysis a
Barkas effect in the semiclassical approximation
In this paper, it has been shown that the inclusion of the position of an atomic electron with respect to a projectile particle modifies the contribution from the adiabatic interaction. This is a reason for the reduction of energy loss of slow particles as compared to the Bohr theory. It has been found that the energy loss per unit length can be represented as a product of two functions: the Bohr energy losses and the dynamic function representing the corrections associated with the features of the motion of an electron in a target atom
Approximation of distributed delays
Lu, Hao; Eberard, Damien; Simon, Jean-Pierre
2010-01-01
We address in this paper the approximation problem of distributed delays. Such elements are convolution operators with kernel having bounded support, and appear in the control of time-delay systems. From the rich literature on this topic, we propose a general methodology to achieve such an approximation. For this, we enclose the approximation problem in the graph topology, and work with the norm defined over the convolution Banach algebra. The class of rational approximates is described, and a constructive approximation is proposed. Analysis in time and frequency domains is provided. This methodology is illustrated on the stabilization control problem, for which simulations results show the effectiveness of the proposed methodology.
Sparse approximation with bases
2015-01-01
This book systematically presents recent fundamental results on greedy approximation with respect to bases. Motivated by numerous applications, the last decade has seen great successes in studying nonlinear sparse approximation. Recent findings have established that greedy-type algorithms are suitable methods of nonlinear approximation in both sparse approximation with respect to bases and sparse approximation with respect to redundant systems. These insights, combined with some previous fundamental results, form the basis for constructing the theory of greedy approximation. Taking into account the theoretical and practical demand for this kind of theory, the book systematically elaborates a theoretical framework for greedy approximation and its applications. The book addresses the needs of researchers working in numerical mathematics, harmonic analysis, and functional analysis. It quickly takes the reader from classical results to the latest frontier, but is written at the level of a graduate course and do...
YueShihong; ZhangKecun
2002-01-01
In a dot product space with the reproducing kernel (r. k. S. ) ,a fuzzy system with the estimation approximation errors is proposed ,which overcomes the defect that the existing fuzzy control system is difficult to estimate the errors of approximation for a desired function,and keeps the characteristics of fuzzy system as an inference approach. The structure of the new fuzzy approximator benefits a course got by other means.
Malvina Baica
1985-01-01
The author uses a new modification of Jacobi-Perron Algorithm which holds for complex fields of any degree (abbr. ACF), and defines it as Generalized Euclidean Algorithm (abbr. GEA) to approximate irrationals.This paper deals with approximation of irrationals of degree n=2,3,5. Though approximations of these irrationals in a variety of patterns are known, the results are new and practical, since there is used an algorithmic method.
Expectation Consistent Approximate Inference
Opper, Manfred; Winther, Ole
2005-01-01
We propose a novel framework for approximations to intractable probabilistic models which is based on a free energy formulation. The approximation can be understood from replacing an average over the original intractable distribution with a tractable one. It requires two tractable probability distributions which are made consistent on a set of moments and encode different features of the original intractable distribution. In this way we are able to use Gaussian approximations for models with ...
Approximation techniques for engineers
Komzsik, Louis
2006-01-01
Presenting numerous examples, algorithms, and industrial applications, Approximation Techniques for Engineers is your complete guide to the major techniques used in modern engineering practice. Whether you need approximations for discrete data of continuous functions, or you''re looking for approximate solutions to engineering problems, everything you need is nestled between the covers of this book. Now you can benefit from Louis Komzsik''s years of industrial experience to gain a working knowledge of a vast array of approximation techniques through this complete and self-contained resource.
The Fisher-Shannon information and a statistical measure of complexity are calculated in position and momentum spaces for the wavefunctions of the quantum isotropic harmonic oscillator. We show that these quantities are independent of the strength of the harmonic potential. Moreover, for each level of energy, it is found that these two indicators take their minimum values on the orbitals that correspond to the classical (circular) orbits in the Bohr-like quantum image, just those with the highest orbital angular momentum
Expectation Consistent Approximate Inference
Opper, Manfred; Winther, Ole
2005-01-01
We propose a novel framework for approximations to intractable probabilistic models which is based on a free energy formulation. The approximation can be understood from replacing an average over the original intractable distribution with a tractable one. It requires two tractable probability dis...
Heyrovska, R.; Narayan, S.
2005-10-01
Recently, the ground state Bohr radius (aB) of hydrogen was shown to be divided into two Golden sections, aB,p = aB/ø2 and aB,e = aB/ø at the point of electrical neutrality, where ø = 1.618 is the Golden ratio (R. Heyrovska, Molecular Physics 103: 877-882, and the literature cited therein). The origin of the difference of two energy terms in the Rydberg equation was thus shown to be in the ground state energy itself, as shown below: EH = (1/2)e2/(κaB) = (1/2)(e2/κ) [(1/aB,p - (1/aB,e)] (1). This work brings some new results that 1) a unit charge in vacuum has a magnetic moment, 2) (e2/2κ) in eq. (1) is an electromagnetic condenser constant, 3) the de Broglie wavelengths of the proton and electron correspond to the Golden arcs of a circle with the Bohr radius, 4) the fine structure constant (α) is the ratio of the Planck's constants without and with the interaction of light with matter, 5) the g-factors of the electron and proton, ge/2 and gp/2 divide the Bohr radius at the magnetic center and 6) the ``mysterious'' value (137.036) of α -1 = (360/ø2) - (2/ø3), where (2/ø3) arises from the difference, (gp - ge).
Ordered cones and approximation
Keimel, Klaus
1992-01-01
This book presents a unified approach to Korovkin-type approximation theorems. It includes classical material on the approximation of real-valuedfunctions as well as recent and new results on set-valued functions and stochastic processes, and on weighted approximation. The results are notonly of qualitative nature, but include quantitative bounds on the order of approximation. The book is addressed to researchers in functional analysis and approximation theory as well as to those that want to applythese methods in other fields. It is largely self- contained, but the readershould have a solid background in abstract functional analysis. The unified approach is based on a new notion of locally convex ordered cones that are not embeddable in vector spaces but allow Hahn-Banach type separation and extension theorems. This concept seems to be of independent interest.
Approximate Modified Policy Iteration
Scherrer, Bruno; Ghavamzadeh, Mohammad; Geist, Matthieu
2012-01-01
Modified policy iteration (MPI) is a dynamic programming (DP) algorithm that contains the two celebrated policy and value iteration methods. Despite its generality, MPI has not been thoroughly studied, especially its approximation form which is used when the state and/or action spaces are large or infinite. In this paper, we propose three approximate MPI (AMPI) algorithms that are extensions of the well-known approximate DP algorithms: fitted-value iteration, fitted-Q iteration, and classification-based policy iteration. We provide an error propagation analysis for AMPI that unifies those for approximate policy and value iteration. We also provide a finite-sample analysis for the classification-based implementation of AMPI (CBMPI), which is more general (and somehow contains) than the analysis of the other presented AMPI algorithms. An interesting observation is that the MPI's parameter allows us to control the balance of errors (in value function approximation and in estimating the greedy policy) in the fina...
Approximations to toroidal harmonics
Toroidal harmonics P/sub n-1/2/1(cosh μ) and Q/sub n-1/2/1(cosh μ) are useful in solutions to Maxwell's equations in toroidal coordinates. In order to speed their computation, a set of approximations has been developed that is valid over the range 0 -10. The simple method used to determine the approximations is described. Relative error curves are also presented, obtained by comparing approximations to the more accurate values computed by direct summation of the hypergeometric series
Jensen, F B
2004-11-01
The discovery of the S-shaped O2 equilibrium curve and the Bohr effect in 1904 stimulated a fertile and continued research into respiratory functions of blood and allosteric mechanisms in haemoglobin (Hb). The Bohr effect (influence of pH/CO2 on Hb O2 affinity) and the reciprocal Haldane effect (influence of HbO2 saturation on H+/CO2 binding) originate in the Hb oxy-deoxy conformational change and allosteric interactions between O2 and H+/CO2 binding sites. In steady state, H+ is passively distributed across the vertebrate red blood cell (RBC) membrane, and intracellular pH (pHi) changes are related to changes in extracellular pH, Hb-O2 saturation and RBC organic phosphate content. As the Hb molecule shifts between the oxy and deoxy conformation in arterial-venous gas transport, it delivers O2 and takes up CO2 and H+ in tissue capillaries (elegantly aided by the Bohr effect). Concomitantly, the RBC may sense local O2 demand via the degree of Hb deoxygenation and release vasodilatory agents to match local blood flow with requirements. Three recent hypotheses suggest (1) release of NO from S-nitroso-Hb upon deoxygenation, (2) reduction of nitrite to vasoactive NO by deoxy haems, and (3) release of ATP. Inside RBCs, carbonic anhydrase (CA) provides fast hydration of metabolic CO2 and ensures that the Bohr shift occurs during capillary transit. The formed H+ is bound to Hb (Haldane effect) while HCO3- is shifted to plasma via the anion exchanger (AE1). The magnitude of the oxylabile H+ binding shows characteristic differences among vertebrates. Alternative strategies for CO2 transport include direct HCO3- binding to deoxyHb in crocodilians, and high intracellular free [HCO3-] (due to high pHi) in lampreys. At the RBC membrane, CA, AE1 and other proteins may associate into what appears to be an integrated gas exchange metabolon. Oxygenation-linked binding of Hb to the membrane may regulate glycolysis in mammals and perhaps also oxygen-sensitive ion transport involved in
Approximations in Inspection Planning
Engelund, S.; Sørensen, John Dalsgaard; Faber, M. H.; Bloch, Allan
2000-01-01
. One of the more important of these approximations is the assumption that all inspections will reveal no defects. Using this approximation the optimal inspection plan may be determined on the basis of conditional probabilities, i.e. the probability of failure given no defects have been found by the......Planning of inspections of civil engineering structures may be performed within the framework of Bayesian decision analysis. The effort involved in a full Bayesian decision analysis is relatively large. Therefore, the actual inspection planning is usually performed using a number of approximations...... inspection. In this paper the quality of this approximation is investigated. The inspection planning is formulated both as a full Bayesian decision problem and on the basis of the assumption that the inspection will reveal no defects....
The Karlqvist approximation revisited
Tannous, C.
2015-01-01
The Karlqvist approximation signaling the historical beginning of magnetic recording head theory is reviewed and compared to various approaches progressing from Green, Fourier, Conformal mapping that obeys the Sommerfeld edge condition at angular points and leads to exact results.
Approximation Behooves Calibration
da Silva Ribeiro, André Manuel; Poulsen, Rolf
2013-01-01
Calibration based on an expansion approximation for option prices in the Heston stochastic volatility model gives stable, accurate, and fast results for S&P500-index option data over the period 2005–2009.......Calibration based on an expansion approximation for option prices in the Heston stochastic volatility model gives stable, accurate, and fast results for S&P500-index option data over the period 2005–2009....
Gautschi, Walter; Rassias, Themistocles M
2011-01-01
Approximation theory and numerical analysis are central to the creation of accurate computer simulations and mathematical models. Research in these areas can influence the computational techniques used in a variety of mathematical and computational sciences. This collection of contributed chapters, dedicated to renowned mathematician Gradimir V. Milovanovia, represent the recent work of experts in the fields of approximation theory and numerical analysis. These invited contributions describe new trends in these important areas of research including theoretic developments, new computational alg
Dutta, Soumitra
1988-01-01
Much of human reasoning is approximate in nature. Formal models of reasoning traditionally try to be precise and reject the fuzziness of concepts in natural use and replace them with non-fuzzy scientific explicata by a process of precisiation. As an alternate to this approach, it has been suggested that rather than regard human reasoning processes as themselves approximating to some more refined and exact logical process that can be carried out with mathematical precision, the essence and power of human reasoning is in its capability to grasp and use inexact concepts directly. This view is supported by the widespread fuzziness of simple everyday terms (e.g., near tall) and the complexity of ordinary tasks (e.g., cleaning a room). Spatial reasoning is an area where humans consistently reason approximately with demonstrably good results. Consider the case of crossing a traffic intersection. We have only an approximate idea of the locations and speeds of various obstacles (e.g., persons and vehicles), but we nevertheless manage to cross such traffic intersections without any harm. The details of our mental processes which enable us to carry out such intricate tasks in such apparently simple manner are not well understood. However, it is that we try to incorporate such approximate reasoning techniques in our computer systems. Approximate spatial reasoning is very important for intelligent mobile agents (e.g., robots), specially for those operating in uncertain or unknown or dynamic domains.
Rao, M J; Acharya, A S
1992-08-18
Glu-43(beta) of hemoglobin A exhibits a high degree of chemical reactivity around neutral pH for amidation with nucleophiles in the presence of carbodiimide. Such a reactivity is unusual for the side-chain carboxyl groups of proteins. In addition, the reactivity of Glu-43(beta) is also sensitive to the ligation state of the protein [Rao, M. J., & Acharya, A. S. (1991) J. Protein Chem. 10, 129-138]. The influence of deoxygenation of hemoglobin A on the chemical reactivity of the gamma-carboxyl group of Glu-43(beta) has now been investigated as a function of pH (from 5.5 to 7.5). The chemical reactivity of Glu-43(beta) for amidation increases upon deoxygenation only when the modification reaction is carried out above pH 6.0. The pH-chemical reactivity profile of the amidation of hemoglobin A in the deoxy conformation reflects an apparent pKa of 7.0 for the gamma-carboxyl group of Glu-43(beta). This pKa is considerably higher than the pKa of 6.35 for the oxy conformation. The deoxy conformational transition mediated increase in the pKa of the gamma-carboxyl group of Glu-43(beta) implicates this carboxyl group as an alkaline Bohr group. The amidated derivative of hemoglobin A with 2 mol of glycine ethyl ester covalently bound to the protein was isolated by CM-cellulose chromatography.(ABSTRACT TRUNCATED AT 250 WORDS) PMID:1354984
Diophantine approximations on fractals
Einsiedler, Manfred; Shapira, Uri
2009-01-01
We exploit dynamical properties of diagonal actions to derive results in Diophantine approximations. In particular, we prove that the continued fraction expansion of almost any point on the middle third Cantor set (with respect to the natural measure) contains all finite patterns (hence is well approximable). Similarly, we show that for a variety of fractals in [0,1]^2, possessing some symmetry, almost any point is not Dirichlet improvable (hence is well approximable) and has property C (after Cassels). We then settle by similar methods a conjecture of M. Boshernitzan saying that there are no irrational numbers x in the unit interval such that the continued fraction expansions of {nx mod1 : n is a natural number} are uniformly eventually bounded.
Covariant approximation averaging
Shintani, Eigo; Blum, Thomas; Izubuchi, Taku; Jung, Chulwoo; Lehner, Christoph
2014-01-01
We present a new class of statistical error reduction techniques for Monte-Carlo simulations. Using covariant symmetries, we show that correlation functions can be constructed from inexpensive approximations without introducing any systematic bias in the final result. We introduce a new class of covariant approximation averaging techniques, known as all-mode averaging (AMA), in which the approximation takes account of contributions of all eigenmodes through the inverse of the Dirac operator computed from the conjugate gradient method with a relaxed stopping condition. In this paper we compare the performance and computational cost of our new method with traditional methods using correlation functions and masses of the pion, nucleon, and vector meson in $N_f=2+1$ lattice QCD using domain-wall fermions. This comparison indicates that AMA significantly reduces statistical errors in Monte-Carlo calculations over conventional methods for the same cost.
Accuracy of Approximate Eigenstates
Lucha, Wolfgang; Lucha, Wolfgang
2000-01-01
Besides perturbation theory, which requires, of course, the knowledge of the exact unperturbed solution, variational techniques represent the main tool for any investigation of the eigenvalue problem of some semibounded operator H in quantum theory. For a reasonable choice of the employed trial subspace of the domain of H, the lowest eigenvalues of H usually can be located with acceptable precision whereas the trial-subspace vectors corresponding to these eigenvalues approximate, in general, the exact eigenstates of H with much less accuracy. Accordingly, various measures for the accuracy of the approximate eigenstates derived by variational techniques are scrutinized. In particular, the matrix elements of the commutator of the operator H and (suitably chosen) different operators, with respect to degenerate approximate eigenstates of H obtained by some variational method, are proposed here as new criteria for the accuracy of variational eigenstates. These considerations are applied to that Hamiltonian the eig...
Synthesis of approximation errors
Bareiss, E.H.; Michel, P.
1977-07-01
A method is developed for the synthesis of the error in approximations in the large of regular and irregular functions. The synthesis uses a small class of dimensionless elementary error functions which are weighted by the coefficients of the expansion of the regular part of the function. The question is answered whether a computer can determine the analytical nature of a solution by numerical methods. It is shown that continuous least-squares approximations of irregular functions can be replaced by discrete least-squares approximation and how to select the discrete points. The elementary error functions are used to show how the classical convergence criterions can be markedly improved. There are eight numerical examples included, 30 figures and 74 tables.
White, Martin
2014-01-01
This year marks the 100th anniversary of the birth of Yakov Zel'dovich. Amongst his many legacies is the Zel'dovich approximation for the growth of large-scale structure, which remains one of the most successful and insightful analytic models of structure formation. We use the Zel'dovich approximation to compute the two-point function of the matter and biased tracers, and compare to the results of N-body simulations and other Lagrangian perturbation theories. We show that Lagrangian perturbation theories converge well and that the Zel'dovich approximation provides a good fit to the N-body results except for the quadrupole moment of the halo correlation function. We extend the calculation of halo bias to 3rd order and also consider non-local biasing schemes, none of which remove the discrepancy. We argue that a part of the discrepancy owes to an incorrect prediction of inter-halo velocity correlations. We use the Zel'dovich approximation to compute the ingredients of the Gaussian streaming model and show that ...
Prestack wavefield approximations
Alkhalifah, Tariq
2013-09-01
The double-square-root (DSR) relation offers a platform to perform prestack imaging using an extended single wavefield that honors the geometrical configuration between sources, receivers, and the image point, or in other words, prestack wavefields. Extrapolating such wavefields, nevertheless, suffers from limitations. Chief among them is the singularity associated with horizontally propagating waves. I have devised highly accurate approximations free of such singularities which are highly accurate. Specifically, I use Padé expansions with denominators given by a power series that is an order lower than that of the numerator, and thus, introduce a free variable to balance the series order and normalize the singularity. For the higher-order Padé approximation, the errors are negligible. Additional simplifications, like recasting the DSR formula as a function of scattering angle, allow for a singularity free form that is useful for constant-angle-gather imaging. A dynamic form of this DSR formula can be supported by kinematic evaluations of the scattering angle to provide efficient prestack wavefield construction. Applying a similar approximation to the dip angle yields an efficient 1D wave equation with the scattering and dip angles extracted from, for example, DSR ray tracing. Application to the complex Marmousi data set demonstrates that these approximations, although they may provide less than optimal results, allow for efficient and flexible implementations. © 2013 Society of Exploration Geophysicists.
Madsen, Rasmus Elsborg
2005-01-01
The Dirichlet compound multinomial (DCM), which has recently been shown to be well suited for modeling for word burstiness in documents, is here investigated. A number of conceptual explanations that account for these recent results, are provided. An exponential family approximation of the DCM that...
Assessment of the roles of the carboxyl-terminal β146 histidyl residues in the alkaline Bohr effect in human and normal adult hemoglobin by high-resolution proton nuclear magnetic resonance spectroscopy requires assignment of the resonances corresponding to these residues. By a careful spectroscopic study of human normal adult hemoglobin, enzymatically prepared des(His146β)-hemoglobin, and the mutant hemoglobins Cowtown (β146His → Leu) and York (β146His → Pro), the authors have resolved some of these conflicting results. By a close incremental variation of pH over a wide range in chloride-free 0.1 M N-(2-hydroxyethyl)piperazine-N'-2-ethanesulfonic acid buffer, a single resonance has been found to be consistently missing in the proton nuclear magnetic resonance spectra of these hemoglobin variants. The results indicate that the contribution of the β146 histidyl residues is 0.52 H+/hemoglobin tetramer at pH 7.6, markedly less than 0.8 H+/hemoglobin tetramer estimated by study of the mutant hemoglobin Cowtown (β146His → Leu) by Shih and Perutz. They have found that at least two histidyl residues in the carbonmonoxy form of this mutant have pK values that are perturbed, and they suggest that these pK differences may in part account for this discrepancy. The results show that the pK values of β146 histidyl residues in the carbonmonoxy form of hemoglobin are substantially affected by the presence of chloride and other anions in the solvent, and thus, the contribution of this amino acid residue to the alkaline Bohr effect can be shown to vary widely in magnitude, depending on the solvent composition. These results demonstrate that the detailed molecular mechanisms of the alkaline Bohr effect are not unique but are affected both by the hemoglobin structure and by the interactions with the solvent components in which the hemoglobin molecule resides
Prestack traveltime approximations
Alkhalifah, Tariq Ali
2011-01-01
Most prestack traveltime relations we tend work with are based on homogeneous (or semi-homogenous, possibly effective) media approximations. This includes the multi-focusing or double square-root (DSR) and the common reflection stack (CRS) equations. Using the DSR equation, I analyze the associated eikonal form in the general source-receiver domain. Like its wave-equation counterpart, it suffers from a critical singularity for horizontally traveling waves. As a result, I derive expansion based solutions of this eikonal based on polynomial expansions in terms of the reflection and dip angles in a generally inhomogenous background medium. These approximate solutions are free of singularities and can be used to estimate travetimes for small to moderate offsets (or reflection angles) in a generally inhomogeneous medium. A Marmousi example demonstrates the usefulness of the approach. © 2011 Society of Exploration Geophysicists.
Richtárik, Peter
2008-01-01
In this paper we propose and analyze a variant of the level method [4], which is an algorithm for minimizing nonsmooth convex functions. The main work per iteration is spent on 1) minimizing a piecewise-linear model of the objective function and on 2) projecting onto the intersection of the feasible region and a polyhedron arising as a level set of the model. We show that by replacing exact computations in both cases by approximate computations, in relative scale, the theoretical ...
Approximate Bayesian recursive estimation
Kárný, Miroslav
2014-01-01
Roč. 285, č. 1 (2014), s. 100-111. ISSN 0020-0255 R&D Projects: GA ČR GA13-13502S Institutional support: RVO:67985556 Keywords : Approximate parameter estimation * Bayesian recursive estimation * Kullback–Leibler divergence * Forgetting Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 4.038, year: 2014 http://library.utia.cas.cz/separaty/2014/AS/karny-0425539.pdf
Local approximate inference algorithms
Jung, Kyomin; Shah, Devavrat
2006-01-01
We present a new local approximation algorithm for computing Maximum a Posteriori (MAP) and log-partition function for arbitrary exponential family distribution represented by a finite-valued pair-wise Markov random field (MRF), say $G$. Our algorithm is based on decomposition of $G$ into {\\em appropriately} chosen small components; then computing estimates locally in each of these components and then producing a {\\em good} global solution. We show that if the underlying graph $G$ either excl...
Fragments of approximate counting
Buss, S.R.; Kolodziejczyk, L.. A.; Thapen, Neil
2014-01-01
Roč. 79, č. 2 (2014), s. 496-525. ISSN 0022-4812 R&D Projects: GA AV ČR IAA100190902 Institutional support: RVO:67985840 Keywords : approximate counting * bounded arithmetic * ordering principle Subject RIV: BA - General Mathematics Impact factor: 0.541, year: 2014 http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9287274&fileId=S0022481213000376
Highlights: • Development of optimization rules for S2 quadrature sets. • Studying the dependency of optimized S2 quadratures on composition and geometry. • Demonstrating S2 procedures preserving the features of higher approximations. - Abstract: Discrete ordinates method relies on approximating the integral term of the transport equation with the aid of quadrature summation rules. These quadratures are usually based on certain assumptions which assure specific symmetry rules and transport/diffusion limits. Generally, these assumptions are not problem-dependent which results in inaccuracies in some instances. Here, various methods have been developed for more accurate estimation of the independent angle in S2 approximation, as it is tightly related to valid estimation of the diffusion coefficient/length. We proposed and examined a method to reduce a complicated problem that usually is consisting many energy groups and discrete directions (SN) to an equivalent one-group S2 problem while it mostly preserves general features of the original model. Some numerical results are demonstrated to show the accuracy of proposed method
Chalasani, P.; Saias, I. [Los Alamos National Lab., NM (United States); Jha, S. [Carnegie Mellon Univ., Pittsburgh, PA (United States)
1996-04-08
As increasingly large volumes of sophisticated options (called derivative securities) are traded in world financial markets, determining a fair price for these options has become an important and difficult computational problem. Many valuation codes use the binomial pricing model, in which the stock price is driven by a random walk. In this model, the value of an n-period option on a stock is the expected time-discounted value of the future cash flow on an n-period stock price path. Path-dependent options are particularly difficult to value since the future cash flow depends on the entire stock price path rather than on just the final stock price. Currently such options are approximately priced by Monte carlo methods with error bounds that hold only with high probability and which are reduced by increasing the number of simulation runs. In this paper the authors show that pricing an arbitrary path-dependent option is {number_sign}-P hard. They show that certain types f path-dependent options can be valued exactly in polynomial time. Asian options are path-dependent options that are particularly hard to price, and for these they design deterministic polynomial-time approximate algorithms. They show that the value of a perpetual American put option (which can be computed in constant time) is in many cases a good approximation to the value of an otherwise identical n-period American put option. In contrast to Monte Carlo methods, the algorithms have guaranteed error bounds that are polynormally small (and in some cases exponentially small) in the maturity n. For the error analysis they derive large-deviation results for random walks that may be of independent interest.
A simple approach employing properties of solutions of differential equations is adopted to derive an appropriate extension of the WKBJ method. Some of the earlier techniques that are commonly in use are unified, whereby the general approximate solution to a second-order homogeneous linear differential equation is presented in a standard form that is valid for all orders. In comparison to other methods, the present one is shown to be leading in the order of iteration, and thus possibly has the ability of accelerating the convergence of the solution. The method is also extended for the solution of inhomogeneous equations. (author)
Approximation by Cylinder Surfaces
Randrup, Thomas
1997-01-01
We present a new method for approximation of a given surface by a cylinder surface. It is a constructive geometric method, leading to a monorail representation of the cylinder surface. By use of a weighted Gaussian image of the given surface, we determine a projection plane. In the orthogonal...... projection of the surface onto this plane, a reference curve is determined by use of methods for thinning of binary images. Finally, the cylinder surface is constructed as follows: the directrix of the cylinder surface is determined by a least squares method minimizing the distance to the points in the...
Finite elements and approximation
Zienkiewicz, O C
2006-01-01
A powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises.Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual methods in the context of continuous trial functions, and piecewise defined trial functions and the finite element method. Additional topics include higher o
Approximations to Euler's constant
We study a problem of finding good approximations to Euler's constant γ=lim→∞ Sn, where Sn = Σk=Ln (1)/k-log(n+1), by linear forms in logarithms and harmonic numbers. In 1995, C. Elsner showed that slow convergence of the sequence Sn can be significantly improved if Sn is replaced by linear combinations of Sn with integer coefficients. In this paper, considering more general linear transformations of the sequence Sn we establish new accelerating convergence formulae for γ. Our estimates sharpen and generalize recent Elsner's, Rivoal's and author's results. (author)
Chen, Dan
2012-01-01
We consider the problem of approximating the majority depth (Liu and Singh, 1993) of a point q with respect to an n-point set, S, by random sampling. At the heart of this problem is a data structures question: How can we preprocess a set of n lines so that we can quickly test whether a randomly selected vertex in the arrangement of these lines is above or below the median level. We describe a Monte-Carlo data structure for this problem that can be constructed in O(nlog n$ time, can answer queries O((log n)^{4/3}) expected time, and answers correctly with high probability.
The Compact Approximation Property does not imply the Approximation Property
Willis, George A.
1992-01-01
It is shown how to construct, given a Banach space which does not have the approximation property, another Banach space which does not have the approximation property but which does have the compact approximation property.
Prestack traveltime approximations
Alkhalifah, Tariq Ali
2012-05-01
Many of the explicit prestack traveltime relations used in practice are based on homogeneous (or semi-homogenous, possibly effective) media approximations. This includes the multifocusing, based on the double square-root (DSR) equation, and the common reflection stack (CRS) approaches. Using the DSR equation, I constructed the associated eikonal form in the general source-receiver domain. Like its wave-equation counterpart, it suffers from a critical singularity for horizontally traveling waves. As a result, I recasted the eikonal in terms of the reflection angle, and thus, derived expansion based solutions of this eikonal in terms of the difference between the source and receiver velocities in a generally inhomogenous background medium. The zero-order term solution, corresponding to ignoring the lateral velocity variation in estimating the prestack part, is free of singularities and can be used to estimate traveltimes for small to moderate offsets (or reflection angles) in a generally inhomogeneous medium. The higher-order terms include limitations for horizontally traveling waves, however, we can readily enforce stability constraints to avoid such singularities. In fact, another expansion over reflection angle can help us avoid these singularities by requiring the source and receiver velocities to be different. On the other hand, expansions in terms of reflection angles result in singularity free equations. For a homogenous background medium, as a test, the solutions are reasonably accurate to large reflection and dip angles. A Marmousi example demonstrated the usefulness and versatility of the formulation. © 2012 Society of Exploration Geophysicists.
Interacting boson approximation
Lectures notes on the Interacting Boson Approximation are given. Topics include: angular momentum tensors; properties of T/sub i//sup (n)/ matrices; T/sub i//sup (n)/ matrices as Clebsch-Gordan coefficients; construction of higher rank tensors; normalization: trace of products of two s-rank tensors; completeness relation; algebra of U(N); eigenvalue of the quadratic Casimir operator for U(3); general result for U(N); angular momentum content of U(3) representation; p-Boson model; Hamiltonian; quadrupole transitions; S,P Boson model; expectation value of dipole operator; S-D model: U(6); quadratic Casimir operator; an O(5) subgroup; an O(6) subgroup; properties of O(5) representations; quadratic Casimir operator; quadratic Casimir operator for U(6); decomposition via SU(5) chain; a special O(3) decomposition of SU(3); useful identities; a useful property of D/sub αβγ/(α,β,γ = 4-8) as coupling coefficients; explicit construction of T/sub x//sup (2)/ and d/sub αβγ/; D-coefficients; eigenstates of T3; and summary of T = 2 states
Operators of Approximations and Approximate Power Set Spaces
ZHANG Xian-yong; MO Zhi-wen; SHU Lan
2004-01-01
Boundary inner and outer operators are introduced; and union, intersection, complement operators of approximations are redefined. The approximation operators have a good property of maintaining union, intersection, complement operators, so the rough set theory has been enriched from the operator-oriented and set-oriented views. Approximate power set spaces are defined, and it is proved that the approximation operators are epimorphisms from power set space to approximate power set spaces. Some basic properties of approximate power set space are got by epimorphisms in contrast to power set space.
Tkalya, E V
2016-01-01
The magnetic hyperfine (MHF) structure of the $5/2^+$(0.0 eV) ground state and the low-lying $3/2^+$(7.8 eV) isomeric state of the $^{229}$Th nucleus in highly charged ions Th$^{89+}$ and Th$^{87+}$ is calculated. The distribution of the nuclear magnetization (the Bohr-Weisskopf effect) is accounted for in the framework of the collective nuclear model with the wave functions of the Nilsson model for the unpaired neutron. The deviations of the MHF structure for the ground and isomeric states from their values in the model of point-like nuclear magnetic dipole are calculated. The influence of the mixing of the states with the same quantum number $F$ on the energy of sublevels is studied. Taking into account the mixing of states, the probabilities of the transitions between the components of MHF structure are found.
Approximation algorithms and hardness of approximation for knapsack problems
Buhrman, H.; Loff, B.; Torenvliet, L.
2012-01-01
We show various hardness of approximation algorithms for knapsack and related problems; in particular we will show that unless the Exponential-Time Hypothesis is false, then subset-sum cannot be approximated any better than with an FPTAS. We also give a simple new algorithm for approximating knapsac
Approximate nonlinear self-adjointness and approximate conservation laws
In this paper, approximate nonlinear self-adjointness for perturbed PDEs is introduced and its properties are studied. Consequently, approximate conservation laws which cannot be obtained by the approximate Noether theorem are constructed by means of the method. As an application, a class of perturbed nonlinear wave equations is considered to illustrate the effectiveness. (paper)
$\\sigma $ -Approximately Contractible Banach Algebras
Momeni, M; Yazdanpanah, T.; Mardanbeigi, M. R.
2012-01-01
We investigate $\\sigma $ -approximate contractibility and $\\sigma $ -approximate amenability of Banach algebras, which are extensions of usual notions of contractibility and amenability, respectively, where $\\sigma $ is a dense range or an idempotent bounded endomorphism of the corresponding Banach algebra.
Approximation by planar elastic curves
Brander, David; Gravesen, Jens; Nørbjerg, Toke Bjerge
2015-01-01
We give an algorithm for approximating a given plane curve segment by a planar elastic curve. The method depends on an analytic representation of the space of elastic curve segments, together with a geometric method for obtaining a good initial guess for the approximating curve. A gradient......-driven optimization is then used to find the approximating elastic curve....
Approximate sine-Gordon solitons
Stratopoulos, G.N. (Dept. of Mathematical Sciences, Durham Univ. (United Kingdom)); Zakrzewski, W.J. (Dept. of Mathematical Sciences, Durham Univ. (United Kingdom))
1993-08-01
We look at the recently proposed scheme of approximating a sine-Gordon soliton by an expression derived from two dimensional instantons. We point out that the scheme of Sutcliffe in which he uses two dimensional instantons can be generalised to higher dimensions and that these generalisations produce even better approximations than the original approximation. We also comment on generalisations to other models. (orig.)
Exact constants in approximation theory
Korneichuk, N
1991-01-01
This book is intended as a self-contained introduction for non-specialists, or as a reference work for experts, to the particular area of approximation theory that is concerned with exact constants. The results apply mainly to extremal problems in approximation theory, which in turn are closely related to numerical analysis and optimization. The book encompasses a wide range of questions and problems: best approximation by polynomials and splines; linear approximation methods, such as spline-approximation; optimal reconstruction of functions and linear functionals. Many of the results are base
International Conference Approximation Theory XIV
Schumaker, Larry
2014-01-01
This volume developed from papers presented at the international conference Approximation Theory XIV, held April 7–10, 2013 in San Antonio, Texas. The proceedings contains surveys by invited speakers, covering topics such as splines on non-tensor-product meshes, Wachspress and mean value coordinates, curvelets and shearlets, barycentric interpolation, and polynomial approximation on spheres and balls. Other contributed papers address a variety of current topics in approximation theory, including eigenvalue sequences of positive integral operators, image registration, and support vector machines. This book will be of interest to mathematicians, engineers, and computer scientists working in approximation theory, computer-aided geometric design, numerical analysis, and related approximation areas.
Approximate solutions for the skyrmion
Ponciano, J A; Fanchiotti, H; Canal-Garcia, C A
2001-01-01
We reconsider the Euler-Lagrange equation for the Skyrme model in the hedgehog ansatz and study the analytical properties of the solitonic solution. In view of the lack of a closed form solution to the problem, we work on approximate analytical solutions. We show that Pade approximants are well suited to continue analytically the asymptotic representation obtained in terms of a power series expansion near the origin, obtaining explicit approximate solutions for the Skyrme equations. We improve the approximations by applying the 2-point Pade approximant procedure whereby the exact behaviour at spatial infinity is incorporated. An even better convergence to the exact solution is obtained by introducing a modified form for the approximants. The new representations share the same analytical properties with the exact solution at both small and large values of the radial variable r.
The Smoothed Approximate Linear Program
Desai, V V; Moallemi, C C
2009-01-01
We present a novel linear program for the approximation of the dynamic programming cost-to-go function in high-dimensional stochastic control problems. LP approaches to approximate DP have typically relied on a natural `projection' of a well studied linear program for exact dynamic programming. Such programs restrict attention to approximations that are lower bounds to the optimal cost-to-go function. Our program--the `smoothed approximate linear program'--is distinct from such approaches and relaxes the restriction to lower bounding approximations in an appropriate fashion while remaining computationally tractable. Doing so appears to have several advantages: First, we demonstrate substantially superior bounds on the quality of approximation to the optimal cost-to-go function afforded by our approach. Second, experiments with our approach on a challenging problem (the game of Tetris) show that the approach outperforms the existing LP approach (which has previously been shown to be competitive with several AD...
Approximate Grammar for Information Extraction
Sriram, V; Reddy, B. Ravi Sekar; Sangal, R.
2003-01-01
In this paper, we present the concept of Approximate grammar and how it can be used to extract information from a documemt. As the structure of informational strings cannot be defined well in a document, we cannot use the conventional grammar rules to represent the information. Hence, the need arises to design an approximate grammar that can be used effectively to accomplish the task of Information extraction. Approximate grammars are a novel step in this direction. The rules of an approximat...
BDD Minimization for Approximate Computing
Soeken, Mathias; Grosse, Daniel; Chandrasekharan, Arun; Drechsler, Rolf
2016-01-01
We present Approximate BDD Minimization (ABM) as a problem that has application in approximate computing. Given a BDD representation of a multi-output Boolean function, ABM asks whether there exists another function that has a smaller BDD representation but meets a threshold w.r.t. an error metric. We present operators to derive approximated functions and present algorithms to exactly compute the error metrics directly on the BDD representation. An experimental evaluation demonstrates the app...
Dajnowicz, Steven; Seaver, Sean; Hanson, B Leif; Fisher, S Zoë; Langan, Paul; Kovalevsky, Andrey Y; Mueser, Timothy C
2016-07-01
Neutron crystallography provides direct visual evidence of the atomic positions of deuterium-exchanged H atoms, enabling the accurate determination of the protonation/deuteration state of hydrated biomolecules. Comparison of two neutron structures of hemoglobins, human deoxyhemoglobin (T state) and equine cyanomethemoglobin (R state), offers a direct observation of histidine residues that are likely to contribute to the Bohr effect. Previous studies have shown that the T-state N-terminal and C-terminal salt bridges appear to have a partial instead of a primary overall contribution. Four conserved histidine residues [αHis72(EF1), αHis103(G10), αHis89(FG1), αHis112(G19) and βHis97(FG4)] can become protonated/deuterated from the R to the T state, while two histidine residues [αHis20(B1) and βHis117(G19)] can lose a proton/deuteron. αHis103(G10), located in the α1:β1 dimer interface, appears to be a Bohr group that undergoes structural changes: in the R state it is singly protonated/deuterated and hydrogen-bonded through a water network to βAsn108(G10) and in the T state it is doubly protonated/deuterated with the network uncoupled. The very long-term H/D exchange of the amide protons identifies regions that are accessible to exchange as well as regions that are impermeable to exchange. The liganded relaxed state (R state) has comparable levels of exchange (17.1% non-exchanged) compared with the deoxy tense state (T state; 11.8% non-exchanged). Interestingly, the regions of non-exchanged protons shift from the tetramer interfaces in the T-state interface (α1:β2 and α2:β1) to the cores of the individual monomers and to the dimer interfaces (α1:β1 and α2:β2) in the R state. The comparison of regions of stability in the two states allows a visualization of the conservation of fold energy necessary for ligand binding and release. PMID:27377386
Beyond the random phase approximation
Olsen, Thomas; Thygesen, Kristian S.
2013-01-01
We assess the performance of a recently proposed renormalized adiabatic local density approximation (rALDA) for ab initio calculations of electronic correlation energies in solids and molecules. The method is an extension of the random phase approximation (RPA) derived from time-dependent density...
Matrix-Free Approximate Equilibration
Bradley, Andrew M.; Murray, Walter
2011-01-01
The condition number of a diagonally scaled matrix, for appropriately chosen scaling matrices, is often less than that of the original. Equilibration scales a matrix so that the scaled matrix's row and column norms are equal. Scaling can be approximate. We develop approximate equilibration algorithms for nonsymmetric and symmetric matrices having signed elements that access a matrix only by matrix-vector products.
Approximate circuits for increased reliability
Hamlet, Jason R.; Mayo, Jackson R.
2015-08-18
Embodiments of the invention describe a Boolean circuit having a voter circuit and a plurality of approximate circuits each based, at least in part, on a reference circuit. The approximate circuits are each to generate one or more output signals based on values of received input signals. The voter circuit is to receive the one or more output signals generated by each of the approximate circuits, and is to output one or more signals corresponding to a majority value of the received signals. At least some of the approximate circuits are to generate an output value different than the reference circuit for one or more input signal values; however, for each possible input signal value, the majority values of the one or more output signals generated by the approximate circuits and received by the voter circuit correspond to output signal result values of the reference circuit.
Approximate circuits for increased reliability
Hamlet, Jason R.; Mayo, Jackson R.
2015-12-22
Embodiments of the invention describe a Boolean circuit having a voter circuit and a plurality of approximate circuits each based, at least in part, on a reference circuit. The approximate circuits are each to generate one or more output signals based on values of received input signals. The voter circuit is to receive the one or more output signals generated by each of the approximate circuits, and is to output one or more signals corresponding to a majority value of the received signals. At least some of the approximate circuits are to generate an output value different than the reference circuit for one or more input signal values; however, for each possible input signal value, the majority values of the one or more output signals generated by the approximate circuits and received by the voter circuit correspond to output signal result values of the reference circuit.
N-variable rational approximants
''Desirable properties'' of a two-variable generalization of Pade approximants are laid down. The ''Chisholm approximants'' are defined and are shown to obey nearly all of these properties; the alternative ways of completing a unique definition are discussed, and the ''prong structure'' of the defining equations is elucidated. Several generalizations and variants of Chisholm approximants are described: N-variable diagonal, 2-variable simple off-diagonal, N-variable simple and general off-diagonal, and rotationally covariant 2-variable approximants. All of the 2-variable approximants are capable of representing singularities of functions of two variables, and of analytically continuing beyond the polycylinder of convergence of the double series. 8 figures
Chebyshev polynomial approximation to approximate partial differential equations
Caporale, Guglielmo Maria; Cerrato, Mario
2008-01-01
This pa per suggests a simple method based on Chebyshev approximation at Chebyshev nodes to approximate partial differential equations. The methodology simply consists in determining the value function by using a set of nodes and basis functions. We provide two examples. Pricing an European option and determining the best policy for chatting down a machinery. The suggested method is flexible, easy to program and efficient. It is also applicable in other fields, providing efficient solutions t...
This study was undertaken to evaluate the lysosomal accumulation of radioactive metal ions in tumor and liver, using tumor-bearing animals. From the experimental of lysosomal accumulation and binding substance for nineteen radioactive metal ions, the following results were obtained. Hard and borderline acids which have incomplete d-shells accumulated extensively in lysosomes of tumor and liver with time after administration of these ions. They were bound in these tissues to the acid mucopolysaccharides whose molecular weights exceed 40,000 daltons. Trivalent hard acids (Ga3+, In3+, Yb3+, Tm3+) which have complete d-shells accumulated extensively in the lysosomes of liver, but very little in lysososmes of tumor, and were bound to the acid mucopolysaccharide with a molecular weight of about 10,000 daltons in tissues. It was clear based on these results and the facts reported previously that a very interesting relationship existed between the location of elements in the Thomsen-Bohr type periodic table and the lysosomal accumulation of metal ions
The efficiency of Flory approximation
The Flory approximation for the self-avoiding chain problem is compared with a conventional perturbation theory expansion. While in perturbation theory each term is averaged over the unperturbed set of configurations, the Flory approximation is equivalent to the perturbation theory with the averaging over the stretched set of configurations. This imposes restrictions on the integration domain in higher order terms and they can be treated self-consistently. The accuracy δν/ν of Flory approximation for self-avoiding chain problems is estimated to be 2-5% for 1 < d < 4. (orig.)
Approximate Reanalysis in Topology Optimization
Amir, Oded; Bendsøe, Martin P.; Sigmund, Ole
2009-01-01
In the nested approach to structural optimization, most of the computational effort is invested in the solution of the finite element analysis equations. In this study, the integration of an approximate reanalysis procedure into the framework of topology optimization of continuum structures is...... investigated. The nested optimization problem is re-formulated to accommodate the use of an approximate displacement vector and the design sensitivities are derived accordingly. It is shown that relatively rough approximations are acceptable since the errors are taken into account in the sensitivity analysis...
Weighted approximation with varying weight
Totik, Vilmos
1994-01-01
A new construction is given for approximating a logarithmic potential by a discrete one. This yields a new approach to approximation with weighted polynomials of the form w"n"(" "= uppercase)P"n"(" "= uppercase). The new technique settles several open problems, and it leads to a simple proof for the strong asymptotics on some L p(uppercase) extremal problems on the real line with exponential weights, which, for the case p=2, are equivalent to power- type asymptotics for the leading coefficients of the corresponding orthogonal polynomials. The method is also modified toyield (in a sense) uniformly good approximation on the whole support. This allows one to deduce strong asymptotics in some L p(uppercase) extremal problems with varying weights. Applications are given, relating to fast decreasing polynomials, asymptotic behavior of orthogonal polynomials and multipoint Pade approximation. The approach is potential-theoretic, but the text is self-contained.
Approximate maximizers of intricacy functionals
Buzzi, Jerome
2009-01-01
G. Edelman, O. Sporns, and G. Tononi introduced in theoretical biology the neural complexity of a family of random variables. This functional is a special case of intricacy, i.e., an average of the mutual information of subsystems whose weights have good mathematical properties. Moreover, its maximum value grows at a definite speed with the size of the system. In this work, we compute exactly this speed of growth by building "approximate maximizers" subject to an entropy condition. These approximate maximizers work simultaneously for all intricacies. We also establish some properties of arbitrary approximate maximizers, in particular the existence of a threshold in the size of subsystems of approximate maximizers: most smaller subsystems are almost equidistributed, most larger subsystems determine the full system. The main ideas are a random construction of almost maximizers with a high statistical symmetry and the consideration of entropy profiles, i.e., the average entropies of sub-systems of a given size. ...
Metrical Diophantine approximation for quaternions
Dodson, Maurice
2011-01-01
The metrical theory of Diophantine approximation for quaternions is developed using recent results in the general theory. In particular, Quaternionic analogues of the classical theorems of Khintchine, Jarnik and Jarnik-Besicovitch are established.
Metrical Diophantine approximation for quaternions
Dodson, Maurice; Everitt, Brent
2014-11-01
Analogues of the classical theorems of Khintchine, Jarnik and Jarnik-Besicovitch in the metrical theory of Diophantine approximation are established for quaternions by applying results on the measure of general `lim sup' sets.
Reinforcement Learning via AIXI Approximation
Veness, Joel; Ng, Kee Siong; Hutter, Marcus; Silver, David
2010-01-01
This paper introduces a principled approach for the design of a scalable general reinforcement learning agent. This approach is based on a direct approximation of AIXI, a Bayesian optimality notion for general reinforcement learning agents. Previously, it has been unclear whether the theory of AIXI could motivate the design of practical algorithms. We answer this hitherto open question in the affirmative, by providing the first computationally feasible approximation to the AIXI agent. To deve...
Binary nucleation beyond capillarity approximation
Kalikmanov, V.I.
2010-01-01
Large discrepancies between binary classical nucleation theory (BCNT) and experiments result from adsorption effects and inability of BCNT, based on the phenomenological capillarity approximation, to treat small clusters. We propose a model aimed at eliminating both of these deficiencies. Adsorption is taken into account within Gibbsian approximation. Binary clusters are treated by means of statistical-mechanical considerations: tracing out the molecular degrees of freedom of the more volatil...
Approximate factorization with source terms
Shih, T. I.-P.; Chyu, W. J.
1991-01-01
A comparative evaluation is made of three methodologies with a view to that which offers the best approximate factorization error. While two of these methods are found to lead to more efficient algorithms in cases where factors which do not contain source terms can be diagonalized, the third method used generates the lowest approximate factorization error. This method may be preferred when the norms of source terms are large, and transient solutions are of interest.
Chebyshev approximation for multivariate functions
Sukhorukova, Nadezda; Ugon, Julien; Yost, David
2015-01-01
In this paper, we derive optimality conditions (Chebyshev approximation) for multivariate functions. The theory of Chebyshev (uniform) approximation for univariate functions is very elegant. The optimality conditions are based on the notion of alternance (maximal deviation points with alternating deviation signs). It is not very straightforward, however, how to extend the notion of alternance to the case of multivariate functions. There have been several attempts to extend the theory of Cheby...
Analytic Approximations for Spread Options
Carol Alexander; Aanand Venkatramanan
2007-01-01
Even in the simple case that two price processes follow correlated geometric Brownian motions with constant volatility no analytic formula for the price of a standard European spread option has been derived, except when the strike is zero in which case the option becomes an exchange option. This paper expresses the price of a spread option as the price of a compound exchange option and hence derives a new analytic approximation for its price and hedge ratios. This approximation has several ad...
Wavelet Sparse Approximate Inverse Preconditioners
Chan, Tony F.; Tang, W.-P.; Wan, W. L.
1996-01-01
There is an increasing interest in using sparse approximate inverses as preconditioners for Krylov subspace iterative methods. Recent studies of Grote and Huckle and Chow and Saad also show that sparse approximate inverse preconditioner can be effective for a variety of matrices, e.g. Harwell-Boeing collections. Nonetheless a drawback is that it requires rapid decay of the inverse entries so that sparse approximate inverse is possible. However, for the class of matrices that, come from elliptic PDE problems, this assumption may not necessarily hold. Our main idea is to look for a basis, other than the standard one, such that a sparse representation of the inverse is feasible. A crucial observation is that the kind of matrices we are interested in typically have a piecewise smooth inverse. We exploit this fact, by applying wavelet techniques to construct a better sparse approximate inverse in the wavelet basis. We shall justify theoretically and numerically that our approach is effective for matrices with smooth inverse. We emphasize that in this paper we have only presented the idea of wavelet approximate inverses and demonstrated its potential but have not yet developed a highly refined and efficient algorithm.
Shearlets and Optimally Sparse Approximations
Kutyniok, Gitta; Lim, Wang-Q
2011-01-01
Multivariate functions are typically governed by anisotropic features such as edges in images or shock fronts in solutions of transport-dominated equations. One major goal both for the purpose of compression as well as for an efficient analysis is the provision of optimally sparse approximations of such functions. Recently, cartoon-like images were introduced in 2D and 3D as a suitable model class, and approximation properties were measured by considering the decay rate of the $L^2$ error of the best $N$-term approximation. Shearlet systems are to date the only representation system, which provide optimally sparse approximations of this model class in 2D as well as 3D. Even more, in contrast to all other directional representation systems, a theory for compactly supported shearlet frames was derived which moreover also satisfy this optimality benchmark. This chapter shall serve as an introduction to and a survey about sparse approximations of cartoon-like images by band-limited and also compactly supported sh...
Relativistic regular approximations revisited: An infinite-order relativistic approximation
The concept of the regular approximation is presented as the neglect of the energy dependence of the exact Foldy - Wouthuysen transformation of the Dirac Hamiltonian. Expansion of the normalization terms leads immediately to the zeroth-order regular approximation (ZORA) and first-order regular approximation (FORA) Hamiltonians as the zeroth- and first-order terms of the expansion. The expansion may be taken to infinite order by using an un-normalized Foldy - Wouthuysen transformation, which results in the ZORA Hamiltonian and a non-unit metric. This infinite-order regular approximation, IORA, has eigenvalues which differ from the Dirac eigenvalues by order E3/c4 for a hydrogen-like system, which is a considerable improvement over the ZORA eigenvalues, and similar to the non-variational FORA energies. A further perturbation analysis yields a third-order correction to the IORA energies, TIORA. Results are presented for several systems including the neutral U atom. The IORA eigenvalues for all but the 1s spinor of the neutral system are superior even to the scaled ZORA energies, which are exact for the hydrogenic system. The third-order correction reduces the IORA error for the inner orbitals to a very small fraction of the Dirac eigenvalue. copyright 1999 American Institute of Physics
Approximation methods in probability theory
Čekanavičius, Vydas
2016-01-01
This book presents a wide range of well-known and less common methods used for estimating the accuracy of probabilistic approximations, including the Esseen type inversion formulas, the Stein method as well as the methods of convolutions and triangle function. Emphasising the correct usage of the methods presented, each step required for the proofs is examined in detail. As a result, this textbook provides valuable tools for proving approximation theorems. While Approximation Methods in Probability Theory will appeal to everyone interested in limit theorems of probability theory, the book is particularly aimed at graduate students who have completed a standard intermediate course in probability theory. Furthermore, experienced researchers wanting to enlarge their toolkit will also find this book useful.
Concept Approximation between Fuzzy Ontologies
无
2006-01-01
Fuzzy ontologies are efficient tools to handle fuzzy and uncertain knowledge on the semantic web; but there are heterogeneity problems when gaining interoperability among different fuzzy ontologies. This paper uses concept approximation between fuzzy ontologies based on instances to solve the heterogeneity problems. It firstly proposes an instance selection technology based on instance clustering and weighting to unify the fuzzy interpretation of different ontologies and reduce the number of instances to increase the efficiency. Then the paper resolves the problem of computing the approximations of concepts into the problem of computing the least upper approximations of atom concepts. It optimizes the search strategies by extending atom concept sets and defining the least upper bounds of concepts to reduce the searching space of the problem. An efficient algorithm for searching the least upper bounds of concept is given.
An Approximation Ratio for Biclustering
Puolamäki, Kai; Hanhijärvi, Sami; Garriga, Gemma C
2007-01-01
The problem of biclustering consists of the simultaneous clustering of rows and columns of a matrix such that each of the submatrices induced by a pair of row and column clusters is as uniform as possible. In this paper we approximate the optimal biclustering by applying one-way clustering algorithms independently on the rows and on the columns of the input matrix. We show that such a solution yields a worst-case approximation ratio of 1+sqrt(2) under L1-norm for 0-1 valued matrices, and of 2...
An Approximation Ratio for Biclustering
Puolamäki, Kai; Garriga, Gemma C
2007-01-01
The problem of biclustering consists of the simultaneous clustering of rows and columns of a matrix such that each of the submatrices induced by a pair of row and column clusters is as uniform as possible. In this paper we approximate the optimal biclustering by applying one-way clustering algorithms independently on the rows and on the columns of the input matrix. We show that such a solution yields a worst-case approximation ratio of 1+sqrt(2) under L1-norm for 0-1 valued matrices, and of 2 under L2-norm for real valued matrices.
Shearlets and Optimally Sparse Approximations
Kutyniok, Gitta; Lemvig, Jakob; Lim, Wang-Q
Multivariate functions are typically governed by anisotropic features such as edges in images or shock fronts in solutions of transport-dominated equations. One major goal both for the purpose of compression as well as for an efficient analysis is the provision of optimally sparse approximations of...... provide optimally sparse approximations of this model class in 2D as well as 3D. Even more, in contrast to all other directional representation systems, a theory for compactly supported shearlet frames was derived which moreover also satisfy this optimality benchmark. This chapter shall serve as an...
Tkalya, E. V.; Nikolaev, A. V.
2016-07-01
Background: The search for new opportunities to investigate the low-energy level in the 229Th nucleus, which is nowadays intensively studied experimentally, has motivated us to theoretical studies of the magnetic hyperfine (MHF) structure of the 5 /2+ (0.0 eV) ground state and the low-lying 3 /2+ (7.8 eV) isomeric state in highly charged 89+229Th and 87+229Th ions. Purpose: The aim is to calculate, with the maximal precision presently achievable, the energy of levels of the hyperfine structure of the 229Th ground-state doublet in highly charged ions and the probability of radiative transitions between these levels. Methods: The distribution of the nuclear magnetization (the Bohr-Weisskopf effect) is accounted for in the framework of the collective nuclear model with Nilsson model wave functions for the unpaired neutron. Numerical calculations using precise atomic density functional theory methods, with full account of the electron self-consistent field, have been performed for the electron structure inside and outside the nuclear region. Results: The deviations of the MHF structure for the ground and isomeric states from their values in a model of a pointlike nuclear magnetic dipole are calculated. The influence of the mixing of the states with the same quantum number F on the energy of sublevels is studied. Taking into account the mixing of states, the probabilities of the transitions between the components of the MHF structure are calculated. Conclusions: Our findings are relevant for experiments with highly ionized 229Th ions in a storage ring at an accelerator facility.
Approximate Reasoning with Fuzzy Booleans
Broek, van den P.M.; Noppen, J.A.R.
2004-01-01
This paper introduces, in analogy to the concept of fuzzy numbers, the concept of fuzzy booleans, and examines approximate reasoning with the compositional rule of inference using fuzzy booleans. It is shown that each set of fuzzy rules is equivalent to a set of fuzzy rules with singleton crisp ante
Truthful approximations to range voting
Filos-Ratsika, Aris; Miltersen, Peter Bro
We consider the fundamental mechanism design problem of approximate social welfare maximization under general cardinal preferences on a finite number of alternatives and without money. The well-known range voting scheme can be thought of as a non-truthful mechanism for exact social welfare maximi...
Analytical Approximations to Galaxy Clustering
Mo, H. J.
1997-01-01
We discuss some recent progress in constructing analytic approximations to the galaxy clustering. We show that successful models can be constructed for the clustering of both dark matter and dark matter haloes. Our understanding of galaxy clustering and galaxy biasing can be greatly enhanced by these models.
Ultrafast Approximation for Phylogenetic Bootstrap
Bui Quang Minh, [No Value; Nguyen, Thi; von Haeseler, Arndt
2013-01-01
Nonparametric bootstrap has been a widely used tool in phylogenetic analysis to assess the clade support of phylogenetic trees. However, with the rapidly growing amount of data, this task remains a computational bottleneck. Recently, approximation methods such as the RAxML rapid bootstrap (RBS) and
Approximation by Penultimate Stable Laws
L.F.M. de Haan (Laurens); L. Peng (Liang); H. Iglesias Pereira
1997-01-01
textabstractIn certain cases partial sums of i.i.d. random variables with finite variance are better approximated by a sequence of stable distributions with indices \\\\alpha_n \\\\to 2 than by a normal distribution. We discuss when this happens and how much the convergence rate can be improved by using
Approximation properties of haplotype tagging
Dreiseitl Stephan
2006-01-01
Full Text Available Abstract Background Single nucleotide polymorphisms (SNPs are locations at which the genomic sequences of population members differ. Since these differences are known to follow patterns, disease association studies are facilitated by identifying SNPs that allow the unique identification of such patterns. This process, known as haplotype tagging, is formulated as a combinatorial optimization problem and analyzed in terms of complexity and approximation properties. Results It is shown that the tagging problem is NP-hard but approximable within 1 + ln((n2 - n/2 for n haplotypes but not approximable within (1 - ε ln(n/2 for any ε > 0 unless NP ⊂ DTIME(nlog log n. A simple, very easily implementable algorithm that exhibits the above upper bound on solution quality is presented. This algorithm has running time O((2m - p + 1 ≤ O(m(n2 - n/2 where p ≤ min(n, m for n haplotypes of size m. As we show that the approximation bound is asymptotically tight, the algorithm presented is optimal with respect to this asymptotic bound. Conclusion The haplotype tagging problem is hard, but approachable with a fast, practical, and surprisingly simple algorithm that cannot be significantly improved upon on a single processor machine. Hence, significant improvement in computatational efforts expended can only be expected if the computational effort is distributed and done in parallel.
Low Rank Approximation in $G_0W_0$ Approximation
Shao, Meiyue; Yang, Chao; Liu, Fang; da Jornada, Felipe H; Deslippe, Jack; Louie, Steven G
2016-01-01
The single particle energies obtained in a Kohn--Sham density functional theory (DFT) calculation are generally known to be poor approximations to electron excitation energies that are measured in transport, tunneling and spectroscopic experiments such as photo-emission spectroscopy. The correction to these energies can be obtained from the poles of a single particle Green's function derived from a many-body perturbation theory. From a computational perspective, the accuracy and efficiency of such an approach depends on how a self energy term that properly accounts for dynamic screening of electrons is approximated. The $G_0W_0$ approximation is a widely used technique in which the self energy is expressed as the convolution of a non-interacting Green's function ($G_0$) and a screened Coulomb interaction ($W_0$) in the frequency domain. The computational cost associated with such a convolution is high due to the high complexity of evaluating $W_0$ at multiple frequencies. In this paper, we discuss how the cos...
Approximate Matching of Hierarchial Data
Augsten, Nikolaus
formally proof that the pq-gram index can be incrementally updated based on the log of edit operations without reconstructing intermediate tree versions. The incremental update is independent of the data size and scales to a large number of changes in the data. We introduce windowed pq-grams for the......-gram based distance between streets, introduces a global greedy matching that guarantees stable pairs, and links addresses that are stored with different granularity. The connector has been successfully tested with public administration databases. Our extensive experiments on both synthetic and real world......The goal of this thesis is to design, develop, and evaluate new methods for the approximate matching of hierarchical data represented as labeled trees. In approximate matching scenarios two items should be matched if they are similar. Computing the similarity between labeled trees is hard as in...
Approximate Privacy: Foundations and Quantification
Feigenbaum, Joan; Schapira, Michael
2009-01-01
Increasing use of computers and networks in business, government, recreation, and almost all aspects of daily life has led to a proliferation of online sensitive data about individuals and organizations. Consequently, concern about the privacy of these data has become a top priority, particularly those data that are created and used in electronic commerce. There have been many formulations of privacy and, unfortunately, many negative results about the feasibility of maintaining privacy of sensitive data in realistic networked environments. We formulate communication-complexity-based definitions, both worst-case and average-case, of a problem's privacy-approximation ratio. We use our definitions to investigate the extent to which approximate privacy is achievable in two standard problems: the second-price Vickrey auction and the millionaires problem of Yao. For both the second-price Vickrey auction and the millionaires problem, we show that not only is perfect privacy impossible or infeasibly costly to achieve...
Hydrogen: Beyond the Classic Approximation
The classical nucleus approximation is the most frequently used approach for the resolution of problems in condensed matter physics.However, there are systems in nature where it is necessary to introduce the nuclear degrees of freedom to obtain a correct description of the properties.Examples of this, are the systems with containing hydrogen.In this work, we have studied the resolution of the quantum nuclear problem for the particular case of the water molecule.The Hartree approximation has been used, i.e. we have considered that the nuclei are distinguishable particles.In addition, we have proposed a model to solve the tunneling process, which involves the resolution of the nuclear problem for configurations of the system away from its equilibrium position
Concentration Bounds for Stochastic Approximations
Frikha, Noufel
2012-01-01
We obtain non asymptotic concentration bounds for two kinds of stochastic approximations. We first consider the deviations between the expectation of a given function of the Euler scheme of some diffusion process at a fixed deterministic time and its empirical mean obtained by the Monte-Carlo procedure. We then give some estimates concerning the deviation between the value at a given time-step of a stochastic approximation algorithm and its target. Under suitable assumptions both concentration bounds turn out to be Gaussian. The key tool consists in exploiting accurately the concentration properties of the increments of the schemes. For the first case, as opposed to the previous work of Lemaire and Menozzi (EJP, 2010), we do not have any systematic bias in our estimates. Also, no specific non-degeneracy conditions are assumed.
Waveless Approximation Theories of Gravity
Isenberg, J A
2007-01-01
The analysis of a general multibody physical system governed by Einstein's equations in quite difficult, even if numerical methods (on a computer) are used. Some of the difficulties -- many coupled degrees of freedom, dynamic instability -- are associated with the presence of gravitational waves. We have developed a number of ``waveless approximation theories'' (WAT) which repress the gravitational radiation and thereby simplify the analysis. The matter, according to these theories, evolves dynamically. The gravitational field, however, is determined at each time step by a set of elliptic equations with matter sources. There is reason to believe that for many physical systems, the WAT-generated system evolution is a very accurate approximation to that generated by the full Einstein theory.
On Approximability of Block Sorting
Narayanaswamy, N S
2011-01-01
Block Sorting is a well studied problem, motivated by its applications in Optical Character Recognition (OCR), and Computational Biology. Block Sorting has been shown to be NP-Hard, and two separate polynomial time 2-approximation algorithms have been designed for the problem. But questions like whether a better approximation algorithm can be designed, and whether the problem is APX-Hard have been open for quite a while now. In this work we answer the latter question by proving Block Sorting to be Max-SNP-Hard (APX-Hard). The APX-Hardness result is based on a linear reduction of Max-3SAT to Block Sorting. We also provide a new lower bound for the problem via a new parametrized problem k-Block Merging.
Variance approximation under balanced sampling
Deville, Jean-Claude; Tillé, Yves
2016-01-01
A balanced sampling design has the interesting property that Horvitz–Thompson estimators of totals for a set of balancing variables are equal to the totals we want to estimate, therefore the variance of Horvitz–Thompson estimators of variables of interest are reduced in function of their correlations with the balancing variables. Since it is hard to derive an analytic expression for the joint inclusion probabilities, we derive a general approximation of variance based on a residual technique....
Approximating Metal-Insulator Transitions
Danieli, C.; Rayanov, K.; Pavlov, B.; Martin, G.; Flach, S
2014-01-01
We consider quantum wave propagation in one-dimensional quasiperiodic lattices. We propose an iterative construction of quasiperiodic potentials from sequences of potentials with increasing spatial period. At each finite iteration step the eigenstates reflect the properties of the limiting quasiperiodic potential properties up to a controlled maximum system size. We then observe approximate metal-insulator transitions (MIT) at the finite iteration steps. We also report evidence on mobility ed...
Saddlepoint approximations to option prices
Rogers, L. C. G.; Zane, O.
1999-01-01
The use of saddlepoint approximations in statistics is a well-established technique for computing the distribution of a random variable whose moment generating function is known. In this paper, we apply the methodology to computing the prices of various European-style options, whose returns processes are not the Brownian motion with drift assumed in the Black-Scholes paradigm. Through a number of examples, we show that the methodology is generally accurate and fast.
Approximate maximizers of intricacy functionals
Buzzi, Jerome; Zambotti, Lorenzo
2009-01-01
G. Edelman, O. Sporns, and G. Tononi introduced in theoretical biology the neural complexity of a family of random variables. This functional is a special case of intricacy, i.e., an average of the mutual information of subsystems whose weights have good mathematical properties. Moreover, its maximum value grows at a definite speed with the size of the system. In this work, we compute exactly this speed of growth by building "approximate maximizers" subject to an entropy condition. These appr...
Stochastic approximation algorithms and applications
Kushner, Harold J
1997-01-01
In recent years algorithms of the stochastic approximation type have found applications in new and diverse areas, and new techniques have been developed for proofs of convergence and rate of convergence. The actual and potential applications in signal processing have exploded. New challenges have arisen in applications to adaptive control. This book presents a thorough coverage of the ODE method used to analyze these algorithms.
Quantum Tunneling Beyond Semiclassical Approximation
Banerjee, Rabin; Majhi, Bibhas Ranjan
2008-01-01
Hawking radiation as tunneling by Hamilton-Jacobi method beyond semiclassical approximation is analysed. We compute all quantum corrections in the single particle action revealing that these are proportional to the usual semiclassical contribution. We show that a simple choice of the proportionality constants reproduces the one loop back reaction effect in the spacetime, found by conformal field theory methods, which modifies the Hawking temperature of the black hole. Using the law of black h...
Approximate quantum and acoustic cloaking
Greenleaf, Allan; Lassas, Matti; Uhlmann, Gunther
2008-01-01
At any energy E > 0, we construct a sequence of bounded potentials $V^E_{n}, n\\in\\N$, supported in an annular region $B_{out}\\setminus B_{inn}$ in three-space, which act as approximate cloaks for solutions of Schr\\"odinger's equation: For any potential $V_0\\in L^\\infty(B_{inn})$ such that E is not a Neumann eigenvalue of $-\\Delta+V_0$ in $B_{inn}$, the scattering amplitudes $a_{V_0+V_n^E}(E,\\theta,\\omega)\\to 0$ as $n\\to\\infty$. The $V^E_{n}$ thus not only form a family of approximately transparent potentials, but also function as approximate invisibility cloaks in quantum mechanics. On the other hand, for $E$ close to interior eigenvalues, resonances develop and there exist {\\it almost trapped states} concentrated in $B_{inn}$. We derive the $V_n^E$ from singular, anisotropic transformation optics-based cloaks by a de-anisotropization procedure, which we call \\emph{isotropic transformation optics}. This technique uses truncation, inverse homogenization and spectral theory to produce nonsingular, isotropic app...
Computer Experiments for Function Approximations
Chang, A; Izmailov, I; Rizzo, S; Wynter, S; Alexandrov, O; Tong, C
2007-10-15
This research project falls in the domain of response surface methodology, which seeks cost-effective ways to accurately fit an approximate function to experimental data. Modeling and computer simulation are essential tools in modern science and engineering. A computer simulation can be viewed as a function that receives input from a given parameter space and produces an output. Running the simulation repeatedly amounts to an equivalent number of function evaluations, and for complex models, such function evaluations can be very time-consuming. It is then of paramount importance to intelligently choose a relatively small set of sample points in the parameter space at which to evaluate the given function, and then use this information to construct a surrogate function that is close to the original function and takes little time to evaluate. This study was divided into two parts. The first part consisted of comparing four sampling methods and two function approximation methods in terms of efficiency and accuracy for simple test functions. The sampling methods used were Monte Carlo, Quasi-Random LP{sub {tau}}, Maximin Latin Hypercubes, and Orthogonal-Array-Based Latin Hypercubes. The function approximation methods utilized were Multivariate Adaptive Regression Splines (MARS) and Support Vector Machines (SVM). The second part of the study concerned adaptive sampling methods with a focus on creating useful sets of sample points specifically for monotonic functions, functions with a single minimum and functions with a bounded first derivative.
Product Approximation of Grade and Precision
ZHANG Xian-yong; MO Zhi-wen
2005-01-01
The normal graded approximation and variable precision approximation are defined in approximate space. The relationship between graded approximation and variable precision approximation is studied, and an important formula of conversion between them is achieved. The product approximation of gradeand precision is defined and its basic properties are studied.
On the Gaussian overlap approximation for the collective excitations of odd nuclei
Rohoziński, Stanisław G.
2015-02-01
The multi-dimensional generator coordinate method is applied to describe the quadrupole collective states of odd nuclei. The laboratory Cartesian components of the quadrupole deformation tensor are used as the generator coordinates. The two mean-field states of an odd nucleus constituting a Kramers’ doublet are taken as the two intrinsic generating states which can rotate in the laboratory reference frame. The time-signature invariance of these intrinsic states is assumed. A version of the Gaussian overlap approximation (GOA) for the two generating states is constructed. A system of two coupled differential equations for the collective excitations of odd nuclei is derived from the variational principle using the GOA. The system forms a generalized eigenvalue differential equation in the two-dimensional ‘alispin’ space. Breaking the time-reversal symmetry and alignment of the angular momentum in the mean-field states modifies the rotational part of the Hamiltonian compared to that of the standard Bohr Hamiltonian, whereas the quadrupole vibrations are modified through the coupling of the Kramers states.
Generalized gradient approximation made simple
Generalized gradient approximations Exc = ∫ d3 r f(n↑, n↓, triangledown n↑, triangledown n↓) for the exchange-correlation energy typically surpass the accuracy of the local spin density approximation and compete with standard quantum-chemical methods in electronic-structure calculations. But the derivation and analytic expression for the integrand f tend to be complicated and over-parametrized. We present a simple derivation of a simple but accurate expression for f, involving no parameter other than fundamental-constants. The derivation invoices only general ideas (not details) of the real-space cutoff construction, and agrees closely with the result of this construction. Besides its greater simplicity, this PBE96 functional has other advantages over PW91: (1) The correct behavior of the correlation energy is recovered under uniform scaling to the high-density limit. (2) The linear response of the uniform electron gas agrees with the accurate local spin density prediction. 96:006128*1 Paper TuI 6 Many-body effects are hidden in the universal density functional. The interaction of degenerate states via two-body operators, such as the electron-electron repulsion (for describing multiplets or the interaction of molecular fragments at large separations) are thus not explicitly considered in the Kohn-Sham scheme. In practice the density functionals have to be approximated, and there is a fundamental difficulty which arises in the case of degeneracy. While density functionals should be universal, the effect of degeneracy is linked to the potential characteristic to the atom, molecule, or crystal. There are, however, several possibilities to treat degeneracy effects within density functional theory, a few of which will be discussed. These take profit of the use of two-body operators, which can be, but must not be, the physical electron-electron interaction
Quantum Tunneling Beyond Semiclassical Approximation
Banerjee, Rabin
2008-01-01
Hawking radiation as tunneling by Hamilton-Jacobi method beyond semiclassical approximation is analysed. We compute all quantum corrections in the single particle action revealing that these are proportional to the usual semiclassical contribution. We show that a simple choice of the proportionality constants reproduces the one loop back reaction effect in the spacetime, found by conformal field theory methods, which modifies the Hawking temperature of the black hole. Using the law of black hole mechanics we give the corrections to the Bekenstein-Hawking area law following from the modified Hawking temperature. Some examples are explicitly worked out.
Quantum tunneling beyond semiclassical approximation
Banerjee, Rabin; Ranjan Majhi, Bibhas
2008-06-01
Hawking radiation as tunneling by Hamilton-Jacobi method beyond semiclassical approximation is analysed. We compute all quantum corrections in the single particle action revealing that these are proportional to the usual semiclassical contribution. We show that a simple choice of the proportionality constants reproduces the one loop back reaction effect in the spacetime, found by conformal field theory methods, which modifies the Hawking temperature of the black hole. Using the law of black hole mechanics we give the corrections to the Bekenstein-Hawking area law following from the modified Hawking temperature. Some examples are explicitly worked out.
Fermion Tunneling Beyond Semiclassical Approximation
Majhi, Bibhas Ranjan
2008-01-01
Applying the Hamilton-Jacobi method beyond the semiclassical approximation prescribed in \\cite{Majhi3} for the scalar particle, Hawking radiation as tunneling of Dirac particle through an event horizon is analysed. We show that, as before, all quantum corrections in the single particle action are proportional to the usual semiclassical contribution. We also compute the modifications to the Hawking temperature and Bekenstein-Hawking entropy for the Schwarzschild black hole. Finally, the coefficient of the logarithmic correction to entropy is shown to be related with the trace anomaly.
Fermion tunneling beyond semiclassical approximation
Majhi, Bibhas Ranjan
2009-02-01
Applying the Hamilton-Jacobi method beyond the semiclassical approximation prescribed in R. Banerjee and B. R. Majhi, J. High Energy Phys.JHEPFG1029-8479 06 (2008) 09510.1088/1126-6708/2008/06/095 for the scalar particle, Hawking radiation as tunneling of the Dirac particle through an event horizon is analyzed. We show that, as before, all quantum corrections in the single particle action are proportional to the usual semiclassical contribution. We also compute the modifications to the Hawking temperature and Bekenstein-Hawking entropy for the Schwarzschild black hole. Finally, the coefficient of the logarithmic correction to entropy is shown to be related with the trace anomaly.
Rollout Sampling Approximate Policy Iteration
Dimitrakakis, Christos
2008-01-01
Several researchers have recently investigated the connection between reinforcement learning and classification. We are motivated by proposals of approximate policy iteration schemes without value functions which focus on policy representation using classifiers and address policy learning as a supervised learning problem. This paper proposes variants of an improved policy iteration scheme which addresses the core sampling problem in evaluating a policy through simulation as a multi-armed bandit machine. The resulting algorithm offers comparable performance to the previous algorithm achieved, however, with significantly less computational effort. An order of magnitude improvement is demonstrated experimentally in two standard reinforcement learning domains: inverted pendulum and mountain-car.
The distorted wave Glauber approximation
A solution of the Pauli equation with non-zero potentials defines quantum scalar and vector potentials and magnetic fields and quantum trajectories. If a line integral of perturbing potentials and fields along these quantum trajectories is added to the phase of this solution, an approximate solution of the perturbed equation is found. Glauber theory is a special case and the conditions of applicability are similar. Applications given start from the harmonic oscillator and from a homogeneous magnetic field and add a perturbation. (author)
The structural physical approximation conjecture
Shultz, Fred
2016-01-01
It was conjectured that the structural physical approximation (SPA) of an optimal entanglement witness is separable (or equivalently, that the SPA of an optimal positive map is entanglement breaking). This conjecture was disproved, first for indecomposable maps and more recently for decomposable maps. The arguments in both cases are sketched along with important related results. This review includes background material on topics including entanglement witnesses, optimality, duality of cones, decomposability, and the statement and motivation for the SPA conjecture so that it should be accessible for a broad audience.
Rotating wave approximation and entropy
This Letter studies composite quantum systems, like atom-cavity systems and coupled optical resonators, in the absence of external driving by resorting to methods from quantum field theory. Going beyond the rotating wave approximation, it is shown that the usually neglected counter-rotating part of the Hamiltonian relates to the entropy operator and generates an irreversible time evolution. The vacuum state of the system is shown to evolve into a generalized coherent state exhibiting entanglement of the modes in which the counter-rotating terms are expressed. Possible consequences at observational level in quantum optics experiments are currently under study.