Goldstone (GDSCC) administrative computing

NASA Technical Reports Server (NTRS)

Martin, H.

1981-01-01

The GDSCC Data Processing Unit provides various administrative computing services for Goldstone. Those activities, including finance, manpower and station utilization, deep-space station scheduling and engineering change order (ECO) control are discussed.

The origin of the mass of the Nambu-Goldstone bosons

NASA Astrophysics Data System (ADS)

Arraut, Ivan

2018-03-01

We explain the origin of the mass for the Nambu-Goldstone bosons when there is a chemical potential in the action which explicitly breaks the symmetry. The method is based on the number of independent histories for the interaction of the pair of Nambu-Goldstone bosons with the degenerate vacuum (triangle relations). The analysis suggests that under some circumstances, pairs of massive Nambu-Goldstone bosons can become a single degree of freedom with an effective mass defined by the superposition of the individual masses of each boson. Possible mass oscillations for the Nambu-Goldstone bosons are discussed.

A generalized Uhlenbeck and Beth formula for the third cluster coefficient

DOE Office of Scientific and Technical Information (OSTI.GOV)

Larsen, Sigurd Yves; Lassaut, Monique; Amaya-Tapia, Alejandro, E-mail: jano@icf.unam.mx

2016-11-15

Relatively recently (Amaya-Tapia et al., 2011), we presented a formula for the evaluation of the third Bose fugacity coefficient–leading to the third virial coefficient–in terms of three-body eigenphase shifts, for particles subject to repulsive forces. An analytical calculation for a 1-dim. model, for which the result is known, confirmed the validity of this approach. We now extend the formalism to particles with attractive forces, and therefore must allow for the possibility that the particles have bound states. We thus obtain a true generalization of the famous formula of Uhlenbeck and Beth (Uhlenbeck and Beth, 1936; Beth and Uhlenbeck, 1937) and ofmore » Gropper (Gropper, 1936, 1937) for the second virial. We illustrate our formalism by a calculation, in an adiabatic approximation, of the third cluster in one dimension, using McGuire’s model as in our previous paper, but with attractive forces. The inclusion of three-body bound states is trivial; taking into account states having asymptotically two particles bound, and one free, is not.« less

Lorentzian Goldstone modes shared among photons and gravitons

NASA Astrophysics Data System (ADS)

Chkareuli, J. L.; Jejelava, J.; Kepuladze, Z.

2018-02-01

It has long been known that photons and gravitons may appear as vector and tensor Goldstone modes caused by spontaneous Lorentz invariance violation (SLIV). Usually this approach is considered for photons and gravitons separately. We develop the emergent electrogravity theory consisting of the ordinary QED and the tensor-field gravity model which mimics the linearized general relativity in Minkowski spacetime. In this theory, Lorentz symmetry appears incorporated into higher global symmetries of the length-fixing constraints put on the vector and tensor fields involved, A_{μ }2=± MA2 and H_{μ ν }2=± MH2 (MA and MH are the proposed symmetry breaking scales). We show that such a SLIV pattern being related to breaking of global symmetries underlying these constraints induces the massless Goldstone and pseudo-Goldstone modes shared by photon and graviton. While for a vector field case the symmetry of the constraint coincides with Lorentz symmetry SO(1, 3) of the electrogravity Lagrangian, the tensor-field constraint itself possesses much higher global symmetry SO(7, 3), whose spontaneous violation provides a sufficient number of zero modes collected in a graviton. Accordingly, while the photon may only contain true Goldstone modes, the graviton appears at least partially to be composed of pseudo-Goldstone modes rather than of pure Goldstone ones. When expressed in terms of these modes, the theory looks essentially nonlinear and contains a variety of Lorentz and CPT violating couplings. However, all SLIV effects turn out to be strictly cancelled in the lowest order processes considered in some detail. How this emergent electrogravity theory could be observationally different from conventional QED and GR theories is also briefly discussed.

Goldstone Tracking the Echo Satelloon.

NASA Image and Video Library

2016-10-27

This archival image was released as part of a gallery comparing JPL’s past and present, commemorating the 80th anniversary of NASA’s Jet Propulsion Laboratory on Oct. 31, 2016. This photograph shows the first pass of Echo 1, NASA's first communications satellite, over the Goldstone Tracking Station managed by NASA's Jet Propulsion Laboratory, in Pasadena, California, in the early morning of Aug. 12, 1960. The movement of the antenna, star trails (shorter streaks), and Echo 1 (the long streak in the middle) are visible in this image. Project Echo bounced radio signals off a 10-story-high, aluminum-coated balloon orbiting the Earth. This form of "passive" satellite communication -- which mission managers dubbed a "satelloon" -- was an idea conceived by an engineer from NASA's Langley Research Center in Hampton, Virginia, and was a project managed by NASA's Goddard Space Flight Center in Greenbelt, Maryland. JPL's role involved sending and receiving signals through two of its 85-foot-diameter (26-meter-diameter) antennas at the Goldstone Tracking Station in California's Mojave Desert. The Goldstone station later became part of NASA's Deep Space Network. JPL, a division of Caltech in Pasadena, California, manages the Deep Space Network for NASA. http://photojournal.jpl.nasa.gov/catalog/PIA21114

Hans Bethe, Powering the Stars, and Nuclear Physics

Science.gov Websites

dropdown arrow Site Map A-Z Index Menu Synopsis Hans Bethe, Energy Production in Stars, and Nuclear Physics physics, built atomic weapons, and called for a halt to their proliferation. Bethe's dual legacy is one of Laboratory] from 1943 to 1946. Prior to joining the Manhattan Project, Bethe taught physics at Cornell

Study of molecular N D bound states in the Bethe-Salpeter equation approach

NASA Astrophysics Data System (ADS)

Wang, Zhen-Yang; Qi, Jing-Juan; Guo, Xin-Heng; Wei, Ke-Wei

2018-05-01

We study the Λc(2595 )+ and Σc(2800 )0 states as the N D bound systems in the Bethe-Salpeter formalism in the ladder and instantaneous approximations. With the kernel induced by ρ , ω and σ exchanges, we solve the Bethe-Salpeter equations for the N D bound systems numerically and find that the bound states may exist. We assume that the observed states Λc(2595 )+ and Σc(2800 )0 are S -wave N D molecular bound states and calculate the decay widths of Λc(2595 )+→Σc0π+ and Σc(2800 )0→Λc+π-.

Goldstone-like phonon modes in a (111)-strained perovskite

NASA Astrophysics Data System (ADS)

Marthinsen, A.; Griffin, S. M.; Moreau, M.; Grande, T.; Tybell, T.; Selbach, S. M.

2018-01-01

Goldstone modes are massless particles resulting from spontaneous symmetry breaking. Although such modes are found in elementary particle physics as well as in condensed-matter systems like superfluid helium, superconductors, and magnons, structural Goldstone modes are rare. Epitaxial strain in thin films can induce structures and properties not accessible in bulk and has been intensively studied for (001)-oriented perovskite oxides. Here we predict Goldstone-like phonon modes in (111)-strained SrMn O3 by first-principles calculations. Under compressive strain the coupling between two in-plane rotational instabilities gives rise to a Mexican hat-shaped energy surface characteristic of a Goldstone mode. Conversely, large tensile strain induces in-plane polar instabilities with no directional preference, giving rise to a continuous polar ground state. Such phonon modes with U (1) symmetry could emulate structural condensed-matter Higgs modes. The mass of this Higgs boson, given by the shape of the Mexican hat energy surface, can be tuned by strain through proper choice of substrate.

In Memoriam: Hans Bethe

NASA Astrophysics Data System (ADS)

Garwin, Richard L.; Von Hippel, Frank

Hans Bethe, who died on March 6 at the age of 98, was exemplary as a scientist; a citizen-advocate seeking to stem the arms race; and an individual of warmth, generosity, tenacity, and modest habits. Bethe made major contributions to several areas of physics during his academic career. He earned a Nobel Prize in 1967 for his research into how the sun generates its energy by converting hydrogen to helium using carbon as a nuclear catalyst. A few years later, he made central contributions to the secret US World War II nuclear-weapon development programs (the "Manhattan Project").

Bethe vectors for XXX-spin chain

NASA Astrophysics Data System (ADS)

Burdík, Čestmír; Fuksa, Jan; Isaev, Alexei

2014-11-01

The paper deals with algebraic Bethe ansatz for XXX-spin chain. Generators of Yang-Baxter algebra are expressed in basis of free fermions and used to calculate explicit form of Bethe vectors. Their relation to N-component models is used to prove conjecture about their form in general. Some remarks on inhomogeneous XXX-spin chain are included.

Relative planetary radar sensitivities: Arecibo and Goldstone

NASA Technical Reports Server (NTRS)

Renzetti, N. A.; Thompson, T. W.; Slade, M. A.

1988-01-01

The increase of the Deep Space Network antennas from 64 meter to 70 meter diameter represents the first of several improvements that will be made over the next decade to enhance earth based radar sensitivity to solar system targets. The aperture increase at the Goldstone DSS-14 site, coupled with a proposed increase in transmitter power to 1000 kW, will improve the 3.5 cm radar by about one order of magnitude. Similarly, proposed Arecibo Observatory upgrades of a Gregorian feed structure and an increase of transmitter power to 1000 kW will increase the sensitivity of this radar about 20 fold. In addition, a Goldstone to Very Large Array bistatic observation with horizon to horizon tracking will have 3.5 times more sensitivity than will a Goldstone horizon to horizon monostatic observation. All of these improvements, which should be in place within the next decade, will enrich an already fertile field of planetary exploration.

Goldstone Gauginos.

PubMed

Alves, Daniele S M; Galloway, Jamison; McCullough, Matthew; Weiner, Neal

2015-10-16

Models of supersymmetry with Dirac gauginos provide an attractive scenario for physics beyond the standard model. The "supersoft" radiative corrections and suppressed supersymmetry production at colliders provide for more natural theories and an understanding of why no new states have been seen. Unfortunately, these models are handicapped by a tachyon which is naturally present in existing models of Dirac gauginos. We argue that this tachyon is absent, with the phenomenological successes of the model preserved, if the right-handed gaugino is a (pseudo-)Goldstone field of a spontaneously broken anomalous flavor symmetry.

A tale of two Bethe ansätze

NASA Astrophysics Data System (ADS)

Lima-Santos, Antonio; Nepomechie, Rafael I.; Pimenta, Rodrigo A.

2018-04-01

We revisit the construction of the eigenvectors of the single and double-row transfer matrices associated with the Zamolodchikov–Fateev model, within the algebraic Bethe ansatz method. The left and right eigenvectors are constructed using two different methods: the fusion technique and Tarasov’s construction. A simple explicit relation between the eigenvectors from the two Bethe ansätze is obtained. As a consequence, we obtain the Slavnov formula for the scalar product between on-shell and off-shell Tarasov–Bethe vectors.

Where are the roots of the Bethe Ansatz equations?

NASA Astrophysics Data System (ADS)

Vieira, R. S.; Lima-Santos, A.

2015-10-01

Changing the variables in the Bethe Ansatz Equations (BAE) for the XXZ six-vertex model we had obtained a coupled system of polynomial equations. This provided a direct link between the BAE deduced from the Algebraic Bethe Ansatz (ABA) and the BAE arising from the Coordinate Bethe Ansatz (CBA). For two magnon states this polynomial system could be decoupled and the solutions given in terms of the roots of some self-inversive polynomials. From theorems concerning the distribution of the roots of self-inversive polynomials we made a thorough analysis of the two magnon states, which allowed us to find the location and multiplicity of the Bethe roots in the complex plane, to discuss the completeness and singularities of Bethe's equations, the ill-founded string-hypothesis concerning the location of their roots, as well as to find an interesting connection between the BAE with Salem's polynomials.

47 CFR 27.73 - WCS, AMT, and Goldstone coordination requirements.

Code of Federal Regulations, 2014 CFR

2014-10-01

... 202-741-6030, or go to: http://www/archives.gov/federal_ register/code_of_federal_regulations/ibr... Aeronautics and Space Administration (NASA) within 145 kilometers of the Goldstone, CA earth station site (35... the NASA Goldstone, CA earth station or from an AMT site, operating in the 2305-2320 or 2345-2360 MHz...

47 CFR 27.73 - WCS, AMT, and Goldstone coordination requirements.

Code of Federal Regulations, 2013 CFR

2013-10-01

... 202-741-6030, or go to: http://www/archives.gov/federal_ register/code_of_federal_regulations/ibr... Aeronautics and Space Administration (NASA) within 145 kilometers of the Goldstone, CA earth station site (35... the NASA Goldstone, CA earth station or from an AMT site, operating in the 2305-2320 or 2345-2360 MHz...

Combinatorics of Generalized Bethe Equations

NASA Astrophysics Data System (ADS)

Kozlowski, Karol K.; Sklyanin, Evgeny K.

2013-10-01

A generalization of the Bethe ansatz equations is studied, where a scalar two-particle S-matrix has several zeroes and poles in the complex plane, as opposed to the ordinary single pole/zero case. For the repulsive case (no complex roots), the main result is the enumeration of all distinct solutions to the Bethe equations in terms of the Fuss-Catalan numbers. Two new combinatorial interpretations of the Fuss-Catalan and related numbers are obtained. On the one hand, they count regular orbits of the permutation group in certain factor modules over {{Z}^M}, and on the other hand, they count integer points in certain M-dimensional polytopes.

47 CFR 27.73 - WCS, AMT, and Goldstone coordination requirements.

Code of Federal Regulations, 2012 CFR

2012-10-01

... protect AMT receive systems consistent with Recommendation ITU-R M.1459. The locations of the current and...) within 145 kilometers of the Goldstone, CA earth station site (35°25′33″ N, 116°53′23″ W). (c) After base...) receiving the complaint, no matter the distance from the NASA Goldstone, CA earth station or from an AMT...

Monitoring and manipulating Higgs and Goldstone modes in a supersolid quantum gas.

PubMed

Léonard, Julian; Morales, Andrea; Zupancic, Philip; Donner, Tobias; Esslinger, Tilman

2017-12-15

Higgs and Goldstone modes are collective excitations of the amplitude and phase of an order parameter that is related to the breaking of a continuous symmetry. We directly studied these modes in a supersolid quantum gas created by coupling a Bose-Einstein condensate to two optical cavities, whose field amplitudes form the real and imaginary parts of a U(1)-symmetric order parameter. Monitoring the cavity fields in real time allowed us to observe the dynamics of the associated Higgs and Goldstone modes and revealed their amplitude and phase nature. We used a spectroscopic method to measure their frequencies, and we gave a tunable mass to the Goldstone mode by exploring the crossover between continuous and discrete symmetry. Our experiments link spectroscopic measurements to the theoretical concept of Higgs and Goldstone modes. Copyright © 2017 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works.

Scattering amplitudes of massive Nambu-Goldstone bosons

NASA Astrophysics Data System (ADS)

Brauner, Tomáš; Jakobsen, Martin F.

2018-01-01

Massive Nambu-Goldstone (mNG) bosons are quasiparticles the gap of which is determined exactly by symmetry. They appear whenever a symmetry is broken spontaneously in the ground state of a quantum many-body system and at the same time explicitly by the system's chemical potential. In this paper, we revisit mNG bosons and show that apart from their gap symmetry also protects their scattering amplitudes. Just like for ordinary gapless Nambu-Goldstone (NG) bosons, the scattering amplitudes of mNG bosons vanish in the long-wavelength limit. Unlike for gapless NG bosons, this statement holds for any scattering process involving one or more external mNG states; there are no kinematic singularities associated with the radiation of a soft mNG boson from an on-shell initial or final state.

Goldstone mode and pair-breaking excitations in atomic Fermi superfluids

NASA Astrophysics Data System (ADS)

Hoinka, Sascha; Dyke, Paul; Lingham, Marcus G.; Kinnunen, Jami J.; Bruun, Georg M.; Vale, Chris J.

2017-10-01

Spontaneous symmetry breaking is a central paradigm of elementary particle physics, magnetism, superfluidity and superconductivity. According to Goldstone's theorem, phase transitions that break continuous symmetries lead to the existence of gapless excitations in the long-wavelength limit. These Goldstone modes can become the dominant low-energy excitation, showing that symmetry breaking has a profound impact on the physical properties of matter. Here, we present a comprehensive study of the elementary excitations in a homogeneous strongly interacting Fermi gas through the crossover from a Bardeen-Cooper-Schrieffer (BCS) superfluid to a Bose-Einstein condensate (BEC) of molecules using two-photon Bragg spectroscopy. The spectra exhibit a discrete Goldstone mode, associated with the broken-symmetry superfluid phase, as well as pair-breaking single-particle excitations. Our techniques yield a direct determination of the superfluid pairing gap and speed of sound in close agreement with strong-coupling theories.

Centenary Birth Anniversary of E. W. Beth (1908-1964)

ERIC Educational Resources Information Center

Bagni, Giorgio T.

2008-01-01

Evert Willem Beth (1908-1964) was a Dutch logician, mathematician and philosopher, whose work mainly concerned the foundations of mathematics. Beth was among the founders of the Commission Internationale pour l'Etude et l'Amelioration de l'Enseignement des Mathematiques and was a member of the Central Committee of the International Commission on…

Algebraic geometry and Bethe ansatz. Part I. The quotient ring for BAE

NASA Astrophysics Data System (ADS)

Jiang, Yunfeng; Zhang, Yang

2018-03-01

In this paper and upcoming ones, we initiate a systematic study of Bethe ansatz equations for integrable models by modern computational algebraic geometry. We show that algebraic geometry provides a natural mathematical language and powerful tools for understanding the structure of solution space of Bethe ansatz equations. In particular, we find novel efficient methods to count the number of solutions of Bethe ansatz equations based on Gröbner basis and quotient ring. We also develop analytical approach based on companion matrix to perform the sum of on-shell quantities over all physical solutions without solving Bethe ansatz equations explicitly. To demonstrate the power of our method, we revisit the completeness problem of Bethe ansatz of Heisenberg spin chain, and calculate the sum rules of OPE coefficients in planar N=4 super-Yang-Mills theory.

Algebraic Bethe ansatz for the XXX chain with triangular boundaries and Gaudin model

NASA Astrophysics Data System (ADS)

Cirilo António, N.; Manojlović, N.; Salom, I.

2014-12-01

We implement fully the algebraic Bethe ansatz for the XXX Heisenberg spin chain in the case when both boundary matrices can be brought to the upper-triangular form. We define the Bethe vectors which yield the strikingly simple expression for the off shell action of the transfer matrix, deriving the spectrum and the relevant Bethe equations. We explore further these results by obtaining the off shell action of the generating function of the Gaudin Hamiltonians on the corresponding Bethe vectors through the so-called quasi-classical limit. Moreover, this action is as simple as it could possibly be, yielding the spectrum and the Bethe equations of the Gaudin model.

Goldston syndrome in a fetus: case report and literature review.

PubMed

Avcu, Serhat; Akdeniz, Hüseyin; Unal, Ozkan; Kurdoğlu, Mertihan

2010-01-01

We present a case of the Goldston syndrome which is the association of polycystic kidneys with Dandy-Walker malformation. The diagnosis was made by ultrasound in twenty second week of gestation. Obstetric ultrasound and fetal MRI studies showed hydrocephalus, agenesis of the cerebellar hemispheres, vermian hypoplasia, cystic dilatation of the 4(th) ventricle, enlargement of the posterior fossa, abdominal distension, and oligohydramnios.. The kidneys were symmetrically enlarged and multicystic. To our knowledge this is the third reported case of Goldston syndrome which was diagnosed during intrauterine life.

Goldstone solar system radar

NASA Technical Reports Server (NTRS)

Jurgens, R. F.; Clark, P. E.; Goldstein, R. M.; Ostro, S. J.; Slade, M. A.; Thompson, T. W.; Saunders, R. S.

1986-01-01

Information is provided about physical nature planetary surfaces and their topography as well as dynamical properties such as orbits and spin states using ground based radar as a remote sensing tool. Accessible targets are the terrestrial planets: the Earth's Moon, Mercury, Venus and Mars, the outer planets rings and major moons, and many transient objects such as asteroids and comets. Data acquisition utilizes the unique facilities of the Goldstone Deep Space Network, occasionally the Arecibo radar, and proposed use of the VLA (very large array).

Spontaneously broken spacetime symmetries and the role of inessential Goldstones

NASA Astrophysics Data System (ADS)

Klein, Remko; Roest, Diederik; Stefanyszyn, David

2017-10-01

In contrast to internal symmetries, there is no general proof that the coset construction for spontaneously broken spacetime symmetries leads to universal dynamics. One key difference lies in the role of Goldstone bosons, which for spacetime symmetries includes a subset which are inessential for the non-linear realisation and hence can be eliminated. In this paper we address two important issues that arise when eliminating inessential Goldstones. The first concerns the elimination itself, which is often performed by imposing so-called inverse Higgs constraints. Contrary to claims in the literature, there are a series of conditions on the structure constants which must be satisfied to employ the inverse Higgs phenomenon, and we discuss which parametrisation of the coset element is the most effective in this regard. We also consider generalisations of the standard inverse Higgs constraints, which can include integrating out inessential Goldstones at low energies, and prove that under certain assumptions these give rise to identical effective field theories for the essential Goldstones. Secondly, we consider mappings between non-linear realisations that differ both in the coset element and the algebra basis. While these can always be related to each other by a point transformation, remarkably, the inverse Higgs constraints are not necessarily mapped onto each other under this transformation. We discuss the physical implications of this non-mapping, with a particular emphasis on the coset space corresponding to the spontaneous breaking of the Anti-De Sitter isometries by a Minkowski probe brane.

Goldstone Radar Images of Asteroid 2013 ET

NASA Image and Video Library

2013-03-18

This sequence of radar images of asteroid 2013 ET was obtained on Mar. 10, 2013, by NASA scientists using the 230-foot 70-meter DSN antenna at Goldstone, CA, when the asteroid was about 693,000 mi 1.1 million km from Earth.

Obituary: Beth Brown (1969-2008)

NASA Astrophysics Data System (ADS)

Bregman, Joel

2011-12-01

The astronomical community lost one of its most buoyant and caring individuals when Beth Brown died, unexpectedly, at the age of 39 from a pulmonary embolism. Beth Brown was born in Roanoke, Virginia where she developed a deep interest in astronomy, science, and science fiction (Star Trek). After graduating as the valedictorian of William Fleming High School's Class of 1987, she attended Howard University, where she graduated summa cum laude in 1991 with a bachelor's degree in astrophysics. Following a year in the graduate physics program at Howard, she entered the graduate program in the Department of Astronomy at the University of Michigan, the first African-American woman in the program. She received her PhD in 1998, working with X-ray observations of elliptical galaxies from the Röntgen Satellite (ROSAT; Joel Bregman was her advisor). She compiled and analyzed the first large complete sample of such galaxies with ROSAT and her papers in this area made an impact in the field. Following her PhD, Beth Brown held a National Academy of Science & National Research Council Postdoctoral Research Fellowship at NASA's Goddard Space Flight Center. Subsequently, she became a civil servant at the National Space Science Data Center at GSFC, where she was involved in data archival activities as well as education and outreach, a continuing passion in her life. In 2006, Brown became an Astrophysics Fellow at GSFC, during which time she worked as a visiting Assistant Professor at Howard University, where she taught and worked with students and faculty to improve the teaching observatory. At the time of her death, she was eagerly looking forward to a new position at GSFC as the Assistant Director for Science Communications and Higher Education. Beth Brown was a joyous individual who loved to work with people, especially in educating them about our remarkable field. Her warmth and openness was a great aid in making accessible explanations of otherwise daunting astrophysical

Tetraquark bound states in a Bethe-Salpeter approach

NASA Astrophysics Data System (ADS)

Heupel, Walter; Eichmann, Gernot; Fischer, Christian S.

2012-12-01

We determine the mass of tetraquark bound states from a coupled system of covariant Bethe-Salpeter equations. Similar in spirit to the quark-diquark model of the nucleon, we approximate the full four-body equation for the tetraquark by a coupled set of two-body equations with meson and diquark constituents. These are calculated from their quark and gluon substructure using a phenomenologically well-established quark-gluon interaction. For the lightest scalar tetraquark we find a mass of the order of 400 MeV and a wave function dominated by the pion-pion constituents. Both results are in agreement with a meson molecule picture for the f0 (600). Our results furthermore suggest the presence of a potentially narrow all-charm tetraquark in the mass region 5-6 GeV.

Algebraic Bethe ansatz for the sℓ (2) Gaudin model with boundary

NASA Astrophysics Data System (ADS)

Cirilo António, N.; Manojlović, N.; Ragoucy, E.; Salom, I.

2015-04-01

Following Sklyanin's proposal in the periodic case, we derive the generating function of the Gaudin Hamiltonians with boundary terms. Our derivation is based on the quasi-classical expansion of the linear combination of the transfer matrix of the XXX Heisenberg spin chain and the central element, the so-called Sklyanin determinant. The corresponding Gaudin Hamiltonians with boundary terms are obtained as the residues of the generating function. By defining the appropriate Bethe vectors which yield strikingly simple off shell action of the generating function, we fully implement the algebraic Bethe ansatz, obtaining the spectrum of the generating function and the corresponding Bethe equations.

Hans Bethe's early life

NASA Astrophysics Data System (ADS)

Bernstein, Jeremy

2012-10-01

In 1937, two years after he moved to the US to escape Nazi persecution, the physicist Hans Bethe sent a letter to his mother in Germany. In it, he wrote, "I think I am about the leading theoretician in America. [Eugene] Wigner is certainly better and [Robert] Oppenheimer and [Edward] Teller probably just as good. But I do more and talk more and that counts too."

X (3872 ) as a molecular D D\\xAF * state in the Bethe-Salpeter equation approach

NASA Astrophysics Data System (ADS)

Wang, Zhen-Yang; Qi, Jing-Juan; Guo, Xin-Heng; Wang, Chao

2018-01-01

We discuss the possibility that the X (3872 ) can be a D D¯* molecular bound state in the Bethe-Salpeter equation approach in the ladder and instantaneous approximations. We show that the D D¯ * bound state with quantum numbers JP C=1++ exists. We also calculate the decay width of X (3872 )→γ J /ψ channel and compare our result with those from previous calculations.

Gauge Invariance and the Goldstone Theorem

NASA Astrophysics Data System (ADS)

Guralnik, Gerald S.

This paper was originally created for and printed in the "Proceedings of seminar on unified theories of elementary particles" held in Feldafing, Germany from July 5 to 16, 1965 under the auspices of the Max-Planck-Institute for Physics and Astrophysics in Munich. It details and expands upon the 1964 Guralnik, Hagen, and Kibble paper demonstrating that the Goldstone theorem does not require physical zero mass particles in gauge theories.

Higgs boson as a top-mode pseudo-Nambu-Goldstone boson

NASA Astrophysics Data System (ADS)

Fukano, Hidenori S.; Kurachi, Masafumi; Matsuzaki, Shinya; Yamawaki, Koichi

2014-09-01

In the spirit of the top-quark condensation, we propose a model which has a naturally light composite Higgs boson, "tHiggs" (ht0), to be identified with the 126 GeV Higgs discovered at the LHC. The tHiggs, a bound state of the top quark and its flavor (vectorlike) partner, emerges as a pseudo-Nambu-Goldstone boson (NGB), "top-mode pseudo-Nambu-Goldstone boson," together with the exact NGBs to be absorbed into the W and Z bosons as well as another (heavier) top-mode pseudo-Nambu-Goldstone bosons (CP-odd composite scalar, At0). Those five composite (exact/pseudo-) NGBs are dynamically produced simultaneously by a single supercritical four-fermion interaction having U(3)×U(1) symmetry which includes the electroweak symmetry, where the vacuum is aligned by a small explicit breaking term so as to break the symmetry down to a subgroup, U(2)×U(1)', in a way not to retain the electroweak symmetry, in sharp contrast to the little Higgs models. The explicit breaking term for the vacuum alignment gives rise to a mass of the tHiggs, which is protected by the symmetry and hence naturally controlled against radiative corrections. Realistic top-quark mass is easily realized similarly to the top-seesaw mechanism by introducing an extra (subcritical) four-fermion coupling which explicitly breaks the residual U(2)'×U(1)' symmetry with U(2)' being an extra symmetry besides the above U(3)L×U(1). We present a phenomenological Lagrangian of the top-mode pseudo-Nambu-Goldstone bosons along with the Standard Model particles, which will be useful for the study of the collider phenomenology. The coupling property of the tHiggs is shown to be consistent with the currently available data reported from the LHC. Several phenomenological consequences and constraints from experiments are also addressed.

Planck satellite constraints on pseudo-Nambu-Goldstone boson quintessence

NASA Astrophysics Data System (ADS)

Smer-Barreto, Vanessa; Liddle, Andrew R.

2017-01-01

The pseudo-Nambu-Goldstone Boson (PNGB) potential, defined through the amplitude M4 and width f of its characteristic potential V(phi) = M4[1 + cos(phi/f)], is one of the best-suited models for the study of thawing quintessence. We analyse its present observational constraints by direct numerical solution of the scalar field equation of motion. Observational bounds are obtained using Supernovae data, cosmic microwave background temperature, polarization and lensing data from Planck, direct Hubble constant constraints, and baryon acoustic oscillations data. We find the parameter ranges for which PNGB quintessence gives a viable theory for dark energy. This exact approach is contrasted with the use of an approximate equation-of-state parametrization for thawing theories. We also discuss other possible parameterization choices, as well as commenting on the accuracy of the constraints imposed by Planck alone. Overall our analysis highlights a significant prior dependence to the outcome coming from the choice of modelling methodology, which current data are not sufficient to override.

Use of the Bethe equation for inner-shell ionization by electron impact

DOE Office of Scientific and Technical Information (OSTI.GOV)

Powell, Cedric J.; Llovet, Xavier; Salvat, Francesc

2016-05-14

We analyzed calculated cross sections for K-, L-, and M-shell ionization by electron impact to determine the energy ranges over which these cross sections are consistent with the Bethe equation for inner-shell ionization. Our analysis was performed with K-shell ionization cross sections for 26 elements, with L-shell ionization cross sections for seven elements, L{sub 3}-subshell ionization cross sections for Xe, and M-shell ionization cross sections for three elements. The validity (or otherwise) of the Bethe equation could be checked with Fano plots based on a linearized form of the Bethe equation. Our Fano plots, which display theoretical cross sections andmore » available measured cross sections, reveal two linear regions as predicted by de Heer and Inokuti [in Electron Impact Ionization, edited by T. D. Märk and G. H. Dunn, (Springer-Verlag, Vienna, 1985), Chap. 7, pp. 232–276]. For each region, we made linear fits and determined values of the two element-specific Bethe parameters. We found systematic variations of these parameters with atomic number for both the low- and the high-energy linear regions of the Fano plots. We also determined the energy ranges over which the Bethe equation can be used.« less

Bethe states of the trigonometric SU(3) spin chain with generic open boundaries

NASA Astrophysics Data System (ADS)

Sun, Pei; Xin, Zhirong; Qiao, Yi; Wen, Fakai; Hao, Kun; Cao, Junpeng; Li, Guang-Liang; Yang, Tao; Yang, Wen-Li; Shi, Kangjie

2018-06-01

By combining the algebraic Bethe ansatz and the off-diagonal Bethe ansatz, we investigate the trigonometric SU (3) model with generic open boundaries. The eigenvalues of the transfer matrix are given in terms of an inhomogeneous T - Q relation, and the corresponding eigenstates are expressed in terms of nested Bethe-type eigenstates which have well-defined homogeneous limit. This exact solution provides a basis for further analyzing the thermodynamic properties and correlation functions of the anisotropic models associated with higher rank algebras.

Degeneration of Bethe subalgebras in the Yangian of gl_n

NASA Astrophysics Data System (ADS)

Ilin, Aleksei; Rybnikov, Leonid

2018-04-01

We study degenerations of Bethe subalgebras B( C) in the Yangian Y(gl_n), where C is a regular diagonal matrix. We show that closure of the parameter space of the family of Bethe subalgebras, which parameterizes all possible degenerations, is the Deligne-Mumford moduli space of stable rational curves \\overline{M_{0,n+2}}. All subalgebras corresponding to the points of \\overline{M_{0,n+2}} are free and maximal commutative. We describe explicitly the "simplest" degenerations and show that every degeneration is the composition of the simplest ones. The Deligne-Mumford space \\overline{M_{0,n+2}} generalizes to other root systems as some De Concini-Procesi resolution of some toric variety. We state a conjecture generalizing our results to Bethe subalgebras in the Yangian of arbitrary simple Lie algebra in terms of this De Concini-Procesi resolution.

Goldstone-Apple Valley Radio Telescope System Theory of Operation

NASA Technical Reports Server (NTRS)

Stephan, George R.

1997-01-01

The purpose of this learning module is to enable learners to describe how the Goldstone-Apple Valley Radio Telescope (GAVRT) system functions in support of Apple Valley Science and Technology Center's (AVSTC) client schools' radio astronomy activities.

Collective-Goldstone-mode-induced ultralow lattice thermal conductivity in Sn-filled skutterudite SnFe4Sb12

NASA Astrophysics Data System (ADS)

Fu, Yuhao; He, Xin; Zhang, Lijun; Singh, David J.

2018-01-01

We demonstrate that the concept of Goldstone bosons can be exploited for phonon control and thermal conductivity reduction of materials. By studying lattice dynamics of the Sn filled skutterudite SnFe4Sb12 , we find Sn off-centers in its coordination cage in contrast to the common rare earth fillers. This leads to low-frequency Goldstone-like modes below 1 THz associated mainly with Sn motions. Importantly, these involve collective motion of other atoms, especially Sb, in the host skutterudite lattice. The optical modes transversing to the Sn off-centering direction are identified as Goldstone type modes in association with a three-dimensional Mexican-hat-like potential energy surface. The interaction of these collective Goldstone modes with the host heat-carrying phonons is shown to lead to ultralow lattice thermal conductivity.

A Conversation with Hans Bethe

NASA Astrophysics Data System (ADS)

Goodstein, Judith

1999-10-01

A Nobel laureate in physics speaks candidly about C. C. Lauritsen, Robert Millikan, and a number of other prominent physicists he has known and worked with at Cornell University, the California Institute of Technology, and the University of Rome. Bethe also describes his first impressions of nuclear physics, the political climate in Italy in the 1930s, and the Rome school of physics.

Geology of Southern Guinevere Planitia, Venus, based on analyses of Goldstone radar data

NASA Technical Reports Server (NTRS)

Arvidson, R. E.; Plaut, J. J.; Jurgens, R. F.; Saunders, R. S.; Slade, M. A.

1989-01-01

The ensemble of 41 backscatter images of Venus acquired by the S Band (12.6 cm) Goldstone radar system covers approx. 35 million km and includes the equatorial portion of Guinevere Planitia, Navka Planitia, Heng-O Chasma, and Tinatin Planitia, and parts of Devana Chasma and Phoebe Regio. The images and associated altimetry data combine relatively high spatial resolution (1 to 10 km) with small incidence angles (less than 10 deg) for regions not covered by either Venera Orbiter or Arecibo radar data. Systematic analyses of the Goldstone data show that: (1) Volcanic plains dominate, including groups of small volcanic constructs, radar bright flows on a NW-SE arm of Phoebe Regio and on Ushas Mons and circular volcano-tectonic depressions; (2) Some of the regions imaged by Goldstone have high radar cross sections, including the flows on Ushas Mons and the NW-SE arm of Phoebe Regio, and several other unnamed hills, ridged terrains, and plains areas; (3) A 1000 km diameter multiringed structure is observed and appears to have a morphology not observed in Venera data (The northern section corresponds to Heng-O Chasma); (4) A 150 km wide, 2 km deep, 1400 km long rift valley with upturned flanks is located on the western flank of Phoebe Regio and extends into Devana Chasma; (5) A number of structures can be discerned in the Goldstone data, mainly trending NW-SE and NE-SW, directions similar to those discerned in Pioneer-Venus topography throughout the equatorial region; and (6) The abundance of circular and impact features is similar to the plains global average defined from Venera and Arecibo data, implying that the terrain imaged by Goldstone has typical crater retention ages, measured in hundreds of millions of years. The rate of resurfacing is less than or equal to 4 km/Ga.

The goldstone and goldstino of supersymmetric inflation

DOE PAGES

Kahn, Yonatan; Roberts, Daniel A.; Thaler, Jesse

2015-10-01

Here, we construct the minimal effective field theory (EFT) of supersymmetric inflation, whose field content is a real scalar, the goldstone for time-translation breaking, and a Weyl fermion, the goldstino for supersymmetry (SUSY) breaking. The inflating background can be viewed as a single SUSY-breaking sector, and the degrees of freedom can be efficiently parameterized using constrained superfields. Our EFT is comprised of a chiral superfield X NL containing the goldstino and satisfying X 2 NL = 0, and a real superfield B NL containing both the goldstino and the goldstone, satisfying X NL B NL = B 3 NL =more » 0. We match results from our EFT formalism to existing results for SUSY broken by a fluid background, showing that the goldstino propagates with subluminal velocities. The same effect can also be derived from the unitary gauge gravitino action after embedding our EFT in supergravity. If the gravitino mass is comparable to the Hubble scale during inflation, we identify a new parameter in the EFT related to a time-dependent phase of the gravitino mass parameter. We briefly comment on the leading contributions of goldstino loops to inflationary observables.« less

Collective-Goldstone-mode-induced ultralow lattice thermal conductivity in Sn-filled skutterudite SnFe 4 Sb 12

DOE PAGES

Fu, Yuhao; He, Xin; Zhang, Lijun; ...

2018-01-03

Here, we demonstrate that the concept of Goldstone bosons can be exploited for phonon control and thermal conductivity reduction of materials. By studying lattice dynamics of the Sn filled skutterudite SnFe 4Sb 12, we find Sn off-centers in its coordination cage in contrast to the common rare earth fillers. This leads to low-frequency Goldstone-like modes below 1 THz associated mainly with Sn motions. Importantly, these involve collective motion of other atoms, especially Sb, in the host skutterudite lattice. The optical modes transversing to the Sn off-centering direction are identified as Goldstone type modes in association with a three-dimensional Mexican-hat-like potentialmore » energy surface. The interaction of these collective Goldstone modes with the host heat-carrying phonons is shown to lead to ultralow lattice thermal conductivity.« less

Collective-Goldstone-mode-induced ultralow lattice thermal conductivity in Sn-filled skutterudite SnFe 4 Sb 12

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fu, Yuhao; He, Xin; Zhang, Lijun

Here, we demonstrate that the concept of Goldstone bosons can be exploited for phonon control and thermal conductivity reduction of materials. By studying lattice dynamics of the Sn filled skutterudite SnFe 4Sb 12, we find Sn off-centers in its coordination cage in contrast to the common rare earth fillers. This leads to low-frequency Goldstone-like modes below 1 THz associated mainly with Sn motions. Importantly, these involve collective motion of other atoms, especially Sb, in the host skutterudite lattice. The optical modes transversing to the Sn off-centering direction are identified as Goldstone type modes in association with a three-dimensional Mexican-hat-like potentialmore » energy surface. The interaction of these collective Goldstone modes with the host heat-carrying phonons is shown to lead to ultralow lattice thermal conductivity.« less

Natural inflation with pseudo Nambu-Goldstone bosons

NASA Technical Reports Server (NTRS)

Freese, Katherine; Frieman, Joshua A.; Olinto, Angela V.

1990-01-01

It is shown that a pseudo-Nambu-Goldstone boson of given potential can naturally give rise to an epoch of inflation in the early universe. Mass scales which arise in particle physics models with a gauge group that becomes strongly interacting at a certain scales are shown to be conditions for successful inflation. The density fluctuation spectrum is nonscale-invariant, with extra power on large length scales.

Scalar products of Bethe vectors in models with {\\mathfrak{gl}}(2| 1) symmetry 1. Super-analog of Reshetikhin formula

NASA Astrophysics Data System (ADS)

Hutsalyuk, A.; Liashyk, A.; Pakuliak, S. Z.; Ragoucy, E.; Slavnov, N. A.

2016-11-01

We study the scalar products of Bethe vectors in integrable models solvable by the nested algebraic Bethe ansatz and possessing {gl}(2| 1) symmetry. Using explicit formulas of the monodromy matrix entries’ multiple actions onto Bethe vectors we obtain a representation for the scalar product in the most general case. This explicit representation appears to be a sum over partitions of the Bethe parameters. It can be used for the analysis of scalar products involving on-shell Bethe vectors. As a by-product, we obtain a determinant representation for the scalar products of generic Bethe vectors in integrable models with {gl}(1| 1) symmetry. Dedicated to the memory of Petr Petrovich Kulish.

Planck satellite constraints on pseudo-Nambu-Goldstone boson quintessence

DOE Office of Scientific and Technical Information (OSTI.GOV)

Smer-Barreto, Vanessa; Liddle, Andrew R., E-mail: vsm@roe.ac.uk, E-mail: arl@roe.ac.uk

2017-01-01

The pseudo-Nambu-Goldstone Boson (PNGB) potential, defined through the amplitude M {sup 4} and width f of its characteristic potential V (φ) = M {sup 4}[1 + cos(φ/ f )], is one of the best-suited models for the study of thawing quintessence. We analyse its present observational constraints by direct numerical solution of the scalar field equation of motion. Observational bounds are obtained using Supernovae data, cosmic microwave background temperature, polarization and lensing data from Planck , direct Hubble constant constraints, and baryon acoustic oscillations data. We find the parameter ranges for which PNGB quintessence gives a viable theory for darkmore » energy. This exact approach is contrasted with the use of an approximate equation-of-state parametrization for thawing theories. We also discuss other possible parameterization choices, as well as commenting on the accuracy of the constraints imposed by Planck alone. Overall our analysis highlights a significant prior dependence to the outcome coming from the choice of modelling methodology, which current data are not sufficient to override.« less

Algebraic Bethe ansatz for the XXZ Heisenberg spin chain with triangular boundaries and the corresponding Gaudin model

NASA Astrophysics Data System (ADS)

Manojlović, N.; Salom, I.

2017-10-01

The implementation of the algebraic Bethe ansatz for the XXZ Heisenberg spin chain in the case, when both reflection matrices have the upper-triangular form is analyzed. The general form of the Bethe vectors is studied. In the particular form, Bethe vectors admit the recurrent procedure, with an appropriate modification, used previously in the case of the XXX Heisenberg chain. As expected, these Bethe vectors yield the strikingly simple expression for the off-shell action of the transfer matrix of the chain as well as the spectrum of the transfer matrix and the corresponding Bethe equations. As in the XXX case, the so-called quasi-classical limit gives the off-shell action of the generating function of the corresponding trigonometric Gaudin Hamiltonians with boundary terms.

The goldstone energy project

NASA Technical Reports Server (NTRS)

Bartos, K. P.

1978-01-01

The Golstone Energy Project was established in 1974 to investigate ways in which the Goldstone Deep Space Complex in California could be made partly or completely energy-sufficient, especially through the use of solar- and wind-derived energy resources. Ways in which energy could be conserved at the Complex were also studied. Findings included data on both wind and solar energy. Obstacles to demonstrating energy self-sufficiency are: (1) operation and maintenance costs of solar energy systems are estimated to be much higher than conventional energy systems, (2) initial capital costs of present-day technology solar collectors are high and are compounded by low collector efficiency, and (3) no significant market force exists to create the necessary industry to reduce costs through mass production and broad open-market competition.

Radar investigations of near-Earth asteroids at Arecibo and Goldstone

NASA Astrophysics Data System (ADS)

Brozovic, M.; Nolan, M.; Benner, L.; Busch, M.; Howell, E.; Taylor, P.; Springmann, A.; Giorgini, J.; Margot, J.; Magri, C.; Sheppard, M.; Naidu, S.

2014-07-01

Radar observations are a powerful technique to study near-Earth asteroids (NEAs). The Arecibo and Goldstone planetary radars can provide delay-Doppler images that can directly resolve surface features such as concavities, hills, ridges, and boulders. Goldstone's 3.75-m resolution capability is invaluable when attempting to image NEAs with diameters smaller than 50 m. To date, over 430 near-Earth asteroids and 136 main-belt asteroids have been observed with radar. 80 % of the radar-detected NEAs have been observed within the last 10 years. The radar detection rate in the last three years has tripled relative to the average in the previous decade due to an increase in funding and greater scheduling flexibility. Currently, ˜400 observing hours per year at Goldstone and ˜600 observing hours per year at Arecibo are devoted to observing asteroids. We strive to observe all strong and moderately strong imaging targets, Yarkovsky drift candidates, NEOWISE targets, asteroids with very low perihelia that can be used to measure solar oblateness, and as many other detectable asteroids as resources allow. We also regularly attempt to observe any asteroid that is flagged by the Near-Earth Object Human Spaceflight Accessible Targets Study (NHATS) list (http://neo.jpl.nasa.gov/nhats/). To date, we have observed more than 60 NHATS objects at Arecibo and Goldstone. In the past three years, ˜1/3 of the detected asteroids were targets of opportunity (TOOs), some of which we observed within 24 h from when the discoveries were announced. Many TOOs are small, rapidly moving objects that are detectable by radar only within few lunar distances. Radar astrometry is particularly important for these asteroids because they are too faint to be followed for long with optical telescopes. A radar-range measurement often secures their orbit for decades or centuries, where otherwise the object would be lost and require rediscovery. In one of the extreme cases, two delay and two Doppler

Beth Reis and the Safe Schools Coalition

ERIC Educational Resources Information Center

Vaught, Sabina E.

2007-01-01

This article chronicles the formation and organization of the Safe Schools Coalition (SCC) through the experiences of Beth Reis, co-founder and co-Chair. The article suggests ways in which the SCC can serve as a model for both collective and individual work in promoting safe schools.

Electrical load management at the Goldstone DSN Complex

NASA Technical Reports Server (NTRS)

Rayburn, J. C.

1981-01-01

A Power Load Management Plan was deveoped which utilizes the unique power generating capabilities of the stations to reduce the stress on the local utility's reserve capacity and reduce the cost of electrical power at the stations. The plan has greatly reduced the cost of Goldstone electrical power by completely eliminating the use of commercial power during the local utility's high usage periods each day.

Introduction to the thermodynamic Bethe ansatz

NASA Astrophysics Data System (ADS)

van Tongeren, Stijn J.

2016-08-01

We give a pedagogical introduction to the thermodynamic Bethe ansatz, a method that allows us to describe the thermodynamics of integrable models whose spectrum is found via the (asymptotic) Bethe ansatz. We set the stage by deriving the Fermi-Dirac distribution and associated free energy of free electrons, and then in a similar though technically more complicated fashion treat the thermodynamics of integrable models, focusing first on the one-dimensional Bose gas with delta function interaction as a clean pedagogical example, secondly the XXX spin chain as an elementary (lattice) model with prototypical complicating features in the form of bound states, and finally the {SU}(2) chiral Gross-Neveu model as a field theory example. Throughout this discussion we emphasize the central role of particle and hole densities, whose relations determine the model under consideration. We then discuss tricks that allow us to use the same methods to describe the exact spectra of integrable field theories on a circle, in particular the chiral Gross-Neveu model. We moreover discuss the simplification of TBA equations to Y systems, including the transition back to integral equations given sufficient analyticity data, in simple examples.

Supersymmetric and non-supersymmetric models without catastrophic Goldstone bosons

NASA Astrophysics Data System (ADS)

Braathen, Johannes; Goodsell, Mark D.; Staub, Florian

2017-11-01

The calculation of the Higgs mass in general renormalisable field theories has been plagued by the so-called "Goldstone Boson Catastrophe," where light (would-be) Goldstone bosons give infra-red divergent loop integrals. In supersymmetric models, previous approaches included a workaround that ameliorated the problem for most, but not all, parameter space regions; while giving divergent results everywhere for non-supersymmetric models! We present an implementation of a general solution to the problem in the public code SARAH, along with new calculations of some necessary loop integrals and generic expressions. We discuss the validation of our code in the Standard Model, where we find remarkable agreement with the known results. We then show new applications in Split SUSY, the NMSSM, the Two-Higgs-Doublet Model, and the Georgi-Machacek model. In particular, we take some first steps to exploring where the habit of using tree-level mass relations in non-supersymmetric models breaks down, and show that the loop corrections usually become very large well before naive perturbativity bounds are reached.

Goldstone and Higgs modes of photons inside a cavity

NASA Astrophysics Data System (ADS)

Yi-Xiang, Yu; Ye, Jinwu; Liu, Wu-Ming

2013-12-01

Goldstone and Higgs modes have been detected in various condensed matter, cold atom and particle physics experiments. Here, we demonstrate that the two modes can also be observed in optical systems with only a few (artificial) atoms inside a cavity. We establish this connection by studying the U(1)/Z2 Dicke model where N qubits (atoms) coupled to a single photon mode. We determine the Goldstone and Higgs modes inside the super-radiant phase and their corresponding spectral weights by performing both 1/J = 2/N expansion and exact diagonalization (ED) study at a finite N. We find nearly perfect agreements between the results achieved by the two approaches when N gets down even to N = 2. The quantum finite size effects at a few qubits make the two modes quite robust against an effectively small counterrotating wave term. We present a few schemes to reduce the critical coupling strength, so the two modes can be observed in several current available experimental systems by just conventional optical measurements.

Goldstone field test activities: Target search

NASA Technical Reports Server (NTRS)

Tarter, J.

1986-01-01

In March of this year prototype SETI equipment was installed at DSS13, the 26 meter research and development antenna at NASA's Goldstone complex of satellite tracking dishes. The SETI equipment will remain at this site at least through the end of the summer so that the hardware and software developed for signal detection and recognition can be fully tested in a dynamic observatory environment. The field tests are expected to help understand which strategies for observing and which signal recognition algorithms perform best in the presence of strong man-made interfering signals (RFI) and natural astronomical sources.

Boundary Quantum Knizhnik-Zamolodchikov Equations and Bethe Vectors

NASA Astrophysics Data System (ADS)

Reshetikhin, Nicolai; Stokman, Jasper; Vlaar, Bart

2015-06-01

Solutions to boundary quantum Knizhnik-Zamolodchikov equations are constructed as bilateral sums involving "off-shell" Bethe vectors in case the reflection matrix is diagonal and only the 2-dimensional representation of is involved. We also consider their rational and classical degenerations.

Performance of the image statistics decoder in conjunction with the Goldstone-VLA array

NASA Technical Reports Server (NTRS)

Wang, H. C.; Pitt, G. H., III

1989-01-01

During Voyager's Neptune encounter, the National Radio Astronomy Observatory's Very Large Array (VLA) will be arrayed with Goldstone antennas to receive the transmitted telemetry data from the spacecraft. The telemetry signal from the VLA will drop out periodically, resulting in a periodic drop in the received signal-to-noise ratio (SNR). The Image Statistics Decoder (ISD), which assumes a correlation between pixels, can improve the bit error rate (BER) for images during these dropout periods. Simulation results have shown that the ISD, in conjunction with the Goldstone-VLA array can provide a 3-dB gain for uncompressed images at a BER of 5.0 x 10(exp -3).

GW and Bethe-Salpeter study of small water clusters

DOE Office of Scientific and Technical Information (OSTI.GOV)

Blase, Xavier, E-mail: xavier.blase@neel.cnrs.fr; Boulanger, Paul; Bruneval, Fabien

We study within the GW and Bethe-Salpeter many-body perturbation theories the electronic and optical properties of small (H{sub 2}O){sub n} water clusters (n = 1-6). Comparison with high-level CCSD(T) Coupled-Cluster at the Single Double (Triple) levels and ADC(3) Green’s function third order algebraic diagrammatic construction calculations indicates that the standard non-self-consistent G{sub 0}W{sub 0}@PBE or G{sub 0}W{sub 0}@PBE0 approaches significantly underestimate the ionization energy by about 1.1 eV and 0.5 eV, respectively. Consequently, the related Bethe-Salpeter lowest optical excitations are found to be located much too low in energy when building transitions from a non-self-consistent G{sub 0}W{sub 0} description ofmore » the quasiparticle spectrum. Simple self-consistent schemes, with update of the eigenvalues only, are shown to provide a weak dependence on the Kohn-Sham starting point and a much better agreement with reference calculations. The present findings rationalize the theory to experiment possible discrepancies observed in previous G{sub 0}W{sub 0} and Bethe-Salpeter studies of bulk water. The increase of the optical gap with increasing cluster size is consistent with the evolution from gas to dense ice or water phases and results from an enhanced screening of the electron-hole interaction.« less

Algebraic Bethe ansatz for the two species ASEP with different hopping rates

NASA Astrophysics Data System (ADS)

Cantini, Luigi

2008-03-01

An ASEP with two species of particles and different hopping rates is considered on a ring. Its integrability is proved, and the nested algebraic Bethe ansatz is used to derive the Bethe equations for states with arbitrary numbers of particles of each type, generalizing the results of Derrida and Evans [10]. We also present formulae for the total velocity of particles of a given type and their limit given the large size of the system and the finite densities of the particles.

Random Blume-Emery-Griffiths model on the Bethe lattice

NASA Astrophysics Data System (ADS)

Albayrak, Erhan

2015-12-01

The random phase transitions of the Blume-Emery-Griffiths (BEG) model for the spin-1 system are investigated on the Bethe lattice and the phase diagrams of the model are obtained. The biquadratic exchange interaction (K) is turned on, i.e. the BEG model, with probability p either attractively (K > 0) or repulsively (K < 0) and turned off, which leads to the BC model, with the probability (1 - p) throughout the Bethe lattice. By taking the bilinear exchange interaction parameter J as a scaling parameter, the effects of the competitions between the reduced crystal fields (D / J), reduced biquadratic exchange interaction parameter (K / J) and the reduced temperature (kT / J) for given values of the probability when the coordination number is q=4, i.e. on a square lattice, are studied in detail.

Nambu-Goldstone theorem and spin-statistics theorem

NASA Astrophysics Data System (ADS)

Fujikawa, Kazuo

On December 19-21 in 2001, we organized a yearly workshop at Yukawa Institute for Theoretical Physics in Kyoto on the subject of "Fundamental Problems in Field Theory and their Implications". Prof. Yoichiro Nambu attended this workshop and explained a necessary modification of the Nambu-Goldstone theorem when applied to nonrelativistic systems. At the same workshop, I talked on a path integral formulation of the spin-statistics theorem. The present essay is on this memorable workshop, where I really enjoyed the discussions with Nambu, together with a short comment on the color freedom of quarks.

A Tour of the Goldstone-Apple Valley Radio Telescope

NASA Technical Reports Server (NTRS)

Ardenski, Brooke; Stephan, George R.

1997-01-01

Goldstone-Apple Valley Radio Telescope (GAVRT) is located in a remote area of the Mojave Desert, 40 miles north of Barstow, California. The antenna, identified as DSS-12, is a 34-meter diameter dish, 11 times the diameter of a ten foot microwave dish used for satellite television. DSS-12 has been used by NASA to communicate with robotic space probes for more than thirty years.

Goldstone Solar System Radar (GSSR)

NASA Technical Reports Server (NTRS)

Renzetti, N. A.

1991-01-01

The primary objective of the Goldstone Solar System Radar is the investigation of solar system bodies by means of Earth-based radar. Targets of primary interest include the Galilean moons, Saturn's rings and moons, and Earth-approaching asteroids and comets. Planets are also of interest, particularly Mercury and the planets to which NASA has not yet planned spacecraft visits. Based on a history of solid achievement, including the definition of the Astronomical Unit, imaging and topography of Mars, Venus, and Mercury, and contributions to the general theory of relativity, the program will continue to support flight project requirements and its primary objectives. The individual target objectives are presented, and information on the following topics are presented in tabular form: Deep Space Network support, compatibility tests, telemetry, command, and tracking support responsibility.

An ultra-weak sector, the strong CP problem and the pseudo-Goldstone dilaton

DOE PAGES

Allison, Kyle; Hill, Christopher T.; Ross, Graham G.

2014-12-29

In the context of a Coleman–Weinberg mechanism for the Higgs boson mass, we address the strong CP problem. We show that a DFSZ-like invisible axion model with a gauge-singlet complex scalar field S, whose couplings to the Standard Model are naturally ultra-weak, can solve the strong CP problem and simultaneously generate acceptable electroweak symmetry breaking. The ultra-weak couplings of the singlet S are associated with underlying approximate shift symmetries that act as custodial symmetries and maintain technical naturalness. The model also contains a very light pseudo-Goldstone dilaton that is consistent with cosmological Polonyi bounds, and the axion can be themore » dark matter of the universe. As a result, we further outline how a SUSY version of this model, which may be required in the context of Grand Unification, can avoid introducing a hierarchy problem.« less

An ultra-weak sector, the strong CP problem and the pseudo-Goldstone dilaton

DOE Office of Scientific and Technical Information (OSTI.GOV)

Allison, Kyle; Hill, Christopher T.; Ross, Graham G.

In the context of a Coleman–Weinberg mechanism for the Higgs boson mass, we address the strong CP problem. We show that a DFSZ-like invisible axion model with a gauge-singlet complex scalar field S, whose couplings to the Standard Model are naturally ultra-weak, can solve the strong CP problem and simultaneously generate acceptable electroweak symmetry breaking. The ultra-weak couplings of the singlet S are associated with underlying approximate shift symmetries that act as custodial symmetries and maintain technical naturalness. The model also contains a very light pseudo-Goldstone dilaton that is consistent with cosmological Polonyi bounds, and the axion can be themore » dark matter of the universe. As a result, we further outline how a SUSY version of this model, which may be required in the context of Grand Unification, can avoid introducing a hierarchy problem.« less

Development of realtime connected element interferometry at the Goldstone Deep Space Communications Complex

NASA Technical Reports Server (NTRS)

Edwards, C. D.

1990-01-01

Connected-element interferometry (CEI) has the potential to provide high-accuracy angular spacecraft tracking on short baselines by making use of the very precise phase delay observable. Within the Goldstone Deep Space Communications Complex (DSCC), one of three tracking complexes in the NASA Deep Space Network, baselines of up to 21 km in length are available. Analysis of data from a series of short-baseline phase-delay interferometry experiments are presented to demonstrate the potential tracking accuracy on these baselines. Repeated differential observations of pairs of angularly close extragalactic radio sources were made to simulate differential spacecraft-quasar measurements. Fiber-optic data links and a correlation processor are currently being developed and installed at Goldstone for a demonstration of real-time CEI in 1990.

Quantum fluctuations and gapped Goldstone modes in spinor Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Beekman, Aron

2015-03-01

The classical Heisenberg ferromagnet is an exact eigenstate of the quantum Hamiltonian and therefore has no quantum fluctuations. Furthermore it has a reduced number of Goldstone modes, an order parameter that is itself a symmetry generator, is a highest-weight state for the spin algebra, and has no tower of states of vanishing energy. We derive the connection between all these properties and provide general criteria for their presence in other spontaneously-broken symmetry states. The phletora of groundstates in spinor Bose-Einstein condensates is an ideal testing ground for these predictions. In particular the phases with non-maximal polarization (e.g. the F-phase in spin-3 condensates) have an additional gapped mode that is a partner to the quadratically dispersing Goldstone mode, as compared to the maximally polarized, ferromagnetic phase. Furthermore there is a fundamental limit to the coherence time of superpositions in the non-maximally polarized state, which should manifest itself for small-size systems.

Can a pseudo-Nambu-Goldstone Higgs lead to symmetry non-restoration?

NASA Astrophysics Data System (ADS)

Kilic, Can; Swaminathan, Sivaramakrishnan

2016-01-01

The calculation of finite temperature contributions to the scalar potential in a quantum field theory is similar to the calculation of loop corrections at zero temperature. In natural extensions of the Standard Model where loop corrections to the Higgs potential cancel between Standard Model degrees of freedom and their symmetry partners, it is interesting to contemplate whether finite temperature corrections also cancel, raising the question of whether a broken phase of electroweak symmetry may persist at high temperature. It is well known that this does not happen in supersymmetric theories because the thermal contributions of bosons and fermions do not cancel each other. However, for theories with same spin partners, the answer is less obvious. Using the Twin Higgs model as a benchmark, we show that although thermal corrections do cancel at the level of quadratic divergences, subleading corrections still drive the system to a restored phase. We further argue that our conclusions generalize to other well-known extensions of the Standard Model where the Higgs is rendered natural by being the pseudo-Nambu-Goldstone mode of an approximate global symmetry.

Twisting singular solutions of Betheʼs equations

NASA Astrophysics Data System (ADS)

Nepomechie, Rafael I.; Wang, Chunguang

2014-12-01

The Bethe equations for the periodic XXX and XXZ spin chains admit singular solutions, for which the corresponding eigenvalues and eigenvectors are ill-defined. We use a twist regularization to derive conditions for such singular solutions to be physical, in which case they correspond to genuine eigenvalues and eigenvectors of the Hamiltonian.

Nambu-Goldstone theorem and spin-statistics theorem

NASA Astrophysics Data System (ADS)

Fujikawa, Kazuo

2016-05-01

On December 19-21 in 2001, we organized a yearly workshop at Yukawa Institute for Theoretical Physics in Kyoto on the subject of “Fundamental Problems in Field Theory and their Implications”. Prof. Yoichiro Nambu attended this workshop and explained a necessary modification of the Nambu-Goldstone theorem when applied to non-relativistic systems. At the same workshop, I talked on a path integral formulation of the spin-statistics theorem. The present essay is on this memorable workshop, where I really enjoyed the discussions with Nambu, together with a short comment on the color freedom of quarks.

Collisional excitation of the highly excited hydrogen atoms in the dipole form of the semiclassical impact parameter and Born approximations

NASA Technical Reports Server (NTRS)

Omidvar, K.

1971-01-01

Expressions for the excitation cross section of the highly excited states of the hydrogenlike atoms by fast charged particles have been derived in the dipole approximation of the semiclassical impact parameter and the Born approximations, making use of a formula for the asymptotic expansion of the oscillator strength of the hydrogenlike atoms given by Menzel. When only the leading term in the asymptotic expansion is retained, the expression for the cross section becomes identical to the expression obtained by the method of the classical collision and correspondence principle given by Percival and Richards. Comparisons are made between the Bethe coefficients obtained here and the Bethe coefficients of the Born approximation for transitions where the Born calculation is available. Satisfactory agreement is obtained only for n yields n + 1 transitions, with n the principal quantum number of the excited state.

Bayesian extraction of the parton distribution amplitude from the Bethe-Salpeter wave function

NASA Astrophysics Data System (ADS)

Gao, Fei; Chang, Lei; Liu, Yu-xin

2017-07-01

We propose a new numerical method to compute the parton distribution amplitude (PDA) from the Euclidean Bethe-Salpeter wave function. The essential step is to extract the weight function in the Nakanishi representation of the Bethe-Salpeter wave function in Euclidean space, which is an ill-posed inversion problem, via the maximum entropy method (MEM). The Nakanishi weight function as well as the corresponding light-front parton distribution amplitude (PDA) can be well determined. We confirm prior work on PDA computations, which was based on different methods.

Goldstone Radar Observations of the 1999 Mars Opposition and other Observing Opportunities

NASA Astrophysics Data System (ADS)

Slade, M. A.

1997-07-01

As part of the International Mars Watch, Goldstone radar observations of Mars are planned during the 1999 Opposition ( Feb.'99-Aug'99). While some observing time is already allocated, a number of tracks could be made available for well-focused scientific objectives. Since the Deep Space Network plans far in advance, now is the time to develop your plans. During the next Mars opposition, the sub-Earth latitudes are in Mars' Northern hemisphere over the most northerly terrain accessible, which has not been previously examined with current sensitivity. The North residual ice cap is of particular interest. As a reminder to the Planetary Science community, observing proposals from any scientist with peer-reviewed planetary funding are solicited and should be forwarded to Martin.A.Slade@jpl.nasa.gov by email. Data reduction can, in principle, be carried out over the Internet. A graduate student or postdoctoral fellow resident at JPL for short period is recommended, however, to become familiar with suite of software for data analysis. Unfortunately, JPL cannot guarantee travel reimbursement due to funding limitations. We urge your consideration of becoming involved with the acquisition and analysis of Goldstone radar data. In the recent past, P.I.'s or co-I.s from Cornell, Arecibo/NAIC, Washington State University, Univ. Cal. Berkeley, Harvard -Smithsonian Center for Astrophysics, Univ. of Chicago, the DLR, Kashima SRC, ISAS, the Russian Academy of Science, the Russian Space Agency, and the USGS, have participated in radar experiments with Goldstone transmitting. This work is supported by the California Institute of Technology, under contract with NASA.

Height probabilities in the Abelian sandpile model on the generalized finite Bethe lattice

NASA Astrophysics Data System (ADS)

Chen, Haiyan; Zhang, Fuji

2013-08-01

In this paper, we study the sandpile model on the generalized finite Bethe lattice with a particular boundary condition. Using a combinatorial method, we give the exact expressions for all single-site probabilities and some two-site joint probabilities. As a by-product, we prove that the height probabilities of bulk vertices are all the same for the Bethe lattice with certain given boundary condition, which was found from numerical evidence by Grassberger and Manna ["Some more sandpiles," J. Phys. (France) 51, 1077-1098 (1990)], 10.1051/jphys:0199000510110107700 but without a proof.

Symmetry preserving truncations of the gap and Bethe-Salpeter equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Binosi, Daniele; Chang, Lei; Papavassiliou, Joannis

2016-05-01

Ward-Green-Takahashi (WGT) identities play a crucial role in hadron physics, e.g. imposing stringent relationships between the kernels of the one-and two-body problems, which must be preserved in any veracious treatment of mesons as bound states. In this connection, one may view the dressed gluon-quark vertex, Gamma(alpha)(mu), as fundamental. We use a novel representation of Gamma(alpha)(mu), in terms of the gluon-quark scattering matrix, to develop a method capable of elucidating the unique quark-antiquark Bethe-Salpeter kernel, K, that is symmetry consistent with a given quark gap equation. A strength of the scheme is its ability to expose and capitalize on graphic symmetriesmore » within the kernels. This is displayed in an analysis that reveals the origin of H-diagrams in K, which are two-particle-irreducible contributions, generated as two-loop diagrams involving the three-gluon vertex, that cannot be absorbed as a dressing of Gamma(alpha)(mu) in a Bethe-Salpeter kernel nor expressed as a member of the class of crossed-box diagrams. Thus, there are no general circumstances under which the WGT identities essential for a valid description of mesons can be preserved by a Bethe-Salpeter kernel obtained simply by dressing both gluon-quark vertices in a ladderlike truncation; and, moreover, adding any number of similarly dressed crossed-box diagrams cannot improve the situation.« less

Goldstone and Arecibo radar observations of (99942) Apophis in 2012-2013

NASA Astrophysics Data System (ADS)

Brozović, Marina; Benner, Lance A. M.; McMichael, Joseph G.; Giorgini, Jon D.; Pravec, Petr; Scheirich, Petr; Magri, Christopher; Busch, Michael W.; Jao, Joseph S.; Lee, Clement G.; Snedeker, Lawrence G.; Silva, Marc A.; Slade, Martin A.; Semenov, Boris; Nolan, Michael C.; Taylor, Patrick A.; Howell, Ellen S.; Lawrence, Kenneth J.

2018-01-01

We report radar observations of Apophis obtained during the 2012-2013 apparition. We observed Apophis on fourteen days at Goldstone (8560 MHz, 3.5 cm) and on five days at Arecibo (2380 MHz, 12.3 cm) between 2012 December 21 to 2013 March 16. Closest approach occurred on January 9 at a distance of 0.097 au. We obtained relatively weak echo power spectra and delay-Doppler images. The highest range resolution was achieved at Goldstone, 0.125 μs or ∼20 m/px. The data suggest that Apophis is an elongated, asymmetric, and possibly bifurcated object. The images place a lower bound on the long axis of 450 m. We used the Pravec et al. (2014) lightcurve-derived shape and spin state model of Apophis to test for short axis mode (SAM) non-principal axis rotation (NPA) and to estimate the asteroid's dimensions. The radar data are consistent with the NPA spin state and they constrain the equivalent diameter to be D = 0.34 ± 0.04 km (1σ bound). This is slightly smaller than the most recent IR observation estimates of 375(-10)(+14) m and 380-393 m, reported by Müller et al. (2014) and Licandro et al. (2016) respectively. We estimated a radar albedo of 0.25 ± 0.11 based on Goldstone data, and an optical albedo, pV, of 0.35 ± 0.10. Licandro et al. (2016) reported pV in the range of 0.24-0.33. The radar astrometry has been updated using a 3-D shape model. The Yarkovsky acceleration has not been detected in the current orbital fit, but if the position error during the 2021 encounter exceeds 8-12 km, this could signal a detection of the Yarkovsky effect.

Bethe ansatz for two-magnon scattering states in 2D and 3D Heisenberg–Ising ferromagnets

NASA Astrophysics Data System (ADS)

Bibikov, P. N.

2018-04-01

Two different versions of Bethe ansatz are suggested for evaluation of scattering two-magnon states in 2D and 3D Heisenberg–Ising ferromagnets on square and simple cubic lattices. It is shown that the two-magnon sector is subdivided on two subsectors related to non-interacting and scattering magnons. The former subsector possess an integrable regular dynamics and may be described by a natural modification of the usual Bethe Ansatz. The latter one is characterized by a non-integrable chaotic dynamics and may be treated only within discrete degenerative version of Bethe Ansatz previously suggested by the author. Some of these results are generalized for multi-magnon states of the Heisenberg–Ising ferromagnet on a D dimensional hyper cubic lattice. Dedicated to the memory of L D Faddeev.

Review of “orthopaedic biomechanics” edited by Beth A. Winkelstein

PubMed Central

2013-01-01

This article is a review of the book “orthopaedic biomechanics” edited by Beth A. Winkelstein. This book (hardcover) was published by CRC Press, Taylor & Francis Group, FL in 2012. The contents of the book and its relevance to orthopedic research or practice is discussed in this invited review.

Elementary functions in thermodynamic Bethe ansatz

NASA Astrophysics Data System (ADS)

Suzuki, J.

2015-05-01

Some years ago, Fendley found an explicit solution to the thermodynamic Bethe ansatz (TBA) equation for an N=2 supersymmetric theory in 2D with a specific F-term. Motivated by this, we seek explicit solutions for other super-potential cases utilizing the idea from the ODE/IM correspondence. We find that the TBA equations, corresponding to a wider class of super-potentials, admit solutions in terms of elementary functions such as modified Bessel functions and confluent hyper-geometric series. Based on talks given at ‘Infinite Analysis 2014’ (Tokyo, 2014) and at ‘Integrable lattice models and quantum field theories’ (Bad Honnef, 2014).

Numerical studies of the Bethe-Salpeter equation for a two-fermion bound state

NASA Astrophysics Data System (ADS)

de Paula, W.; Frederico, T.; Salmè, G.; Viviani, M.

2018-03-01

Some recent advances on the solution of the Bethe-Salpeter equation (BSE) for a two-fermion bound system directly in Minkowski space are presented. The calculations are based on the expression of the Bethe-Salpeter amplitude in terms of the so-called Nakanishi integral representation and on the light-front projection (i.e. the integration of the light-front variable k - = k 0 - k 3). The latter technique allows for the analytically exact treatment of the singularities plaguing the two-fermion BSE in Minkowski space. The good agreement observed between our results and those obtained using other existing numerical methods, based on both Minkowski and Euclidean space techniques, fully corroborate our analytical treatment.

Classification of three-state Hamiltonians solvable by the coordinate Bethe ansatz

NASA Astrophysics Data System (ADS)

Crampé, N.; Frappat, L.; Ragoucy, E.

2013-10-01

We classify ‘all’ Hamiltonians with rank 1 symmetry and nearest-neighbour interactions, acting on a periodic three-state spin chain, and solvable through (generalization of) the coordinate Bethe ansatz (CBA). In this way we obtain four multi-parametric extensions of the known 19-vertex Hamiltonians (such as Zamolodchikov-Fateev, Izergin-Korepin and Bariev Hamiltonians). Apart from the 19-vertex Hamiltonians, there exist 17-vertex and 14-vertex Hamiltonians that cannot be viewed as subcases of the 19-vertex ones. In the case of 17-vertex Hamiltonians, we get a generalization of the genus 5 special branch found by Martins, plus three new ones. We also get two 14-vertex Hamiltonians. We solve all these Hamiltonians using CBA, and provide their spectrum, eigenfunctions and Bethe equations. Special attention is given to provide the specifications of our multi-parametric Hamiltonians that give back known Hamiltonians.

The design and implementation of the Technical Facilities Controller (TFC) for the Goldstone deep space communications complex

NASA Technical Reports Server (NTRS)

Killian, D. A.; Menninger, F. J.; Gorman, T.; Glenn, P.

1988-01-01

The Technical Facilities Controller is a microprocessor-based energy management system that is to be implemented in the Deep Space Network facilities. This system is used in conjunction with facilities equipment at each of the complexes in the operation and maintenance of air-conditioning equipment, power generation equipment, power distribution equipment, and other primary facilities equipment. The implementation of the Technical Facilities Controller was completed at the Goldstone Deep Space Communications Complex and is now operational. The installation completed at the Goldstone Complex is described and the utilization of the Technical Facilities Controller is evaluated. The findings will be used in the decision to implement a similar system at the overseas complexes at Canberra, Australia, and Madrid, Spain.

Bethe Ansatz solutions for highest states in Script N = 4 SYM and AdS/CFT duality

NASA Astrophysics Data System (ADS)

Beccaria, Matteo; DelDebbio, Luigi

2006-09-01

We consider the operators with highest anomalous dimension Δ in the compact rank-one sectors fraktur sfraktur u(1|1) and fraktur sfraktur u(2) of Script N = 4 super Yang-Mills. We study the flow of Δ from weak to strong 't Hooft coupling λ by solving (i) the all-loop gauge Bethe Ansatz, (ii) the quantum string Bethe Ansatz. The two calculations are carefully compared in the strong coupling limit and exhibit different exponents ν in the leading order expansion Δ ~ λν. We find ν = 1/2 and ν = 1/4 for the gauge or string solution. This strong coupling discrepancy is not unexpected, and it provides an explicit example where the gauge Bethe Ansatz solution cannot be trusted at large λ. Instead, the string solution perfectly reproduces the Gubser-Klebanov-Polyakov law Δ = 2n1/2 λ1/4. In particular, we provide an analytic expression for the integer level n as a function of the U(1) charge in both sectors.

Objectives and first results of the NASA SETI sky survey field tests at Goldstone

NASA Technical Reports Server (NTRS)

Gulkis, S.; Klein, M. J.; Olsen, E. T.; Crow, R. B.; Gosline, R. M.; Downs, G. S.; Quirk, M. P.; Lokshin, A.; Solomon, J.

1986-01-01

Field tests of SETI (Search for Extraterrestrial Intelligence) prototype hardware and software began in March 1985 at Goldstone. With emphasis on the sky survey component of the NASA SETI search strategy, the article describes the survey characteristics, the detection strategy, and preliminary results of system tests.

Nuclear matter from effective quark-quark interaction.

PubMed

Baldo, M; Fukukawa, K

2014-12-12

We study neutron matter and symmetric nuclear matter with the quark-meson model for the two-nucleon interaction. The Bethe-Bruckner-Goldstone many-body theory is used to describe the correlations up to the three hole-line approximation with no extra parameters. At variance with other nonrelativistic realistic interactions, the three hole-line contribution turns out to be non-negligible and to have a substantial saturation effect. The saturation point of nuclear matter, the compressibility, the symmetry energy, and its slope are within the phenomenological constraints. Since the interaction also reproduces fairly well the properties of the three-nucleon system, these results indicate that the explicit introduction of the quark degrees of freedom within the considered constituent quark model is expected to reduce the role of three-body forces.

One-loop pseudo-Goldstone masses in the minimal S O (10 ) Higgs model

NASA Astrophysics Data System (ADS)

Gráf, Lukáš; Malinský, Michal; Mede, Timon; Susič, Vasja

2017-04-01

We calculate the prominent perturbative contributions shaping the one-loop scalar spectrum of the minimal renormalizable nonsupersymmetric S O (10 ) Higgs model whose unified gauge symmetry is spontaneously broken by an adjoint scalar. Focusing on its potentially realistic 45 ⊕126 variant in which the rank is reduced by a vacuum expectation value of the 5-index antisymmetric self-dual tensor, we provide a thorough analysis of the corresponding Coleman-Weinberg one-loop effective potential, paying particular attention to the masses of the potentially tachyonic pseudo-Goldstone bosons transforming as (1, 3, 0) and (8, 1, 0) under the standard model (SM) gauge group. The results confirm the assumed existence of extended regions in the parameter space supporting a locally stable SM-like quantum vacuum inaccessible at the tree level. The effective potential tedium is compared to that encountered in the previously studied 45 ⊕16 S O (10 ) Higgs model where the polynomial corrections to the relevant pseudo-Goldstone masses turn out to be easily calculable within a very simplified purely diagrammatic approach.

Semiclassics, Goldstone bosons and CFT data

NASA Astrophysics Data System (ADS)

Monin, A.; Pirtskhalava, D.; Rattazzi, R.; Seibold, F. K.

2017-06-01

Hellerman et al. (arXiv:1505.01537) have shown that in a generic CFT the spectrum of operators carrying a large U(1) charge can be analyzed semiclassically in an expansion in inverse powers of the charge. The key is the operator state correspondence by which such operators are associated with a finite density superfluid phase for the theory quantized on the cylinder. The dynamics is dominated by the corresponding Goldstone hydrodynamic mode and the derivative expansion coincides with the inverse charge expansion. We illustrate and further clarify this situation by first considering simple quantum mechanical analogues. We then systematize the approach by employing the coset construction for non-linearly realized space-time symmetries. Focussing on CFT3 we illustrate the case of higher rank and non-abelian groups and the computation of higher point functions. Three point function coefficients turn out to satisfy universal scaling laws and correlations as the charge and spin are varied.

Low-density homogeneous symmetric nuclear matter: Disclosing dinucleons in coexisting phases

NASA Astrophysics Data System (ADS)

Arellano, Hugo F.; Delaroche, Jean-Paul

2015-01-01

The effect of in-medium dinucleon bound states on self-consistent single-particle fields in Brueckner, Bethe and Goldstone theory is investigated in symmetric nuclear matter at zero temperature. To this end, dinucleon bound state occurences in the 1 S 0 and 3 SD 1 channels are explicitly accounted for --within the continuous choice for the auxiliary fields-- while imposing self-consistency in Brueckner-Hartree-Fock approximation calculations. Searches are carried out at Fermi momenta in the range fm-1, using the Argonne bare nucleon-nucleon potential without resorting to the effective-mass approximation. As a result, two distinct solutions meeting the self-consistency requirement are found with overlapping domains in the interval 0.130 fm-1 0.285 fm-1, corresponding to mass densities between and g cm-3. Effective masses as high as three times the nucleon mass are found in the coexistence domain. The emergence of superfluidity in relationship with BCS pairing gap solutions is discussed.

High-Resolution Bistatic Radar Imaging of Near-Earth Asteroids in 2015 using New Capabilities of Goldstone and Green Bank Telescopes

NASA Astrophysics Data System (ADS)

Naidu, S.; Benner, L.; Brozovic, M.; Giorgini, J. D.; Jao, J. S.; Lee, C. G.; Busch, M.; Ghigo, F. D.; Ford, A.; Kobelski, A.; Marshall, S.

2015-12-01

We present new results from bistatic Goldstone to Green Bank Telescope (GBT) high-resolution radar imaging of near-Earth asteroids (NEAs). Previously, most radar observations used either the 305-m Arecibo radar or the 70-m DSS-14 radar at Goldstone. Following the installation of new data-taking equipment at the GBT in late 2014, the number of bistatic Goldstone/GBT observations has increased substantially. Receiving Goldstone radar echoes at the 100-m GBT improves the signal-to-noise ratios (SNRs) two- to three-fold relative to monostatic reception at DSS-14. The higher SNRs allow us to obtain higher resolution images than is possible with DSS-14 both transmitting and receiving. Thus far in 2015, we have used the GBT receiver in combination with the 450 kW DSS-14 antenna and a new low-power 80kW transmitter on the 34-m DSS-13 antenna at the Goldstone complex to image five and two NEAs respectively. Asteroids 2005 YQ96, 2004 BL86, and 1994 AW1 are binary systems. 2011 UW158 has a spin period of 36 minutes that is unusually fast among asteroids its size (~500 m). 1999 JD6 is a deeply bifurcated double-lobed object. 2015 HM10 is an elongated 80 m asteroid with a spin period of 22 minutes. Our best images of these objects resolve the surface with resolutions of 3.75 m and reveal numerous features. Such images are useful to estimate the 3D shape, spin state, and other physical and dynamical properties of the objects. This knowledge is of particular interest for spacecraft mission planning, impact threat assessment, and resource utilization. Over the long term, such observations will help answer fundamental questions regarding the origin of the diversity in asteroid morphologies, the importance of spin-up mechanisms and collisional influences, the interior structure and thermal properties of asteroids, and the variety of dynamical states.

Potential Interference from Wireless Water Tank Transmitters at Goldstone

NASA Astrophysics Data System (ADS)

Ho, C.

2008-02-01

The Deep Space Network (DSN) facility in the Goldstone, California, area is considering installation of a new type of wireless transmitter (M2400S) within the facility. The transmitters will be used to monitor the water levels in several water tanks. Then these water-level signals will be transmitted to the nearby DSN facilities using transmitters operating in the UHF band (900-MHz) or S-band (2.4-GHz). This study is to evaluate the interference effects from the transmitters in adjacent DSN receiving stations. First we perform a terrain profile analysis to identify if there is a line of sight between each transmitter and the nearby DSN stations. After taking into account terrain shielding using high-resolution data, total propagation losses are calculated along each path. Then we perform the link analysis for each site to identify if the interference power exceeds the protection threshold of DSN receiving stations. As a result, we find that, because there is no bandpass filter installed in the transmitter system, interference power from the new transmitter at S-band will greatly exceed the protection criteria of broadband radio astronomy services (RAS) at S-band, such as Deep Space Station (DSS) 12 and DSS 28, by about 50 dB. The interference may also cause problems on all deep-space research stations at S-band, such as the Mars, Apollo, Venus, and Gemini sites. Without a sharp bandpass filter to suppress the out-of-band emissions in the frequency bands that the DSN station and RAS use, the author recommends not installing this type of transmitter within the Goldstone DSN facility area.

Cosmological constraints on pseudo-Nambu-Goldstone bosons

NASA Technical Reports Server (NTRS)

Frieman, Joshua A.; Jaffe, Andrew H.

1991-01-01

Particle physics models with pseudo-Nambu-Goldstone bosons (PNGBs) are characterized by two mass scales: a global spontaneous symmetry breaking scale, f, and a soft (explicit) symmetry breaking scale, Lambda. General model insensitive constraints were studied on this 2-D parameter space arising from the cosmological and astrophysical effects of PNGBs. In particular, constraints were studied arising from vacuum misalignment and thermal production of PNGBs, topological defects, and the cosmological effects of PNGB decay products, as well as astrophysical constraints from stellar PNGB emission. Bounds on the Peccei-Quinn axion scale, 10(exp 10) GeV approx. = or less than f sub pq approx. = or less than 10(exp 10) to 10(exp 12) GeV, emerge as a special case, where the soft breaking scale is fixed at Lambda sub QCD approx. = 100 MeV.

Rigged String Configurations, Bethe Ansatz Qubits, and Conservation of Parity

NASA Astrophysics Data System (ADS)

Lulek, T.

Bethe Ansatz solutions for the Heisenberg Hamiltonian of a one - dimensional magnetic ring of N nodes, each with the spin 1/2, within the XXX model, have been presented as some composite systems, in a spirit of quantum information theory. The constituents are single - node spin states, which organize into strings of various length, and "seas of holes". The former are responsible for dynamics, whereas the latter determine the range of riggings for strings. Another aim was to demonstrate a unification of Bethe Ansatz eigenstates by means of Galois symmetries of finite field extensions. The key observation is that the original eigenproblem is expressible in integers, and thus, for a finite fixed N, the splitting field of the characteristic polynom of the Heisenberg Hamiltonian is also finite. The Galois group of the latter field permutes, by definition, roots of this polynom, which implies permutation of eigenstates. General considerations are demonstrated on the example of heptagon (N = 7), which admits an implementation of a collection of arithmetic qubits, and also demonstrates a special case of degeneration of the spectrum of the Hamiltonian, resulting from conservation of parity, within the realm of rigged string configurations.

An approach to improve management visibility within the procurement and financial group at Goldstone

NASA Technical Reports Server (NTRS)

Maiocco, F. R.; Rozek, J. B.

1976-01-01

Improvements in the operational efficiency of the data management systems at the Goldstone Deep Space Communications Complex (GDSCC) are discussed. This addresses the existing procurement and financial management data system at GDSCC, identifies management requirements for better visibility, describes a proposed computerized data management system, summarizes results to data, and identifies plans for future development.

[Carl Friedrich von Weizsäcker and the Bethe-Weizsäcker cycle].

PubMed

Wiescher, Michael

2014-01-01

The Carbon- or Bethe-Weizsäcker Cycle plays an important role in astrophysics as one of the most important energy sources for a quiescent and explosive hydrogen burning in stars. This paper presents the historical background and the contributions by Carl Friedrich von Weizsäcker and Hans Bethe who provided the first predictions of the cycle. Furthermore, it discussed the experimental verification of the predicted process in the following decades. Also discussed is the extension of the initial Carbon cycle to the CNO multi-cycles and the hot CNO cycles which followed from the detailed experimental studies of the associated nuclear reactions. Finally discussed is the impact of the experimental and theoretical results on our present understanding of hydrogen burning in different stellar environments and on our understanding of the chemical evolution of our universe.

Simultaneous Ka-Band Site Characterization: Goldstone, CA, White Sands, NM, and Guam, USA

NASA Technical Reports Server (NTRS)

Acosta, Roberto; Morse, Jacquelynne; Zemba, Michael; Nessel, James; Morabito, David; Caroglanian, Armen

2011-01-01

To statistically characterize atmospheric effects on Ka-band links at NASA operational sites, NASA has constructed site test interferometers (STI s) which directly measure the tropospheric phase stability and rain attenuation. These instruments observe an unmodulated beacon signal broadcast from a geostationary satellite (e.g., Anik F2) and measure the phase difference between the signals received by the two antennas and its signal attenuation. Three STI s have been deployed so far: the first one at the NASA Deep Space Network Tracking Complex in Goldstone, California (May 2007); the second at the NASA White Sands Complex, in Las Cruses, New Mexico (February 2009); and the third at the NASA Tracking and Data Relay Satellite (TDRS) Remote Ground Terminal (GRGT) complex in Guam (May 2010). Two station-years of simultaneous atmospheric phase fluctuation data have been collected at Goldstone and White Sands, while one year of data has been collected in Guam. With identical instruments operating simultaneously, we can directly compare the phase stability and rain attenuation at the three sites. Phase stability is analyzed statistically in terms of the root-mean-square (rms) of the tropospheric induced time delay fluctuations over 10 minute blocks. For two years, the time delay fluctuations at the DSN site in Goldstone, CA, have been better than 2.5 picoseconds (ps) for 90% of the time (with reference to zenith), meanwhile at the White Sands, New Mexico site, the time delay fluctuations have been better than 2.2 ps with reference to zenith) for 90% of time. For Guam, the time delay fluctuations have been better than 12 ps (reference to zenith) at 90% of the time, the higher fluctuations are as expected from a high humidity tropical rain zone. This type of data analysis, as well as many other site quality characteristics (e.g., rain attenuation, infrastructure, etc.) will be used to determine the suitability of all the sites for NASA s future communication services at Ka-band.

Magnonic qudit and algebraic Bethe Ansatz

NASA Astrophysics Data System (ADS)

Lulek, B.; Lulek, T.

2010-03-01

A magnonic qudit is proposed as the memory unit of a register of a quantum computer. It is the N-dimensional space, extracted from the 2N-dimensional space of all quantum states of the magnetic Heisenberg ring of N spins 1/2, as the space of all states of a single magnon. Three bases: positional, momentum, and that of Weyl duality are described, together with appropriate Fourier and Kostka transforms. It is demonstrated how exact Bethe Ansatz (BA) eigenfunctions, classified in terms of rigged string configurations, can be coded using a collection of magnonic qudits. To this aim, the algebraic BA is invoked, such that a single magnonic qudit is prepared in a state corresponding to a magnon in one of the states provided by spectral parameters emerging from the corresponding BA equations.

Fast analytic solver of rational Bethe equations

NASA Astrophysics Data System (ADS)

Marboe, C.; Volin, D.

2017-05-01

In this note we propose an approach for a fast analytic determination of all possible sets of Bethe roots corresponding to eigenstates of rational {GL}({N}\\vert {M}) integrable spin chains of given not too large length, in terms of Baxter Q-functions. We observe that all exceptional solutions, if any, are automatically correctly accounted. The key intuition behind the approach is that the equations on the Q-functions are determined solely by the Young diagram, and not by the choice of the rank of the {GL} symmetry. Hence we can choose arbitrary {N} and {M} that accommodate the desired representation. Then we consider all distinguished Q-functions at once, not only those following a certain Kac-Dynkin path.

GW/Bethe-Salpeter calculations for charged and model systems from real-space DFT

NASA Astrophysics Data System (ADS)

Strubbe, David A.

GW and Bethe-Salpeter (GW/BSE) calculations use mean-field input from density-functional theory (DFT) calculations to compute excited states of a condensed-matter system. Many parts of a GW/BSE calculation are efficiently performed in a plane-wave basis, and extensive effort has gone into optimizing and parallelizing plane-wave GW/BSE codes for large-scale computations. Most straightforwardly, plane-wave DFT can be used as a starting point, but real-space DFT is also an attractive starting point: it is systematically convergeable like plane waves, can take advantage of efficient domain parallelization for large systems, and is well suited physically for finite and especially charged systems. The flexibility of a real-space grid also allows convenient calculations on non-atomic model systems. I will discuss the interfacing of a real-space (TD)DFT code (Octopus, www.tddft.org/programs/octopus) with a plane-wave GW/BSE code (BerkeleyGW, www.berkeleygw.org), consider performance issues and accuracy, and present some applications to simple and paradigmatic systems that illuminate fundamental properties of these approximations in many-body perturbation theory.

Bethe-Salpeter Eigenvalue Solver Package (BSEPACK) v0.1

DOE Office of Scientific and Technical Information (OSTI.GOV)

SHAO, MEIYEU; YANG, CHAO

2017-04-25

The BSEPACK contains a set of subroutines for solving the Bethe-Salpeter Eigenvalue (BSE) problem. This type of problem arises in this study of optical excitation of nanoscale materials. The BSE problem is a structured non-Hermitian eigenvalue problem. The BSEPACK software can be used to compute all or subset of eigenpairs of a BSE Hamiltonian. It can also be used to compute the optical absorption spectrum without computing BSE eigenvalues and eigenvectors explicitly. The package makes use of the ScaLAPACK, LAPACK and BLAS.

Nonrelativistic Nambu-Goldstone Modes Associated with Spontaneously Broken Space-Time and Internal Symmetries

NASA Astrophysics Data System (ADS)

Kobayashi, Michikazu; Nitta, Muneto

2014-09-01

We show that a momentum operator of a translational symmetry may not commute with an internal symmetry operator in the presence of a topological soliton in nonrelativistic theories. As a striking consequence, there appears a coupled Nambu-Goldstone mode with a quadratic dispersion consisting of translational and internal zero modes in the vicinity of a domain wall in an O(3) σ model, a magnetic domain wall in ferromagnets with an easy axis.

Clinical trials of boron neutron capture therapy [in humans] [at Beth Israel Deaconess Medical Center][at Brookhaven National Laboratory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wallace, Christine

2001-05-29

Assessment of research records of Boron Neutron Capture Therapy was conducted at Brookhaven National Laboratory and Beth Israel Deaconess Medical Center using the Code of Federal Regulations, FDA Regulations and Good Clinical Practice Guidelines. Clinical data were collected from subjects' research charts, and differences in conduct of studies at both centers were examined. Records maintained at Brookhaven National Laboratory were not in compliance with regulatory standards. Beth Israel's records followed federal regulations. Deficiencies discovered at both sites are discussed in the reports.

Three Weeks with Hans Bethe

NASA Astrophysics Data System (ADS)

Adami, Christoph

Hans Bethe started visiting the Kellogg Radiation Laboratory, accompanied by Gerry Brown, every winter starting in the late eighties. My first visit to Kellogg was in 1991 as a final year graduate student. I returned in January of 1992, while a postdoc with Gerry Brown at SUNY Stony Brook, and this would be my first of many winter months spent in the company of both Hans and Gerry. The following notes are literally "mental downloads" that I wrote down every evening after leaving dinner with Hans, Gerry, and sometimes other invited guests that year. I indiscriminately wrote down everything that I could remember from that day, whether it seemed important or not, hoping to edit it later. In the end, I decided to keep the editing very minimal in order to preserve the original text's immediacy and spontaneity. Besides grammar and punctuation, a few facts that I remembered incorrectly were restored. I also added references and footnotes that add explanations where necessary. The following is a transcript of the conversations that took place between 20 January and 20 February, 1992.

Experimental observation of Bethe strings

NASA Astrophysics Data System (ADS)

Wang, Zhe; Wu, Jianda; Yang, Wang; Bera, Anup Kumar; Kamenskyi, Dmytro; Islam, A. T. M. Nazmul; Xu, Shenglong; Law, Joseph Matthew; Lake, Bella; Wu, Congjun; Loidl, Alois

2018-02-01

Almost a century ago, string states—complex bound states of magnetic excitations—were predicted to exist in one-dimensional quantum magnets. However, despite many theoretical studies, the experimental realization and identification of string states in a condensed-matter system have yet to be achieved. Here we use high-resolution terahertz spectroscopy to resolve string states in the antiferromagnetic Heisenberg-Ising chain SrCo2V2O8 in strong longitudinal magnetic fields. In the field-induced quantum-critical regime, we identify strings and fractional magnetic excitations that are accurately described by the Bethe ansatz. Close to quantum criticality, the string excitations govern the quantum spin dynamics, whereas the fractional excitations, which are dominant at low energies, reflect the antiferromagnetic quantum fluctuations. Today, Bethe’s result is important not only in the field of quantum magnetism but also more broadly, including in the study of cold atoms and in string theory; hence, we anticipate that our work will shed light on the study of complex many-body systems in general.

The goldstone real-time connected element interferometer

NASA Technical Reports Server (NTRS)

Edwards, C., Jr.; Rogstad, D.; Fort, D.; White, L.; Iijima, B.

1992-01-01

Connected element interferometry (CEI) is a technique of observing a celestial radio source at two spatially separated antennas and then interfering the received signals to extract the relative phase of the signal at the two antennas. The high precision of the resulting phase delay data type can provide an accurate determination of the angular position of the radio source relative to the baseline vector between the two stations. This article describes a recently developed connected element interferometer on a 21-km baseline between two antennas at the Deep Space Network's Goldstone, California, tracking complex. Fiber-optic links are used to transmit the data to a common site for processing. The system incorporates a real-time correlator to process these data in real time. The architecture of the system is described, and observational data are presented to characterize the potential performance of such a system. The real-time processing capability offers potential advantages in terms of increased reliability and improved delivery of navigational data for time-critical operations. Angular accuracies of 50-100 nrad are achievable on this baseline.

G W (Γ ) method without the Bethe-Salpeter equation for photoabsorption energies of spin-polarized systems

NASA Astrophysics Data System (ADS)

Isobe, Tomoharu; Kuwahara, Riichi; Ohno, Kaoru

2018-06-01

The one-shot G W method, beginning with the local density approximation (LDA), enables one to calculate photoemission and inverse photoemission spectra. In order to calculate photoabsorption spectra, one had to additionally solve the Bethe-Salpeter equation (BSE) for the two-particle (electron-hole) Green's function, which doubly induces evaluation errors. It has been recently reported that the G W +BSE method significantly underestimates the experimental photoabsorption energies (PAEs) of small molecules. In order to avoid these problems, we propose to apply the G W (Γ ) method not to the neutral ground state but to the cationic state to calculate PAEs without solving the BSE, which allows a rigorous one-to-one correspondence between the photoabsorption peak and the "extended" quasiparticle level. We applied the self-consistent linearized G W Γ method including the vertex correction Γ to our method, and found that this method gives the PAEs of B, Na3, and Li3 to within 0.1 eV accuracy.

Bethe/Gauge correspondence in odd dimension: modular double, non-perturbative corrections and open topological strings

NASA Astrophysics Data System (ADS)

Sciarappa, Antonio

2016-10-01

Bethe/Gauge correspondence as it is usually stated is ill-defined in five dimensions and needs a "non-perturbative" completion; a related problem also appears in three dimensions. It has been suggested that this problem, probably due to incompleteness of Omega background regularization in odd dimension, may be solved if we consider gauge theory on compact S 5 and S 3 geometries. We will develop this idea further by giving a full Bethe/Gauge correspondence dictionary on S 5 and S 3 focussing mainly on the eigenfunctions of (open and closed) relativistic 2-particle Toda chain and its quantized spectral curve: these are most properly written in terms of non-perturbatively completed NS open topological strings. A key ingredient is Faddeev's modular double structure which is naturally implemented by the S 5 and S 3 geometries.

Benchmark of Ab Initio Bethe-Salpeter Equation Approach with Numeric Atom-Centered Orbitals

NASA Astrophysics Data System (ADS)

Liu, Chi; Kloppenburg, Jan; Kanai, Yosuke; Blum, Volker

The Bethe-Salpeter equation (BSE) approach based on the GW approximation has been shown to be successful for optical spectra prediction of solids and recently also for small molecules. We here present an all-electron implementation of the BSE using numeric atom-centered orbital (NAO) basis sets. In this work, we present benchmark of BSE implemented in FHI-aims for low-lying excitation energies for a set of small organic molecules, the well-known Thiel's set. The difference between our implementation (using an analytic continuation of the GW self-energy on the real axis) and the results generated by a fully frequency dependent GW treatment on the real axis is on the order of 0.07 eV for the benchmark molecular set. We study the convergence behavior to the complete basis set limit for excitation spectra, using a group of valence correlation consistent NAO basis sets (NAO-VCC-nZ), as well as for standard NAO basis sets for ground state DFT with extended augmentation functions (NAO+aug). The BSE results and convergence behavior are compared to linear-response time-dependent DFT, where excellent numerical convergence is shown for NAO+aug basis sets.

Geological Interpretations of the Topography of Selected Regions of Venus from Arecibo to Goldstone Radar Interferometry

NASA Technical Reports Server (NTRS)

Jurgens, R. F.; Margot, J-L.; Simons, M.; Pritchard, M. E.; Slade, M. A.

2002-01-01

Radar interferometry using Arecibo to transmit and three antennas at the Goldstone to receive was conducted on 14 dates in Spring, 2001. This data has been used so far to generate DEMs (digital elevation models) for several of the dates with pixel resolution of 0.5-1.0 km. Additional information is contained in the original extended abstract.

Critical Casimir forces, Goldstone modes and anomalous wetting

NASA Astrophysics Data System (ADS)

Balibar, Sebastien

2004-03-01

We have measured the contact angle of a ^3He - ^4He interface on a sapphire window, near the tricritical temperature Tt of liquid helium mixtures (T. Ueno et al., J. Low Temp. Phys. 130, 543, 2003). We have found the first experimental evidence of a violation of "critical point wetting", the general phenomenon introduced by J.W. Cahn in 1977. We then proposed that Fisher and de Gennes' "critical Casimir effect" provides the necessary long range force for this anomalous wetting behavior to occur (T. Ueno et al. Phys. Rev. Lett. 90, 116102, 2003). Our measurements are now extended to the superfluid region far below the tricritical temperature T_t. Our goal is to test the prediction by M. Kardar and R. Golestanian that the confinement of Goldstone modes in superfluid films leads to an additionnal contribution to the Casimir force (M. Kardar and R. Golestanian, Rev. Mod. Phys. 71, 1233, 1999). We compare theoretical predictions to experimental results.

On quantum integrable models related to nonlinear quantum optics. An algebraic Bethe ansatz approach

NASA Astrophysics Data System (ADS)

Jurčo, Branislav

1989-08-01

A unified approach based on Bethe ansatz in a large variety of integrable models in quantum optics is given. Second harmonics generation, three-boson interaction, the Dicke model, and some cases of four-boson interaction as special cases of su(2)⊕su(1,1)-Gaudin models are included.

Double elementary Goldstone Higgs boson production in future linear colliders

NASA Astrophysics Data System (ADS)

Guo, Yu-Chen; Yue, Chong-Xing; Liu, Zhi-Cheng

2018-03-01

The Elementary Goldstone Higgs (EGH) model is a perturbative extension of the Standard Model (SM), which identifies the EGH boson as the observed Higgs boson. In this paper, we study pair production of the EGH boson in future linear electron positron colliders. The cross-sections in the TeV region can be changed to about ‑27%, 163% and ‑34% for the e+e‑→ Zhh, e+e‑→ νν¯hh and e+e‑→ tt¯hh processes with respect to the SM predictions, respectively. According to the expected measurement precisions, such correction effects might be observed in future linear colliders. In addition, we compare the cross-sections of double SM-like Higgs boson production with the predictions in other new physics models.

Radar RFI at Goldstone DSS 12 and DSS 16

NASA Astrophysics Data System (ADS)

Slobin, S. D.; Peng, T. K.

1990-02-01

Radio frequency interference (RFI) from the DSS 14 Goldstone Solar System Radar (GSSR) was investigated at DSS 12 and DSS 16 with the goal of assisting in the choice of the location of future DSN antennas. Total power measurements at both locations were made at the S-band carrier frequency of 2320 MHz. X-band measurements at the carrier frequency of 8495 MHz could not be made. Exciter-chain output spectrum and klystron output spectrum measurements were made at S- and X-bands using a probable worst-case modulation of the radar signal (short pseudorandom number (PN) code length and short pulse length). Based on these measurements, it is estimated that RFI levels in the DSN receiving bands at both sites (above 10-deg elevation) would be below -192 dBm for a 1-Hz bandwidth

Radar RFI at Goldstone DSS 12 and DSS 16

NASA Technical Reports Server (NTRS)

Slobin, S. D.; Peng, T. K.

1990-01-01

Radio frequency interference (RFI) from the DSS 14 Goldstone Solar System Radar (GSSR) was investigated at DSS 12 and DSS 16 with the goal of assisting in the choice of the location of future DSN antennas. Total power measurements at both locations were made at the S-band carrier frequency of 2320 MHz. X-band measurements at the carrier frequency of 8495 MHz could not be made. Exciter-chain output spectrum and klystron output spectrum measurements were made at S- and X-bands using a probable worst-case modulation of the radar signal (short pseudorandom number (PN) code length and short pulse length). Based on these measurements, it is estimated that RFI levels in the DSN receiving bands at both sites (above 10-deg elevation) would be below -192 dBm for a 1-Hz bandwidth

The phase diagrams of the ± K model on the Bethe lattice

NASA Astrophysics Data System (ADS)

Albayrak, Erhan

2015-07-01

The biquadratic exchange interaction is randomized in a bimodal form with probabilities (p) and (1 - p) for the cases with K > 0 (attractive case) and K < 0 (repulsive case), respectively, and its effects on the phase diagrams of the spin-1 Blume-Emery-Griffiths model are studied on the Bethe lattice by using the recursion relations. It was found that the critical behaviors of the model change drastically.

S parameter and pseudo Nambu-Goldstone boson mass from lattice QCD.

PubMed

Shintani, E; Aoki, S; Fukaya, H; Hashimoto, S; Kaneko, T; Matsufuru, H; Onogi, T; Yamada, N

2008-12-12

We present a lattice calculation of L10, one of the low-energy constants in chiral perturbation theory, and the charged-neutral pion squared-mass splitting, using dynamical overlap fermion. The exact chiral symmetry of the overlap fermion allows us to reliably extract these quantities from the difference of the vacuum polarization functions for vector and axial-vector currents. In the context of the technicolor models, these two quantities are read as the S parameter and the pseudo Nambu-Goldstone boson mass, respectively, and play an important role in discriminating the models from others. This calculation can serve as a feasibility study of the lattice techniques for more general technicolor gauge theories.

Supersymmetry breaking and Nambu-Goldstone fermions with cubic dispersion

NASA Astrophysics Data System (ADS)

Sannomiya, Noriaki; Katsura, Hosho; Nakayama, Yu

2017-03-01

We introduce a lattice fermion model in one spatial dimension with supersymmetry (SUSY) but without particle number conservation. The Hamiltonian is defined as the anticommutator of two nilpotent supercharges Q and Q†. Each supercharge is built solely from spinless fermion operators and depends on a parameter g . The system is strongly interacting for small g , and in the extreme limit g =0 , the number of zero-energy ground states grows exponentially with the system size. By contrast, in the large-g limit, the system is noninteracting and SUSY is broken spontaneously. We study the model for modest values of g and show that under certain conditions spontaneous SUSY breaking occurs in both finite and infinite chains. We analyze the low-energy excitations both analytically and numerically. Our analysis suggests that the Nambu-Goldstone fermions accompanying the spontaneous SUSY breaking have cubic dispersion at low energies.

Cyclotomic Gaudin Models: Construction and Bethe Ansatz

NASA Astrophysics Data System (ADS)

Vicedo, Benoît; Young, Charles

2016-05-01

To any finite-dimensional simple Lie algebra g and automorphism {σ: gto g we associate a cyclotomic Gaudin algebra. This is a large commutative subalgebra of {U(g)^{⊗ N}} generated by a hierarchy of cyclotomic Gaudin Hamiltonians. It reduces to the Gaudin algebra in the special case {σ =id}. We go on to construct joint eigenvectors and their eigenvalues for this hierarchy of cyclotomic Gaudin Hamiltonians, in the case of a spin chain consisting of a tensor product of Verma modules. To do so we generalize an approach to the Bethe ansatz due to Feigin, Frenkel and Reshetikhin involving vertex algebras and the Wakimoto construction. As part of this construction, we make use of a theorem concerning cyclotomic coinvariants, which we prove in a companion paper. As a byproduct, we obtain a cyclotomic generalization of the Schechtman-Varchenko formula for the weight function.

Algebraic Bethe ansatz for U(1) invariant integrable models: Compact and non-compact applications

NASA Astrophysics Data System (ADS)

Martins, M. J.; Melo, C. S.

2009-10-01

We apply the algebraic Bethe ansatz developed in our previous paper [C.S. Melo, M.J. Martins, Nucl. Phys. B 806 (2009) 567] to three different families of U(1) integrable vertex models with arbitrary N bond states. These statistical mechanics systems are based on the higher spin representations of the quantum group U[SU(2)] for both generic and non-generic values of q as well as on the non-compact discrete representation of the SL(2,R) algebra. We present for all these models the explicit expressions for both the on-shell and the off-shell properties associated to the respective transfer matrices eigenvalue problems. The amplitudes governing the vectors not parallel to the Bethe states are shown to factorize in terms of elementary building blocks functions. The results for the non-compact SL(2,R) model are argued to be derived from those obtained for the compact systems by taking suitable N→∞ limits. This permits us to study the properties of the non-compact SL(2,R) model starting from systems with finite degrees of freedom.

Hospital CIO Explains Blockchain Potential: An Interview with Beth Israel Deaconess Medical Center's John Halamka.

PubMed

Mertz, Leslie

2018-01-01

Work is already underway to bring blockchain technology to the healthcare industry, and hospital administrators are trying to figure out what it can do for them, their clinicians, and their patients. That includes administrators at Beth Israel Deaconess Medical Center, a leading academic medical center located in Boston.

Web-based description of the space radiation environment using the Bethe-Bloch model

NASA Astrophysics Data System (ADS)

Cazzola, Emanuele; Calders, Stijn; Lapenta, Giovanni

2016-01-01

Space weather is a rapidly growing area of research not only in scientific and engineering applications but also in physics education and in the interest of the public. We focus especially on space radiation and its impact on space exploration. The topic is highly interdisciplinary, bringing together fundamental concepts of nuclear physics with aspects of radiation protection and space science. We give a new approach to presenting the topic by developing a web-based application that combines some of the fundamental concepts from these two fields into a single tool that can be used in the context of advanced secondary or undergraduate university education. We present DREADCode, an outreach or teaching tool to rapidly assess the current conditions of the radiation field in space. DREADCode uses the available data feeds from a number of ongoing space missions (ACE, GOES-13, GOES-15) to produce a first order approximation of the radiation dose an astronaut would receive during a mission of exploration in deep space (i.e. far from the Earth’s shielding magnetic field and from the radiation belts). DREADCode is based on an easy-to-use GUI interface available online from the European Space Weather Portal (www.spaceweather.eu/dreadcode). The core of the radiation transport computation to produce the radiation dose from the observed fluence of radiation observed by the spacecraft fleet considered is based on a relatively simple approximation: the Bethe-Bloch equation. DREADCode also assumes a simplified geometry and material configuration for the shields used to compute the dose. The approach is approximate and sacrifices some important physics on the altar of rapid execution time, which allows a real-time operation scenario. There is no intention here to produce an operational tool for use in space science and engineering. Rather, we present an educational tool at undergraduate level that uses modern web-based and programming methods to learn some of the most important

A Call to Action: JoBeth Allen, NCTE's 2012 Outstanding Educator in the Language Arts

ERIC Educational Resources Information Center

Tisdale, Carmen

2012-01-01

This article is a tribute to JoBeth Allen, recipient of the Elementary Section's 2012 award for Outstanding Educator in the English Language Arts. Each year, this award recognizes a distinguished educator who has made major contributions to the field of language arts in elementary education. This article was written by second-grade teacher and…

Two Years of Simultaneous K(sub a)-Band Measurements: Goldstone, CA; White Sands, NM; and Guam, USA

NASA Technical Reports Server (NTRS)

Acosta, Roberto J.; Zemba, M.; Morse, J.; Nessel, J.

2012-01-01

In order to statistically characterize the effect of the Earth's atmosphere on Ka-Band links, site test interferometers (STIs) have been deployed at three of NASA s operational sites to directly measure each site's tropospheric phase stability and rain attenuation. These STIs are composed of two antennas on a short baseline (less than 1km) that observe the same unmodulated beacon signal broadcast from a geostationary satellite (e.g., Anik F2). The STIs are used to measure the differential phase between the two received signals as well as the individual signal attenuation at each terminal. There are currently three NASA sites utilizing STIs; the Goldstone Deep Space Communications Complex near Barstow, California; the White Sands Complex in Las Cruces, New Mexico; and the Guam Remote Ground Terminal on the island of Guam. The first two sites are both located in desert regions that have highly similar climates in terms of their seasonal temperatures, average humidity, and annual rain fall (the primary factors in determining phase stability). In contrast, Guam is in a tropical region with drastically higher annual rainfall and humidity. Five station years of data have been collected in Goldstone, three in White Sands, and two in Guam, yielding two years of simultaneous data collection across all three sites. During this period of simultaneous data collection, the root-mean-square (RMS) of the time delay fluctuations stayed under 2.40 picoseconds for 90% of the time in Goldstone, under 2.07 picoseconds for 90% of the time in White Sands, and under 10.13 picoseconds for 90% of the time in Guam. For the 99th percentile, the statistics were 6.32 ps, 6.03 ps, and 24.85 ps, respectively. These values, as well as various other site quality characteristics, will be used to determine the suitability of these sites for NASA s future communication services at Ka-Band.

State transition storyboards: A tool for designing the Goldstone solar system radar data acquisition system user interface software

NASA Technical Reports Server (NTRS)

Howard, S. D.

1987-01-01

Effective user interface design in software systems is a complex task that takes place without adequate modeling tools. By combining state transition diagrams and the storyboard technique of filmmakers, State Transition Storyboards were developed to provide a detailed modeling technique for the Goldstone Solar System Radar Data Acquisition System human-machine interface. Illustrations are included with a description of the modeling technique.

The linear -- non-linear frontier for the Goldstone Higgs

DOE PAGES

Gavela, M. B.; Kanshin, K.; Machado, P. A. N.; ...

2016-12-01

The minimalmore » $SO(5)/SO(4)$ sigma model is used as a template for the ultraviolet completion of scenarios in which the Higgs particle is a low-energy remnant of some high-energy dynamics, enjoying a (pseudo) Nambu-Goldstone boson ancestry. Varying the $$\\sigma$$ mass allows to sweep from the perturbative regime to the customary non-linear implementations. The low-energy benchmark effective non-linear Lagrangian for bosons and fermions is obtained, determining as well the operator coefficients including linear corrections. At first order in the latter, three effective bosonic operators emerge which are independent of the explicit soft breaking assumed. The Higgs couplings to vector bosons and fermions turn out to be quite universal: the linear corrections are proportional to the explicit symmetry breaking parameters. Furthermore, we define an effective Yukawa operator which allows a simple parametrization and comparison of different heavy fermion ultraviolet completions. In addition, one particular fermionic completion is explored in detail, obtaining the corresponding leading low-energy fermionic operators.« less

The Role of the Goldstone Apple Valley Radio Telescope Project in Promoting Scientific Efficacy among Middle and High School Students.

ERIC Educational Resources Information Center

Ibe, Mary; Deutscher, Rebecca

This study investigated the effects on student scientific efficacy after participation in the Goldstone Apple Valley Radio Telescope (GAVRT) project. In the GAVRT program, students use computers to record extremely faint radio waves collected by the telescope and analyze real data. Scientific efficacy is a type of self-knowledge a person uses to…

Goldstone radar evidence for short-axis mode non-principal-axis rotation of near-Earth asteroid (214869) 2007 PA8

NASA Astrophysics Data System (ADS)

Brozović, Marina; Benner, Lance A. M.; Magri, Christopher; Scheeres, Daniel J.; Busch, Michael W.; Giorgini, Jon D.; Nolan, Michael C.; Jao, Joseph S.; Lee, Clement G.; Snedeker, Lawrence G.; Silva, Marc A.; Lawrence, Kenneth J.; Slade, Martin A.; Hicks, Michael D.; Howell, Ellen S.; Taylor, Patrick A.; Sanchez, Juan A.; Reddy, Vishnu; Dykhuis, Melissa; Le Corre, Lucille

2017-04-01

We report radar and optical photometric observations of near-Earth asteroid (214869) 2007 PA8 obtained during October 2-November 13, 2012. We observed 2007 PA8 on sixteen days with Goldstone (8560 MHz, 3.5 cm) and on five days with the 0.6 m telescope at Table Mountain Observatory. Closest approach was on November 5 at a distance of 0.043 au. Images obtained with Goldstone's new chirp system achieved range resolutions as fine as 3.75 m, placing thousands of pixels on the asteroid's surface, and revealing that 2007 PA8 is an elongated, asymmetric object. Surface features include angularities, facets, and a concavity approximately 400 m in diameter. We used the Shape software to estimate the asteroid's 3D shape and spin state. 2007 PA8 has a broad, rounded end and a tapered, angular end with sharp-crested ridges. The asteroid's effective diameter is 1.35 ± 0.07 km, which in combination with the absolute magnitude of 16.30 ± 0.52 gives an optical albedo of pV = 0.29 ± 0.14. The shape modeling of the radar data revealed that 2007 PA8 is a non-principal axis (NPA) rotator in the short-axis mode with an average period of precession by the long axis around the angular momentum vector of 4.26 ± 0.02 days and an oscillatory period around the long axis of 20.55 ± 3.75 days. The amplitude of rolling around the long axis is 42 ± 7° . The angular momentum vector points toward ecliptic longitude and latitude of 273.6 ± 10°, +16.9 ± 5°. 2007 PA8 is only the second confirmed short-axis mode NPA rotator known in the near-Earth asteroid population after (99942) Apophis (Pravec et al., 2014). 2007 PA8 has a geopotential high at the equator, where the equator is defined as the plane that contains the long and intermediate axis. This geopotential extreme could be interpreted as a large, hidden surface depression, or as evidence that 2007 PA8 is a multi-component body.

Lattice density functional theory for confined Ising fluids: comparison between different functional approximations in slit pore

NASA Astrophysics Data System (ADS)

Chen, Xueqian; Feng, Wei; Liu, Honglai; Hu, Ying

2016-09-01

In this paper, Lafuente and Cuesta's cluster density functional theory (CDFT) and lattice mean field approximation (LMFA) are formulated and compared within the framework of lattice density functional theory (LDFT). As a comparison, an LDFT based on our previous work on nonrandom correction to LMFA is also developed, where local density approximation is adopted on the correction. The numerical results of density distributions of an Ising fluid confined in a slit pore obtained from Monte Carlo simulation are used to check these functional approximations. Due to rational treatment on the coupling between site-excluding entropic effect and contact-attracting enthalpic effect by CDFT with Bethe-Peierls approximation (named as BPA-CDFT for short), the improvement of BPA-CDFT beyond LMFA is checked as expected. And it is interesting that our LDFT has a comparative accuracy with BPA-CDFT. Apparent differences between the profiles such as solvation force, excess adsorption quantity and interfacial tension from LMFA and non-LMFAs are found in our calculations. We also discuss some possible theoretical extensions of BPA-CDFT.

Study of Y and Lu iron garnets using Bethe-Peierls-Weiss method

NASA Astrophysics Data System (ADS)

Goveas, Neena; Mukhopadhyay, G.; Mukhopadhyay, P.

1994-11-01

We study here the magnetic properties of Y- and Lu- Iron Garnets using the Bethe- Peierls-Weiss method modified to suit complex systems like these Garnets. We consider these Garnets as described by Heisenberg Hamiltonian with two sublattices (a,d) and determine the exchange interaction parameters Jad, Jaa and Jdd by matching the exerimental susceptibility curves. We find Jaa and Jdd to be much smaller than those determined by Néel theory, and consistent with those obtained by the study of spin wave spectra; the spin wave dispersion relation constant obtained using these parameters gives good agreement with the experimental values.

The Goldstone solar system radar: A science instrument for planetary research

NASA Technical Reports Server (NTRS)

Dvorsky, J. D.; Renzetti, N. A.; Fulton, D. E.

1992-01-01

The Goldstone Solar System Radar (GSSR) station at NASA's Deep Space Communications Complex in California's Mojave Desert is described. A short chronological account of the GSSR's technical development and scientific discoveries is given. This is followed by a basic discussion of how information is derived from the radar echo and how the raw information can be used to increase understanding of the solar system. A moderately detailed description of the radar system is given, and the engineering performance of the radar is discussed. The operating characteristics of the Arcibo Observatory in Puerto Rico are briefly described and compared with those of the GSSR. Planned and in-process improvements to the existing radar, as well as the performance of a hypothetical 128-m diameter antenna radar station, are described. A comprehensive bibliography of referred scientific and engineering articles presenting results that depended on data gathered by the instrument is provided.

Goldstone models of modified gravity

NASA Astrophysics Data System (ADS)

Brax, Philippe; Valageas, Patrick

2017-02-01

We investigate scalar-tensor theories where matter couples to the scalar field via a kinetically dependent conformal coupling. These models can be seen as the low-energy description of invariant field theories under a global Abelian symmetry. The scalar field is then identified with the Goldstone mode of the broken symmetry. It turns out that the properties of these models are very similar to the ones of ultralocal theories where the scalar-field value is directly determined by the local matter density. This leads to a complete screening of the fifth force in the Solar System and between compact objects, through the ultralocal screening mechanism. On the other hand, the fifth force can have large effects in extended structures with large-scale density gradients, such as galactic halos. Interestingly, it can either amplify or damp Newtonian gravity, depending on the model parameters. We also study the background cosmology and the linear cosmological perturbations. The background cosmology is hardly different from its Λ -CDM counterpart while cosmological perturbations crucially depend on whether the coupling function is convex or concave. For concave functions, growth is hindered by the repulsiveness of the fifth force while it is enhanced in the convex case. In both cases, the departures from the Λ -CDM cosmology increase on smaller scales and peak for galactic structures. For concave functions, the formation of structure is largely altered below some characteristic mass, as smaller structures are delayed and would form later through fragmentation, as in some warm dark matter scenarios. For convex models, small structures form more easily than in the Λ -CDM scenario. This could lead to an over-abundance of small clumps. We use a thermodynamic analysis and show that although convex models have a phase transition between homogeneous and inhomogeneous phases, on cosmological scales the system does not enter the inhomogeneous phase. On the other hand, for galactic

Approach to calculation of mass spectra and two-photon decays of c c¯ mesons in the framework of Bethe-Salpeter equation

NASA Astrophysics Data System (ADS)

Bhatnagar, Shashank; Alemu, Lmenew

2018-02-01

In this work we calculate the mass spectra of charmonium for 1 P ,…,4 P states of 0++ and 1++, for 1 S ,…,5 S states of 0-+, and for 1 S ,…,4 D states of 1- along with the two-photon decay widths of the ground and first excited states of 0++ quarkonia for the process O++→γ γ in the framework of a QCD-motivated Bethe-Salpeter equation (BSE). In this 4 ×4 BSE framework, the coupled Salpeter equations are first shown to decouple for the confining part of the interaction (under the heavy-quark approximation) and are analytically solved, and later the one-gluon-exchange interaction is perturbatively incorporated, leading to mass spectral equations for various quarkonia. The analytic forms of wave functions obtained are used for the calculation of the two-photon decay widths of χc 0. Our results are in reasonable agreement with data (where available) and other models.

Modified n-level, n - 1-mode Tavis-Cummings model and algebraic Bethe ansatz

NASA Astrophysics Data System (ADS)

Skrypnyk, T.

2018-01-01

Using the quantum group technique we construct a one-parametric family of integrable modifications of the n-level, n-1 mode Tavis-Cummings Hamiltonian possessing an additional Stark-type term. We show that in the ‘quasiclassical’ limit the constructed Hamiltonian transforms into the integrable Hamiltonian of the quantum n-level, n-1 mode Tavis-Cummings model with the equal interaction strengths considered in Skrypnyk (2008 J. Phys. A: Math. Theor. 41 475202, 2009 J. Math. Phys. 50 103523). We diagonalize the constructed ‘modified’ Tavis-Cummings Hamiltonian and its second order integrals of motion using the nested Bethe ansatz.

Bethe-Boltzmann hydrodynamics and spin transport in the XXZ chain

NASA Astrophysics Data System (ADS)

Bulchandani, Vir B.; Vasseur, Romain; Karrasch, Christoph; Moore, Joel E.

2018-01-01

Quantum integrable systems, such as the interacting Bose gas in one dimension and the XXZ quantum spin chain, have an extensive number of local conserved quantities that endow them with exotic thermalization and transport properties. We discuss recently introduced hydrodynamic approaches for such integrable systems from the viewpoint of kinetic theory and extend the previous works by proposing a numerical scheme to solve the hydrodynamic equations for finite times and arbitrary locally equilibrated initial conditions. We then discuss how such methods can be applied to describe nonequilibrium steady states involving ballistic heat and spin currents. In particular, we show that the spin Drude weight in the XXZ chain, previously accessible only by rigorous techniques of limited scope or controversial thermodynamic Bethe ansatz arguments, may be evaluated from hydrodynamics in very good agreement with density-matrix renormalization group calculations.

Log-gamma directed polymer with fixed endpoints via the replica Bethe Ansatz

NASA Astrophysics Data System (ADS)

Thiery, Thimothée; Le Doussal, Pierre

2014-10-01

We study the model of a discrete directed polymer (DP) on a square lattice with homogeneous inverse gamma distribution of site random Boltzmann weights, introduced by Seppalainen (2012 Ann. Probab. 40 19-73). The integer moments of the partition sum, \\overline{Z^n} , are studied using a transfer matrix formulation, which appears as a generalization of the Lieb-Liniger quantum mechanics of bosons to discrete time and space. In the present case of the inverse gamma distribution the model is integrable in terms of a coordinate Bethe Ansatz, as discovered by Brunet. Using the Brunet-Bethe eigenstates we obtain an exact expression for the integer moments of \\overline{Z^n} for polymers of arbitrary lengths and fixed endpoint positions. Although these moments do not exist for all integer n, we are nevertheless able to construct a generating function which reproduces all existing integer moments and which takes the form of a Fredholm determinant (FD). This suggests an analytic continuation via a Mellin-Barnes transform and we thereby propose a FD ansatz representation for the probability distribution function (PDF) of Z and its Laplace transform. In the limit of a very long DP, this ansatz yields that the distribution of the free energy converges to the Gaussian unitary ensemble (GUE) Tracy-Widom distribution up to a non-trivial average and variance that we calculate. Our asymptotic predictions coincide with a result by Borodin et al (2013 Commun. Math. Phys. 324 215-32) based on a formula obtained by Corwin et al (2011 arXiv:1110.3489) using the geometric Robinson-Schensted-Knuth (gRSK) correspondence. In addition we obtain the dependence on the endpoint position and the exact elastic coefficient at a large time. We argue the equivalence between our formula and that of Borodin et al. As we will discuss, this provides a connection between quantum integrability and tropical combinatorics.

Numerical Solutions of One Reduced Bethe-Salpeter Equation for the Coulombic Bound States Composed of Virtual Constituents

NASA Astrophysics Data System (ADS)

Chen, Jiao-Kai

2018-04-01

We present one reduction of the Bethe-Salpeter equation for the bound states composed of two off-mass-shell constituents. Both the relativistic effects and the virtuality effects can be considered in the obtained spinless virtuality distribution equation. The eigenvalues of the spinless virtuality distribution equation are perturbatively calculated and the bound states e+e-, μ+μ-, τ+τ-, μ+e-, and τ+e- are discussed.

Mayer-cluster expansion of instanton partition functions and thermodynamic bethe ansatz

NASA Astrophysics Data System (ADS)

Meneghelli, Carlo; Yang, Gang

2014-05-01

In [19] Nekrasov and Shatashvili pointed out that the = 2 instanton partition function in a special limit of the Ω-deformation parameters is characterized by certain thermodynamic Bethe ansatz (TBA) like equations. In this work we present an explicit derivation of this fact as well as generalizations to quiver gauge theories. To do so we combine various techniques like the iterated Mayer expansion, the method of expansion by regions, and the path integral tricks for non-perturbative summation. The TBA equations derived entirely within gauge theory have been proposed to encode the spectrum of a large class of quantum integrable systems. We hope that the derivation presented in this paper elucidates further this completely new point of view on the origin, as well as on the structure, of TBA equations in integrable models.

Inspiring the next generation of scientists with their observations of quasars, black holes, Jupiter, and SETI with the Goldstone Apple Valley Radio Telescope, GAVRT

NASA Astrophysics Data System (ADS)

Jauncey, D. L.; Levin, S.; Teitelbaum, L.; Hofstadter, M.; Arballo, J.; McConnell, S.; Dorcey, R.; Cole, K.; Kreuser-Jenkins, N.; Leflang, J.; Kruzins, E.; Ricardo, L.; Horiuchi, S.; Nagle, G.; Miro, C. G.

2017-04-01

This paper describes a radio astronomy programfor schools, the Goldstone-AppleValley Radio Telescope,GAVRT. The GAVRT program is designed to bring the inspiration and enthusiasm to a younger generation of teachers and children who learn about science by doing real science, just as Iosif Shklovsky brought to an older generation.

The Klystron Engineering Model Development (KEMD) Task - A New Design for the Goldstone Solar System Radar (GSR)

NASA Astrophysics Data System (ADS)

Teitelbaum, L.; Liou, R.; Vodonos, Y.; Velazco, J.; Andrews, K.; Kelley, D.

2017-08-01

The Goldstone Solar System Radar (GSSR) is one of the world's great planetary radar facilities. The heart of the GSSR is its high-power transmitter, which radiates 450 kW from DSS-14, the Deep Space Network's 70-m antenna at Goldstone, by combining the output from two 250-kW klystrons. Klystrons are vacuum tube electron beam devices that are the key amplifying elements of most radio frequency telecommunications and radar transmitter systems. NASA's Science Mission Directorate sponsored the development of a new design for a 250-kW power, 50-MHz bandwidth, reliable klystron, intended to replace the aging operational devices that were developed in the mid-1990s. The design, developed in partnership with Communications & Power Industries, was verified by implementing and testing a first article prototype, the engineering model. Key elements of the design are new beam optics and focusing magnet, a seven-cavity RF body, and a modern collector able to reliably dissipate the full power of the electron beam. The first klystron based on the new VKX-7864C design was delivered to the DSN High-Power Transmitter Test Facility on November 1, 2016, the culmination of a six-year effort initiated to explore higher-resolution imaging of potentially hazardous near-Earth asteroids. The new design met or exceeded all requirements, including supporting advanced GSSR ranging modulations. The first article prototype was placed into operational service on July 26, 2017, after failure of one of the older klystrons, restoring the GSSR to full-power operations.

Neutrino phenomenology, dark energy and leptogenesis from pseudo-Nambu Goldstone bosons

NASA Astrophysics Data System (ADS)

Hill, C. T.; Mocioiu, I.; Paschos, E. A.; Sarkar, U.

2007-07-01

We consider a model of dynamical neutrino masses via the see-saw mechanism. Nambu-Goldstone bosons (majorons) arise associated with the formation of the heavy right-handed Majorana masses. These bosons then acquire naturally soft masses (become pNGB's) at loop level via the Higgs-Yukawa mass terms. These models, like the original neutrino pNGB quintessence schemes of the 1980's [C.T. Hill, D.N. Schramm, J.N. Fry, Nucl. Part. Phys. 19 (1989) 25; J.A. Frieman, C.T. Hill, R. Watkins, Phys. Rev. D 46 (1992) 1226; A.K. Gupta, C.T. Hill, R. Holman, E.W. Kolb, Phys. Rev. D 45 (1992) 441; J.A. Frieman, C.T. Hill, A. Stebbins, I. Waga, Phys. Rev. Lett. 75 (1995) 2077, astro-ph/9505060] that proceed through the Dirac masses, are natural, have cosmological implications through mass varying neutrinos, long range forces, and provide a soft potential for dark energy. We further argue that these models can explain leptogenesis naturally through the decays of the right-handed neutrinos.

Stochastic, real-space, imaginary-time evaluation of third-order Feynman-Goldstone diagrams

NASA Astrophysics Data System (ADS)

Willow, Soohaeng Yoo; Hirata, So

2014-01-01

A new, alternative set of interpretation rules of Feynman-Goldstone diagrams for many-body perturbation theory is proposed, which translates diagrams into algebraic expressions suitable for direct Monte Carlo integrations. A vertex of a diagram is associated with a Coulomb interaction (rather than a two-electron integral) and an edge with the trace of a Green's function in real space and imaginary time. With these, 12 diagrams of third-order many-body perturbation (MP3) theory are converted into 20-dimensional integrals, which are then evaluated by a Monte Carlo method. It uses redundant walkers for convergence acceleration and a weight function for importance sampling in conjunction with the Metropolis algorithm. The resulting Monte Carlo MP3 method has low-rank polynomial size dependence of the operation cost, a negligible memory cost, and a naturally parallel computational kernel, while reproducing the correct correlation energies of small molecules within a few mEh after 106 Monte Carlo steps.

The cosmic microwave background and pseudo-Nambu-Goldstone bosons: Searching for Lorentz violations in the cosmos

NASA Astrophysics Data System (ADS)

Leon, David; Kaufman, Jonathan; Keating, Brian; Mewes, Matthew

2017-01-01

One of the most powerful probes of new physics is the polarized cosmic microwave background (CMB). The detection of a nonzero polarization angle rotation between the CMB surface of last scattering and today could provide evidence of Lorentz-violating physics. The purpose of this paper is two-fold. First, we review one popular mechanism for polarization rotation of CMB photons: the pseudo-Nambu-Goldstone boson (PNGB). Second, we propose a method to use the POLARBEAR experiment to constrain Lorentz-violating physics in the context of the Standard Model Extension (SME), a framework to standardize a large class of potential Lorentz-violating terms in particle physics.

Brueckner-AMD Study of Light Nuclei

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kato, Kiyoshi; Yamamoto, Yuhei; Togashi, Tomoaki

2011-06-28

We applied the Brueckner theory to the Antisymmetrized Molecular Dynamics (AMD) and examined the reliability of the AMD calculations based on realistic nuclear interactions. In this method, the Bethe-Goldstone equation in the Brueckner theory is solved for every nucleon pair described by wave packets of AMD, and the G-matrix is calculated with single-particle orbits in AMD self-consistently. We apply this framework to not only {alpha}-nuclei but also N{ne}Z nuclei with A{approx}10. It is confirmed that these results present the description of reasonable cluster structures and energy-level schemes comparable with the experimental ones in light nuclei.

Interference from the Deep Space Network's 70-m High Power Transmitter in Goldstone, CA to 3G Mobile Users Operating in the Surrounding Area

NASA Technical Reports Server (NTRS)

Ho, Christian

2004-01-01

The International Telecommunications Union (ITU) has allocated 2110-2200 MHz for the third generation (3G) mobile services. Part of the spectrum (2110-2120 MHz) is allocated for space research service and has been used by the DSN for years for sending command uplinks to deep space missions. Due to the extremely high power transmitted, potential interference to 3G users in areas surrounding DSN Goldstone exists. To address this issue, a preliminary analytical study has been performed and computer models have been developed. The goal is to provide theoretical foundation and tools to estimate the strength of interference as a function of distance from the transmitter for various interference mechanisms, (or propagation modes), and then determine the size of the area in which 3G users are susceptible to interference from the 400-kW transmitter in Goldstone. The focus is non-line-of-sight interference, taking into account of terrain shielding, anomalous propagation mechanisms, and technical and operational characteristics of the DSN and the 3G services.

On Condensation Properties of Bethe Roots Associated with the XXZ Chain

NASA Astrophysics Data System (ADS)

Kozlowski, Karol K.

2018-02-01

I prove that the Bethe roots describing either the ground state or a certain class of "particle-hole" excited states of the XXZ spin-1/2 chain in any sector with magnetisation m \\in [0;1/2] exist, are uniquely defined, and form, in the infinite volume limit, a dense distribution on a subinterval of R. The results hold for any value of the anisotropy {Δ ≥ -1}. In fact, I establish an even stronger result, namely the existence of an all order asymptotic expansion of the counting function associated with such roots. As a corollary, these results allow one to prove the existence and form of the infinite volume limit of various observables attached to the model -the excitation energy, momentum, the zero temperature correlation functions, so as to name a few- that were argued earlier in the literature.

A systematic approach to sketch Bethe-Salpeter equation

NASA Astrophysics Data System (ADS)

Qin, Si-xue

2016-03-01

To study meson properties, one needs to solve the gap equation for the quark propagator and the Bethe-Salpeter (BS) equation for the meson wavefunction, self-consistently. The gluon propagator, the quark-gluon vertex, and the quark-anti-quark scattering kernel are key pieces to solve those equations. Predicted by lattice-QCD and Dyson-Schwinger analyses of QCD's gauge sector, gluons are non-perturbatively massive. In the matter sector, the modeled gluon propagator which can produce a veracious description of meson properties needs to possess a mass scale, accordingly. Solving the well-known longitudinal Ward-Green-Takahashi identities (WGTIs) and the less-known transverse counterparts together, one obtains a nontrivial solution which can shed light on the structure of the quark-gluon vertex. It is highlighted that the phenomenologically proposed anomalous chromomagnetic moment (ACM) vertex originates from the QCD Lagrangian symmetries and its strength is proportional to the magnitude of dynamical chiral symmetry breaking (DCSB). The color-singlet vector and axial-vector WGTIs can relate the BS kernel and the dressed quark-gluon vertex to each other. Using the relation, one can truncate the gap equation and the BS equation, systematically, without violating crucial symmetries, e.g., gauge symmetry and chiral symmetry.

Mutual capture of dipolar molecules at low and very low energies. I. Approximate analytical treatment.

PubMed

Nikitin, E E; Troe, J

2010-09-16

Approximate analytical expressions are derived for the low-energy rate coefficients of capture of two identical dipolar polarizable rigid rotors in their lowest nonresonant (j(1) = 0 and j(2) = 0) and resonant (j(1) = 0,1 and j(2) = 1,0) states. The considered range extends from the quantum, ultralow energy regime, characterized by s-wave capture, to the classical regime described within fly wheel and adiabatic channel approaches, respectively. This is illustrated by the table of contents graphic (available on the Web) that shows the scaled rate coefficients for the mutual capture of rotors in the resonant state versus the reduced wave vector between the Bethe zero-energy (left arrows) and classical high-energy (right arrow) limits for different ratios δ of the dipole-dipole to dispersion interaction.

How Inhomogeneous Site Percolation Works on Bethe Lattices: Theory and Application

NASA Astrophysics Data System (ADS)

Ren, Jingli; Zhang, Liying; Siegmund, Stefan

2016-03-01

Inhomogeneous percolation, for its closer relationship with real-life, can be more useful and reasonable than homogeneous percolation to illustrate the critical phenomena and dynamical behaviour of complex networks. However, due to its intricacy, the theoretical framework of inhomogeneous percolation is far from being complete and many challenging problems are still open. In this paper, we first investigate inhomogeneous site percolation on Bethe Lattices with two occupation probabilities, and then extend the result to percolation with m occupation probabilities. The critical behaviour of this inhomogeneous percolation is shown clearly by formulating the percolation probability with given occupation probability p, the critical occupation probability , and the average cluster size where p is subject to . Moreover, using the above theory, we discuss in detail the diffusion behaviour of an infectious disease (SARS) and present specific disease-control strategies in consideration of groups with different infection probabilities.

Unusual magnetic excitations in the weakly ordered spin- 1 2 chain antiferromagnet Sr 2 CuO 3 : Possible evidence for Goldstone magnon coupled with the amplitude mode

DOE PAGES

Sergeicheva, E. G.; Sosin, S. S.; Prozorova, L. A.; ...

2017-01-18

We report on an electron spin resonance (ESR) study of a nearly one-dimensional (1D) spin-1/2 chain antiferromagnet, Sr 2CuO 3, with extremely weak magnetic ordering. The ESR spectra at T > T N, in the disordered Luttinger-spin-liquid phase, reveal nearly ideal Heisenberg-chain behavior with only a very small, field-independent linewidth, ~1/T. In the ordered state, below T N, we identify field-dependent antiferromagnetic resonance modes, which are well described by pseudo-Goldstone magnons in the model of a collinear biaxial antiferromagnet. Additionally, we observe a major resonant mode with unusual and strongly anisotropic properties, which is not anticipated by the conventional theorymore » of Goldstone spin waves. Lastly, we propose that this unexpected magnetic excitation can be attributed to a field-independent magnon mode renormalized due to its interaction with the high-energy amplitude (Higgs) mode in the regime of weak spontaneous symmetry breaking.« less

Surveying the Lunar Surface for New Craters with Mini-RF/Goldstone X-Band Bistatic Observations

NASA Astrophysics Data System (ADS)

Cahill, J. T.; Patterson, G.; Turner, F. S.; Morgan, G.; Stickle, A. M.; Speyerer, E. J.; Espiritu, R. C.; Thomson, B. J.

2017-12-01

A multi-look temporal imaging survey by Speyerer et al. (2016) using Lunar Reconnaissance Orbiter Camera (LROC) Narrow Angle Camera (NAC) has highlighted detectable and frequent impact bombardment processes actively modifying the lunar surface. Over 220 new resolvable impacts have been detected since NASA's Lunar Reconnaissance Orbiter (LRO) entered orbit around the Moon, at a flux that is substantially higher than anticipated from previous studies (Neukum et al., 2001). The Miniature Radio Frequency (Mini-RF) instrument aboard LRO is a hybrid dual-polarized synthetic aperture radar (SAR) that now operates in concert with the Arecibo Observatory (AO) and the Goldstone deep space communications complex 34-meter antenna DSS-13 to collect S- and X-band (12.6 and 4.2 cm, respectively) bistatic radar data of the Moon, respectively. Here we targeted some of the larger (>30 m) craters identified by Speyerer et al. (2016) and executed bistatic X-band radar observations both to evaluate our ability to detect and resolve these impact features and further characterize the spatial extent and material size of their ejecta outside optical wavelengths. Data acquired during Mini-RF monostatic operations, when the transmitter was active, show no coverage of the regions in question before or after two of the new impacts occurred. This makes Mini-RF and Earth-based bistatic observations all the more valuable for examination of these fresh new geologic features. Preliminary analyses of Arecibo/Greenbank and Mini-RF/Goldstone observations are unable to resolve the new crater cavities (due to our current resolving capability of 100 m/px), but they further confirm lunar surface roughness changes occurred between 2008 and 2017. Mini-RF X-band observations show newly ejected material was dispersed on the order of 100-300 meters from the point of impact. Scattering observed in the X-band data suggests the presence of rocky ejecta 4 - 45 cm in diameter on the surface and buried to depths of

Comparing Goldstone Solar System Radar Earth-based Observations of Mars with Orbital Datasets

NASA Technical Reports Server (NTRS)

Haldemann, A. F. C.; Larsen, K. W.; Jurgens, R. F.; Slade, M. A.

2005-01-01

The Goldstone Solar System Radar (GSSR) has collected a self-consistent set of delay-Doppler near-nadir radar echo data from Mars since 1988. Prior to the Mars Global Surveyor (MGS) Mars Orbiter Laser Altimeter (MOLA) global topography for Mars, these radar data provided local elevation information, along with radar scattering information with global coverage. Two kinds of GSSR Mars delay-Doppler data exist: low 5 km x 150 km resolution and, more recently, high (5 to 10 km) spatial resolution. Radar data, and non-imaging delay-Doppler data in particular, requires significant data processing to extract elevation, reflectivity and roughness of the reflecting surface. Interpretation of these parameters, while limited by the complexities of electromagnetic scattering, provide information directly relevant to geophysical and geomorphic analyses of Mars. In this presentation we want to demonstrate how to compare GSSR delay-Doppler data to other Mars datasets, including some idiosyncracies of the radar data. Additional information is included in the original extended abstract.

Prospects for discovering the Higgs-like pseudo-Nambu-Goldstone boson of the classical scale symmetry

NASA Astrophysics Data System (ADS)

Farzinnia, Arsham

2015-11-01

We examine the impact of the expected reach of the LHC and the XENON1T experiments on the parameter space of the minimal classically scale invariant extension of the standard model (SM), where all the mass scales are induced dynamically by means of the Coleman-Weinberg mechanism. In this framework, the SM content is enlarged by the addition of one complex gauge-singlet scalar with a scale invariant and C P -symmetric potential. The massive pseudoscalar component, protected by the C P symmetry, forms a viable dark matter candidate, and three flavors of the right-handed Majorana neutrinos are included to account for the nonzero masses of the SM neutrinos via the seesaw mechanism. The projected constraints on the parameter space arise by applying the ATLAS heavy Higgs discovery prospects, with an integrated luminosity of 300 and 3000 fb-1 at √{s }=14 TeV , to the pseudo-Nambu-Goldstone boson of the (approximate) scale symmetry, as well as by utilizing the expected reach of the XENON1T direct detection experiment for the discovery of the pseudoscalar dark matter candidate. A null-signal discovery by these future experiments implies that vast regions of the model's parameter space can be thoroughly explored; the combined projections are expected to confine a mixing between the SM and the singlet sector to very small values while probing the viability of the TeV scale pseudoscalar's thermal relic abundance as the dominant dark matter component in the Universe. Furthermore, the vacuum stability and triviality requirements of the framework up to the Planck scale are studied, and the viable region of the parameter space is identified. The results are summarized in extensive exclusion plots, incorporating additionally the prior theoretical and experimental bounds for comparison.

Phase diagram of the isotropic spin-(3)/(2) model on the z=3 Bethe lattice

NASA Astrophysics Data System (ADS)

Depenbrock, Stefan; Pollmann, Frank

2013-07-01

We study an SU(2) symmetric spin-3/2 model on the z=3 Bethe lattice using the infinite time evolving block decimation (iTEBD) method. This model is shown to exhibit a rich phase diagram. We compute several order parameters which allow us to identify a ferromagnetic, a ferrimagnetic, an antiferromagnetic, as well as a dimerized phase. We calculate the entanglement spectra from which we conclude the existence of a symmetry protected topological phase that is characterized by S=1/2 edge spins. Details of the iTEBD algorithm used for the simulations are included.

"Her mouth is medicine": Beth Brant and Paula Gunn Allen's decolonizing queer erotics.

PubMed

Burford, Arianne

2013-01-01

This article asserts the need to recognize the complexity of the theoretical work of more lesbian Native American writers, focusing specifically Beth Brant (Bay of Quinte Mohawk) and Paula Gunn Allen (Laguna Pueblo). Their poetry and short stories provide a theoretically nuanced analysis of how heteronormativity is intertwined in and dependent on colonialism, and thus a methodology for Queer Theory that requires an understanding of it in relation to colonialism. They reject heteronormative Pocahontas fantasies about Native women, offering a lesbian-based tactic for decolonization through the expression of erotic desire. This article demonstrates the endless possibilities for fierce queer resistance, revolutionary change, and healing from the trauma of genocide and the accompanying colonialist heteropatriarchal disciplining of Native women's bodies.

Aspects of AdS/CFT: Conformal Deformations and the Goldstone Equivalence Theorem

NASA Astrophysics Data System (ADS)

Cantrell, Sean Andrew

The AdS/CFT correspondence provides a map from the states of theories situated in AdSd+1 to those in dual conformal theories in a d-dimensional space. The correspondence can be used to establish certain universal properties of some theories in one space by examining the behave of general objects in the other. In this thesis, we develop various formal aspects of AdS/CFT. Conformal deformations manifest in the AdS/CFT correspondence as boundary conditions on the AdS field. Heretofore, double-trace deformations have been the primary focus in this context. To better understand multitrace deformations, we revisit the relationship between the generating AdS partition function for a free bulk theory and the boundary CFT partition function subject to arbitrary conformal deformations. The procedure leads us to a formalism that constructs bulk fields from boundary operators. We independently replicate the holographic RG flow narrative to go on to interpret the brane used to regulate the AdS theory as a renormalization scale. The scale-dependence of the dilatation spectrum of a boundary theory in the presence of general deformations can be thus understood on the AdS side using this formalism. The Goldstone equivalence theorem allows one to relate scattering amplitudes of massive gauge fields to those of scalar fields in the limit of large scattering energies. We generalize this theorem under the framework of the AdS/CFT correspondence. First, we obtain an expression of the equivalence theorem in terms of correlation functions of creation and annihilation operators by using an AdS wave function approach to the AdS/CFT dictionary. It is shown that the divergence of the non-conserved conformal current dual to the bulk gauge field is approximately primary when computing correlators for theories in which the masses of all the exchanged particles are sufficiently large. The results are then generalized to higher spin fields. We then go on to generalize the theorem using conformal

R matrices of three-state Hamiltonians solvable by coordinate Bethe ansatz

NASA Astrophysics Data System (ADS)

Fonseca, T.; Frappat, L.; Ragoucy, E.

2015-01-01

We review some of the strategies that can be implemented to infer an R-matrix from the knowledge of its Hamiltonian. We apply them to the classification achieved in Crampé, Frappat, and Ragoucy, J. Phys. A 46, 405001 (2013), on three state U(1)-invariant Hamiltonians solvable by coordinate Bethe ansatz, focusing on models for which the S-matrix is not trivial. For the 19-vertex solutions, we recover the R-matrices of the well-known Zamolodchikov-Fateev and Izergin-Korepin models. We point out that the generalized Bariev Hamiltonian is related to both main and special branches studied by Martins in Nucl. Phys. B 874, 243 (2013), that we prove to generate the same Hamiltonian. The 19-vertex SpR model still resists to the analysis, although we are able to state some no-go theorems on its R-matrix. For 17-vertex Hamiltonians, we produce a new R-matrix.

Bethe lattice approach and relaxation dynamics study of spin-crossover materials

NASA Astrophysics Data System (ADS)

Oke, Toussaint Djidjoho; Hontinfinde, Félix; Boukheddaden, Kamel

2015-07-01

Dynamical properties of Prussian blue analogs and spin-crossover materials are investigated in the framework of a Blume-Emery-Griffiths (BEG) spin-1 model, where states ±1 and 0 represent the high-spin (HS) state and the low-spin state, respectively. The quadrupolar interaction depends on the temperature in the form . Magnetic interactions are controlled by a factor such that for (), magnetic ordering is not expected. The model is exactly solved using the Bethe lattice approach for the equilibrium properties. The results are closer to those calculated by numerical simulations with suitable Arrhenius-type transition rates. The study of relaxation processes of non-equilibrium HS states revealed one-step nonlinear sigmoidal relaxation curves of the HS fraction at low temperatures. We found that increasing the magnetic interactions leads to the appearance of a plateau in the thermal hysteresis as well as in the relaxation curves of the HS fraction at low temperature.

Three-body Coulomb problem probed by mapping the Bethe surface in ionizing ion-atom collisions.

PubMed

Moshammer, R; Perumal, A; Schulz, M; Rodríguez, V D; Kollmus, H; Mann, R; Hagmann, S; Ullrich, J

2001-11-26

The three-body Coulomb problem has been explored in kinematically complete experiments on single ionization of helium by 100 MeV/u C(6+) and 3.6 MeV/u Au(53+) impact. Low-energy electron emission ( E(e)<150 eV) as a function of the projectile deflection theta(p) (momentum transfer), i.e., the Bethe surface [15], has been mapped with Delta theta(p)+/-25 nanoradian resolution at extremely large perturbations ( 3.6 MeV/u Au(53+)) where single ionization occurs at impact parameters of typically 10 times the He K-shell radius. The experimental data are not in agreement with state-of-the-art continuum distorted wave-eikonal initial state theory.

Bond Dilution Effects on Bethe Lattice the Spin-1 Blume-Capel Model

NASA Astrophysics Data System (ADS)

Albayrak, Erhan

2017-09-01

The bond dilution effects are investigated for the spin-1 Blume-Capel model on the Bethe lattice by using the exact recursion relations. The bilinear interaction parameter is either turned on ferromagnetically with probability p or turned off with probability 1 - p between the nearest-neighbor spins. The thermal variations of the order-parameters are studied in detail to obtain the phase diagrams on the possible planes spanned by the temperature (T), probability (p) and crystal field (D) for the coordination numbers q = 3, 4, and 6. The lines of the second-order phase transitions, Tc-lines, combined with the first-order ones, Tt-lines, at the tricritical points (TCP) are always found for any p and q on the (T, D)-planes. It is also found that the model gives only Tc-lines, Tc-lines combined with the Tt-lines at the TCP’s and only Tt-lines with the consecutively decreasing values of D on the (T, p)-planes for all q.

Bethe Ansatz for the Weakly Asymmetric Simple Exclusion Process and Phase Transition in the Current Distribution

NASA Astrophysics Data System (ADS)

Simon, Damien

2011-03-01

The probability distribution of the current in the asymmetric simple exclusion process is expected to undergo a phase transition in the regime of weak asymmetry of the jumping rates. This transition was first predicted by Bodineau and Derrida using a linear stability analysis of the hydrodynamical limit of the process and further arguments have been given by Mallick and Prolhac. However it has been impossible so far to study what happens after the transition. The present paper presents an analysis of the large deviation function of the current on both sides of the transition from a Bethe Ansatz approach of the weak asymmetry regime of the exclusion process.

Scalar pseudo-Nambu-Goldstone boson in nuclei and dense nuclear matter

NASA Astrophysics Data System (ADS)

Lee, Hyun Kyu; Paeng, Won-Gi; Rho, Mannque

2015-12-01

The notion that the scalar listed as f0(500 ) in the particle data booklet is a pseudo-Nambu-Goldstone (NG) boson of spontaneously broken scale symmetry, explicitly broken by a small departure from an infrared fixed point, is explored in nuclear dynamics. This notion—which puts the scalar (which we shall identify as the "dilaton") on the same footing as the pseudoscalar pseudo-NG bosons, i.e., octet π , while providing a simple explanation for the Δ I =1 /2 rule for kaon decay—generalizes the standard chiral perturbation theory (χ PT ) to "scale chiral perturbation theory," denoted χPT σ , with one infrared mass scale for both symmetries, with the σ figuring as a chiral singlet NG mode in the nonstrange sector. Applied to nuclear dynamics, it is seen to provide answers to various hitherto unclarified nuclear phenomena, such as the success of one-boson-exchange potentials, the large cancellation of a strongly attractive scalar potential by a strongly repulsive vector potential in relativistic mean-field theory of nuclear systems and in-medium QCD sum rules, the interplay of the dilaton and the vector meson ω in dense Skyrmion matter, the Bogomol'nyi-Prasad-Sommerfeld Skyrmion structure of nuclei accounting for small binding energies of medium-heavy nuclei, and the suppression of hyperon degrees of freedom in compact-star matter.

Simple many-body based screening mixing ansatz for improvement of G W /Bethe-Salpeter equation excitation energies of molecular systems

NASA Astrophysics Data System (ADS)

Ziaei, Vafa; Bredow, Thomas

2017-11-01

We propose a simple many-body based screening mixing strategy to considerably enhance the performance of the Bethe-Salpeter equation (BSE) approach for prediction of excitation energies of molecular systems. This strategy enables us to closely reproduce results of highly correlated equation of motion coupled cluster singles and doubles (EOM-CCSD) through optimal use of cancellation effects. We start from the Hartree-Fock (HF) reference state and take advantage of local density approximation (LDA) based random phase approximation (RPA) screening, denoted as W0-RPA@LDA with W0 as the dynamically screened interaction built upon LDA wave functions and energies. We further use this W0-RPA@LDA screening as an initial screening guess for calculation of quasiparticle energies in the framework of G0W0 @HF. The W0-RPA@LDA screening is further injected into the BSE. By applying such an approach on a set of 22 molecules for which the traditional G W /BSE approaches fail, we observe good agreement with respect to EOM-CCSD references. The reason for the observed good accuracy of this mixing ansatz (scheme A) lies in an optimal damping of HF exchange effect through the W0-RPA@LDA strong screening, leading to substantial decrease of typically overestimated HF electronic gap, and hence to better excitation energies. Further, we present a second multiscreening ansatz (scheme B), which is similar to scheme A with the exception that now the W0-RPA@HF screening is used in the BSE in order to further improve the overestimated excitation energies of carbonyl sulfide (COS) and disilane (Si2H6 ). The reason for improvement of the excitation energies in scheme B lies in the fact that W0-RPA@HF screening is less effective (and weaker than W0-RPA@LDA), which gives rise to stronger electron-hole effects in the BSE.

Density matrix renormalization group simulations of SU(N ) Heisenberg chains using standard Young tableaus: Fundamental representation and comparison with a finite-size Bethe ansatz

NASA Astrophysics Data System (ADS)

Nataf, Pierre; Mila, Frédéric

2018-04-01

We develop an efficient method to perform density matrix renormalization group simulations of the SU(N ) Heisenberg chain with open boundary conditions taking full advantage of the SU(N ) symmetry of the problem. This method is an extension of the method previously developed for exact diagonalizations and relies on a systematic use of the basis of standard Young tableaux. Concentrating on the model with the fundamental representation at each site (i.e., one particle per site in the fermionic formulation), we have benchmarked our results for the ground-state energy up to N =8 and up to 420 sites by comparing them with Bethe ansatz results on open chains, for which we have derived and solved the Bethe ansatz equations. The agreement for the ground-state energy is excellent for SU(3) (12 digits). It decreases with N , but it is still satisfactory for N =8 (six digits). Central charges c are also extracted from the entanglement entropy using the Calabrese-Cardy formula and agree with the theoretical values expected from the SU (N) 1 Wess-Zumino-Witten conformal field theories.

Arecibo and Goldstone radar images of near-Earth Asteroid (469896) 2005 WC1

NASA Astrophysics Data System (ADS)

Lawrence, Kenneth J.; Benner, Lance A. M.; Brozovic, Marina; Ostro, Steven J.; Jao, Joseph S.; Giorgini, Jon D.; Slade, Martin A.; Jurgens, Raymond F.; Nolan, Michael C.; Howell, Ellen S.; Taylor, Patrick A.

2018-01-01

We report radar observations of near-Earth asteroid (469896) 2005 WC1 that were obtained at Arecibo (2380 MHz, 13 cm) and Goldstone (8560 MHz, 3.5 cm) on 2005 December 14-15 during the asteroid's approach within 0.020 au The asteroid was a strong radar target. Delay-Doppler images with resolutions as fine as 15 m/pixel were obtained with 2 samples per baud giving a correlated pixel resolution of 7.5 m. The radar images reveal an angular object with 100 m-scale surface facets, radar-dark regions, and an estimated diameter of 400 ± 50 m. The rotation of the facets in the images gives a rotation period of ∼2.6 h that is consistent with the estimated period of 2.582 h ± 0.002 h from optical lightcurves reported by Miles (private communication). 2005 WC1 has a circular polarization ratio of 1.12 ± 0.05 that is one of the highest values known, suggesting a structurally-complex near-surface at centimeter to decimeter spatial scales. It is the first asteroid known with an extremely high circular polarization ratio, relatively low optical albedo, and high radar albedo.

Bethe, Oppenheimer, Teller and the Fermi Award: Norris Bradbury Speaks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Meade, Roger Allen

In 1956 the Enrico Fermi Presidential Award was established to recognize scientists, engineers, and science policymakers who gave unstintingly over their careers to advance energy science and technology. The first recipient was John von Neumann. .1 Among those scientists who were thought eligible for the award were Hans Bethe, J. Robert Oppenheimer, and Edward Teller. In 1959 Norris Bradbury was asked to comment on the relative merits of each these three men, whom he knew well from their affiliation with Los Alamos. Below is a reproduction of the letter Bradbury sent to Dr. Warren C. Johnson of the AEC’s Generalmore » Advisory Committee(GAC) containing his evaluation of each man. The letter might surprise those not accustomed to Bradbury’s modus operandi of providing very detailed and forthright answers to the AEC. The letter, itself, was found in cache of old microfilm. Whether because of the age of the microfilm or the quality of the filming process, portions of the letter are not legible. Where empty brackets appear, the word or words could not be read or deduced. Words appearing in brackets are guesses that appear, from the image, to be what was written. These guesses, of course, are just that – guesses.« less

Solutions of the Bethe ansatz equations for XXX antiferromagnet of arbitrary spin in the case of a finite number of sites

DOE Office of Scientific and Technical Information (OSTI.GOV)

Avdeev, L.V.; Doerfel, B.D.

1987-11-01

The exactly integrable isotropic Heisenberg chain of N spins s is studied, and numerical solutions to the Bethe ansatz equations corresponding to the antiferromagnetic vacuum (for sN less than or equal to 128) and the simplest excitations have been obtained. For s = 1, a complete set of states for N = 6 is given, and the vacuum solution for finite N is estimated analytically. The deviations from the string picture at large N are discussed.

Power Spectrum of Atmospheric Scintillation for the Deep Space Network Goldstone Ka-Band Downlink

NASA Technical Reports Server (NTRS)

Ho, C.; Wheelon, A.

2004-01-01

Dynamic signal fluctuations due to atmospheric scintillations may impair the Ka-band (around 32-GHz) link sensitivities for a low-margin Deep Space Network (DSN) receiving system. The ranges of frequency and power of the fast fluctuating signals (time scale less than 1 min) are theoretically investigated using the spatial covariance and turbulence theory. Scintillation power spectrum solutions are derived for both a point receiver and a finite-aperture receiver. The aperture-smoothing frequency ((omega(sub s)), corner frequency ((omega(sub c)), and damping rate are introduced to define the shape of the spectrum for a finite-aperture antenna. The emphasis is put on quantitatively describing the aperture-smoothing effects and graphically estimating the corner frequency for a large aperture receiver. Power spectral shapes are analyzed parametrically in detail through both low- and high-frequency approximations. It is found that aperture-averaging effects become significant when the transverse correlation length of the scintillation is smaller than the antenna radius. The upper frequency or corner frequency for a finite-aperture receiver is controlled by both the Fresnel frequency and aperture-smoothing frequency. Above the aperture-smoothing frequency, the spectrum rolls off at a much faster rate of exp (-omega(sup 2)/omega(sup 2, sub s), rather than omega(sup -8/3), which is customary for a point receiver. However, a relatively higher receiver noise level can mask the fast falling-off shape and make it hard to be identified. We also predict that when the effective antenna radius a(sub r) less than or = 6 m, the corner frequency of its power spectrum becomes the same as that for a point receiver. The aperture-smoothing effects are not obvious. We have applied these solutions to the scenario of a DSN Goldstone 34-m-diameter antenna and predicted the power spectrum shape for the receiving station. The maximum corner frequency for the receiver (with omega(sub s) = 0

Debris Flux Comparisons From The Goldstone Radar, Haystack Radar, and Hax Radar Prior, During, and After the Last Solar Maximum

NASA Technical Reports Server (NTRS)

Stokely, C. L.; Stansbery, E. G.; Goldstein, R. M.

2006-01-01

The continual monitoring of low Earth orbit (LEO) debris environment using highly sensitive radars is essential for an accurate characterization of these dynamic populations. Debris populations are continually evolving since there are new debris sources, previously unrecognized debris sources, and debris loss mechanisms that are dependent on the dynamic space environment. Such radar data are used to supplement, update, and validate existing orbital debris models. NASA has been utilizing radar observations of the debris environment for over a decade from three complementary radars: the NASA JPL Goldstone radar, the MIT Lincoln Laboratory (MIT/LL) Long Range Imaging Radar (known as the Haystack radar), and the MIT/LL Haystack Auxiliary radar (HAX). All of these systems are highly sensitive radars that operate in a fixed staring mode to statistically sample orbital debris in the LEO environment. Each of these radars is ideally suited to measure debris within a specific size region. The Goldstone radar generally observes objects with sizes from 2 mm to 1 cm. The Haystack radar generally measures from 5 mm to several meters. The HAX radar generally measures from 2 cm to several meters. These overlapping size regions allow a continuous measurement of cumulative debris flux versus diameter from 2 mm to several meters for a given altitude window. This is demonstrated for all three radars by comparing the debris flux versus diameter over 200 km altitude windows for 3 nonconsecutive years from 1998 through 2003. These years correspond to periods before, during, and after the peak of the last solar cycle. Comparing the year to year flux from Haystack for each of these altitude regions indicate statistically significant changes in subsets of the debris populations. Potential causes of these changes are discussed. These analysis results include error bars that represent statistical sampling errors, and are detailed in this paper.

Ka-Band Atmospheric Phase Stability Measurements in Goldstone, CA; White Sands, NM; and Guam

NASA Technical Reports Server (NTRS)

Zemba, Michael J.; Morse, Jacquelynne Rose; Nessel, James A.

2014-01-01

As spacecraft communication links are driven to higher frequencies (e.g. Ka-band) both by spectrum congestion and the appeal of higher data rates, the propagation phenomena at these frequencies must be well characterized for effective system design. In particular, the phase stability of a site at a given frequency will govern whether or not the site is a practical location for an antenna array, particularly if uplink capabilities are desired. Propagation studies to characterize such phenomena must be done on a site-by-site basis due to the wide variety of climates and weather conditions at each ground terminal. Accordingly, in order to statistically characterize the atmospheric effects on Ka-Band links, site test interferometers (STIs) have been deployed at three of NASA's operational sites to directly measure each site's tropospheric phase stability. Using three years of results from these experiments, this paper will statistically characterize the simultaneous atmospheric phase noise measurements recorded by the STIs deployed at the following ground station sites: the Goldstone Deep Space Communications Complex near Barstow, CA; the White Sands Ground Terminal near Las Cruces, NM; and the Guam Remote Ground Terminal on the island of Guam.

Efficient implementation of core-excitation Bethe-Salpeter equation calculations

NASA Astrophysics Data System (ADS)

Gilmore, K.; Vinson, John; Shirley, E. L.; Prendergast, D.; Pemmaraju, C. D.; Kas, J. J.; Vila, F. D.; Rehr, J. J.

2015-12-01

We present an efficient implementation of the Bethe-Salpeter equation (BSE) method for obtaining core-level spectra including X-ray absorption (XAS), X-ray emission (XES), and both resonant and non-resonant inelastic X-ray scattering spectra (N/RIXS). Calculations are based on density functional theory (DFT) electronic structures generated either by ABINIT or QuantumESPRESSO, both plane-wave basis, pseudopotential codes. This electronic structure is improved through the inclusion of a GW self energy. The projector augmented wave technique is used to evaluate transition matrix elements between core-level and band states. Final two-particle scattering states are obtained with the NIST core-level BSE solver (NBSE). We have previously reported this implementation, which we refer to as OCEAN (Obtaining Core Excitations from Ab initio electronic structure and NBSE) (Vinson et al., 2011). Here, we present additional efficiencies that enable us to evaluate spectra for systems ten times larger than previously possible; containing up to a few thousand electrons. These improvements include the implementation of optimal basis functions that reduce the cost of the initial DFT calculations, more complete parallelization of the screening calculation and of the action of the BSE Hamiltonian, and various memory reductions. Scaling is demonstrated on supercells of SrTiO3 and example spectra for the organic light emitting molecule Tris-(8-hydroxyquinoline)aluminum (Alq3) are presented. The ability to perform large-scale spectral calculations is particularly advantageous for investigating dilute or non-periodic systems such as doped materials, amorphous systems, or complex nano-structures.

Theory of self-resonance after inflation. I. Adiabatic and isocurvature Goldstone modes

NASA Astrophysics Data System (ADS)

Hertzberg, Mark P.; Karouby, Johanna; Spitzer, William G.; Becerra, Juana C.; Li, Lanqing

2014-12-01

We develop a theory of self-resonance after inflation. We study a large class of models involving multiple scalar fields with an internal symmetry. For illustration, we often specialize to dimension-four potentials, but we derive results for general potentials. This is the first part of a two part series of papers. Here in Part 1 we especially focus on the behavior of long-wavelength modes, which are found to govern most of the important physics. Since the inflaton background spontaneously breaks the time-translation symmetry and the internal symmetry, we obtain Goldstone modes; these are the adiabatic and isocurvature modes. We find general conditions on the potential for when a large instability band exists for these modes at long wavelengths. For the adiabatic mode, this is determined by a sound speed derived from the time-averaged potential, while for the isocurvature mode, this is determined by a speed derived from a time-averaged auxiliary potential. Interestingly, we find that this instability band usually exists for one of these classes of modes, rather than both simultaneously. We focus on backgrounds that evolve radially in field space, as set up by inflation, and also mention circular orbits, as relevant to Q -balls. In Part 2 [M. P. Hertzberg et al., Phys. Rev. D 90, 123529 (2014)] we derive the central behavior from the underlying description of many-particle quantum mechanics, and introduce a weak breaking of the symmetry to study corrections to particle-antiparticle production from preheating.

Environmental projects. Volume 13: Underground storage tanks, removal and replacement. Goldstone Deep Space Communications Complex

NASA Technical Reports Server (NTRS)

Bengelsdorf, Irv

1991-01-01

The Goldstone Deep Space Communications Complex (GDSCC), located in the Mojave Desert about 40 miles north of Barstow, California, and about 160 miles northeast of Pasadena, is part of the National Aeronautics and Space Administration's (NASA's) Deep Space Network, one of the world's largest and most sensitive scientific telecommunications and radio navigation networks. Activities at the GDSCC are carried out in support of six large parabolic dish antennas. As a large-scale facility located in a remote, isolated desert region, the GDSCC operations require numerous on-site storage facilities for gasoline, diesel oil, hydraulic oil, and waste oil. These fluids are stored in underground storage tanks (USTs). This present volume describes what happened to the 26 USTs that remained at the GDSCC. Twenty-four of these USTs were constructed of carbon steel without any coating for corrosion protection, and without secondary containment or leak detection. Two remaining USTs were constructed of fiberglass-coated carbon steel but without secondary containment or leak protection. Of the 26 USTs that remained at the GDSCC, 23 were cleaned, removed from the ground, cut up, and hauled away from the GDSCC for environmentally acceptable disposal. Three USTs were permanently closed (abandoned in place).

Local free energies for the coarse-graining of adsorption phenomena: The interacting pair approximation

NASA Astrophysics Data System (ADS)

Pazzona, Federico G.; Pireddu, Giovanni; Gabrieli, Andrea; Pintus, Alberto M.; Demontis, Pierfranco

2018-05-01

We investigate the coarse-graining of host-guest systems under the perspective of the local distribution of pore occupancies, along with the physical meaning and actual computability of the coarse-interaction terms. We show that the widely accepted approach, in which the contributions to the free energy given by the molecules located in two neighboring pores are estimated through Monte Carlo simulations where the two pores are kept separated from the rest of the system, leads to inaccurate results at high sorbate densities. In the coarse-graining strategy that we propose, which is based on the Bethe-Peierls approximation, density-independent interaction terms are instead computed according to local effective potentials that take into account the correlations between the pore pair and its surroundings by means of mean-field correction terms without the need for simulating the pore pair separately. Use of the interaction parameters obtained this way allows the coarse-grained system to reproduce more closely the equilibrium properties of the original one. Results are shown for lattice-gases where the local free energy can be computed exactly and for a system of Lennard-Jones particles under the effect of a static confining field.

The infrared behaviour of QCD Green's functions. Confinement, dynamical symmetry breaking, and hadrons as relativistic bound states

NASA Astrophysics Data System (ADS)

Alkofer, Reinhard; von Smekal, Lorenz

2001-11-01

Recent studies of QCD Green's functions and their applications in hadronic physics are reviewed. We discuss the definition of the generating functional in gauge theories, in particular, the rôle of redundant degrees of freedom, possibilities of a complete gauge fixing versus gauge fixing in presence of Gribov copies, BRS invariance and positivity. The apparent contradiction between positivity and colour antiscreening in combination with BRS invariance in QCD is considered. Evidence for the violation of positivity by quarks and transverse gluons in the covariant gauge is collected, and it is argued that this is one manifestation of confinement. We summarise the derivation of the Dyson-Schwinger equations (DSEs) of QED and QCD. For the latter, the implications of BRS invariance on the Green's functions are explored. The possible influence of instantons on DSEs is discussed in a two-dimensional model. In QED in (2+1) and (3+1) dimensions, the solutions for Green's functions provide tests of truncation schemes which can under certain circumstances be extended to the DSEs of QCD. We discuss some limitations of such extensions and assess the validity of assumptions for QCD as motivated from studies in QED. Truncation schemes for DSEs are discussed in axial and related gauges, as well as in the Landau gauge. Furthermore, we review the available results from a systematic non-perturbative expansion scheme established for Landau gauge QCD. Comparisons to related lattice results, where available, are presented. The applications of QCD Green's functions to hadron physics are summarised. Properties of ground state mesons are discussed on the basis of the ladder Bethe-Salpeter equation for quarks and antiquarks. The Goldstone nature of pseudoscalar mesons and a mechanism for diquark confinement beyond the ladder approximation are reviewed. We discuss some properties of ground state baryons based on their description as Bethe-Salpeter/Faddeev bound states of quark

Reliability of the one-crossing approximation in describing the Mott transition

NASA Astrophysics Data System (ADS)

Vildosola, V.; Pourovskii, L. V.; Manuel, L. O.; Roura-Bas, P.

2015-12-01

We assess the reliability of the one-crossing approximation (OCA) approach in a quantitative description of the Mott transition in the framework of the dynamical mean field theory (DMFT). The OCA approach has been applied in conjunction with DMFT to a number of heavy-fermion, actinide, transition metal compounds and nanoscale systems. However, several recent studies in the framework of impurity models pointed out serious deficiencies of OCA and raised questions regarding its reliability. Here we consider a single band Hubbard model on the Bethe lattice at finite temperatures and compare the results of OCA to those of a numerically exact quantum Monte Carlo (QMC) method. The temperature-local repulsion U phase diagram for the particle-hole symmetric case obtained by OCA is in good agreement with that of QMC, with the metal-insulator transition captured very well. We find, however, that the insulator to metal transition is shifted to higher values of U and, simultaneously, correlations in the metallic phase are significantly overestimated. This counter-intuitive behaviour is due to simultaneous underestimations of the Kondo scale in the metallic phase and the size of the insulating gap. We trace the underestimation of the insulating gap to that of the second moment of the high-frequency expansion of the impurity spectral density. Calculations of the system away from the particle-hole symmetric case are also presented and discussed.

A structure preserving Lanczos algorithm for computing the optical absorption spectrum

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shao, Meiyue; Jornada, Felipe H. da; Lin, Lin

2016-11-16

We present a new structure preserving Lanczos algorithm for approximating the optical absorption spectrum in the context of solving full Bethe-Salpeter equation without Tamm-Dancoff approximation. The new algorithm is based on a structure preserving Lanczos procedure, which exploits the special block structure of Bethe-Salpeter Hamiltonian matrices. A recently developed technique of generalized averaged Gauss quadrature is incorporated to accelerate the convergence. We also establish the connection between our structure preserving Lanczos procedure with several existing Lanczos procedures developed in different contexts. Numerical examples are presented to demonstrate the effectiveness of our Lanczos algorithm.

Beth-Uhlenbeck approach for repulsive interactions between baryons in a hadron gas

NASA Astrophysics Data System (ADS)

Vovchenko, Volodymyr; Motornenko, Anton; Gorenstein, Mark I.; Stoecker, Horst

2018-03-01

The quantum mechanical Beth-Uhlenbeck (BU) approach for repulsive hard-core interactions between baryons is applied to the thermodynamics of a hadron gas. The second virial coefficient a2—the "excluded volume" parameter—calculated within the BU approach is found to be temperature dependent, and it differs dramatically from the classical excluded volume (EV) model result. At temperatures T =100 -200 MeV, the widely used classical EV model underestimates the EV parameter for nucleons at a given value of the nucleon hard-core radius by large factors of 3-4. Previous studies, which employed the hard-core radii of hadrons as an input into the classical EV model, have to be re-evaluated using the appropriately rescaled EV parameters. The BU approach is used to model the repulsive baryonic interactions in the hadron resonance gas (HRG) model. Lattice data for the second- and fourth-order net baryon susceptibilities are described fairly well when the temperature dependent BU baryonic excluded volume parameter corresponds to nucleon hard-core radii of rc=0.25 -0.3 fm. Role of the attractive baryonic interactions is also considered. It is argued that HRG model with a constant baryon-baryon EV parameter vN N≃1 fm3 provides a simple yet efficient description of baryon-baryon interaction in the crossover temperature region.

Axion-familon model with a harmless 17 keV neutrino

NASA Astrophysics Data System (ADS)

Nelson, Ann E.

1985-09-01

A model is discussed in which e + τ-μ emerges as an approximate, but very good, accidental symmetry of the lepton mass matrices. Consequently a heavy neutrino can be accommodated without conflicts with νμ oscillation or neutrinoless double β decay data. The model has a Goldstone boson which may be interpreted as the axion, the majoron, or a familon. The decay of the heavy neutrino can proceed at a rate just compatible with cosmology if the K+ --> π+ + Goldstone boson branching ratio is at the present experimental limit. Junior Fellow, Harvard Society of Fellows.

Grand-canonical solution of semiflexible self-avoiding trails on the Bethe lattice.

PubMed

Dantas, W G; Oliveira, Tiago J; Stilck, Jürgen F; Prellberg, Thomas

2017-02-01

We consider a model of semiflexible interacting self-avoiding trails (sISATs) on a lattice, where the walks are constrained to visit each lattice edge at most once. Such models have been studied as an alternative to the self-attracting self-avoiding walks (SASAWs) to investigate the collapse transition of polymers, with the attractive interactions being on site as opposed to nearest-neighbor interactions in SASAWs. The grand-canonical version of the sISAT model is solved on a four-coordinated Bethe lattice, and four phases appear: non-polymerized (NP), regular polymerized (P), dense polymerized (DP), and anisotropic nematic (AN), the last one present in the phase diagram only for sufficiently stiff chains. The last two phases are dense, in the sense that all lattice sites are visited once in the AN phase and twice in the DP phase. In general, critical NP-P and DP-P transition surfaces meet with a NP-DP coexistence surface at a line of bicritical points. The region in which the AN phase is stable is limited by a discontinuous critical transition to the P phase, and we study this somewhat unusual transition in some detail. In the limit of rods, where the chains are totally rigid, the P phase is absent and the three coexistence lines (NP-AN, AN-DP, and NP-DP) meet at a triple point, which is the endpoint of the bicritical line.

The NASA/JPL 64-meter-diameter antenna at Goldstone, California: Project report, technical staff, tracking and data acquisition organization

NASA Technical Reports Server (NTRS)

1974-01-01

The significant management and technical aspects of the JPL Project to develop and implement a 64-meter-diameter antenna at the Goldstone Deep Space Communications Complex in California, which was the first of the Advanced Antenna Systems of the National Aeronautics and Space Administration/Jet Propulsion Laboratory Deep Space Network are described. The original need foreseen for a large-diameter antenna to accomplish communication and tracking support of NASA's solar system exploration program is reviewed, and the translation of those needs into the technical specification of an appropriate ground station antenna is described. The antenna project is delineated by phases to show the key technical and managerial skills and the technical facility resources involved. There is a brief engineering description of the antenna and its closely related facilities. Some difficult and interesting engineering problems, then at the state-of-the-art level, which were met in the accomplishment of the Project, are described. The key performance characteristics of the antenna, in relation to the original specifications and the methods of their determination, are stated.

Goldstone/VLA 3.5cm Mars Radar Observations - "Stealths" and South Polar Regions

NASA Astrophysics Data System (ADS)

Butler, Bryan; Chizek, M. R.; Slade, M. A.; Haldemann, A. F.; Muhleman, D. O.; Mao, T. F.

2006-09-01

The opposition of Mars in 2003 provided a fantastic opportunity to use the combined Goldstone/VLA radar to probe the surface with the highest resolution ever obtained on Mars with that instrument (as good as 70 km). Observations were made on August 11, 19, 28, and September 8. Details of data reduction and analysis of the radar echoes from the volcanic regions of the planet are presented in a companion paper in these proceedings (Chizek et al.). We will present results related to "Stealth" (and other radar-dark regions of the planet, including the Argyre and Hellas Planitiae, and a region to the west of the Elysium Mons caldera), and the south polar residual and seasonal ice caps. The size, shape, and reflectivity characteristics of Stealth and "mega-Stealth" (Edgett et al. 1997) are reaffirmed, with a better viewing geometry of the western extent of the feature than had been obtained previously. It had been speculated previously that Hellas Planitia should also be radar dark - this is confirmed by our imaging, though the reflectivity is not as low as for Stealth. We find a new radar dark area to the west of Elysium Mons, which is likely an ash fall from that volcano (similar to the relationship between Stealth and the Tharsis volcanoes). The south polar residual ice cap is a very bright reflector, as seen previously, but we now also see a very bright reflection from the seasonal cap, not seen previously. The cap is not uniformly bright, however, and the extent of the bright reflection does not correspond to that expected from the retreat of the cap as measured either from albedo or thermal emission characteristics. The NRAO is a facility of the National Science Foundation, operated under cooperative agreement by Associated Universities, Inc.

A Binary-Encounter-Bethe Approach to Simulate DNA Damage by the Direct Effect

NASA Technical Reports Server (NTRS)

Plante, Ianik; Cucinotta, Francis A.

2013-01-01

The DNA damage is of crucial importance in the understanding of the effects of ionizing radiation. The main mechanisms of DNA damage are by the direct effect of radiation (e.g. direct ionization) and by indirect effect (e.g. damage by.OH radicals created by the radiolysis of water). Despite years of research in this area, many questions on the formation of DNA damage remains. To refine existing DNA damage models, an approach based on the Binary-Encounter-Bethe (BEB) model was developed[1]. This model calculates differential cross sections for ionization of the molecular orbitals of the DNA bases, sugars and phosphates using the electron binding energy, the mean kinetic energy and the occupancy number of the orbital. This cross section has an analytic form which is quite convenient to use and allows the sampling of the energy loss occurring during an ionization event. To simulate the radiation track structure, the code RITRACKS developed at the NASA Johnson Space Center is used[2]. This code calculates all the energy deposition events and the formation of the radiolytic species by the ion and the secondary electrons as well. We have also developed a technique to use the integrated BEB cross section for the bases, sugar and phosphates in the radiation transport code RITRACKS. These techniques should allow the simulation of DNA damage by ionizing radiation, and understanding of the formation of double-strand breaks caused by clustered damage in different conditions.

From ‘Nerve Fiber Regeneration’ to ‘Functional Changes’ in the Human Brain—On the Paradigm-Shifting Work of the Experimental Physiologist Albrecht Bethe (1872–1954) in Frankfurt am Main

PubMed Central

Stahnisch, Frank W.

2016-01-01

Until the beginning 1930’s the traditional dogma that the human central nervous system (CNS) did not possess any abilities to adapt functionally to degenerative processes and external injuries loomed large in the field of the brain sciences (Hirnforschung). Cutting-edge neuroanatomists, such as the luminary Wilhelm Waldeyer (1836–1921) in Germany or the Nobel Prize laureate Santiago Ramón y Cajal (1852–1934) in Spain, debated any regenerative and thus “plastic” properties in the human brain. A renewed interest arose in the scientific community to investigate the pathologies and the healing processes in the human CNS after the return of the high number of brain injured war veterans from the fronts during and after the First World War (1914–1918). A leading research center in this area was the “Institute for the Scientific Study of the Effects of Brain Injuries,” which the neurologist Ludwig Edinger (1855–1918) had founded shortly before the war. This article specifically deals with the physiological research on nerve fiber plasticity by Albrecht Bethe (1872–1954) at the respective institute of the University of Frankfurt am Main. Bethe conducted here his paradigmatic experimental studies on the pathophysiological and clinical phenomena of peripheral and CNS regeneration. PMID:26941616

Asymptotic behavior of Nambu-Bethe-Salpeter wave functions for multiparticles in quantum field theories

NASA Astrophysics Data System (ADS)

Aoki, Sinya; Ishii, Noriyoshi; Doi, Takumi; Ikeda, Yoichi; Inoue, Takashi

2013-07-01

We derive asymptotic behaviors of the Nambu-Bethe-Salpeter (NBS) wave function at large space separations for systems with more than two particles in quantum field theories. To deal with n particles in the center-of-mass frame coherently, we introduce the Jacobi coordinates of n particles and then combine their 3(n-1) coordinates into the one spherical coordinate in D=3(n-1) dimensions. We parametrize the on-shell T matrix for n scalar particles at low energy using the unitarity constraint of the S matrix. We then express asymptotic behaviors of the NBS wave function for n particles at low energy in terms of parameters of the T matrix and show that the NBS wave function carries information of the T matrix such as phase shifts and mixing angles of the n-particle system in its own asymptotic behavior, so that the NBS wave function can be considered as the scattering wave of n particles in quantum mechanics. This property is one of the essential ingredients of the HAL QCD scheme to define “potential” from the NBS wave function in quantum field theories such as QCD. Our results, together with an extension to systems with spin 1/2 particles, justify the HAL QCD’s definition of potentials for three or more nucleons (or baryons) in terms of the NBS wave functions.

Triple Asteroid System Triples Asteroid Observers Interest

NASA Image and Video Library

2009-08-06

NASA Deep Space Network, Goldstone radar images show triple asteroid 1994 CC, which consists of a central object approximately 700 meters 2,300 feet in diameter and two smaller moons that orbit the central body. Animation available at the Photojournal

The critical 1-arm exponent for the ferromagnetic Ising model on the Bethe lattice

NASA Astrophysics Data System (ADS)

Heydenreich, Markus; Kolesnikov, Leonid

2018-04-01

We consider the ferromagnetic nearest-neighbor Ising model on regular trees (Bethe lattice), which is well-known to undergo a phase transition in the absence of an external magnetic field. The behavior of the model at critical temperature can be described in terms of various critical exponents; one of them is the critical 1-arm exponent ρ which characterizes the rate of decay of the (root) magnetization as a function of the distance to the boundary. The crucial quantity we analyze in this work is the thermal expectation of the root spin on a finite subtree, where the expected value is taken with respect to a probability measure related to the corresponding finite-volume Hamiltonian with a fixed boundary condition. The spontaneous magnetization, which is the limit of this thermal expectation in the distance between the root and the boundary (i.e., in the height of the subtree), is known to vanish at criticality. We are interested in a quantitative analysis of the rate of this convergence in terms of the critical 1-arm exponent ρ. Therefore, we rigorously prove that ⟨σ0⟩ n +, the thermal expectation of the root spin at the critical temperature and in the presence of the positive boundary condition, decays as ⟨σ0 ⟩ n +≈n-1/2 (in a rather sharp sense), where n is the height of the tree. This establishes the 1-arm critical exponent for the Ising model on regular trees (ρ =1/2 ).

Equation of state of dense nuclear matter and neutron star structure from nuclear chiral interactions

NASA Astrophysics Data System (ADS)

Bombaci, Ignazio; Logoteta, Domenico

2018-02-01

Aims: We report a new microscopic equation of state (EOS) of dense symmetric nuclear matter, pure neutron matter, and asymmetric and β-stable nuclear matter at zero temperature using recent realistic two-body and three-body nuclear interactions derived in the framework of chiral perturbation theory (ChPT) and including the Δ(1232) isobar intermediate state. This EOS is provided in tabular form and in parametrized form ready for use in numerical general relativity simulations of binary neutron star merging. Here we use our new EOS for β-stable nuclear matter to compute various structural properties of non-rotating neutron stars. Methods: The EOS is derived using the Brueckner-Bethe-Goldstone quantum many-body theory in the Brueckner-Hartree-Fock approximation. Neutron star properties are next computed solving numerically the Tolman-Oppenheimer-Volkov structure equations. Results: Our EOS models are able to reproduce the empirical saturation point of symmetric nuclear matter, the symmetry energy Esym, and its slope parameter L at the empirical saturation density n0. In addition, our EOS models are compatible with experimental data from collisions between heavy nuclei at energies ranging from a few tens of MeV up to several hundreds of MeV per nucleon. These experiments provide a selective test for constraining the nuclear EOS up to 4n0. Our EOS models are consistent with present measured neutron star masses and particularly with the mass M = 2.01 ± 0.04 M⊙ of the neutron stars in PSR J0348+0432.

Hans A. Bethe Prize: Cosmic Collisions Online - Compact Binary Mergers, Gravitational Waves and Gamma-Ray Bursts

NASA Astrophysics Data System (ADS)

Shapiro, Stuart

2017-01-01

Hans A. Bethe elucidated our understanding of the fundamental forces of Nature by exploring and explaining countless phenomena occurring in nuclear laboratories and in stars. With the dawn of gravitational wave astronomy we now can probe compact binary mergers - Nature's cosmic collision experiments - to deepen our understanding, especially where strong-field gravitation is involved. In addition to gravitational waves, some mergers are likely to generate observable electromagnetic and/or neutrino radiation, heralding a new era of multimessenger astronomy. Robust numerical algorithms now allow us to simulate these events in full general relativity on supercomputers. We will describe some recent magnetohydrodynamic simulations that show how binary black hole-neutron star and neutron star-neutron star mergers can launch jets, lending support to the idea that such mergers could be the engines that power short gamma-ray bursts. We will also show how the magnetorotational collapse of very massive stars to spinning black holes immersed in magnetized accretion disks can launch jets as well, reinforcing the belief that such ``collapsars'' are the progenitors of long gamma-ray bursts. Computer-generated movies highlighting some of these simulations will be shown. We gratefully acknowledge support from NSF Grants 1300903 and 1602536 and NASA Grant NNX13AH44G.

Relocking of intrinsic angular momenta in collisions of diatoms with ions: Capture of H2(j = 0,1) by H2+

NASA Astrophysics Data System (ADS)

Dashevskaya, E. I.; Litvin, I.; Nikitin, E. E.; Troe, J.

2016-12-01

Rate coefficients for capture of H2(j = 0,1) by H2+ are calculated in perturbed rotor approximation, i.e., at collision energies considerably lower than Bhc (where B denotes the rotational constant of H2). The results are compared with the results from an axially nonadiabatic channel (ANC) approach, the latter providing a very good approximation from the low-temperature Bethe-Wigner to the high temperature Langevin limit. The classical ANC approximation performs satisfactorily at temperatures above 0.1 K. At 0.1 K, the rate coefficient for j =1 is about 25% higher than that for j = 0 while the latter is close to the Langevin rate coefficient. The Bethe-Wigner limit of the rate coefficient for j = 1 is about twice that for j = 0. The analysis of the relocking of the intrinsic angular momentum of H2 during the course of the collision illustrates the significance of relocking in capture dynamics in general.

Investigations of quantum heuristics for optimization

NASA Astrophysics Data System (ADS)

Rieffel, Eleanor; Hadfield, Stuart; Jiang, Zhang; Mandra, Salvatore; Venturelli, Davide; Wang, Zhihui

We explore the design of quantum heuristics for optimization, focusing on the quantum approximate optimization algorithm, a metaheuristic developed by Farhi, Goldstone, and Gutmann. We develop specific instantiations of the of quantum approximate optimization algorithm for a variety of challenging combinatorial optimization problems. Through theoretical analyses and numeric investigations of select problems, we provide insight into parameter setting and Hamiltonian design for quantum approximate optimization algorithms and related quantum heuristics, and into their implementation on hardware realizable in the near term.

Calculation of total electron excitation cross-sections and partial electron ionization cross-sections for the elements. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Green, T. J.

1973-01-01

Computer programs were used to calculate the total electron excitation cross-section for atoms and the partial ionization cross-section. The approximations to the scattering amplitude used are as follows: (1) Born, Bethe, and Modified Bethe for non-exchange excitation; (2) Ochkur for exchange excitation; and (3) Coulomb-Born of non-exchange ionization. The amplitudes are related to the differential cross-sections which are integrated to give the total excitation (or partial ionization) cross-section for the collision. The atomic wave functions used are Hartree-Fock-Slater functions for bound states and the coulomb wave function for the continuum. The programs are presented and the results are examined.

Approximate Dynamic Programming: Combining Regional and Local State Following Approximations.

PubMed

Deptula, Patryk; Rosenfeld, Joel A; Kamalapurkar, Rushikesh; Dixon, Warren E

2018-06-01

An infinite-horizon optimal regulation problem for a control-affine deterministic system is solved online using a local state following (StaF) kernel and a regional model-based reinforcement learning (R-MBRL) method to approximate the value function. Unlike traditional methods such as R-MBRL that aim to approximate the value function over a large compact set, the StaF kernel approach aims to approximate the value function in a local neighborhood of the state that travels within a compact set. In this paper, the value function is approximated using a state-dependent convex combination of the StaF-based and the R-MBRL-based approximations. As the state enters a neighborhood containing the origin, the value function transitions from being approximated by the StaF approach to the R-MBRL approach. Semiglobal uniformly ultimately bounded (SGUUB) convergence of the system states to the origin is established using a Lyapunov-based analysis. Simulation results are provided for two, three, six, and ten-state dynamical systems to demonstrate the scalability and performance of the developed method.

Countably QC-Approximating Posets

PubMed Central

Mao, Xuxin; Xu, Luoshan

2014-01-01

As a generalization of countably C-approximating posets, the concept of countably QC-approximating posets is introduced. With the countably QC-approximating property, some characterizations of generalized completely distributive lattices and generalized countably approximating posets are given. The main results are as follows: (1) a complete lattice is generalized completely distributive if and only if it is countably QC-approximating and weakly generalized countably approximating; (2) a poset L having countably directed joins is generalized countably approximating if and only if the lattice σ c(L)op of all σ-Scott-closed subsets of L is weakly generalized countably approximating. PMID:25165730

Non-Gaussianities in a two-field generalization of natural inflation

NASA Astrophysics Data System (ADS)

Riquelme M., Simon

2018-04-01

We describe a two-field model that generalizes natural inflation, in which the inflaton is the pseudo-Goldstone boson of an approximate symmetry that is spontaneously broken, and the radial mode is dynamical. We analyze how the dynamics fundamentally depends on the mass of the radial mode and calculate/estimate the non-Gaussianities arising from such a scenario.

Natural electroweak breaking from a mirror symmetry.

PubMed

Chacko, Z; Goh, Hock-Seng; Harnik, Roni

2006-06-16

We present "twin Higgs models," simple realizations of the Higgs boson as a pseudo Goldstone boson that protect the weak scale from radiative corrections up to scales of order 5-10 TeV. In the ultraviolet these theories have a discrete symmetry which interchanges each standard model particle with a corresponding particle which transforms under a twin or a mirror standard model gauge group. In addition, the Higgs sector respects an approximate global symmetry. When this global symmetry is broken, the discrete symmetry tightly constrains the form of corrections to the pseudo Goldstone Higgs potential, allowing natural electroweak symmetry breaking. Precision electroweak constraints are satisfied by construction. These models demonstrate that, contrary to the conventional wisdom, stabilizing the weak scale does not require new light particles charged under the standard model gauge groups.

Emergent gauge theories and supersymmetry: A QED primer

NASA Astrophysics Data System (ADS)

Chkareuli, J. L.

2013-04-01

We argue that a generic trigger for photon and other gauge fields to emerge as massless Nambu-Goldstone modes could be spontaneously broken supersymmetry rather than physically manifested Lorentz violation. We consider supersymmetric QED model extended by an arbitrary polynomial potential of vector superfield that induces the spontaneous SUSY violation in the visible sector. As a consequence, massless photon appears as a companion of massless photino being Goldstone fermion state in tree approximation. Remarkably, the photon masslessness appearing at tree level is further protected against radiative corrections due to the simultaneously generated special gauge invariance in the broken SUSY phase. Meanwhile, photino being mixed with another goldstino appearing from a spontaneous SUSY violation in the hidden sector largely turns into light pseudo-goldstino whose physics seems to be of special interest.

A systematic benchmark of the ab initio Bethe-Salpeter equation approach for low-lying optical excitations of small organic molecules

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bruneval, Fabien; Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California 94720; Department of Physics, University of California, Berkeley, California 94720

2015-06-28

The predictive power of the ab initio Bethe-Salpeter equation (BSE) approach, rigorously based on many-body Green’s function theory but incorporating information from density functional theory, has already been demonstrated for the optical gaps and spectra of solid-state systems. Interest in photoactive hybrid organic/inorganic systems has recently increased and so has the use of the BSE for computing neutral excitations of organic molecules. However, no systematic benchmarks of the BSE for neutral electronic excitations of organic molecules exist. Here, we study the performance of the BSE for the 28 small molecules in Thiel’s widely used time-dependent density functional theory benchmark setmore » [Schreiber et al., J. Chem. Phys. 128, 134110 (2008)]. We observe that the BSE produces results that depend critically on the mean-field starting point employed in the perturbative approach. We find that this starting point dependence is mainly introduced through the quasiparticle energies obtained at the intermediate GW step and that with a judicious choice of starting mean-field, singlet excitation energies obtained from BSE are in excellent quantitative agreement with higher-level wavefunction methods. The quality of the triplet excitations is slightly less satisfactory.« less

Solution on the Bethe lattice of a hard core athermal gas with two kinds of particles.

PubMed

Oliveira, Tiago J; Stilck, Jürgen F

2011-11-14

Athermal lattice gases of particles with first neighbor exclusion have been studied for a long time as simple models exhibiting a fluid-solid transition. At low concentration the particles occupy randomly both sublattices, but as the concentration is increased one of the sublattices is occupied preferentially. Here, we study a mixed lattice gas with excluded volume interactions only in the grand-canonical formalism with two kinds of particles: small ones, which occupy a single lattice site and large ones, which, when placed on a site, do not allow other particles to occupy its first neighbors also. We solve the model on a Bethe lattice of arbitrary coordination number q. In the parameter space defined by the activities of both particles, at low values of the activity of small particles (z(1)) we find a continuous transition from the fluid to the solid phase as the activity of large particles (z(2)) is increased. At higher values of z(1) the transition becomes discontinuous, both regimes are separated by a tricritical point. The critical line has a negative slope at z(1) = 0 and displays a minimum before reaching the tricritical point, so that a re-entrant behavior is observed for constant values of z(2) in the region of low density of small particles. The isobaric curves of the total density of particles as a function of the density or the activity of small particles show a minimum in the fluid phase. © 2011 American Institute of Physics

Approximate symmetries of Hamiltonians

NASA Astrophysics Data System (ADS)

Chubb, Christopher T.; Flammia, Steven T.

2017-08-01

We explore the relationship between approximate symmetries of a gapped Hamiltonian and the structure of its ground space. We start by considering approximate symmetry operators, defined as unitary operators whose commutators with the Hamiltonian have norms that are sufficiently small. We show that when approximate symmetry operators can be restricted to the ground space while approximately preserving certain mutual commutation relations. We generalize the Stone-von Neumann theorem to matrices that approximately satisfy the canonical (Heisenberg-Weyl-type) commutation relations and use this to show that approximate symmetry operators can certify the degeneracy of the ground space even though they only approximately form a group. Importantly, the notions of "approximate" and "small" are all independent of the dimension of the ambient Hilbert space and depend only on the degeneracy in the ground space. Our analysis additionally holds for any gapped band of sufficiently small width in the excited spectrum of the Hamiltonian, and we discuss applications of these ideas to topological quantum phases of matter and topological quantum error correcting codes. Finally, in our analysis, we also provide an exponential improvement upon bounds concerning the existence of shared approximate eigenvectors of approximately commuting operators under an added normality constraint, which may be of independent interest.

Radar Observations of Near-Earth Asteroids 2000 UG11 and 2000 UK11

NASA Technical Reports Server (NTRS)

Nolan, M. C.; Margot, J.-L.; Howell, E. S.; Benner, L. A. M.; Ostro, S. J.; Jurgens, R. F.; Giorgini, J. D.; Campbell, D. B.

2001-01-01

Two small near-Earth asteroids, 2000 UG11 and 2000 UK11 were observed using the Arecibo and Goldstone radars a week after their discovery. 2000 UK11 is a rapidly rotating (3 min) approximately 30 m solid body. 2000 UG11 is two bodies separated by at least 300 m Additional information is contained in the original extended abstract..

Padé Approximant and Minimax Rational Approximation in Standard Cosmology

NASA Astrophysics Data System (ADS)

Zaninetti, Lorenzo

2016-02-01

The luminosity distance in the standard cosmology as given by $\\Lambda$CDM and consequently the distance modulus for supernovae can be defined by the Pad\\'e approximant. A comparison with a known analytical solution shows that the Pad\\'e approximant for the luminosity distance has an error of $4\\%$ at redshift $= 10$. A similar procedure for the Taylor expansion of the luminosity distance gives an error of $4\\%$ at redshift $=0.7 $; this means that for the luminosity distance, the Pad\\'e approximation is superior to the Taylor series. The availability of an analytical expression for the distance modulus allows applying the Levenberg--Marquardt method to derive the fundamental parameters from the available compilations for supernovae. A new luminosity function for galaxies derived from the truncated gamma probability density function models the observed luminosity function for galaxies when the observed range in absolute magnitude is modeled by the Pad\\'e approximant. A comparison of $\\Lambda$CDM with other cosmologies is done adopting a statistical point of view.

Approximate spatial reasoning

NASA Technical Reports Server (NTRS)

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.

Thermodynamic Bethe ansatz for non-equilibrium steady states: exact energy current and fluctuations in integrable QFT

NASA Astrophysics Data System (ADS)

Castro-Alvaredo, Olalla; Chen, Yixiong; Doyon, Benjamin; Hoogeveen, Marianne

2014-03-01

We evaluate the exact energy current and scaled cumulant generating function (related to the large-deviation function) in non-equilibrium steady states with energy flow, in any integrable model of relativistic quantum field theory (IQFT) with diagonal scattering. Our derivations are based on various recent results of Bernard and Doyon. The steady states are built by connecting homogeneously two infinite halves of the system thermalized at different temperatures Tl, Tr, and waiting for a long time. We evaluate the current J(Tl, Tr) using the exact QFT density matrix describing these non-equilibrium steady states and using Zamolodchikov’s method of the thermodynamic Bethe ansatz (TBA). The scaled cumulant generating function is obtained from the extended fluctuation relations which hold in integrable models. We verify our formula in particular by showing that the conformal field theory (CFT) result is obtained in the high-temperature limit. We analyze numerically our non-equilibrium steady-state TBA equations for three models: the sinh-Gordon model, the roaming trajectories model, and the sine-Gordon model at a particular reflectionless point. Based on the numerics, we conjecture that an infinite family of non-equilibrium c-functions, associated with the scaled cumulants, can be defined, which we interpret physically. We study the full scaled distribution function and find that it can be described by a set of independent Poisson processes. Finally, we show that the ‘additivity’ property of the current, which is known to hold in CFT and was proposed to hold more generally, does not hold in general IQFT—that is, J(Tl, Tr) is not of the form f(Tl) - f(Tr).

Symmetry realization via a dynamical inverse Higgs mechanism

NASA Astrophysics Data System (ADS)

Rothstein, Ira Z.; Shrivastava, Prashant

2018-05-01

The Ward identities associated with spontaneously broken symmetries can be saturated by Goldstone bosons. However, when space-time symmetries are broken, the number of Goldstone bosons necessary to non-linearly realize the symmetry can be less than the number of broken generators. The loss of Goldstones may be due to a redundancy or the generation of a gap. In either case the associated Goldstone may be removed from the spectrum. This phenomena is called an Inverse Higgs Mechanism (IHM) and its appearance has a well defined mathematical condition. However, there are cases when a Goldstone boson associated with a broken generator does not appear in the low energy theory despite the lack of the existence of an associated IHM. In this paper we will show that in such cases the relevant broken symmetry can be realized, without the aid of an associated Goldstone, if there exists a proper set of operator constraints, which we call a Dynamical Inverse Higgs Mechanism (DIHM). We consider the spontaneous breaking of boosts, rotations and conformal transformations in the context of Fermi liquids, finding three possible paths to symmetry realization: pure Goldstones, no Goldstones and DIHM, or some mixture thereof. We show that in the two dimensional degenerate electron system the DIHM route is the only consistent way to realize spontaneously broken boosts and dilatations, while in three dimensions these symmetries could just as well be realized via the inclusion of non-derivatively coupled Goldstone bosons. We present the action, including the leading order non-linearities, for the rotational Goldstone (angulon), and discuss the constraint associated with the possible DIHM that would need to be imposed to remove it from the spectrum. Finally we discuss the conditions under which Goldstone bosons are non-derivatively coupled, a necessary condition for the existence of a Dynamical Inverse Higgs Constraint (DIHC), generalizing the results for Vishwanath and Wantanabe.

Modification of the nuclear landscape in the inverse problem framework using the generalized Bethe-Weizsäcker mass formula

NASA Astrophysics Data System (ADS)

Mavrodiev, S. Cht.; Deliyergiyev, M. A.

We formalized the nuclear mass problem in the inverse problem framework. This approach allows us to infer the underlying model parameters from experimental observation, rather than to predict the observations from the model parameters. The inverse problem was formulated for the numerically generalized semi-empirical mass formula of Bethe and von Weizsäcker. It was solved in a step-by-step way based on the AME2012 nuclear database. The established parametrization describes the measured nuclear masses of 2564 isotopes with a maximum deviation less than 2.6MeV, starting from the number of protons and number of neutrons equal to 1. The explicit form of unknown functions in the generalized mass formula was discovered in a step-by-step way using the modified least χ2 procedure, that realized in the algorithms which were developed by Lubomir Aleksandrov to solve the nonlinear systems of equations via the Gauss-Newton method, lets us to choose the better one between two functions with same χ2. In the obtained generalized model, the corrections to the binding energy depend on nine proton (2, 8, 14, 20, 28, 50, 82, 108, 124) and ten neutron (2, 8, 14, 20, 28, 50, 82, 124, 152, 202) magic numbers as well on the asymptotic boundaries of their influence. The obtained results were compared with the predictions of other models.

Two-dimensional Schrödinger symmetry and three-dimensional breathers and Kelvin-ripple complexes as quasi-massive-Nambu-Goldstone modes

NASA Astrophysics Data System (ADS)

Takahashi, Daisuke A.; Ohashi, Keisuke; Fujimori, Toshiaki; Nitta, Muneto

2017-08-01

Bose-Einstein condensates (BECs) confined in a two-dimensional (2D) harmonic trap are known to possess a hidden 2D Schrödinger symmetry, that is, the Schrödinger symmetry modified by a trapping potential. Spontaneous breaking of this symmetry gives rise to a breathing motion of the BEC, whose oscillation frequency is robustly determined by the strength of the harmonic trap. In this paper, we demonstrate that the concept of the 2D Schrödinger symmetry can be applied to predict the nature of three-dimensional (3D) collective modes propagating along a condensate confined in an elongated trap. We find three kinds of collective modes whose existence is robustly ensured by the Schrödinger symmetry, which are physically interpreted as one breather mode and two Kelvin-ripple complex modes, i.e., composite modes in which the vortex core and the condensate surface oscillate interactively. We provide analytical expressions for the dispersion relations (energy-momentum relation) of these modes using the Bogoliubov theory [D. A. Takahashi and M. Nitta, Ann. Phys. 354, 101 (2015), 10.1016/j.aop.2014.12.009]. Furthermore, we point out that these modes can be interpreted as "quasi-massive-Nambu-Goldstone (NG) modes", that is, they have the properties of both quasi-NG and massive NG modes: quasi-NG modes appear when a symmetry of a part of a Lagrangian, which is not a symmetry of a full Lagrangian, is spontaneously broken, while massive NG modes appear when a modified symmetry is spontaneously broken.

Dawn in the Apollo Valley

NASA Image and Video Library

2013-12-18

Beam Wave Guide antennas at Goldstone, known as the Beam Waveguide Cluster. They are located in an area at Goldstone called Apollo Valley. The Goldstone Deep Space Communications Complex is located in the Mojave Desert in California, USA.

Legendre-Tau approximation for functional differential equations. Part 3: Eigenvalue approximations and uniform stability

NASA Technical Reports Server (NTRS)

Ito, K.

1984-01-01

The stability and convergence properties of the Legendre-tau approximation for hereditary differential systems are analyzed. A charactristic equation is derived for the eigenvalues of the resulting approximate system. As a result of this derivation the uniform exponential stability of the solution semigroup is preserved under approximation. It is the key to obtaining the convergence of approximate solutions of the algebraic Riccati equation in trace norm.

Approximate spatial reasoning

NASA Technical Reports Server (NTRS)

Dutta, Soumitra

1988-01-01

A model for approximate spatial reasoning using fuzzy logic to represent the uncertainty in the environment is presented. Algorithms are developed which can be used to reason about spatial information expressed in the form of approximate linguistic descriptions similar to the kind of spatial information processed by humans. Particular attention is given to static spatial reasoning.

CONTRIBUTIONS TO RATIONAL APPROXIMATION,

DTIC Science & Technology

Some of the key results of linear Chebyshev approximation theory are extended to generalized rational functions. Prominent among these is Haar’s...linear theorem which yields necessary and sufficient conditions for uniqueness. Some new results in the classic field of rational function Chebyshev...Furthermore a Weierstrass type theorem is proven for rational Chebyshev approximation. A characterization theorem for rational trigonometric Chebyshev approximation in terms of sign alternation is developed. (Author)

Calculation of water equivalent thickness of materials of arbitrary density, elemental composition and thickness in proton beam irradiation

NASA Astrophysics Data System (ADS)

Zhang, Rui; Newhauser, Wayne D.

2009-03-01

In proton therapy, the radiological thickness of a material is commonly expressed in terms of water equivalent thickness (WET) or water equivalent ratio (WER). However, the WET calculations required either iterative numerical methods or approximate methods of unknown accuracy. The objective of this study was to develop a simple deterministic formula to calculate WET values with an accuracy of 1 mm for materials commonly used in proton radiation therapy. Several alternative formulas were derived in which the energy loss was calculated based on the Bragg-Kleeman rule (BK), the Bethe-Bloch equation (BB) or an empirical version of the Bethe-Bloch equation (EBB). Alternative approaches were developed for targets that were 'radiologically thin' or 'thick'. The accuracy of these methods was assessed by comparison to values from an iterative numerical method that utilized evaluated stopping power tables. In addition, we also tested the approximate formula given in the International Atomic Energy Agency's dosimetry code of practice (Technical Report Series No 398, 2000, IAEA, Vienna) and stopping power ratio approximation. The results of these comparisons revealed that most methods were accurate for cases involving thin or low-Z targets. However, only the thick-target formulas provided accurate WET values for targets that were radiologically thick and contained high-Z material.

Approximate Genealogies Under Genetic Hitchhiking

PubMed Central

Pfaffelhuber, P.; Haubold, B.; Wakolbinger, A.

2006-01-01

The rapid fixation of an advantageous allele leads to a reduction in linked neutral variation around the target of selection. The genealogy at a neutral locus in such a selective sweep can be simulated by first generating a random path of the advantageous allele's frequency and then a structured coalescent in this background. Usually the frequency path is approximated by a logistic growth curve. We discuss an alternative method that approximates the genealogy by a random binary splitting tree, a so-called Yule tree that does not require first constructing a frequency path. Compared to the coalescent in a logistic background, this method gives a slightly better approximation for identity by descent during the selective phase and a much better approximation for the number of lineages that stem from the founder of the selective sweep. In applications such as the approximation of the distribution of Tajima's D, the two approximation methods perform equally well. For relevant parameter ranges, the Yule approximation is faster. PMID:17182733

Approximate kernel competitive learning.

PubMed

Wu, Jian-Sheng; Zheng, Wei-Shi; Lai, Jian-Huang

2015-03-01

Kernel competitive learning has been successfully used to achieve robust clustering. However, kernel competitive learning (KCL) is not scalable for large scale data processing, because (1) it has to calculate and store the full kernel matrix that is too large to be calculated and kept in the memory and (2) it cannot be computed in parallel. In this paper we develop a framework of approximate kernel competitive learning for processing large scale dataset. The proposed framework consists of two parts. First, it derives an approximate kernel competitive learning (AKCL), which learns kernel competitive learning in a subspace via sampling. We provide solid theoretical analysis on why the proposed approximation modelling would work for kernel competitive learning, and furthermore, we show that the computational complexity of AKCL is largely reduced. Second, we propose a pseudo-parallelled approximate kernel competitive learning (PAKCL) based on a set-based kernel competitive learning strategy, which overcomes the obstacle of using parallel programming in kernel competitive learning and significantly accelerates the approximate kernel competitive learning for large scale clustering. The empirical evaluation on publicly available datasets shows that the proposed AKCL and PAKCL can perform comparably as KCL, with a large reduction on computational cost. Also, the proposed methods achieve more effective clustering performance in terms of clustering precision against related approximate clustering approaches. Copyright © 2014 Elsevier Ltd. All rights reserved.

Cosmological applications of Padé approximant

NASA Astrophysics Data System (ADS)

Wei, Hao; Yan, Xiao-Peng; Zhou, Ya-Nan

2014-01-01

As is well known, in mathematics, any function could be approximated by the Padé approximant. The Padé approximant is the best approximation of a function by a rational function of given order. In fact, the Padé approximant often gives better approximation of the function than truncating its Taylor series, and it may still work where the Taylor series does not converge. In the present work, we consider the Padé approximant in two issues. First, we obtain the analytical approximation of the luminosity distance for the flat XCDM model, and find that the relative error is fairly small. Second, we propose several parameterizations for the equation-of-state parameter (EoS) of dark energy based on the Padé approximant. They are well motivated from the mathematical and physical points of view. We confront these EoS parameterizations with the latest observational data, and find that they can work well. In these practices, we show that the Padé approximant could be an useful tool in cosmology, and it deserves further investigation.

Approximate number and approximate time discrimination each correlate with school math abilities in young children.

PubMed

Odic, Darko; Lisboa, Juan Valle; Eisinger, Robert; Olivera, Magdalena Gonzalez; Maiche, Alejandro; Halberda, Justin

2016-01-01

What is the relationship between our intuitive sense of number (e.g., when estimating how many marbles are in a jar), and our intuitive sense of other quantities, including time (e.g., when estimating how long it has been since we last ate breakfast)? Recent work in cognitive, developmental, comparative psychology, and computational neuroscience has suggested that our representations of approximate number, time, and spatial extent are fundamentally linked and constitute a "generalized magnitude system". But, the shared behavioral and neural signatures between number, time, and space may alternatively be due to similar encoding and decision-making processes, rather than due to shared domain-general representations. In this study, we investigate the relationship between approximate number and time in a large sample of 6-8 year-old children in Uruguay by examining how individual differences in the precision of number and time estimation correlate with school mathematics performance. Over four testing days, each child completed an approximate number discrimination task, an approximate time discrimination task, a digit span task, and a large battery of symbolic math tests. We replicate previous reports showing that symbolic math abilities correlate with approximate number precision and extend those findings by showing that math abilities also correlate with approximate time precision. But, contrary to approximate number and time sharing common representations, we find that each of these dimensions uniquely correlates with formal math: approximate number correlates more strongly with formal math compared to time and continues to correlate with math even when precision in time and individual differences in working memory are controlled for. These results suggest that there are important differences in the mental representations of approximate number and approximate time and further clarify the relationship between quantity representations and mathematics. Copyright �

Producing approximate answers to database queries

NASA Technical Reports Server (NTRS)

Vrbsky, Susan V.; Liu, Jane W. S.

1993-01-01

We have designed and implemented a query processor, called APPROXIMATE, that makes approximate answers available if part of the database is unavailable or if there is not enough time to produce an exact answer. The accuracy of the approximate answers produced improves monotonically with the amount of data retrieved to produce the result. The exact answer is produced if all of the needed data are available and query processing is allowed to continue until completion. The monotone query processing algorithm of APPROXIMATE works within the standard relational algebra framework and can be implemented on a relational database system with little change to the relational architecture. We describe here the approximation semantics of APPROXIMATE that serves as the basis for meaningful approximations of both set-valued and single-valued queries. We show how APPROXIMATE is implemented to make effective use of semantic information, provided by an object-oriented view of the database, and describe the additional overhead required by APPROXIMATE.

Topological Defects and Structures in the Early Universe

NASA Astrophysics Data System (ADS)

Zhu, Yong

1997-08-01

This thesis discusses the topological defects generated in the early universe and their contributions to cosmic structure formation. First, we investigate non-Gaussian isocurvature perturbations generated by the evolution of Goldstone modes during inflation. If a global symmetry is broken before inflation, the resulting Goldstone modes are disordered during inflation in a precise and predictable way. After inflation these Goldstone modes order themselves in a self-similar way, much as Goldstone modes in field ordering scenarios based on the Kibble mechanism. For (Hi2/Mpl2)~10- 6, through their gravitational interaction these Goldstone modes generate density perturbations of approximately the right magnitude to explain the cosmic microwave background (CMB) anisotropy and seed the structure seen in the universe today. In such a model non-Gaussian perturbations result because to lowest order density perturbations are sourced by products of Gaussian fields. We explore the issue of phase dispersion and conclude that this non-Gaussian model predicts Doppler peaks in the CMB anisotropy. Topological defects generated from quantum fluctuations during inflation are studied in chapter four. We present a calculation of the power spectrum generated in a classically symmetry-breaking O(N) scalar field through inflationary quantum fluctuations, using the large-N limit. The effective potential of the theory in de Sitter space is obtained from a gap equation which is exact at large N. Quantum fluctuations restore the O(N) symmetry in de Sitter space, but for the finite values of N of interest, there is symmetry breaking and phase ordering after inflation, described by the classical nonlinear sigma model. The scalar field power spectrum is obtained as a function of the scalar field self-coupling. In the second part of the thesis, we investigate non-Abelian topological worm-holes, obtained when winding number one texture field is coupled to Einstein gravity with a conserved global

Environmental projects. Volume 3: Environmental compliance audit

NASA Technical Reports Server (NTRS)

1987-01-01

The Goldstone Deep Space Communications Complex is part of NASA's Deep Space Network, one of the world's largest and most sensitive scientific telecommunications and radio navigation networks. Activities at Goldstone are carried out in support of six large parabolic dish antennas. In support of the national goal of the preservation of the environment and the protection of human health and safety, NASA, JPL and Goldstone have adopted a position that their operating installations shall maintain a high level of compliance with Federal, state, and local laws governing the management of hazardous substances, abestos, and underground storage tanks. A JPL version of a document prepared as an environmental audit of Goldstone operations is presented. Both general and specific items of noncompliance at Goldstone are identified and recommendations are provided for corrective actions.

Structural optimization with approximate sensitivities

NASA Technical Reports Server (NTRS)

Patnaik, S. N.; Hopkins, D. A.; Coroneos, R.

1994-01-01

Computational efficiency in structural optimization can be enhanced if the intensive computations associated with the calculation of the sensitivities, that is, gradients of the behavior constraints, are reduced. Approximation to gradients of the behavior constraints that can be generated with small amount of numerical calculations is proposed. Structural optimization with these approximate sensitivities produced correct optimum solution. Approximate gradients performed well for different nonlinear programming methods, such as the sequence of unconstrained minimization technique, method of feasible directions, sequence of quadratic programming, and sequence of linear programming. Structural optimization with approximate gradients can reduce by one third the CPU time that would otherwise be required to solve the problem with explicit closed-form gradients. The proposed gradient approximation shows potential to reduce intensive computation that has been associated with traditional structural optimization.

Bethe-Salpeter wave functions of ηc(1S, 2S) and ψ(1S, 2S) states: local-potential description of the charmonium system revisited

NASA Astrophysics Data System (ADS)

Nochi, Kazuki; Kawanai, Taichi; Sasaki, Shoichi

2018-03-01

The quark potential models with an energy-independent central potential have been successful for understanding the conventional charmonium states especially below the open charm threshold. As one might consider, however, the interquark potential is in general energy-dependent, and its tendency gets stronger in higher lying states. Confirmation of whether the interquark potential is energy-independent is also important to verify the validity of the quark potential models. In this talk, we examine the energy dependence of the charmonium potential, which can be determined from the Bethe-Salpeter (BS) amplitudes of cc̅ mesons in lattice QCD.We first calculate the BS amplitudes of radially excited charmonium states, the ηc(2S) and ψ(2S) states, using the variational method and then determine both the quark kinetic mass and the charmonium potential within the HAL QCD method. Through a direct comparison of charmonium potentials determined from both the 1S and 2S states, we confirm that neither the central nor spin-spin potential shows visible energy dependence at least up to 2S state.

Bounded-Degree Approximations of Stochastic Networks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Quinn, Christopher J.; Pinar, Ali; Kiyavash, Negar

2017-06-01

We propose algorithms to approximate directed information graphs. Directed information graphs are probabilistic graphical models that depict causal dependencies between stochastic processes in a network. The proposed algorithms identify optimal and near-optimal approximations in terms of Kullback-Leibler divergence. The user-chosen sparsity trades off the quality of the approximation against visual conciseness and computational tractability. One class of approximations contains graphs with speci ed in-degrees. Another class additionally requires that the graph is connected. For both classes, we propose algorithms to identify the optimal approximations and also near-optimal approximations, using a novel relaxation of submodularity. We also propose algorithms to identifymore » the r-best approximations among these classes, enabling robust decision making.« less

Limitations of shallow nets approximation.

PubMed

Lin, Shao-Bo

2017-10-01

In this paper, we aim at analyzing the approximation abilities of shallow networks in reproducing kernel Hilbert spaces (RKHSs). We prove that there is a probability measure such that the achievable lower bound for approximating by shallow nets can be realized for all functions in balls of reproducing kernel Hilbert space with high probability, which is different with the classical minimax approximation error estimates. This result together with the existing approximation results for deep nets shows the limitations for shallow nets and provides a theoretical explanation on why deep nets perform better than shallow nets. Copyright © 2017 Elsevier Ltd. All rights reserved.

More on approximations of Poisson probabilities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kao, C

1980-05-01

Calculation of Poisson probabilities frequently involves calculating high factorials, which becomes tedious and time-consuming with regular calculators. The usual way to overcome this difficulty has been to find approximations by making use of the table of the standard normal distribution. A new transformation proposed by Kao in 1978 appears to perform better for this purpose than traditional transformations. In the present paper several approximation methods are stated and compared numerically, including an approximation method that utilizes a modified version of Kao's transformation. An approximation based on a power transformation was found to outperform those based on the square-root type transformationsmore » as proposed in literature. The traditional Wilson-Hilferty approximation and Makabe-Morimura approximation are extremely poor compared with this approximation. 4 tables. (RWR)« less

Approximate circuits for increased reliability

DOE Office of Scientific and Technical Information (OSTI.GOV)

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 referencemore » 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.« less

Risk approximation in decision making: approximative numeric abilities predict advantageous decisions under objective risk.

PubMed

Mueller, Silke M; Schiebener, Johannes; Delazer, Margarete; Brand, Matthias

2018-01-22

Many decision situations in everyday life involve mathematical considerations. In decisions under objective risk, i.e., when explicit numeric information is available, executive functions and abilities to handle exact numbers and ratios are predictors of objectively advantageous choices. Although still debated, exact numeric abilities, e.g., normative calculation skills, are assumed to be related to approximate number processing skills. The current study investigates the effects of approximative numeric abilities on decision making under objective risk. Participants (N = 153) performed a paradigm measuring number-comparison, quantity-estimation, risk-estimation, and decision-making skills on the basis of rapid dot comparisons. Additionally, a risky decision-making task with exact numeric information was administered, as well as tasks measuring executive functions and exact numeric abilities, e.g., mental calculation and ratio processing skills, were conducted. Approximative numeric abilities significantly predicted advantageous decision making, even beyond the effects of executive functions and exact numeric skills. Especially being able to make accurate risk estimations seemed to contribute to superior choices. We recommend approximation skills and approximate number processing to be subject of future investigations on decision making under risk.

An energy-dependent electron backscattering coefficient

NASA Astrophysics Data System (ADS)

Williamson, W., Jr.; Antolak, A. J.; Meredith, R. J.

1987-05-01

An energy-dependent electron backscattering coefficient is derived based on the continuous slowing down approximation and the Bethe stopping power. Backscattering coefficients are given for 10-50-keV electrons incident on bulk and thin-film aluminum, silver, and gold targets. The results are compared with the Everhart theory and empirical fits to experimental data. The energy-dependent theory agrees better with experimental work.

Community Dynamics and Soil Seed Bank Ecology of Lane Mountain Milkvetch (Astragalus jaegerianus Munz)

DTIC Science & Technology

2012-08-01

concentrated in four geographic areas (Coolgardie Mesa, Paradise Valley, Brinkman Wash-Montana Mine , and the Gemini Conservation Area; Fig. 1) that total...data for 2003, and from 2007 through 2009 were generated by the remote automated weather station (RAWS) at Opal Mountain CA (35°09´N; 117°10´W; 980...m.). This weather station is approximately 30 km SW of UCLA’s milkvetch study sites. Opal Mountain and Goldstone monthly precipitation from 1992

Combining global and local approximations

NASA Technical Reports Server (NTRS)

Haftka, Raphael T.

1991-01-01

A method based on a linear approximation to a scaling factor, designated the 'global-local approximation' (GLA) method, is presented and shown capable of extending the range of usefulness of derivative-based approximations to a more refined model. The GLA approach refines the conventional scaling factor by means of a linearly varying, rather than constant, scaling factor. The capabilities of the method are demonstrated for a simple beam example with a crude and more refined FEM model.

Impact of the terrorist bombings of the Neve Shalom and Beth Israel Synagogues on a hospital in Istanbul, Turkey.

PubMed

Rodoplu, Ulkümen; Arnold, Jeffrey L; Tokyay, Rifat; Ersoy, Gurkan; Cetiner, Serkan; Yücel, Tayfun

2005-02-01

The authors sought to estimate the impact of the open-air mass-casualty terrorist bombings of the Neve Shalom and Beth Israel Synagogues in Istanbul, Turkey, on November 15, 2003, on the American Hospital (AH) in terms of resource utilization, epidemiologic outcomes, and time course of emergency needs. A retrospective descriptive study using data from hospital records of injured survivors who used the emergency department at AH on November 15, 2003, to determine the number and percentage of injured survivors who were hospitalized, received operative care, had specific injury types, had an Injury Severity Score >/=16, died, and arrived within certain time intervals. AH received 69 (91%) injured survivors from the scene, of which nine (12%) were hospitalized and three (4%) received operative care. Starting four hours after the initial blast, seven (9%) injured survivors were transferred to AH from other hospitals, of which five (7%) were hospitalized and four (5%) received operative care. Of the 49 injured survivors from the scene with documented injuries, 43 (88%) had injuries to the head or face, 42 (86%) had lacerations, five (10%) had fractures, one (2%) had a penetrating eye injury, one (2%) had a serious intracranial injury, and none had primary blast injuries. Four (5%) injured survivors at AH had an Injury Severity Score >/=16, and none died. Seventy-six injured survivors used the emergency department at AH, including a delayed wave of injured survivors transferred from other hospitals. The majority of injured survivors with documented injuries had non-life-threatening lacerations of the head or face, and relatively few injured survivors were hospitalized or received operative care.

Spline approximation, Part 1: Basic methodology

NASA Astrophysics Data System (ADS)

Ezhov, Nikolaj; Neitzel, Frank; Petrovic, Svetozar

2018-04-01

In engineering geodesy point clouds derived from terrestrial laser scanning or from photogrammetric approaches are almost never used as final results. For further processing and analysis a curve or surface approximation with a continuous mathematical function is required. In this paper the approximation of 2D curves by means of splines is treated. Splines offer quite flexible and elegant solutions for interpolation or approximation of "irregularly" distributed data. Depending on the problem they can be expressed as a function or as a set of equations that depend on some parameter. Many different types of splines can be used for spline approximation and all of them have certain advantages and disadvantages depending on the approximation problem. In a series of three articles spline approximation is presented from a geodetic point of view. In this paper (Part 1) the basic methodology of spline approximation is demonstrated using splines constructed from ordinary polynomials and splines constructed from truncated polynomials. In the forthcoming Part 2 the notion of B-spline will be explained in a unique way, namely by using the concept of convex combinations. The numerical stability of all spline approximation approaches as well as the utilization of splines for deformation detection will be investigated on numerical examples in Part 3.

Monotone Boolean approximation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hulme, B.L.

1982-12-01

This report presents a theory of approximation of arbitrary Boolean functions by simpler, monotone functions. Monotone increasing functions can be expressed without the use of complements. Nonconstant monotone increasing functions are important in their own right since they model a special class of systems known as coherent systems. It is shown here that when Boolean expressions for noncoherent systems become too large to treat exactly, then monotone approximations are easily defined. The algorithms proposed here not only provide simpler formulas but also produce best possible upper and lower monotone bounds for any Boolean function. This theory has practical application formore » the analysis of noncoherent fault trees and event tree sequences.« less

Testing approximations for non-linear gravitational clustering

NASA Technical Reports Server (NTRS)

Coles, Peter; Melott, Adrian L.; Shandarin, Sergei F.

1993-01-01

The accuracy of various analytic approximations for following the evolution of cosmological density fluctuations into the nonlinear regime is investigated. The Zel'dovich approximation is found to be consistently the best approximation scheme. It is extremely accurate for power spectra characterized by n = -1 or less; when the approximation is 'enhanced' by truncating highly nonlinear Fourier modes the approximation is excellent even for n = +1. The performance of linear theory is less spectrum-dependent, but this approximation is less accurate than the Zel'dovich one for all cases because of the failure to treat dynamics. The lognormal approximation generally provides a very poor fit to the spatial pattern.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Delacrétaz, Luca V.; Senatore, Leonardo; Noumi, Toshifumi, E-mail: lvd@stanford.edu, E-mail: tnoumi@phys.sci.kobe-u.ac.jp, E-mail: senatore@stanford.edu

If time-translations are spontaneously broken, so are boosts. This symmetry breaking pattern can be non-linearly realized by either just the Goldstone boson of time translations, or by four Goldstone bosons associated with time translations and boosts. In this paper we extend the Effective Field Theory of Multifield Inflation to consider the case in which the additional Goldstone bosons associated with boosts are light and coupled to the Goldstone boson of time translations. The symmetry breaking pattern forces a coupling to curvature so that the mass of the additional Goldstone bosons is predicted to be equal to √2 H in themore » vast majority of the parameter space where they are light. This pattern therefore offers a natural way of generating self-interacting particles with Hubble mass during inflation. After constructing the general effective Lagrangian, we study how these particles mix and interact with the curvature fluctuations, generating potentially detectable non-Gaussian signals.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Delacrétaz, Luca V.; Noumi, Toshifumi; Senatore, Leonardo

If time-translations are spontaneously broken, so are boosts. This symmetry breaking pattern can be non-linearly realized by either just the Goldstone boson of time translations, or by four Goldstone bosons associated with time translations and boosts. Here in this paper we extend the Effective Field Theory of Multifield Inflation to consider the case in which the additional Goldstone bosons associated with boosts are light and coupled to the Goldstone boson of time translations. The symmetry breaking pattern forces a coupling to curvature so that the mass of the additional Goldstone bosons is predicted to be equal to √2H in themore » vast majority of the parameter space where they are light. This pattern therefore offers a natural way of generating self-interacting particles with Hubble mass during inflation. After constructing the general effective Lagrangian, we study how these particles mix and interact with the curvature fluctuations, generating potentially detectable non-Gaussian signals.« less

Boost breaking in the EFT of inflation

DOE PAGES

Delacrétaz, Luca V.; Noumi, Toshifumi; Senatore, Leonardo

2017-02-17

If time-translations are spontaneously broken, so are boosts. This symmetry breaking pattern can be non-linearly realized by either just the Goldstone boson of time translations, or by four Goldstone bosons associated with time translations and boosts. Here in this paper we extend the Effective Field Theory of Multifield Inflation to consider the case in which the additional Goldstone bosons associated with boosts are light and coupled to the Goldstone boson of time translations. The symmetry breaking pattern forces a coupling to curvature so that the mass of the additional Goldstone bosons is predicted to be equal to √2H in themore » vast majority of the parameter space where they are light. This pattern therefore offers a natural way of generating self-interacting particles with Hubble mass during inflation. After constructing the general effective Lagrangian, we study how these particles mix and interact with the curvature fluctuations, generating potentially detectable non-Gaussian signals.« less

Analytical approximation schemes for solving exact renormalization group equations in the local potential approximation

NASA Astrophysics Data System (ADS)

Bervillier, C.; Boisseau, B.; Giacomini, H.

2008-02-01

The relation between the Wilson-Polchinski and the Litim optimized ERGEs in the local potential approximation is studied with high accuracy using two different analytical approaches based on a field expansion: a recently proposed genuine analytical approximation scheme to two-point boundary value problems of ordinary differential equations, and a new one based on approximating the solution by generalized hypergeometric functions. A comparison with the numerical results obtained with the shooting method is made. A similar accuracy is reached in each case. Both two methods appear to be more efficient than the usual field expansions frequently used in the current studies of ERGEs (in particular for the Wilson-Polchinski case in the study of which they fail).

Study of RE-garnets using BPW method

NASA Astrophysics Data System (ADS)

Goveas, Neena; Mukhopadhyay, P.; Mukhopadhyay, G.

1995-02-01

The magnetic susceptibility of rare-earth (Y and Lu) iron garnets is studied using a modified Bethe-Peierls-Weiss (BPW) approximation. The modifications enable us to incorporate the three exchange parameters Jad, Jaa and Jdd necessary to describe the systems. We get excellent fits to the experimental susceptibilities from which we determined the J-values. These also give excellent agreement with the spin wave dispersion relation constant D.

An Approximate Approach to Automatic Kernel Selection.

PubMed

Ding, Lizhong; Liao, Shizhong

2016-02-02

Kernel selection is a fundamental problem of kernel-based learning algorithms. In this paper, we propose an approximate approach to automatic kernel selection for regression from the perspective of kernel matrix approximation. We first introduce multilevel circulant matrices into automatic kernel selection, and develop two approximate kernel selection algorithms by exploiting the computational virtues of multilevel circulant matrices. The complexity of the proposed algorithms is quasi-linear in the number of data points. Then, we prove an approximation error bound to measure the effect of the approximation in kernel matrices by multilevel circulant matrices on the hypothesis and further show that the approximate hypothesis produced with multilevel circulant matrices converges to the accurate hypothesis produced with kernel matrices. Experimental evaluations on benchmark datasets demonstrate the effectiveness of approximate kernel selection.

Approximate error conjugation gradient minimization methods

DOEpatents

Kallman, Jeffrey S

2013-05-21

In one embodiment, a method includes selecting a subset of rays from a set of all rays to use in an error calculation for a constrained conjugate gradient minimization problem, calculating an approximate error using the subset of rays, and calculating a minimum in a conjugate gradient direction based on the approximate error. In another embodiment, a system includes a processor for executing logic, logic for selecting a subset of rays from a set of all rays to use in an error calculation for a constrained conjugate gradient minimization problem, logic for calculating an approximate error using the subset of rays, and logic for calculating a minimum in a conjugate gradient direction based on the approximate error. In other embodiments, computer program products, methods, and systems are described capable of using approximate error in constrained conjugate gradient minimization problems.

Topological approximation of the nonlinear Anderson model

NASA Astrophysics Data System (ADS)

Milovanov, Alexander V.; Iomin, Alexander

2014-06-01

We study the phenomena of Anderson localization in the presence of nonlinear interaction on a lattice. A class of nonlinear Schrödinger models with arbitrary power nonlinearity is analyzed. We conceive the various regimes of behavior, depending on the topology of resonance overlap in phase space, ranging from a fully developed chaos involving Lévy flights to pseudochaotic dynamics at the onset of delocalization. It is demonstrated that the quadratic nonlinearity plays a dynamically very distinguished role in that it is the only type of power nonlinearity permitting an abrupt localization-delocalization transition with unlimited spreading already at the delocalization border. We describe this localization-delocalization transition as a percolation transition on the infinite Cayley tree (Bethe lattice). It is found in the vicinity of the criticality that the spreading of the wave field is subdiffusive in the limit t →+∞. The second moment of the associated probability distribution grows with time as a power law ∝ tα, with the exponent α =1/3 exactly. Also we find for superquadratic nonlinearity that the analog pseudochaotic regime at the edge of chaos is self-controlling in that it has feedback on the topology of the structure on which the transport processes concentrate. Then the system automatically (without tuning of parameters) develops its percolation point. We classify this type of behavior in terms of self-organized criticality dynamics in Hilbert space. For subquadratic nonlinearities, the behavior is shown to be sensitive to the details of definition of the nonlinear term. A transport model is proposed based on modified nonlinearity, using the idea of "stripes" propagating the wave process to large distances. Theoretical investigations, presented here, are the basis for consistency analysis of the different localization-delocalization patterns in systems with many coupled degrees of freedom in association with the asymptotic properties of the

Macroscopic and microscopic components of exchange-correlation interactions

NASA Astrophysics Data System (ADS)

Sottile, F.; Karlsson, K.; Reining, L.; Aryasetiawan, F.

2003-11-01

We consider two commonly used approaches for the ab initio calculation of optical-absorption spectra, namely, many-body perturbation theory based on Green’s functions and time-dependent density-functional theory (TDDFT). The former leads to the two-particle Bethe-Salpeter equation that contains a screened electron-hole interaction. We approximate this interaction in various ways, and discuss in particular the results obtained for a local contact potential. This, in fact, allows us to straightforwardly make the link to the TDDFT approach, and to discuss the exchange-correlation kernel fxc that corresponds to the contact exciton. Our main results, illustrated in the examples of bulk silicon, GaAs, argon, and LiF, are the following. (i) The simple contact exciton model, used on top of an ab initio calculated band structure, yields reasonable absorption spectra. (ii) Qualitatively extremely different fxc can be derived approximatively from the same Bethe-Salpeter equation. These kernels can however yield very similar spectra. (iii) A static fxc, both with or without a long-range component, can create transitions in the quasiparticle gap. To the best of our knowledge, this is the first time that TDDFT has been shown to be able to reproduce bound excitons.

Applied Routh approximation

NASA Technical Reports Server (NTRS)

Merrill, W. C.

1978-01-01

The Routh approximation technique for reducing the complexity of system models was applied in the frequency domain to a 16th order, state variable model of the F100 engine and to a 43d order, transfer function model of a launch vehicle boost pump pressure regulator. The results motivate extending the frequency domain formulation of the Routh method to the time domain in order to handle the state variable formulation directly. The time domain formulation was derived and a characterization that specifies all possible Routh similarity transformations was given. The characterization was computed by solving two eigenvalue-eigenvector problems. The application of the time domain Routh technique to the state variable engine model is described, and some results are given. Additional computational problems are discussed, including an optimization procedure that can improve the approximation accuracy by taking advantage of the transformation characterization.

Analysis of corrections to the eikonal approximation

NASA Astrophysics Data System (ADS)

Hebborn, C.; Capel, P.

2017-11-01

Various corrections to the eikonal approximations are studied for two- and three-body nuclear collisions with the goal to extend the range of validity of this approximation to beam energies of 10 MeV/nucleon. Wallace's correction does not improve much the elastic-scattering cross sections obtained at the usual eikonal approximation. On the contrary, a semiclassical approximation that substitutes the impact parameter by a complex distance of closest approach computed with the projectile-target optical potential efficiently corrects the eikonal approximation. This opens the possibility to analyze data measured down to 10 MeV/nucleon within eikonal-like reaction models.

Approximations of Two-Attribute Utility Functions

DTIC Science & Technology

1976-09-01

preferred to") be a bina-zy relation on the set • of simple probability measures or ’gambles’ defined on a set T of consequences. Throughout this study it...simplifying independence assumptions. Although there are several approaches to this problem, the21 present study will focus on approximations of u... study will elicit additional interest in the topic. 2. REMARKS ON APPROXIMATION THEORY This section outlines a few basic ideas of approximation theory

Quantum criticality in the spin-1/2 Heisenberg chain system copper pyrazine dinitrate

PubMed Central

Breunig, Oliver; Garst, Markus; Klümper, Andreas; Rohrkamp, Jens; Turnbull, Mark M.; Lorenz, Thomas

2017-01-01

Low-dimensional quantum magnets promote strong correlations between magnetic moments that lead to fascinating quantum phenomena. A particularly interesting system is the antiferromagnetic spin-1/2 Heisenberg chain because it is exactly solvable by the Bethe-Ansatz method. It is approximately realized in the magnetic insulator copper pyrazine dinitrate, providing a unique opportunity for a quantitative comparison between theory and experiment. We investigate its thermodynamic properties with a particular focus on the field-induced quantum phase transition. Thermal expansion, magnetostriction, specific heat, magnetization, and magnetocaloric measurements are found to be in excellent agreement with exact Bethe-Ansatz predictions. Close to the critical field, thermodynamics obeys the expected quantum critical scaling behavior, and in particular, the magnetocaloric effect and the Grüneisen parameters diverge in a characteristic manner. Beyond its importance for quantum magnetism, our study establishes a paradigm of a quantum phase transition, which illustrates fundamental principles of quantum critical thermodynamics. PMID:29282449

The {{\\rm{D}}\\bar{{\\rm{D}}}}^{{\\rm{* }}} interaction with isospin zero in an extended hidden gauge symmetry approach

NASA Astrophysics Data System (ADS)

Sun, Bao-Xi; Wan, Da-Ming; Zhao, Si-Yu

2018-05-01

The {{{D}}\\bar{{{D}}}}{{* }} interaction via a ρ or ω exchange is constructed within an extended hidden gauge symmetry approach, where the strange quark is replaced by the charm quark in the SU(3) flavor space. With this {{{D}}\\bar{{{D}}}}{{* }} interaction, a bound state slightly lower than the {{{D}}\\bar{{{D}}}}{{* }} threshold is generated dynamically in the isospin zero sector by solving the Bethe-Salpeter equation in the coupled-channel approximation, which might correspond to the X(3872) particle announced by many collaborations. This formulism is also used to study the {{{B}}\\bar{{{B}}}}{{* }} interaction, and a {{{B}}\\bar{{{B}}}}{{* }} bound state with isospin zero is generated dynamically, which has no counterpart listed in the review of the Particle Data Group. Furthermore, the one-pion exchange between the D meson and the {\\bar{{{D}}}}{{* }} is analyzed precisely, and we do not think the one-pion exchange potential need be considered when the Bethe-Salpeter equation is solved.

Spin Hartree-Fock approach to studying quantum Heisenberg antiferromagnets in low dimensions

NASA Astrophysics Data System (ADS)

Werth, A.; Kopietz, P.; Tsyplyatyev, O.

2018-05-01

We construct a new mean-field theory for a quantum (spin-1/2) Heisenberg antiferromagnet in one (1D) and two (2D) dimensions using a Hartree-Fock decoupling of the four-point correlation functions. We show that the solution to the self-consistency equations based on two-point correlation functions does not produce any unphysical finite-temperature phase transition, in accord with the Mermin-Wagner theorem, unlike the common approach based on the mean-field equation for the order parameter. The next-neighbor spin-spin correlation functions, calculated within this approach, reproduce closely the strong renormalization by quantum fluctuations obtained via a Bethe ansatz in 1D and a small renormalization of the classical antiferromagnetic state in 2D. The heat capacity approximates with reasonable accuracy the full Bethe ansatz result at all temperatures in 1D. In 2D, we obtain a reduction of the peak height in the heat capacity at a finite temperature that is accessible by high-order 1 /T expansions.

Statistical analysis of loopy belief propagation in random fields

NASA Astrophysics Data System (ADS)

Yasuda, Muneki; Kataoka, Shun; Tanaka, Kazuyuki

2015-10-01

Loopy belief propagation (LBP), which is equivalent to the Bethe approximation in statistical mechanics, is a message-passing-type inference method that is widely used to analyze systems based on Markov random fields (MRFs). In this paper, we propose a message-passing-type method to analytically evaluate the quenched average of LBP in random fields by using the replica cluster variation method. The proposed analytical method is applicable to general pairwise MRFs with random fields whose distributions differ from each other and can give the quenched averages of the Bethe free energies over random fields, which are consistent with numerical results. The order of its computational cost is equivalent to that of standard LBP. In the latter part of this paper, we describe the application of the proposed method to Bayesian image restoration, in which we observed that our theoretical results are in good agreement with the numerical results for natural images.

Born approximation in linear-time invariant system

NASA Astrophysics Data System (ADS)

Gumjudpai, Burin

2017-09-01

An alternative way of finding the LTI’s solution with the Born approximation, is investigated. We use Born approximation in the LTI and in the transformed LTI in form of Helmholtz equation. General solution are considered as infinite series or Feynman graph. Slow-roll approximation are explored. Transforming the LTI system into Helmholtz equation, approximated general solution can be found for any given forms of force with its initial value.

Approximate Model of Zone Sedimentation

NASA Astrophysics Data System (ADS)

Dzianik, František

2011-12-01

The process of zone sedimentation is affected by many factors that are not possible to express analytically. For this reason, the zone settling is evaluated in practice experimentally or by application of an empirical mathematical description of the process. The paper presents the development of approximate model of zone settling, i.e. the general function which should properly approximate the behaviour of the settling process within its entire range and at the various conditions. Furthermore, the specification of the model parameters by the regression analysis of settling test results is shown. The suitability of the model is reviewed by graphical dependencies and by statistical coefficients of correlation. The approximate model could by also useful on the simplification of process design of continual settling tanks and thickeners.

Energy conservation - A test for scattering approximations

NASA Technical Reports Server (NTRS)

Acquista, C.; Holland, A. C.

1980-01-01

The roles of the extinction theorem and energy conservation in obtaining the scattering and absorption cross sections for several light scattering approximations are explored. It is shown that the Rayleigh, Rayleigh-Gans, anomalous diffraction, geometrical optics, and Shifrin approximations all lead to reasonable values of the cross sections, while the modified Mie approximation does not. Further examination of the modified Mie approximation for the ensembles of nonspherical particles reveals additional problems with that method.

Recognition of computerized facial approximations by familiar assessors.

PubMed

Richard, Adam H; Monson, Keith L

2017-11-01

Studies testing the effectiveness of facial approximations typically involve groups of participants who are unfamiliar with the approximated individual(s). This limitation requires the use of photograph arrays including a picture of the subject for comparison to the facial approximation. While this practice is often necessary due to the difficulty in obtaining a group of assessors who are familiar with the approximated subject, it may not accurately simulate the thought process of the target audience (friends and family members) in comparing a mental image of the approximated subject to the facial approximation. As part of a larger process to evaluate the effectiveness and best implementation of the ReFace facial approximation software program, the rare opportunity arose to conduct a recognition study using assessors who were personally acquainted with the subjects of the approximations. ReFace facial approximations were generated based on preexisting medical scans, and co-workers of the scan donors were tested on whether they could accurately pick out the approximation of their colleague from arrays of facial approximations. Results from the study demonstrated an overall poor recognition performance (i.e., where a single choice within a pool is not enforced) for individuals who were familiar with the approximated subjects. Out of 220 recognition tests only 10.5% resulted in the assessor selecting the correct approximation (or correctly choosing not to make a selection when the array consisted only of foils), an outcome that was not significantly different from the 9% random chance rate. When allowed to select multiple approximations the assessors felt resembled the target individual, the overall sensitivity for ReFace approximations was 16.0% and the overall specificity was 81.8%. These results differ markedly from the results of a previous study using assessors who were unfamiliar with the approximated subjects. Some possible explanations for this disparity in

Consistent Yokoya-Chen Approximation to Beamstrahlung(LCC-0010)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Peskin, M

2004-04-22

I reconsider the Yokoya-Chen approximate evolution equation for beamstrahlung and modify it slightly to generate simple, consistent analytical approximations for the electron and photon energy spectra. I compare these approximations to previous ones, and to simulation data.I reconsider the Yokoya-Chen approximate evolution equation for beamstrahlung and modify it slightly to generate simple, consistent analytical approximations for the electron and photon energy spectra. I compare these approximations to previous ones, and to simulation data.

The Shape of Near-Earth Asteroid 275677 (2000 RS11) From Inversion of Arecibo and Goldstone Radar Images

NASA Astrophysics Data System (ADS)

Brauer, Kaley; Busch, Michael W.; Benner, Lance A. M.; Brozovic, Marina; Howell, Ellen S.; Nolan, Michael C.; Springmann, Alessondra; Giorgini, Jon D.; Taylor, Patrick A.; Jao, Joseph S.

2015-11-01

We observed near-Earth asteroid 2000 RS11 with the Arecibo and Goldstone planetary radars during a 0.035 au approach in March 2014, obtaining delay-Doppler images between March 13 and March 17. The finest-resolution images have range resolution of 7.5 m/pixel and show that RS11 is a contact binary with complex topography. We used the SHAPE software package (Magri et al., Icarus 186, 156-160 2007) to create a physical model of RS11 and its spin state from these delay-Doppler images.The rotation period of RS11 is well constrained from optical lightcurves, P = 4.444 ± 0.001 h (Warner et al., Minor Planet Bulletin 41, 160; 2014 and Benishek, Minor Planet Bulletin 41, 257; 2014). We found two possible pole directions and corresponding shape models, mirror images of one another, which provide equally good fits to the radar data. RS11’s pole direction is either (λ , β) = (155°, 30°) ± 10° or (335°, -30°) ± 10° in J2000 ecliptic coordinates. The most likely pole directions of RS11 are not aligned with the heliocentric orbit normal and instead have an obliquity within 10° of 56° or 124°.Our best-fit shape models are 1400-vertex polyhedra comprising two lobes in contact. The lengths of RS11’s principal axes are 698 ± 71 m, 578 ± 59 m, and 758 ± 77 m. RS11 has a volume of 0.086 ± 0.026 km^3. The long axis of RS11’s larger lobe is 751 ± 77 m and the long axis of the smaller lobe is 398 ± 41 m; the volume ratio between these lobes is roughly 2.7 ± 10%. Spectral data informs us that RS11 is an S-class object (Lazzarin et al., Icarus 169, 379; 2004).RS11's shape is unusual compared with those of other contact binary NEAs imaged by radar. Its larger lobe is flattened. Additionally, while the neck between the smaller and larger lobes of most contact binaries is located near the larger lobe's longest principal axis (such as in the cases of 25143 Itokawa and 4179 Toutatis), RS11's neck is near its larger lobe's shortest principal axis. RS11 is the first

Exponential approximations in optimal design

NASA Technical Reports Server (NTRS)

Belegundu, A. D.; Rajan, S. D.; Rajgopal, J.

1990-01-01

One-point and two-point exponential functions have been developed and proved to be very effective approximations of structural response. The exponential has been compared to the linear, reciprocal and quadratic fit methods. Four test problems in structural analysis have been selected. The use of such approximations is attractive in structural optimization to reduce the numbers of exact analyses which involve computationally expensive finite element analysis.

Combination of the pair density approximation and the Takahashi–Imada approximation for path integral Monte Carlo simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zillich, Robert E., E-mail: robert.zillich@jku.at

2015-11-15

We construct an accurate imaginary time propagator for path integral Monte Carlo simulations for heterogeneous systems consisting of a mixture of atoms and molecules. We combine the pair density approximation, which is highly accurate but feasible only for the isotropic interactions between atoms, with the Takahashi–Imada approximation for general interactions. We present finite temperature simulations results for energy and structure of molecules–helium clusters X{sup 4}He{sub 20} (X=HCCH and LiH) which show a marked improvement over the Trotter approximation which has a 2nd-order time step bias. We show that the 4th-order corrections of the Takahashi–Imada approximation can also be applied perturbativelymore » to a 2nd-order simulation.« less

Better approximation guarantees for job-shop scheduling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Goldberg, L.A.; Paterson, M.; Srinivasan, A.

1997-06-01

Job-shop scheduling is a classical NP-hard problem. Shmoys, Stein & Wein presented the first polynomial-time approximation algorithm for this problem that has a good (polylogarithmic) approximation guarantee. We improve the approximation guarantee of their work, and present further improvements for some important NP-hard special cases of this problem (e.g., in the preemptive case where machines can suspend work on operations and later resume). We also present NC algorithms with improved approximation guarantees for some NP-hard special cases.

Modeling of LEO Orbital Debris Populations in Centimeter and Millimeter Size Regimes

NASA Technical Reports Server (NTRS)

Xu, Y.-L.; Hill, . M.; Horstman, M.; Krisko, P. H.; Liou, J.-C.; Matney, M.; Stansbery, E. G.

2010-01-01

The building of the NASA Orbital Debris Engineering Model, whether ORDEM2000 or its recently updated version ORDEM2010, uses as its foundation a number of model debris populations, each truncated at a minimum object-size ranging from 10 micron to 1 m. This paper discusses the development of the ORDEM2010 model debris populations in LEO (low Earth orbit), focusing on centimeter (smaller than 10 cm) and millimeter size regimes. Primary data sets used in the statistical derivation of the cm- and mm-size model populations are from the Haystack radar operated in a staring mode. Unlike cataloged objects of sizes greater than approximately 10 cm, ground-based radars monitor smaller-size debris only in a statistical manner instead of tracking every piece. The mono-static Haystack radar can detect debris as small as approximately 5 mm at moderate LEO altitudes. Estimation of millimeter debris populations (for objects smaller than approximately 6 mm) rests largely on Goldstone radar measurements. The bi-static Goldstone radar can detect 2- to 3-mm objects. The modeling of the cm- and mm-debris populations follows the general approach to developing other ORDEM2010-required model populations for various components and types of debris. It relies on appropriate reference populations to provide necessary prior information on the orbital structures and other important characteristics of the debris objects. NASA's LEO-to-GEO Environment Debris (LEGEND) model is capable of furnishing such reference populations in the desired size range. A Bayesian statistical inference process, commonly adopted in ORDEM2010 model-population derivations, changes a priori distribution into a posteriori distribution and thus refines the reference populations in terms of data. This paper describes key elements and major steps in the statistical derivations of the cm- and mm-size debris populations and presents results. Due to lack of data for near 1-mm sizes, the model populations of 1- to 3.16-mm

Linear Approximation SAR Azimuth Processing Study

NASA Technical Reports Server (NTRS)

Lindquist, R. B.; Masnaghetti, R. K.; Belland, E.; Hance, H. V.; Weis, W. G.

1979-01-01

A segmented linear approximation of the quadratic phase function that is used to focus the synthetic antenna of a SAR was studied. Ideal focusing, using a quadratic varying phase focusing function during the time radar target histories are gathered, requires a large number of complex multiplications. These can be largely eliminated by using linear approximation techniques. The result is a reduced processor size and chip count relative to ideally focussed processing and a correspondingly increased feasibility for spaceworthy implementation. A preliminary design and sizing for a spaceworthy linear approximation SAR azimuth processor meeting requirements similar to those of the SEASAT-A SAR was developed. The study resulted in a design with approximately 1500 IC's, 1.2 cubic feet of volume, and 350 watts of power for a single look, 4000 range cell azimuth processor with 25 meters resolution.

Chemical Laws, Idealization and Approximation

NASA Astrophysics Data System (ADS)

Tobin, Emma

2013-07-01

This paper examines the notion of laws in chemistry. Vihalemm ( Found Chem 5(1):7-22, 2003) argues that the laws of chemistry are fundamentally the same as the laws of physics they are all ceteris paribus laws which are true "in ideal conditions". In contrast, Scerri (2000) contends that the laws of chemistry are fundamentally different to the laws of physics, because they involve approximations. Christie ( Stud Hist Philos Sci 25:613-629, 1994) and Christie and Christie ( Of minds and molecules. Oxford University Press, New York, pp. 34-50, 2000) agree that the laws of chemistry are operationally different to the laws of physics, but claim that the distinction between exact and approximate laws is too simplistic to taxonomise them. Approximations in chemistry involve diverse kinds of activity and often what counts as a scientific law in chemistry is dictated by the context of its use in scientific practice. This paper addresses the question of what makes chemical laws distinctive independently of the separate question as to how they are related to the laws of physics. From an analysis of some candidate ceteris paribus laws in chemistry, this paper argues that there are two distinct kinds of ceteris paribus laws in chemistry; idealized and approximate chemical laws. Thus, while Christie ( Stud Hist Philos Sci 25:613-629, 1994) and Christie and Christie ( Of minds and molecules. Oxford University Press, New York, pp. 34--50, 2000) are correct to point out that the candidate generalisations in chemistry are diverse and heterogeneous, a distinction between idealizations and approximations can nevertheless be used to successfully taxonomise them.

On Nash-Equilibria of Approximation-Stable Games

NASA Astrophysics Data System (ADS)

Awasthi, Pranjal; Balcan, Maria-Florina; Blum, Avrim; Sheffet, Or; Vempala, Santosh

One reason for wanting to compute an (approximate) Nash equilibrium of a game is to predict how players will play. However, if the game has multiple equilibria that are far apart, or ɛ-equilibria that are far in variation distance from the true Nash equilibrium strategies, then this prediction may not be possible even in principle. Motivated by this consideration, in this paper we define the notion of games that are approximation stable, meaning that all ɛ-approximate equilibria are contained inside a small ball of radius Δ around a true equilibrium, and investigate a number of their properties. Many natural small games such as matching pennies and rock-paper-scissors are indeed approximation stable. We show furthermore there exist 2-player n-by-n approximation-stable games in which the Nash equilibrium and all approximate equilibria have support Ω(log n). On the other hand, we show all (ɛ,Δ) approximation-stable games must have an ɛ-equilibrium of support O(Δ^{2-o(1)}/ɛ2{log n}), yielding an immediate n^{O(Δ^{2-o(1)}/ɛ^2log n)}-time algorithm, improving over the bound of [11] for games satisfying this condition. We in addition give a polynomial-time algorithm for the case that Δ and ɛ are sufficiently close together. We also consider an inverse property, namely that all non-approximate equilibria are far from some true equilibrium, and give an efficient algorithm for games satisfying that condition.

Nuclear force from lattice QCD.

PubMed

Ishii, N; Aoki, S; Hatsuda, T

2007-07-13

The nucleon-nucleon (NN) potential is studied by lattice QCD simulations in the quenched approximation, using the plaquette gauge action and the Wilson quark action on a 32(4) [approximately (4.4 fm)(4)] lattice. A NN potential V(NN)(r) is defined from the equal-time Bethe-Salpeter amplitude with a local interpolating operator for the nucleon. By studying the NN interaction in the (1)S(0) and (3)S(1) channels, we show that the central part of V(NN)(r) has a strong repulsive core of a few hundred MeV at short distances (r approximately < 0.5 fm) surrounded by an attractive well at medium and long distances. These features are consistent with the known phenomenological features of the nuclear force.

Legendre-tau approximations for functional differential equations

NASA Technical Reports Server (NTRS)

Ito, K.; Teglas, R.

1986-01-01

The numerical approximation of solutions to linear retarded functional differential equations are considered using the so-called Legendre-tau method. The functional differential equation is first reformulated as a partial differential equation with a nonlocal boundary condition involving time-differentiation. The approximate solution is then represented as a truncated Legendre series with time-varying coefficients which satisfy a certain system of ordinary differential equations. The method is very easy to code and yields very accurate approximations. Convergence is established, various numerical examples are presented, and comparison between the latter and cubic spline approximation is made.

Legendre-Tau approximations for functional differential equations

NASA Technical Reports Server (NTRS)

Ito, K.; Teglas, R.

1983-01-01

The numerical approximation of solutions to linear functional differential equations are considered using the so called Legendre tau method. The functional differential equation is first reformulated as a partial differential equation with a nonlocal boundary condition involving time differentiation. The approximate solution is then represented as a truncated Legendre series with time varying coefficients which satisfy a certain system of ordinary differential equations. The method is very easy to code and yields very accurate approximations. Convergence is established, various numerical examples are presented, and comparison between the latter and cubic spline approximations is made.

Piecewise linear approximation for hereditary control problems

NASA Technical Reports Server (NTRS)

Propst, Georg

1987-01-01

Finite dimensional approximations are presented for linear retarded functional differential equations by use of discontinuous piecewise linear functions. The approximation scheme is applied to optimal control problems when a quadratic cost integral has to be minimized subject to the controlled retarded system. It is shown that the approximate optimal feedback operators converge to the true ones both in case the cost integral ranges over a finite time interval as well as in the case it ranges over an infinite time interval. The arguments in the latter case rely on the fact that the piecewise linear approximations to stable systems are stable in a uniform sense. This feature is established using a vector-component stability criterion in the state space R(n) x L(2) and the favorable eigenvalue behavior of the piecewise linear approximations.

Approximation concepts for efficient structural synthesis

NASA Technical Reports Server (NTRS)

Schmit, L. A., Jr.; Miura, H.

1976-01-01

It is shown that efficient structural synthesis capabilities can be created by using approximation concepts to mesh finite element structural analysis methods with nonlinear mathematical programming techniques. The history of the application of mathematical programming techniques to structural design optimization problems is reviewed. Several rather general approximation concepts are described along with the technical foundations of the ACCESS 1 computer program, which implements several approximation concepts. A substantial collection of structural design problems involving truss and idealized wing structures is presented. It is concluded that since the basic ideas employed in creating the ACCESS 1 program are rather general, its successful development supports the contention that the introduction of approximation concepts will lead to the emergence of a new generation of practical and efficient, large scale, structural synthesis capabilities in which finite element analysis methods and mathematical programming algorithms will play a central role.

Coherent-Anomaly Method in Critical Phenomena. IV. Study of the Wave-Number-Dependent Susceptibility in the 2D Ising Model

NASA Astrophysics Data System (ADS)

Hu, Xiao; Suzuki, Masuo

1988-03-01

The systematic Weiss-like and Bethe-like approximations based on the mean-field transfer-matrix method are used to investigate the asymptotic behavior of the induced magnetization on a semi-infinite square lattice, and to investigate the wave-number dependence of the susceptibility in a nonuniform external field. The critical exponents ν, ν', ηi and η are estimated following the general CAM prescription. A new scaling relation ν{\\cdot}ηi{=}β is obtained in the framework of the finite-degree-of-approximation scaling. Together with previous papers, all the static critical exponents have been estimated by the CAM, and are shown to satisfy the well-known scaling relations.

Coherent-Anomaly Method in Critical Phenomena. IV.

NASA Astrophysics Data System (ADS)

Hu, Xiao; Suzuki, Masuo

The systematic Weiss-like and Bethe-like approximations based on the mean-field transfer-matrix method are used to investigate the asymptotic behavior of the induced magnetization on a semi-infinite square lattice, and to investigate the wave-number dependence of the susceptibility in a nonuniform external field. The critical exponents ν, ν', ηi and η are estimated following the general CAM prescription. A new scaling relation ν·ηi=β is obtained in the framework of the finite-degree-of-approximation scaling. Together with previous papers, all the static critical exponents have been estimated by the CAM, and are shown to satisfy the well-known scaling relations.

Approximations of e and ?: An Exploration

ERIC Educational Resources Information Center

Brown, Philip R.

2017-01-01

Fractional approximations of e and p are discovered by searching for repetitions or partial repetitions of digit strings in their expansions in different number bases. The discovery of such fractional approximations is suggested for students and teachers as an entry point into mathematics research.

Topics in Multivariate Approximation Theory.

DTIC Science & Technology

1982-05-01

once that a continuous function f can be approximated from Sa :o span (N3 )B63 to within *(f, 131 ), with 13 t- sup3 e3 dian PS The simple approximation...N(C) 3- U P s P3AC 0 0 ) . Then, as in Lebesgue’s inequality, we could conclude that f - Qf - f-p - Q(f-p) , for all p e k k therefore I(f-0f) JCI 4 I

Approximation methods for combined thermal/structural design

NASA Technical Reports Server (NTRS)

Haftka, R. T.; Shore, C. P.

1979-01-01

Two approximation concepts for combined thermal/structural design are evaluated. The first concept is an approximate thermal analysis based on the first derivatives of structural temperatures with respect to design variables. Two commonly used first-order Taylor series expansions are examined. The direct and reciprocal expansions are special members of a general family of approximations, and for some conditions other members of that family of approximations are more accurate. Several examples are used to compare the accuracy of the different expansions. The second approximation concept is the use of critical time points for combined thermal and stress analyses of structures with transient loading conditions. Significant time savings are realized by identifying critical time points and performing the stress analysis for those points only. The design of an insulated panel which is exposed to transient heating conditions is discussed.

Goldstone radar imaging of near-Earth asteroids (469896) 2007 WV4, 2014 JO25, 2017 BQ6, and 2017 CS

NASA Astrophysics Data System (ADS)

Naidu, S.; Benner, L.; Brozovic, M.; Giorgini, J. D.; Busch, M.; Jao, J. S.; Lee, C. G.; Snedeker, L. G.; Silva, M. A.; Slade, M. A.; Lawrence, K. J.

2017-12-01

We present Goldstone radar imaging of four near-Earth asteroids during Feb-Jun 2017. The signal-to-noise ratios were very strong for each object and we obtained detailed images with range resolutions as fine as 3.75 m/pixel. 2017 BQ6 was discovered on Jan 26 and approached Earth within 6.5 lunar distances on Feb 7. Radar images show that it is a strikingly angular object roughly 200 m in diameter with a rotation period of 3 h. Its multi-faceted shape challenges the expectation that it is a rubble pile. 2017 CS was discovered on Feb 2 and approached within 8 lunar distances on May 29. It appears rounded on large scales but has considerable fine-scale topography evident along its leading edges. The images suggest a diameter of 1 km and a spin period consistent with the 40 h period obtained from photometry by P. Pravec (pers. comm.). The highest resolution images show evidence for meter-size boulders, ridges, and broad concavities. 2007 WV4 was imaged in late May and early June, has a diameter of 900 meters, and appears distinctly angular with at least three large facets > 100 m in extent. Tracking of features in the images gives a rotation period of about 12 hours. 2014 JO25 approached within 4.6 lunar distances on April 19. This was the closest encounter by an asteroid with an absolute magnitude brighter than 18 known in advance until 2027, when 1999 AN10 will approach within one lunar distance. Radar imaging shows that 2014 JO25 is an irregular object, consisting of two components connected by a narrow neck. The asteroid has pole on dimensions of roughly 1 x 0.6 km in the images. Imaging with 3.75 m/pixel resolution places thousands of pixels on the object and reveals ridges, concavities, flat regions up to 200 meters long, and radar-bright spots suggestive of boulders. Tracking of features in the images yields a rotation period of about 4.5 hours that is among the fastest of the 50 known contact binaries in the near-Earth population.

A result about scale transformation families in approximation

NASA Astrophysics Data System (ADS)

Apprato, Dominique; Gout, Christian

2000-06-01

Scale transformations are common in approximation. In surface approximation from rapidly varying data, one wants to suppress, or at least dampen the oscillations of the approximation near steep gradients implied by the data. In that case, scale transformations can be used to give some control over overshoot when the surface has large variations of its gradient. Conversely, in image analysis, scale transformations are used in preprocessing to enhance some features present on the image or to increase jumps of grey levels before segmentation of the image. In this paper, we establish the convergence of an approximation method which allows some control over the behavior of the approximation. More precisely, we study the convergence of an approximation from a data set of , while using scale transformations on the values before and after classical approximation. In addition, the construction of scale transformations is also given. The algorithm is presented with some numerical examples.

Quirks of Stirling's Approximation

ERIC Educational Resources Information Center

Macrae, Roderick M.; Allgeier, Benjamin M.

2013-01-01

Stirling's approximation to ln "n"! is typically introduced to physical chemistry students as a step in the derivation of the statistical expression for the entropy. However, naive application of this approximation leads to incorrect conclusions. In this article, the problem is first illustrated using a familiar "toy…

Approximations to camera sensor noise

NASA Astrophysics Data System (ADS)

Jin, Xiaodan; Hirakawa, Keigo

2013-02-01

Noise is present in all image sensor data. Poisson distribution is said to model the stochastic nature of the photon arrival process, while it is common to approximate readout/thermal noise by additive white Gaussian noise (AWGN). Other sources of signal-dependent noise such as Fano and quantization also contribute to the overall noise profile. Question remains, however, about how best to model the combined sensor noise. Though additive Gaussian noise with signal-dependent noise variance (SD-AWGN) and Poisson corruption are two widely used models to approximate the actual sensor noise distribution, the justification given to these types of models are based on limited evidence. The goal of this paper is to provide a more comprehensive characterization of random noise. We concluded by presenting concrete evidence that Poisson model is a better approximation to real camera model than SD-AWGN. We suggest further modification to Poisson that may improve the noise model.

Approximate techniques of structural reanalysis

NASA Technical Reports Server (NTRS)

Noor, A. K.; Lowder, H. E.

1974-01-01

A study is made of two approximate techniques for structural reanalysis. These include Taylor series expansions for response variables in terms of design variables and the reduced-basis method. In addition, modifications to these techniques are proposed to overcome some of their major drawbacks. The modifications include a rational approach to the selection of the reduced-basis vectors and the use of Taylor series approximation in an iterative process. For the reduced basis a normalized set of vectors is chosen which consists of the original analyzed design and the first-order sensitivity analysis vectors. The use of the Taylor series approximation as a first (initial) estimate in an iterative process, can lead to significant improvements in accuracy, even with one iteration cycle. Therefore, the range of applicability of the reanalysis technique can be extended. Numerical examples are presented which demonstrate the gain in accuracy obtained by using the proposed modification techniques, for a wide range of variations in the design variables.

Effect of ladder diagrams on optical absorption spectra in a quasiparticle self-consistent GW framework

NASA Astrophysics Data System (ADS)

Cunningham, Brian; Grüning, Myrta; Azarhoosh, Pooya; Pashov, Dimitar; van Schilfgaarde, Mark

2018-03-01

We present an approach to calculate the optical absorption spectra that combines the quasiparticle self-consistent GW method [Phys. Rev. B 76, 165106 (2007), 10.1103/PhysRevB.76.165106] for the electronic structure with the solution of the ladder approximation to the Bethe-Salpeter equation for the macroscopic dielectric function. The solution of the Bethe-Salpeter equation has been implemented within an all-electron framework, using a linear muffin-tin orbital basis set, with the contribution from the nonlocal self-energy to the transition dipole moments (in the optical limit) evaluated explicitly. This approach addresses those systems whose electronic structure is poorly described within the standard perturbative GW approaches with density-functional theory calculations as a starting point. The merits of this approach have been exemplified by calculating optical absorption spectra of a strongly correlated transition metal oxide, NiO, and a narrow gap semiconductor, Ge. In both cases, the calculated spectrum is in good agreement with the experiment. It is also shown that for systems whose electronic structure is well-described within the standard perturbative GW , such as Si, LiF, and h -BN , the performance of the present approach is in general comparable to the standard GW plus Bethe-Salpeter equation. It is argued that both vertex corrections to the electronic screening and the electron-phonon interaction are responsible for the observed systematic overestimation of the fundamental band gap and spectrum onset.

Approximate Bayesian evaluations of measurement uncertainty

NASA Astrophysics Data System (ADS)

Possolo, Antonio; Bodnar, Olha

2018-04-01

The Guide to the Expression of Uncertainty in Measurement (GUM) includes formulas that produce an estimate of a scalar output quantity that is a function of several input quantities, and an approximate evaluation of the associated standard uncertainty. This contribution presents approximate, Bayesian counterparts of those formulas for the case where the output quantity is a parameter of the joint probability distribution of the input quantities, also taking into account any information about the value of the output quantity available prior to measurement expressed in the form of a probability distribution on the set of possible values for the measurand. The approximate Bayesian estimates and uncertainty evaluations that we present have a long history and illustrious pedigree, and provide sufficiently accurate approximations in many applications, yet are very easy to implement in practice. Differently from exact Bayesian estimates, which involve either (analytical or numerical) integrations, or Markov Chain Monte Carlo sampling, the approximations that we describe involve only numerical optimization and simple algebra. Therefore, they make Bayesian methods widely accessible to metrologists. We illustrate the application of the proposed techniques in several instances of measurement: isotopic ratio of silver in a commercial silver nitrate; odds of cryptosporidiosis in AIDS patients; height of a manometer column; mass fraction of chromium in a reference material; and potential-difference in a Zener voltage standard.

Difference equation state approximations for nonlinear hereditary control problems

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1982-01-01

Discrete approximation schemes for the solution of nonlinear hereditary control problems are constructed. The methods involve approximation by a sequence of optimal control problems in which the original infinite dimensional state equation has been approximated by a finite dimensional discrete difference equation. Convergence of the state approximations is argued using linear semigroup theory and is then used to demonstrate that solutions to the approximating optimal control problems in some sense approximate solutions to the original control problem. Two schemes, one based upon piecewise constant approximation, and the other involving spline functions are discussed. Numerical results are presented, analyzed and used to compare the schemes to other available approximation methods for the solution of hereditary control problems.

Approximation algorithms for planning and control

NASA Technical Reports Server (NTRS)

Boddy, Mark; Dean, Thomas

1989-01-01

A control system operating in a complex environment will encounter a variety of different situations, with varying amounts of time available to respond to critical events. Ideally, such a control system will do the best possible with the time available. In other words, its responses should approximate those that would result from having unlimited time for computation, where the degree of the approximation depends on the amount of time it actually has. There exist approximation algorithms for a wide variety of problems. Unfortunately, the solution to any reasonably complex control problem will require solving several computationally intensive problems. Algorithms for successive approximation are a subclass of the class of anytime algorithms, algorithms that return answers for any amount of computation time, where the answers improve as more time is allotted. An architecture is described for allocating computation time to a set of anytime algorithms, based on expectations regarding the value of the answers they return. The architecture described is quite general, producing optimal schedules for a set of algorithms under widely varying conditions.

Approximation methods in gravitational-radiation theory

NASA Technical Reports Server (NTRS)

Will, C. M.

1986-01-01

The observation of gravitational-radiation damping in the binary pulsar PSR 1913 + 16 and the ongoing experimental search for gravitational waves of extraterrestrial origin have made the theory of gravitational radiation an active branch of classical general relativity. In calculations of gravitational radiation, approximation methods play a crucial role. Recent developments are summarized in two areas in which approximations are important: (a) the quadrupole approxiamtion, which determines the energy flux and the radiation reaction forces in weak-field, slow-motion, source-within-the-near-zone systems such as the binary pulsar; and (b) the normal modes of oscillation of black holes, where the Wentzel-Kramers-Brillouin approximation gives accurate estimates of the complex frequencies of the modes.

Difference equation state approximations for nonlinear hereditary control problems

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1984-01-01

Discrete approximation schemes for the solution of nonlinear hereditary control problems are constructed. The methods involve approximation by a sequence of optimal control problems in which the original infinite dimensional state equation has been approximated by a finite dimensional discrete difference equation. Convergence of the state approximations is argued using linear semigroup theory and is then used to demonstrate that solutions to the approximating optimal control problems in some sense approximate solutions to the original control problem. Two schemes, one based upon piecewise constant approximation, and the other involving spline functions are discussed. Numerical results are presented, analyzed and used to compare the schemes to other available approximation methods for the solution of hereditary control problems. Previously announced in STAR as N83-33589

Approximate number word knowledge before the cardinal principle.

PubMed

Gunderson, Elizabeth A; Spaepen, Elizabet; Levine, Susan C

2015-02-01

Approximate number word knowledge-understanding the relation between the count words and the approximate magnitudes of sets-is a critical piece of knowledge that predicts later math achievement. However, researchers disagree about when children first show evidence of approximate number word knowledge-before, or only after, they have learned the cardinal principle. In two studies, children who had not yet learned the cardinal principle (subset-knowers) produced sets in response to number words (verbal comprehension task) and produced number words in response to set sizes (verbal production task). As evidence of approximate number word knowledge, we examined whether children's numerical responses increased with increasing numerosity of the stimulus. In Study 1, subset-knowers (ages 3.0-4.2 years) showed approximate number word knowledge above their knower-level on both tasks, but this effect did not extend to numbers above 4. In Study 2, we collected data from a broader age range of subset-knowers (ages 3.1-5.6 years). In this sample, children showed approximate number word knowledge on the verbal production task even when only examining set sizes above 4. Across studies, children's age predicted approximate number word knowledge (above 4) on the verbal production task when controlling for their knower-level, study (1 or 2), and parents' education, none of which predicted approximation ability. Thus, children can develop approximate knowledge of number words up to 10 before learning the cardinal principle. Furthermore, approximate number word knowledge increases with age and might not be closely related to the development of exact number word knowledge. Copyright © 2014 Elsevier Inc. All rights reserved.

Computing Functions by Approximating the Input

ERIC Educational Resources Information Center

Goldberg, Mayer

2012-01-01

In computing real-valued functions, it is ordinarily assumed that the input to the function is known, and it is the output that we need to approximate. In this work, we take the opposite approach: we show how to compute the values of some transcendental functions by approximating the input to these functions, and obtaining exact answers for their…

Approximating lens power.

PubMed

Kaye, Stephen B

2009-04-01

To provide a scalar measure of refractive error, based on geometric lens power through principal, orthogonal and oblique meridians, that is not limited to the paraxial and sag height approximations. A function is derived to model sections through the principal meridian of a lens, followed by rotation of the section through orthogonal and oblique meridians. Average focal length is determined using the definition for the average of a function. Average univariate power in the principal meridian (including spherical aberration), can be computed from the average of a function over the angle of incidence as determined by the parameters of the given lens, or adequately computed from an integrated series function. Average power through orthogonal and oblique meridians, can be similarly determined using the derived formulae. The widely used computation for measuring refractive error, the spherical equivalent, introduces non-constant approximations, leading to a systematic bias. The equations proposed provide a good univariate representation of average lens power and are not subject to a systematic bias. They are particularly useful for the analysis of aggregate data, correlating with biological treatment variables and for developing analyses, which require a scalar equivalent representation of refractive power.

Explicit approximations to estimate the perturbative diffusivity in the presence of convectivity and damping. I. Semi-infinite slab approximations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Berkel, M. van; Fellow of the Japan Society for the Promotion of Science; FOM Institute DIFFER-Dutch Institute for Fundamental Energy Research, Association EURATOM- FOM, Trilateral Euregio Cluster, PO Box 1207, 3430 BE Nieuwegein

2014-11-15

In this paper, a number of new approximations are introduced to estimate the perturbative diffusivity (χ), convectivity (V), and damping (τ) in cylindrical geometry. For this purpose, the harmonic components of heat waves induced by localized deposition of modulated power are used. The approximations are based on semi-infinite slab approximations of the heat equation. The main result is the approximation of χ under the influence of V and τ based on the phase of two harmonics making the estimate less sensitive to calibration errors. To understand why the slab approximations can estimate χ well in cylindrical geometry, the relationships betweenmore » heat transport models in slab and cylindrical geometry are studied. In addition, the relationship between amplitude and phase with respect to their derivatives, used to estimate χ, is discussed. The results are presented in terms of the relative error for the different derived approximations for different values of frequency, transport coefficients, and dimensionless radius. The approximations show a significant region in which χ, V, and τ can be estimated well, but also regions in which the error is large. Also, it is shown that some compensation is necessary to estimate V and τ in a cylindrical geometry. On the other hand, errors resulting from the simplified assumptions are also discussed showing that estimating realistic values for V and τ based on infinite domains will be difficult in practice. This paper is the first part (Part I) of a series of three papers. In Part II and Part III, cylindrical approximations based directly on semi-infinite cylindrical domain (outward propagating heat pulses) and inward propagating heat pulses in a cylindrical domain, respectively, will be treated.« less

Pawlak Algebra and Approximate Structure on Fuzzy Lattice

PubMed Central

Zhuang, Ying; Liu, Wenqi; Wu, Chin-Chia; Li, Jinhai

2014-01-01

The aim of this paper is to investigate the general approximation structure, weak approximation operators, and Pawlak algebra in the framework of fuzzy lattice, lattice topology, and auxiliary ordering. First, we prove that the weak approximation operator space forms a complete distributive lattice. Then we study the properties of transitive closure of approximation operators and apply them to rough set theory. We also investigate molecule Pawlak algebra and obtain some related properties. PMID:25152922

Pawlak algebra and approximate structure on fuzzy lattice.

PubMed

Zhuang, Ying; Liu, Wenqi; Wu, Chin-Chia; Li, Jinhai

2014-01-01

The aim of this paper is to investigate the general approximation structure, weak approximation operators, and Pawlak algebra in the framework of fuzzy lattice, lattice topology, and auxiliary ordering. First, we prove that the weak approximation operator space forms a complete distributive lattice. Then we study the properties of transitive closure of approximation operators and apply them to rough set theory. We also investigate molecule Pawlak algebra and obtain some related properties.

A Generalization of the Karush-Kuhn-Tucker Theorem for Approximate Solutions of Mathematical Programming Problems Based on Quadratic Approximation

NASA Astrophysics Data System (ADS)

Voloshinov, V. V.

2018-03-01

In computations related to mathematical programming problems, one often has to consider approximate, rather than exact, solutions satisfying the constraints of the problem and the optimality criterion with a certain error. For determining stopping rules for iterative procedures, in the stability analysis of solutions with respect to errors in the initial data, etc., a justified characteristic of such solutions that is independent of the numerical method used to obtain them is needed. A necessary δ-optimality condition in the smooth mathematical programming problem that generalizes the Karush-Kuhn-Tucker theorem for the case of approximate solutions is obtained. The Lagrange multipliers corresponding to the approximate solution are determined by solving an approximating quadratic programming problem.

Dynamical cluster approximation plus semiclassical approximation study for a Mott insulator and d-wave pairing

NASA Astrophysics Data System (ADS)

Kim, SungKun; Lee, Hunpyo

2017-06-01

Via a dynamical cluster approximation with N c = 4 in combination with a semiclassical approximation (DCA+SCA), we study the doped two-dimensional Hubbard model. We obtain a plaquette antiferromagnetic (AF) Mott insulator, a plaquette AF ordered metal, a pseudogap (or d-wave superconductor) and a paramagnetic metal by tuning the doping concentration. These features are similar to the behaviors observed in copper-oxide superconductors and are in qualitative agreement with the results calculated by the cluster dynamical mean field theory with the continuous-time quantum Monte Carlo (CDMFT+CTQMC) approach. The results of our DCA+SCA differ from those of the CDMFT+CTQMC approach in that the d-wave superconducting order parameters are shown even in the high doped region, unlike the results of the CDMFT+CTQMC approach. We think that the strong plaquette AF orderings in the dynamical cluster approximation (DCA) with N c = 4 suppress superconducting states with increasing doping up to strongly doped region, because frozen dynamical fluctuations in a semiclassical approximation (SCA) approach are unable to destroy those orderings. Our calculation with short-range spatial fluctuations is initial research, because the SCA can manage long-range spatial fluctuations in feasible computational times beyond the CDMFT+CTQMC tool. We believe that our future DCA+SCA calculations should supply information on the fully momentum-resolved physical properties, which could be compared with the results measured by angle-resolved photoemission spectroscopy experiments.

Differential equation based method for accurate approximations in optimization

NASA Technical Reports Server (NTRS)

Pritchard, Jocelyn I.; Adelman, Howard M.

1990-01-01

This paper describes a method to efficiently and accurately approximate the effect of design changes on structural response. The key to this new method is to interpret sensitivity equations as differential equations that may be solved explicitly for closed form approximations, hence, the method is denoted the Differential Equation Based (DEB) method. Approximations were developed for vibration frequencies, mode shapes and static displacements. The DEB approximation method was applied to a cantilever beam and results compared with the commonly-used linear Taylor series approximations and exact solutions. The test calculations involved perturbing the height, width, cross-sectional area, tip mass, and bending inertia of the beam. The DEB method proved to be very accurate, and in msot cases, was more accurate than the linear Taylor series approximation. The method is applicable to simultaneous perturbation of several design variables. Also, the approximations may be used to calculate other system response quantities. For example, the approximations for displacement are used to approximate bending stresses.

Differential equation based method for accurate approximations in optimization

NASA Technical Reports Server (NTRS)

Pritchard, Jocelyn I.; Adelman, Howard M.

1990-01-01

A method to efficiently and accurately approximate the effect of design changes on structural response is described. The key to this method is to interpret sensitivity equations as differential equations that may be solved explicitly for closed form approximations, hence, the method is denoted the Differential Equation Based (DEB) method. Approximations were developed for vibration frequencies, mode shapes and static displacements. The DEB approximation method was applied to a cantilever beam and results compared with the commonly-used linear Taylor series approximations and exact solutions. The test calculations involved perturbing the height, width, cross-sectional area, tip mass, and bending inertia of the beam. The DEB method proved to be very accurate, and in most cases, was more accurate than the linear Taylor series approximation. The method is applicable to simultaneous perturbation of several design variables. Also, the approximations may be used to calculate other system response quantities. For example, the approximations for displacements are used to approximate bending stresses.

Variationally consistent approximation scheme for charge transfer

NASA Technical Reports Server (NTRS)

Halpern, A. M.

1978-01-01

The author has developed a technique for testing various charge-transfer approximation schemes for consistency with the requirements of the Kohn variational principle for the amplitude to guarantee that the amplitude is correct to second order in the scattering wave functions. Applied to Born-type approximations for charge transfer it allows the selection of particular groups of first-, second-, and higher-Born-type terms that obey the consistency requirement, and hence yield more reliable approximation to the amplitude.

Uniform analytic approximation of Wigner rotation matrices

NASA Astrophysics Data System (ADS)

Hoffmann, Scott E.

2018-02-01

We derive the leading asymptotic approximation, for low angle θ, of the Wigner rotation matrix elements, dm1m2 j(θ ) , uniform in j, m1, and m2. The result is in terms of a Bessel function of integer order. We numerically investigate the error for a variety of cases and find that the approximation can be useful over a significant range of angles. This approximation has application in the partial wave analysis of wavepacket scattering.

Inversion and approximation of Laplace transforms

NASA Technical Reports Server (NTRS)

Lear, W. M.

1980-01-01

A method of inverting Laplace transforms by using a set of orthonormal functions is reported. As a byproduct of the inversion, approximation of complicated Laplace transforms by a transform with a series of simple poles along the left half plane real axis is shown. The inversion and approximation process is simple enough to be put on a programmable hand calculator.

Minimal entropy approximation for cellular automata

NASA Astrophysics Data System (ADS)

Fukś, Henryk

2014-02-01

We present a method for the construction of approximate orbits of measures under the action of cellular automata which is complementary to the local structure theory. The local structure theory is based on the idea of Bayesian extension, that is, construction of a probability measure consistent with given block probabilities and maximizing entropy. If instead of maximizing entropy one minimizes it, one can develop another method for the construction of approximate orbits, at the heart of which is the iteration of finite-dimensional maps, called minimal entropy maps. We present numerical evidence that the minimal entropy approximation sometimes outperforms the local structure theory in characterizing the properties of cellular automata. The density response curve for elementary CA rule 26 is used to illustrate this claim.

Laplace approximation for Bessel functions of matrix argument

NASA Astrophysics Data System (ADS)

Butler, Ronald W.; Wood, Andrew T. A.

2003-06-01

We derive Laplace approximations to three functions of matrix argument which arise in statistics and elsewhere: matrix Bessel A[nu]; matrix Bessel B[nu]; and the type II confluent hypergeometric function of matrix argument, [Psi]. We examine the theoretical and numerical properties of the approximations. On the theoretical side, it is shown that the Laplace approximations to A[nu], B[nu] and [Psi] given here, together with the Laplace approximations to the matrix argument functions 1F1 and 2F1 presented in Butler and Wood (Laplace approximations to hyper-geometric functions with matrix argument, Ann. Statist. (2002)), satisfy all the important confluence relations and symmetry relations enjoyed by the original functions.

Approximation Set of the Interval Set in Pawlak's Space

PubMed Central

Wang, Jin; Wang, Guoyin

2014-01-01

The interval set is a special set, which describes uncertainty of an uncertain concept or set Z with its two crisp boundaries named upper-bound set and lower-bound set. In this paper, the concept of similarity degree between two interval sets is defined at first, and then the similarity degrees between an interval set and its two approximations (i.e., upper approximation set R¯(Z) and lower approximation set R_(Z)) are presented, respectively. The disadvantages of using upper-approximation set R¯(Z) or lower-approximation set R_(Z) as approximation sets of the uncertain set (uncertain concept) Z are analyzed, and a new method for looking for a better approximation set of the interval set Z is proposed. The conclusion that the approximation set R 0.5(Z) is an optimal approximation set of interval set Z is drawn and proved successfully. The change rules of R 0.5(Z) with different binary relations are analyzed in detail. Finally, a kind of crisp approximation set of the interval set Z is constructed. We hope this research work will promote the development of both the interval set model and granular computing theory. PMID:25177721

Function approximation using combined unsupervised and supervised learning.

PubMed

Andras, Peter

2014-03-01

Function approximation is one of the core tasks that are solved using neural networks in the context of many engineering problems. However, good approximation results need good sampling of the data space, which usually requires exponentially increasing volume of data as the dimensionality of the data increases. At the same time, often the high-dimensional data is arranged around a much lower dimensional manifold. Here we propose the breaking of the function approximation task for high-dimensional data into two steps: (1) the mapping of the high-dimensional data onto a lower dimensional space corresponding to the manifold on which the data resides and (2) the approximation of the function using the mapped lower dimensional data. We use over-complete self-organizing maps (SOMs) for the mapping through unsupervised learning, and single hidden layer neural networks for the function approximation through supervised learning. We also extend the two-step procedure by considering support vector machines and Bayesian SOMs for the determination of the best parameters for the nonlinear neurons in the hidden layer of the neural networks used for the function approximation. We compare the approximation performance of the proposed neural networks using a set of functions and show that indeed the neural networks using combined unsupervised and supervised learning outperform in most cases the neural networks that learn the function approximation using the original high-dimensional data.

Coherent Anomaly Method Calculation on the Cluster Variation Method. II.

NASA Astrophysics Data System (ADS)

Wada, Koh; Watanabe, Naotosi; Uchida, Tetsuya

The critical exponents of the bond percolation model are calculated in the D(= 2,3,…)-dimensional simple cubic lattice on the basis of Suzuki's coherent anomaly method (CAM) by making use of a series of the pair, the square-cactus and the square approximations of the cluster variation method (CVM) in the s-state Potts model. These simple approximations give reasonable values of critical exponents α, β, γ and ν in comparison with ones estimated by other methods. It is also shown that the results of the pair and the square-cactus approximations can be derived as exact results of the bond percolation model on the Bethe and the square-cactus lattice, respectively, in the presence of ghost field without recourse to the s→1 limit of the s-state Potts model.

Coherent Anomaly Method Calculation on the Cluster Variation Method. II. Critical Exponents of Bond Percolation Model

NASA Astrophysics Data System (ADS)

Wada, Koh; Watanabe, Naotosi; Uchida, Tetsuya

1991-10-01

The critical exponents of the bond percolation model are calculated in the D(=2, 3, \\cdots)-dimensional simple cubic lattice on the basis of Suzuki’s coherent anomaly method (CAM) by making use of a series of the pair, the square-cactus and the square approximations of the cluster variation method (CVM) in the s-state Potts model. These simple approximations give reasonable values of critical exponents α, β, γ and ν in comparison with ones estimated by other methods. It is also shown that the results of the pair and the square-cactus approximations can be derived as exact results of the bond percolation model on the Bethe and the square-cactus lattice, respectively, in the presence of ghost field without recourse to the s→1 limit of the s-state Potts model.

Nonperturbative dynamics of scalar field theories through the Feynman-Schwinger representation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cetin Savkli; Franz Gross; John Tjon

2004-04-01

In this paper we present a summary of results obtained for scalar field theories using the Feynman-Schwinger (FSR) approach. Specifically, scalar QED and {chi}{sup 2}{phi} theories are considered. The motivation behind the applications discussed in this paper is to use the FSR method as a rigorous tool for testing the quality of commonly used approximations in field theory. Exact calculations in a quenched theory are presented for one-, two-, and three-body bound states. Results obtained indicate that some of the commonly used approximations, such as Bethe-Salpeter ladder summation for bound states and the rainbow summation for one body problems, producemore » significantly different results from those obtained from the FSR approach. We find that more accurate results can be obtained using other, simpler, approximation schemes.« less

A Survey of Techniques for Approximate Computing

DOE PAGES

Mittal, Sparsh

2016-03-18

Approximate computing trades off computation quality with the effort expended and as rising performance demands confront with plateauing resource budgets, approximate computing has become, not merely attractive, but even imperative. Here, we present a survey of techniques for approximate computing (AC). We discuss strategies for finding approximable program portions and monitoring output quality, techniques for using AC in different processing units (e.g., CPU, GPU and FPGA), processor components, memory technologies etc., and programming frameworks for AC. Moreover, we classify these techniques based on several key characteristics to emphasize their similarities and differences. Finally, the aim of this paper is tomore » provide insights to researchers into working of AC techniques and inspire more efforts in this area to make AC the mainstream computing approach in future systems.« less

Meta-Regression Approximations to Reduce Publication Selection Bias

ERIC Educational Resources Information Center

Stanley, T. D.; Doucouliagos, Hristos

2014-01-01

Publication selection bias is a serious challenge to the integrity of all empirical sciences. We derive meta-regression approximations to reduce this bias. Our approach employs Taylor polynomial approximations to the conditional mean of a truncated distribution. A quadratic approximation without a linear term, precision-effect estimate with…

Thin-wall approximation in vacuum decay: A lemma

NASA Astrophysics Data System (ADS)

Brown, Adam R.

2018-05-01

The "thin-wall approximation" gives a simple estimate of the decay rate of an unstable quantum field. Unfortunately, the approximation is uncontrolled. In this paper I show that there are actually two different thin-wall approximations and that they bracket the true decay rate: I prove that one is an upper bound and the other a lower bound. In the thin-wall limit, the two approximations converge. In the presence of gravity, a generalization of this lemma provides a simple sufficient condition for nonperturbative vacuum instability.

Exciton self-trapping and Stark effect in the optical response of pentacene crystals from first principles

NASA Astrophysics Data System (ADS)

Strubbe, David A.; Sharifzadeh, Sahar; Neaton, Jeffrey B.; Louie, Steven G.

2012-02-01

Pentacene is a prototypical organic semiconductor with optoelectronic and photovoltaic applications. It is known that the lowest-energy singlet excitation has a Stokes shift between absorption and emission of about 0.14 eV, but the deformation associated with this self-trapped exciton remains unknown. We begin with a calculation of the optical properties via the first-principles GW/Bethe-Salpeter (BSE) theory [ML Tiago, JE Northrup, and SG Louie, Phys. Rev. B 67, 115212 (2003); S Sharifzadeh, A Biller, L Kronik, and JB Neaton, arXiv:1110.4928 (2011)]. We then study the self-trapping phenomenon via our reformulation of the Bethe-Salpeter excited-state forces approximation of Ismail-Beigi and Louie [Phys. Rev. Lett. 90, 076401 (2003)], which can describe the structural relaxation after optical excitation. Whether excitons in pentacene have charge-transfer character has been controversial in electro-absorption experiments. We use the same BSE analytic derivatives approach to calculate the changes in excitation energies due to an applied electric field to understand this experimental controversy.

Smooth function approximation using neural networks.

PubMed

Ferrari, Silvia; Stengel, Robert F

2005-01-01

An algebraic approach for representing multidimensional nonlinear functions by feedforward neural networks is presented. In this paper, the approach is implemented for the approximation of smooth batch data containing the function's input, output, and possibly, gradient information. The training set is associated to the network adjustable parameters by nonlinear weight equations. The cascade structure of these equations reveals that they can be treated as sets of linear systems. Hence, the training process and the network approximation properties can be investigated via linear algebra. Four algorithms are developed to achieve exact or approximate matching of input-output and/or gradient-based training sets. Their application to the design of forward and feedback neurocontrollers shows that algebraic training is characterized by faster execution speeds and better generalization properties than contemporary optimization techniques.

Random-Phase Approximation Methods

NASA Astrophysics Data System (ADS)

Chen, Guo P.; Voora, Vamsee K.; Agee, Matthew M.; Balasubramani, Sree Ganesh; Furche, Filipp

2017-05-01

Random-phase approximation (RPA) methods are rapidly emerging as cost-effective validation tools for semilocal density functional computations. We present the theoretical background of RPA in an intuitive rather than formal fashion, focusing on the physical picture of screening and simple diagrammatic analysis. A new decomposition of the RPA correlation energy into plasmonic modes leads to an appealing visualization of electron correlation in terms of charge density fluctuations. Recent developments in the areas of beyond-RPA methods, RPA correlation potentials, and efficient algorithms for RPA energy and property calculations are reviewed. The ability of RPA to approximately capture static correlation in molecules is quantified by an analysis of RPA natural occupation numbers. We illustrate the use of RPA methods in applications to small-gap systems such as open-shell d- and f-element compounds, radicals, and weakly bound complexes, where semilocal density functional results exhibit strong functional dependence.

Charge symmetry breaking effects in pion and kaon structure

NASA Astrophysics Data System (ADS)

Hutauruk, Parada T. P.; Bentz, Wolfgang; Cloët, Ian C.; Thomas, Anthony W.

2018-05-01

Charge symmetry breaking (CSB) effects associated with the u and d quark mass difference are investigated in the quark distribution functions and spacelike electromagnetic form factors of the pion and kaon. We use a confining version of the Nambu-Jona-Lasinio model, where CSB effects at the infrared scale associated with the model are driven by the dressed u and d quark mass ratio, which because of dynamical chiral symmetry breaking is much closer to unity than the associated current quark mass ratio. The pion and kaon are given as bound states of a dressed quark and a dressed antiquark governed by the Bethe-Salpeter equation, and exhibit the properties of Goldstone bosons, with a pion mass difference given by mπ+2-mπ0 2∝(mu-md)2 as demanded by dynamical chiral symmetry breaking. We find significant CSB effects for realistic current quark mass ratios (mu/md˜0.5 ) in the quark flavor-sector electromagnetic form factors of both the pion and kaon. For example, the difference between the u and d quark contributions to the π+ electromagnetic form factors is about 8% at a momentum transfer of Q2≃10 GeV2 , while the analogous effect for the light quark sector form factors in the K+ and K0 is about twice as large. For the parton distribution functions we find CSB effects which are considerably smaller than those found in the electromagnetic form factors.

Monotonically improving approximate answers to relational algebra queries

NASA Technical Reports Server (NTRS)

Smith, Kenneth P.; Liu, J. W. S.

1989-01-01

We present here a query processing method that produces approximate answers to queries posed in standard relational algebra. This method is monotone in the sense that the accuracy of the approximate result improves with the amount of time spent producing the result. This strategy enables us to trade the time to produce the result for the accuracy of the result. An approximate relational model that characterizes appromimate relations and a partial order for comparing them is developed. Relational operators which operate on and return approximate relations are defined.

Remarks towards the spectrum of the Heisenberg spin chain type models

NASA Astrophysics Data System (ADS)

Burdík, Č.; Fuksa, J.; Isaev, A. P.; Krivonos, S. O.; Navrátil, O.

2015-05-01

The integrable close and open chain models can be formulated in terms of generators of the Hecke algebras. In this review paper, we describe in detail the Bethe ansatz for the XXX and the XXZ integrable close chain models. We find the Bethe vectors for two-component and inhomogeneous models. We also find the Bethe vectors for the fermionic realization of the integrable XXX and XXZ close chain models by means of the algebraic and coordinate Bethe ansatz. Special modification of the XXZ closed spin chain model ("small polaron model") is considered. Finally, we discuss some questions relating to the general open Hecke chain models.

Approximate isotropic cloak for the Maxwell equations

NASA Astrophysics Data System (ADS)

Ghosh, Tuhin; Tarikere, Ashwin

2018-05-01

We construct a regular isotropic approximate cloak for the Maxwell system of equations. The method of transformation optics has enabled the design of electromagnetic parameters that cloak a region from external observation. However, these constructions are singular and anisotropic, making practical implementation difficult. Thus, regular approximations to these cloaks have been constructed that cloak a given region to any desired degree of accuracy. In this paper, we show how to construct isotropic approximations to these regularized cloaks using homogenization techniques so that one obtains cloaking of arbitrary accuracy with regular and isotropic parameters.

Iran’s Youth Bulge and It’s Implications for U.S. National Security

DTIC Science & Technology

2006-04-01

Sciolino, Elaine. “Radicalism: Is the Devil in the Demographics?” New York Times, 9 December 2001. Sen , Amartya . “Mortality as an Indicator of...validating their model and the independent variables’ significance. See Goldstone, et al., 2005, p. 17. 74 Goldstone, 2001, p. 166. See Amartya Sen’s

Innovative Collaborative Learning Strategies for Integrated Interactive E-Learning in the 21st Century

ERIC Educational Resources Information Center

Son, Barbara

2016-01-01

There is a constant challenge for online programs, instructional designers and instructors to tailor eLearning materials for different learning styles. We examined this issue by closely looking at the innovative interactive learning models at the previous AACE Conferences (Son & Goldstone, 2011, Son & Goldstone, 2012, Son & Simonian,…

Radar Observations of the Icy Galilean Satellites During 2000 Opposition

NASA Technical Reports Server (NTRS)

Harcke, L. J.; Zebker, H. A.; Jurgens, R. F.; Slade, M. A.; Butler, B. J.; Harmon, J. K.

2001-01-01

We report results of radar observation campaigns of Europa, Ganymede, and Callisto carried out during the November/December 2000 Jovian opposition using the Arecibo 12.6 cm, Goldstone 3.5 cm, and Goldstone/VLA 3.5 cm bistatic radars. Additional information is contained in the original extended abstract.

Explicit approximations to estimate the perturbative diffusivity in the presence of convectivity and damping. III. Cylindrical approximations for heat waves traveling inwards

DOE Office of Scientific and Technical Information (OSTI.GOV)

Berkel, M. van; Fellow of the Japan Society for the Promotion of Science; FOM Institute DIFFER-Dutch Institute for Fundamental Energy Research, Association EURATOM-FOM, Trilateral Euregio Cluster, P.O. Box 1207, 3430 BE Nieuwegein

In this paper, a number of new explicit approximations are introduced to estimate the perturbative diffusivity (χ), convectivity (V), and damping (τ) in cylindrical geometry. For this purpose, the harmonic components of heat waves induced by localized deposition of modulated power are used. The approximations are based on the heat equation in cylindrical geometry using the symmetry (Neumann) boundary condition at the plasma center. This means that the approximations derived here should be used only to estimate transport coefficients between the plasma center and the off-axis perturbative source. If the effect of cylindrical geometry is small, it is also possiblemore » to use semi-infinite domain approximations presented in Part I and Part II of this series. A number of new approximations are derived in this part, Part III, based upon continued fractions of the modified Bessel function of the first kind and the confluent hypergeometric function of the first kind. These approximations together with the approximations based on semi-infinite domains are compared for heat waves traveling towards the center. The relative error for the different derived approximations is presented for different values of the frequency, transport coefficients, and dimensionless radius. Moreover, it is shown how combinations of different explicit formulas can be used to estimate the transport coefficients over a large parameter range for cases without convection and damping, cases with damping only, and cases with convection and damping. The relative error between the approximation and its underlying model is below 2% for the case, where only diffusivity and damping are considered. If also convectivity is considered, the diffusivity can be estimated well in a large region, but there is also a large region in which no suitable approximation is found. This paper is the third part (Part III) of a series of three papers. In Part I, the semi-infinite slab approximations have been treated. In

Structural Reliability Analysis and Optimization: Use of Approximations

NASA Technical Reports Server (NTRS)

Grandhi, Ramana V.; Wang, Liping

1999-01-01

This report is intended for the demonstration of function approximation concepts and their applicability in reliability analysis and design. Particularly, approximations in the calculation of the safety index, failure probability and structural optimization (modification of design variables) are developed. With this scope in mind, extensive details on probability theory are avoided. Definitions relevant to the stated objectives have been taken from standard text books. The idea of function approximations is to minimize the repetitive use of computationally intensive calculations by replacing them with simpler closed-form equations, which could be nonlinear. Typically, the approximations provide good accuracy around the points where they are constructed, and they need to be periodically updated to extend their utility. There are approximations in calculating the failure probability of a limit state function. The first one, which is most commonly discussed, is how the limit state is approximated at the design point. Most of the time this could be a first-order Taylor series expansion, also known as the First Order Reliability Method (FORM), or a second-order Taylor series expansion (paraboloid), also known as the Second Order Reliability Method (SORM). From the computational procedure point of view, this step comes after the design point identification; however, the order of approximation for the probability of failure calculation is discussed first, and it is denoted by either FORM or SORM. The other approximation of interest is how the design point, or the most probable failure point (MPP), is identified. For iteratively finding this point, again the limit state is approximated. The accuracy and efficiency of the approximations make the search process quite practical for analysis intensive approaches such as the finite element methods; therefore, the crux of this research is to develop excellent approximations for MPP identification and also different

Variational Gaussian approximation for Poisson data

NASA Astrophysics Data System (ADS)

Arridge, Simon R.; Ito, Kazufumi; Jin, Bangti; Zhang, Chen

2018-02-01

The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the posterior distribution arising from the Poisson model with a Gaussian prior. This is achieved by seeking an optimal Gaussian distribution minimizing the Kullback-Leibler divergence from the posterior distribution to the approximation, or equivalently maximizing the lower bound for the model evidence. We derive an explicit expression for the lower bound, and show the existence and uniqueness of the optimal Gaussian approximation. The lower bound functional can be viewed as a variant of classical Tikhonov regularization that penalizes also the covariance. Then we develop an efficient alternating direction maximization algorithm for solving the optimization problem, and analyze its convergence. We discuss strategies for reducing the computational complexity via low rank structure of the forward operator and the sparsity of the covariance. Further, as an application of the lower bound, we discuss hierarchical Bayesian modeling for selecting the hyperparameter in the prior distribution, and propose a monotonically convergent algorithm for determining the hyperparameter. We present extensive numerical experiments to illustrate the Gaussian approximation and the algorithms.

Approximate Computing Techniques for Iterative Graph Algorithms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Panyala, Ajay R.; Subasi, Omer; Halappanavar, Mahantesh

Approximate computing enables processing of large-scale graphs by trading off quality for performance. Approximate computing techniques have become critical not only due to the emergence of parallel architectures but also the availability of large scale datasets enabling data-driven discovery. Using two prototypical graph algorithms, PageRank and community detection, we present several approximate computing heuristics to scale the performance with minimal loss of accuracy. We present several heuristics including loop perforation, data caching, incomplete graph coloring and synchronization, and evaluate their efficiency. We demonstrate performance improvements of up to 83% for PageRank and up to 450x for community detection, with lowmore » impact of accuracy for both the algorithms. We expect the proposed approximate techniques will enable scalable graph analytics on data of importance to several applications in science and their subsequent adoption to scale similar graph algorithms.« less

Pumping approximately integrable systems

PubMed Central

Lange, Florian; Lenarčič, Zala; Rosch, Achim

2017-01-01

Weak perturbations can drive an interacting many-particle system far from its initial equilibrium state if one is able to pump into degrees of freedom approximately protected by conservation laws. This concept has for example been used to realize Bose–Einstein condensates of photons, magnons and excitons. Integrable quantum systems, like the one-dimensional Heisenberg model, are characterized by an infinite set of conservation laws. Here, we develop a theory of weakly driven integrable systems and show that pumping can induce large spin or heat currents even in the presence of integrability breaking perturbations, since it activates local and quasi-local approximate conserved quantities. The resulting steady state is qualitatively captured by a truncated generalized Gibbs ensemble with Lagrange parameters that depend on the structure but not on the overall amplitude of perturbations nor the initial state. We suggest to use spin-chain materials driven by terahertz radiation to realize integrability-based spin and heat pumps. PMID:28598444

Sensitivity analysis and approximation methods for general eigenvalue problems

NASA Technical Reports Server (NTRS)

Murthy, D. V.; Haftka, R. T.

1986-01-01

Optimization of dynamic systems involving complex non-hermitian matrices is often computationally expensive. Major contributors to the computational expense are the sensitivity analysis and reanalysis of a modified design. The present work seeks to alleviate this computational burden by identifying efficient sensitivity analysis and approximate reanalysis methods. For the algebraic eigenvalue problem involving non-hermitian matrices, algorithms for sensitivity analysis and approximate reanalysis are classified, compared and evaluated for efficiency and accuracy. Proper eigenvector normalization is discussed. An improved method for calculating derivatives of eigenvectors is proposed based on a more rational normalization condition and taking advantage of matrix sparsity. Important numerical aspects of this method are also discussed. To alleviate the problem of reanalysis, various approximation methods for eigenvalues are proposed and evaluated. Linear and quadratic approximations are based directly on the Taylor series. Several approximation methods are developed based on the generalized Rayleigh quotient for the eigenvalue problem. Approximation methods based on trace theorem give high accuracy without needing any derivatives. Operation counts for the computation of the approximations are given. General recommendations are made for the selection of appropriate approximation technique as a function of the matrix size, number of design variables, number of eigenvalues of interest and the number of design points at which approximation is sought.

Low-Energy Excitation Spectra in the Excitonic Phase of Cobalt Oxides

NASA Astrophysics Data System (ADS)

Yamaguchi, Tomoki; Sugimoto, Koudai; Ohta, Yukinori

2017-04-01

We study the excitonic phase and low-energy excitation spectra of perovskite cobalt oxides. Constructing the five-orbital Hubbard model defined on the three-dimensional cubic lattice for the 3d bands of Pr0.5Ca0.5CoO3, we calculate the excitonic susceptibility in the normal state in the random-phase approximation (RPA) to show the presence of the instability toward excitonic condensation. On the basis of the excitonic ground state with a magnetic multipole obtained in the mean-field approximation, we calculate the dynamical susceptibility of the excitonic phase in the RPA and find that there appear a gapless collective excitation in the spin-transverse mode (Goldstone mode) and a gapful collective excitation in the spin-longitudinal mode (Higgs mode). The experimental relevance of our results is discussed.

Goldstone radar images of near-Earth asteroids (469896) 2007 WV4, 2014 JO25, 2017 BQ6, and 2017 CS

NASA Astrophysics Data System (ADS)

Brozovic, Marina; Benner, Lance A. M.; Naidu, Shantanu P.; Giorgini, Jon D.; Busch, Michael; Jao, Joseph; Lee, Clement; Snedeker, Lawrence; Silva, Marc; Slade, Martin A.; Lawrence, Kenneth J.

2017-10-01

We report Goldstone delay-Doppler radar imaging of four NEAs obtained during February-June 2017. The signal-to-noise ratios were very strong for each object and we obtained detailed images with range resolutions as fine as 3.75 m/pixel. Delay-Doppler imaging revealed that 2017 BQ6 is a strikingly angular object roughly ~200 m in diameter with a rotation period of ~3 h. The multi-faceted shape is puzzling assuming a rubble-pile structure of this asteroid. 2017 CS was discovered by Pan-STARRS 1 on February 2 and approached within 8 lunar distances on May 29. 2017 CS appears rounded on large scales but has considerable fine-scale topography evident along its leading edges. The images suggest a diameter of ~1 km and rotation visible in the images is consistent with the 40 h rotation period obtained independently by from photometry by P. Pravec (pers. comm.). The highest resolution images show evidence for meter-size boulders, ridges, and broad concavities. 2007 WV4 was imaged in late May and early June. 2007 WV4 appears distinctly angular, with a diameter in the realm of 900 meters, and with at least three large facets more than 100 m in extent. Tracking of features in the images gives a rotation period of about 12 hours. The echoes show a persistent, small topographic feature that extends out from the surface. The nature of this feature is unknown, but it may be a large boulder similar to Yoshinodai seen on 25143 Itokawa. 2014 JO25 approached within 4.6 lunar distances on April 19. This was the closest encounter by an asteroid with an absolute magnitude brighter than 18 known in advance until 2027, when 1999 AN10 will approach within one lunar distance. Radar imaging shows that 2014 JO25 is an irregular object, which consists of two components connected by a narrow neck. The asteroid has a long axis of about 1 km and a short axis of roughly 600 m. The 3.75 m range resolution imaging placed thousands of pixels on the object and reveals ridges, hills, concavities, flat

Convergence Rates of Finite Difference Stochastic Approximation Algorithms

DTIC Science & Technology

2016-06-01

dfferences as gradient approximations. It is shown that the convergence of these algorithms can be accelerated by controlling the implementation of the...descent algorithm, under various updating schemes using finite dfferences as gradient approximations. It is shown that the convergence of these...the Kiefer-Wolfowitz algorithm and the mirror descent algorithm, under various updating schemes using finite differences as gradient approximations. It

Capacitor-Chain Successive-Approximation ADC

NASA Technical Reports Server (NTRS)

Cunningham, Thomas

2003-01-01

A proposed successive-approximation analog-to-digital converter (ADC) would contain a capacitively terminated chain of identical capacitor cells. Like a conventional successive-approximation ADC containing a bank of binary-scaled capacitors, the proposed ADC would store an input voltage on a sample-and-hold capacitor and would digitize the stored input voltage by finding the closest match between this voltage and a capacitively generated sum of binary fractions of a reference voltage (Vref). However, the proposed capacitor-chain ADC would offer two major advantages over a conventional binary-scaled-capacitor ADC: (1) In a conventional ADC that digitizes to n bits, the largest capacitor (representing the most significant bit) must have 2(exp n-1) times as much capacitance, and hence, approximately 2(exp n-1) times as much area as does the smallest capacitor (representing the least significant bit), so that the total capacitor area must be 2(exp n) times that of the smallest capacitor. In the proposed capacitor-chain ADC, there would be three capacitors per cell, each approximately equal to the smallest capacitor in the conventional ADC, and there would be one cell per bit. Therefore, the total capacitor area would be only about 3(exp n) times that of the smallest capacitor. The net result would be that the proposed ADC could be considerably smaller than the conventional ADC. (2) Because of edge effects, parasitic capacitances, and manufacturing tolerances, it is difficult to make capacitor banks in which the values of capacitance are scaled by powers of 2 to the required precision. In contrast, because all the capacitors in the proposed ADC would be identical, the problem of precise binary scaling would not arise.

The Detection of a Striking Increase in the Microwave Emission from Jupiter's Radiation Belts in June and July 2003.

NASA Astrophysics Data System (ADS)

Klein, M. J.; Bolton, S. J.; Levin, S. M.; Mac Laren, D.

2004-12-01

Synchrotron emission from energetic electrons in Jupiter's radiation belts has been routinely measured by ground-based radio telescopes for three decades. The NASA-JPL Jupiter Patrol, using NASA's Deep Space Network (DSN) antennas at Goldstone, CA., has reported significant (5 %-to-30 %) variations in Jupiter's flux density near 13-cm wavelength with timescales from a few days to several months. In this paper we report observations of an unusually sudden increase in flux density from 3.8 to 4.3 Jy that occurred between 20 June and 15 July 2003. The rate of increase (approximately 0.6 percent per day) is the steepest increase that we have detected with the exception of the increase in 1994 following the impacts of fragments from comet Shoemaker-Levy 9. More than half of the reported observations were conducted by middle- and high school students from classrooms across the nation. The students and their teachers are participants in the Goldstone-Apple Valley Radio Telescope (GAVRT) science education project, which is a partnership involving NASA, the Jet Propulsion Laboratory and the Lewis Center for Educational Research (LCER) in Apple Valley, CA. Working with the Lewis Center over the Internet, GAVRT students conduct remotely controlled radio astronomy observations using 34-m antennas at Goldstone. We also report preliminary results from a special GAVRT observing campaign conducted in the fall of 2003 before, during and after the controlled impact of the Galileo spacecraft into the Jovian atmosphere. Simultaneous observations were made at 3.5 and 13 cm wavelengths three-to-four days per week. These data are being incorporated into synchrotron emission studies of the state of the radiation belts during the last weeks of the Galileo mission. The JPL contribution to this paper was performed at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.

Rational Approximations with Hankel-Norm Criterion

DTIC Science & Technology

1980-01-01

REPORT TYPE ANDu DATES COVERED It) L. TITLE AND SLWUIlL Fi901 ia FUNDING NUMOIRS, RATIONAL APPROXIMATIONS WITH HANKEL-NORM CRITERION PE61102F i...problem is proved to be reducible to obtain a two-variable all- pass ration 1 function, interpolating a set of parametric values at specified points inside...PAGES WHICH DO NOT REPRODUCE LEGIBLY. V" C - w RATIONAL APPROXIMATIONS WITH HANKEL-NORM CRITERION* Y. Genin* Philips Research Lab. 2, avenue van

Approximate reasoning using terminological models

NASA Technical Reports Server (NTRS)

Yen, John; Vaidya, Nitin

1992-01-01

Term Subsumption Systems (TSS) form a knowledge-representation scheme in AI that can express the defining characteristics of concepts through a formal language that has a well-defined semantics and incorporates a reasoning mechanism that can deduce whether one concept subsumes another. However, TSS's have very limited ability to deal with the issue of uncertainty in knowledge bases. The objective of this research is to address issues in combining approximate reasoning with term subsumption systems. To do this, we have extended an existing AI architecture (CLASP) that is built on the top of a term subsumption system (LOOM). First, the assertional component of LOOM has been extended for asserting and representing uncertain propositions. Second, we have extended the pattern matcher of CLASP for plausible rule-based inferences. Third, an approximate reasoning model has been added to facilitate various kinds of approximate reasoning. And finally, the issue of inconsistency in truth values due to inheritance is addressed using justification of those values. This architecture enhances the reasoning capabilities of expert systems by providing support for reasoning under uncertainty using knowledge captured in TSS. Also, as definitional knowledge is explicit and separate from heuristic knowledge for plausible inferences, the maintainability of expert systems could be improved.

Comparison of dynamical approximation schemes for nonlinear gravitaional clustering

NASA Technical Reports Server (NTRS)

Melott, Adrian L.

1994-01-01

We have recently conducted a controlled comparison of a number of approximations for gravitational clustering against the same n-body simulations. These include ordinary linear perturbation theory (Eulerian), the lognormal approximation, the adhesion approximation, the frozen-flow approximation, the Zel'dovich approximation (describable as first-order Lagrangian perturbation theory), and its second-order generalization. In the last two cases we also created new versions of the approximation by truncation, i.e., by smoothing the initial conditions with various smoothing window shapes and varying their sizes. The primary tool for comparing simulations to approximation schemes was cross-correlation of the evolved mass density fields, testing the extent to which mass was moved to the right place. The Zel'dovich approximation, with initial convolution with a Gaussian e(exp -k(exp 2)/k(sub G(exp 2)), where k(sub G) is adjusted to be just into the nonlinear regime of the evolved model (details in text) worked extremely well. Its second-order generalization worked slightly better. We recommend either n-body simulations or our modified versions of the Zel'dovich approximation, depending upon the purpose. The theoretical implication is that pancaking is implicit in all cosmological gravitational clustering, at least from Gaussian initial conditions, even when subcondensations are present. This in turn provides a natural explanation for the presence of sheets and filaments in the observed galaxy distribution. Use of the approximation scheme can permit extremely rapid generation of large numbers of realizations of model universes with good accuracy down to galaxy group mass scales.

Embedding impedance approximations in the analysis of SIS mixers

NASA Technical Reports Server (NTRS)

Kerr, A. R.; Pan, S.-K.; Withington, S.

1992-01-01

Future millimeter-wave radio astronomy instruments will use arrays of many SIS receivers, either as focal plane arrays on individual radio telescopes, or as individual receivers on the many antennas of radio interferometers. Such applications will require broadband integrated mixers without mechanical tuners. To produce such mixers, it will be necessary to improve present mixer design techniques, most of which use the three-frequency approximation to Tucker's quantum mixer theory. This paper examines the adequacy of three approximations to Tucker's theory: (1) the usual three-frequency approximation which assumes a sinusoidal LO voltage at the junction, and a short-circuit at all frequencies above the upper sideband; (2) a five-frequency approximation which allows two LO voltage harmonics and five small-signal sidebands; and (3) a quasi five-frequency approximation in which five small-signal sidebands are allowed, but the LO voltage is assumed sinusoidal. These are compared with a full harmonic-Newton solution of Tucker's equations, including eight LO harmonics and their corresponding sidebands, for realistic SIS mixer circuits. It is shown that the accuracy of the three approximations depends strongly on the value of omega R(sub N)C for the SIS junctions used. For large omega R(sub N)C, all three approximations approach the eight-harmonic solution. For omega R(sub N)C values in the range 0.5 to 10, the range of most practical interest, the quasi five-frequency approximation is a considerable improvement over the three-frequency approximation, and should be suitable for much design work. For the realistic SIS mixers considered here, the five-frequency approximation gives results very close to those of the eight-harmonic solution. Use of these approximations, where appropriate, considerably reduces the computational effort needed to analyze an SIS mixer, and allows the design and optimization of mixers using a personal computer.

Exponential Approximations Using Fourier Series Partial Sums

NASA Technical Reports Server (NTRS)

Banerjee, Nana S.; Geer, James F.

1997-01-01

The problem of accurately reconstructing a piece-wise smooth, 2(pi)-periodic function f and its first few derivatives, given only a truncated Fourier series representation of f, is studied and solved. The reconstruction process is divided into two steps. In the first step, the first 2N + 1 Fourier coefficients of f are used to approximate the locations and magnitudes of the discontinuities in f and its first M derivatives. This is accomplished by first finding initial estimates of these quantities based on certain properties of Gibbs phenomenon, and then refining these estimates by fitting the asymptotic form of the Fourier coefficients to the given coefficients using a least-squares approach. It is conjectured that the locations of the singularities are approximated to within O(N(sup -M-2), and the associated jump of the k(sup th) derivative of f is approximated to within O(N(sup -M-l+k), as N approaches infinity, and the method is robust. These estimates are then used with a class of singular basis functions, which have certain 'built-in' singularities, to construct a new sequence of approximations to f. Each of these new approximations is the sum of a piecewise smooth function and a new Fourier series partial sum. When N is proportional to M, it is shown that these new approximations, and their derivatives, converge exponentially in the maximum norm to f, and its corresponding derivatives, except in the union of a finite number of small open intervals containing the points of singularity of f. The total measure of these intervals decreases exponentially to zero as M approaches infinity. The technique is illustrated with several examples.

A Gaussian-based rank approximation for subspace clustering

NASA Astrophysics Data System (ADS)

Xu, Fei; Peng, Chong; Hu, Yunhong; He, Guoping

2018-04-01

Low-rank representation (LRR) has been shown successful in seeking low-rank structures of data relationships in a union of subspaces. Generally, LRR and LRR-based variants need to solve the nuclear norm-based minimization problems. Beyond the success of such methods, it has been widely noted that the nuclear norm may not be a good rank approximation because it simply adds all singular values of a matrix together and thus large singular values may dominant the weight. This results in far from satisfactory rank approximation and may degrade the performance of lowrank models based on the nuclear norm. In this paper, we propose a novel nonconvex rank approximation based on the Gaussian distribution function, which has demanding properties to be a better rank approximation than the nuclear norm. Then a low-rank model is proposed based on the new rank approximation with application to motion segmentation. Experimental results have shown significant improvements and verified the effectiveness of our method.

Fundamentals and Recent Developments in Approximate Bayesian Computation

PubMed Central

Lintusaari, Jarno; Gutmann, Michael U.; Dutta, Ritabrata; Kaski, Samuel; Corander, Jukka

2017-01-01

Abstract Bayesian inference plays an important role in phylogenetics, evolutionary biology, and in many other branches of science. It provides a principled framework for dealing with uncertainty and quantifying how it changes in the light of new evidence. For many complex models and inference problems, however, only approximate quantitative answers are obtainable. Approximate Bayesian computation (ABC) refers to a family of algorithms for approximate inference that makes a minimal set of assumptions by only requiring that sampling from a model is possible. We explain here the fundamentals of ABC, review the classical algorithms, and highlight recent developments. [ABC; approximate Bayesian computation; Bayesian inference; likelihood-free inference; phylogenetics; simulator-based models; stochastic simulation models; tree-based models.] PMID:28175922

A test of the adhesion approximation for gravitational clustering

NASA Technical Reports Server (NTRS)

Melott, Adrian L.; Shandarin, Sergei; Weinberg, David H.

1993-01-01

We quantitatively compare a particle implementation of the adhesion approximation to fully non-linear, numerical 'N-body' simulations. Our primary tool, cross-correlation of N-body simulations with the adhesion approximation, indicates good agreement, better than that found by the same test performed with the Zel-dovich approximation (hereafter ZA). However, the cross-correlation is not as good as that of the truncated Zel-dovich approximation (TZA), obtained by applying the Zel'dovich approximation after smoothing the initial density field with a Gaussian filter. We confirm that the adhesion approximation produces an excessively filamentary distribution. Relative to the N-body results, we also find that: (a) the power spectrum obtained from the adhesion approximation is more accurate than that from ZA or TZA, (b) the error in the phase angle of Fourier components is worse than that from TZA, and (c) the mass distribution function is more accurate than that from ZA or TZA. It appears that adhesion performs well statistically, but that TZA is more accurate dynamically, in the sense of moving mass to the right place.

A test of the adhesion approximation for gravitational clustering

NASA Technical Reports Server (NTRS)

Melott, Adrian L.; Shandarin, Sergei F.; Weinberg, David H.

1994-01-01

We quantitatively compare a particle implementation of the adhesion approximation to fully nonlinear, numerical 'N-body' simulations. Our primary tool, cross-correlation of N-body simulations with the adhesion approximation, indicates good agreement, better than that found by the same test performed with the Zel'dovich approximation (hereafter ZA). However, the cross-correlation is not as good as that of the truncated Zel'dovich approximation (TZA), obtained by applying the Zel'dovich approximation after smoothing the initial density field with a Gaussian filter. We confirm that the adhesion approximation produces an excessively filamentary distribution. Relative to the N-body results, we also find that: (a) the power spectrum obtained from the adhesion approximation is more accurate that that from ZA to TZA, (b) the error in the phase angle of Fourier components is worse that that from TZA, and (c) the mass distribution function is more accurate than that from ZA or TZA. It appears that adhesion performs well statistically, but that TZA is more accurate dynamically, in the sense of moving mass to the right place.

On the origins of approximations for stochastic chemical kinetics.

PubMed

Haseltine, Eric L; Rawlings, James B

2005-10-22

This paper considers the derivation of approximations for stochastic chemical kinetics governed by the discrete master equation. Here, the concepts of (1) partitioning on the basis of fast and slow reactions as opposed to fast and slow species and (2) conditional probability densities are used to derive approximate, partitioned master equations, which are Markovian in nature, from the original master equation. Under different conditions dictated by relaxation time arguments, such approximations give rise to both the equilibrium and hybrid (deterministic or Langevin equations coupled with discrete stochastic simulation) approximations previously reported. In addition, the derivation points out several weaknesses in previous justifications of both the hybrid and equilibrium systems and demonstrates the connection between the original and approximate master equations. Two simple examples illustrate situations in which these two approximate methods are applicable and demonstrate the two methods' efficiencies.

Alternative approximation concepts for space frame synthesis

NASA Technical Reports Server (NTRS)

Lust, R. V.; Schmit, L. A.

1985-01-01

A structural synthesis methodology for the minimum mass design of 3-dimensionall frame-truss structures under multiple static loading conditions and subject to limits on displacements, rotations, stresses, local buckling, and element cross-sectional dimensions is presented. A variety of approximation concept options are employed to yield near optimum designs after no more than 10 structural analyses. Available options include: (A) formulation of the nonlinear mathematcal programming problem in either reciprocal section property (RSP) or cross-sectional dimension (CSD) space; (B) two alternative approximate problem structures in each design space; and (C) three distinct assumptions about element end-force variations. Fixed element, design element linking, and temporary constraint deletion features are also included. The solution of each approximate problem, in either its primal or dual form, is obtained using CONMIN, a feasible directions program. The frame-truss synthesis methodology is implemented in the COMPASS computer program and is used to solve a variety of problems. These problems were chosen so that, in addition to exercising the various approximation concepts options, the results could be compared with previously published work.

Obituary: Elizabeth Katherine Holmes, 1973-2004

NASA Astrophysics Data System (ADS)

Beichman, Charles Arnold

2004-12-01

from Florida in 2002, Beth took up a National Research Council postdoctoral position at the Jet Propulsion Laboratory with Charles Beichman and T. Velusamy with the goal of applying her theoretical knowledge of zodiacal clouds to observations from the Spitzer Space telescope. In advance of the launch of Spitzer, Beth gathered detailed information on over 150 solar type stars and carefully planned a Spitzer observing program to detect faint zodiacal signals. While waiting through numerous launch delays, she prepared models of zodiacal clouds influenced by the presence of planets to be ready when Spitzer images of stars like Vega, Upsilon Andromedae, and Fomalhaut became available. These models were presented as talks and posters at a number of conferences. Her models were a critical part of the Early Release Observations of Fomalhaut and the subsequent Spitzer paper on the possibility that a Jovian-mass planet located approximately 40 AU from the star was responsible for the structures seen in the Fomalhaut disk. The Fomalhaut paper in the special Spitzer edition of the Astrophysical Journal is dedicated to Beth's memory. Beth was an enthusiastic and cheerful colleague who made friends everywhere she worked. In addition to developing friendships and collaborations at JPL, she became a valued member of the Spitzer/MIPS instrument team at the University of Arizona. She was active on the Committee on the Status of Women in Astronomy of the American Astronomical Society, publishing an article on "The Postdoc Perspective on the Women in Astronomy II Conference" in the January 2004 issue of STATUS, the CSWA magazine, and serving as an associate editor of that magazine. She was an inspiring role model for young women in science, befriending and mentoring a number of Caltech women undergraduates, as well as making numerous appearances in K-12 classrooms for science outreach. She pursued her love of plants (cactus in particular), cats and fish, spending her spare time lovingly

Approximating Integrals Using Probability

ERIC Educational Resources Information Center

Maruszewski, Richard F., Jr.; Caudle, Kyle A.

2005-01-01

As part of a discussion on Monte Carlo methods, which outlines how to use probability expectations to approximate the value of a definite integral. The purpose of this paper is to elaborate on this technique and then to show several examples using visual basic as a programming tool. It is an interesting method because it combines two branches of…

A review of electron-nucleus bremsstrahlung cross sections between 1 and 10 MeV

NASA Astrophysics Data System (ADS)

Mangiarotti, A.; Martins, M. N.

2017-12-01

More than 80 years have passed since the first calculations of electron-nucleus bremsstrahlung cross sections were published by Sommerfeld, for non-relativistic electrons, and, independently, by Sauter, Bethe and Heitler, and Racah, for relativistic electrons. The Bethe-Heitler expression, that is based on the first Born approximation and includes the screening of the Coulomb field of the nucleus by the atomic electrons, has proven to work well at moderately high energies where the Landau-Pomeranchuk-Migdal effect is negligible. We review the current theoretical and experimental status with a highlight on electrons with kinetic energies between 1 and 10 MeV. The choice is motivated by the peculiar difficulties present in this energy region, where it is necessary to treat simultaneously the interaction with the Coulomb field beyond the first Born approximation and the effect of screening. A fully numerical approach within the S-matrix formalism has proven to be extremely difficult above a few MeV, because the number of partial waves needed for an accurate evaluation is prohibitively large. Here we focus on analytic results, including the more complex ones employing the Furry-Sommerfeld-Maue wave functions and taking into account the next-to-leading order, and discuss the advantages and limitations in light of the best available data. The influence of multiple scattering in the target is investigated under the actual experimental conditions. A comparison with the widely used cross section tabulations by Seltzer and Berger is also presented.

Spline approximations for nonlinear hereditary control systems

NASA Technical Reports Server (NTRS)

Daniel, P. L.

1982-01-01

A sline-based approximation scheme is discussed for optimal control problems governed by nonlinear nonautonomous delay differential equations. The approximating framework reduces the original control problem to a sequence of optimization problems governed by ordinary differential equations. Convergence proofs, which appeal directly to dissipative-type estimates for the underlying nonlinear operator, are given and numerical findings are summarized.

Approximate supernova remnant dynamics with cosmic ray production

NASA Technical Reports Server (NTRS)

Voelk, H. J.; Drury, L. O.; Dorfi, E. A.

1985-01-01

Supernova explosions are the most violent and energetic events in the galaxy and have long been considered probably sources of Cosmic Rays. Recent shock acceleration models treating the Cosmic Rays (CR's) as test particles nb a prescribed Supernova Remnant (SNR) evolution, indeed indicate an approximate power law momentum distribution f sub source (p) approximation p(-a) for the particles ultimately injected into the Interstellar Medium (ISM). This spectrum extends almost to the momentum p = 1 million GeV/c, where the break in the observed spectrum occurs. The calculated power law index approximately less than 4.2 agrees with that inferred for the galactic CR sources. The absolute CR intensity can however not be well determined in such a test particle approximation.

(Small) Resonant non-Gaussianities: Signatures of a Discrete Shift Symmetry in the Effective Field Theory of Inflation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Behbahani, Siavosh R.; /SLAC /Stanford U., Phys. Dept. /Boston U.; Dymarsky, Anatoly

2012-06-06

We apply the Effective Field Theory of Inflation to study the case where the continuous shift symmetry of the Goldstone boson {pi} is softly broken to a discrete subgroup. This case includes and generalizes recently proposed String Theory inspired models of Inflation based on Axion Monodromy. The models we study have the property that the 2-point function oscillates as a function of the wavenumber, leading to oscillations in the CMB power spectrum. The non-linear realization of time diffeomorphisms induces some self-interactions for the Goldstone boson that lead to a peculiar non-Gaussianity whose shape oscillates as a function of the wavenumber.more » We find that in the regime of validity of the effective theory, the oscillatory signal contained in the n-point correlation functions, with n > 2, is smaller than the one contained in the 2-point function, implying that the signature of oscillations, if ever detected, will be easier to find first in the 2-point function, and only then in the higher order correlation functions. Still the signal contained in higher-order correlation functions, that we study here in generality, could be detected at a subleading level, providing a very compelling consistency check for an approximate discrete shift symmetry being realized during inflation.« less

Properties of the Boltzmann equation in the classical approximation

DOE PAGES

Epelbaum, Thomas; Gelis, François; Tanji, Naoto; ...

2014-12-30

We examine the Boltzmann equation with elastic point-like scalar interactions in two different versions of the the classical approximation. Although solving numerically the Boltzmann equation with the unapproximated collision term poses no problem, this allows one to study the effect of the ultraviolet cutoff in these approximations. This cutoff dependence in the classical approximations of the Boltzmann equation is closely related to the non-renormalizability of the classical statistical approximation of the underlying quantum field theory. The kinetic theory setup that we consider here allows one to study in a much simpler way the dependence on the ultraviolet cutoff, since onemore » has also access to the non-approximated result for comparison.« less

Recent advances in approximation concepts for optimum structural design

NASA Technical Reports Server (NTRS)

Barthelemy, Jean-Francois M.; Haftka, Raphael T.

1991-01-01

The basic approximation concepts used in structural optimization are reviewed. Some of the most recent developments in that area since the introduction of the concept in the mid-seventies are discussed. The paper distinguishes between local, medium-range, and global approximations; it covers functions approximations and problem approximations. It shows that, although the lack of comparative data established on reference test cases prevents an accurate assessment, there have been significant improvements. The largest number of developments have been in the areas of local function approximations and use of intermediate variable and response quantities. It also appears that some new methodologies are emerging which could greatly benefit from the introduction of new computer architecture.

Is approximated de-epithelized glanuloplasty beneficial for hypospadiologist?

PubMed

ZakiEldahshoury, M; Gamal, W; Salem, E; Rashed, E; Mamdouh, A

2016-05-01

Further evaluation of the cosmetic and functional results of approximated de-epithelized glanuloplasty in different degree of hypospadias. This study included 96 male patients (DPH=68 & MPH=28). Patients selected for repair with glans approximation should have wide urethral plate & grooved glans. All cases were repaired with the classic TIP and glans approximation technique. Follow up was for one year by clinical examination of the meatal shape, size & site, glans shape, skin covering, suture line, urethral catheter, edema & fistula in addition to parent satisfaction. Mean operative time was 49±9minutes. As regards the functional and cosmetic outcomes, success was reported in 95.8%, while failure was in 4.16% in the form of glanular disruption in two patients and subcoronal urethrocutaneous fistula in another two patients. Glans approximation has many advantages, good cosmetic and functional results, short operative time, less blood loss, no need for tourniquet. Study of a large number of cases and comparing glans approximation with the classic TIP technique. Copyright © 2015 AEU. Publicado por Elsevier España, S.L.U. All rights reserved.

Adaptive control using neural networks and approximate models.

PubMed

Narendra, K S; Mukhopadhyay, S

1997-01-01

The NARMA model is an exact representation of the input-output behavior of finite-dimensional nonlinear discrete-time dynamical systems in a neighborhood of the equilibrium state. However, it is not convenient for purposes of adaptive control using neural networks due to its nonlinear dependence on the control input. Hence, quite often, approximate methods are used for realizing the neural controllers to overcome computational complexity. In this paper, we introduce two classes of models which are approximations to the NARMA model, and which are linear in the control input. The latter fact substantially simplifies both the theoretical analysis as well as the practical implementation of the controller. Extensive simulation studies have shown that the neural controllers designed using the proposed approximate models perform very well, and in many cases even better than an approximate controller designed using the exact NARMA model. In view of their mathematical tractability as well as their success in simulation studies, a case is made in this paper that such approximate input-output models warrant a detailed study in their own right.

Rational trigonometric approximations using Fourier series partial sums

NASA Technical Reports Server (NTRS)

Geer, James F.

1993-01-01

A class of approximations (S(sub N,M)) to a periodic function f which uses the ideas of Pade, or rational function, approximations based on the Fourier series representation of f, rather than on the Taylor series representation of f, is introduced and studied. Each approximation S(sub N,M) is the quotient of a trigonometric polynomial of degree N and a trigonometric polynomial of degree M. The coefficients in these polynomials are determined by requiring that an appropriate number of the Fourier coefficients of S(sub N,M) agree with those of f. Explicit expressions are derived for these coefficients in terms of the Fourier coefficients of f. It is proven that these 'Fourier-Pade' approximations converge point-wise to (f(x(exp +))+f(x(exp -)))/2 more rapidly (in some cases by a factor of 1/k(exp 2M)) than the Fourier series partial sums on which they are based. The approximations are illustrated by several examples and an application to the solution of an initial, boundary value problem for the simple heat equation is presented.

Status of Goldstone solar energy system study of the first Goldstone energy project

NASA Technical Reports Server (NTRS)

Lansing, F. L.

1977-01-01

The results reached by the DSN engineering section and private consultants in the review of the initial plan of the Golstone Energy Project are summarized. The main objectives were in the areas of energy conservation and the application of solar-driven systems for power and hydrogen generation. This summary will provide background data for management planning decisions both to the DSN engineering section and other organizations planning a similar program. The review showed that an add-on solar driven absorption refrigeration unit with its associated changes to the existing system was not cost-effective, having a payback period of 29 years. Similar economically unattractive results were found for both a solar-hydrogen and a wind-hydrogen generation plant. However, cutting the hydrogen generation linkage from this plant improved its economic feasibility.

Self-consistent approximation beyond the CPA: Part II

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kaplan, T.; Gray, L.J.

1981-08-01

In Part I, Professor Leath has described the substantial efforts to generalize the CPA. In this second part, a particular self-consistent approximation for random alloys developed by Kaplan, Leath, Gray, and Diehl is described. This approximation is applicable to diagonal, off-diagonal and environmental disorder, includes cluster scattering, and yields a translationally invariant and analytic (Herglotz) average Green's function. Furthermore Gray and Kaplan have shown that an approximation for alloys with short-range order can be constructed from this theory.

A Gaussian Approximation Potential for Silicon

NASA Astrophysics Data System (ADS)

Bernstein, Noam; Bartók, Albert; Kermode, James; Csányi, Gábor

We present an interatomic potential for silicon using the Gaussian Approximation Potential (GAP) approach, which uses the Gaussian process regression method to approximate the reference potential energy surface as a sum of atomic energies. Each atomic energy is approximated as a function of the local environment around the atom, which is described with the smooth overlap of atomic environments (SOAP) descriptor. The potential is fit to a database of energies, forces, and stresses calculated using density functional theory (DFT) on a wide range of configurations from zero and finite temperature simulations. These include crystalline phases, liquid, amorphous, and low coordination structures, and diamond-structure point defects, dislocations, surfaces, and cracks. We compare the results of the potential to DFT calculations, as well as to previously published models including Stillinger-Weber, Tersoff, modified embedded atom method (MEAM), and ReaxFF. We show that it is very accurate as compared to the DFT reference results for a wide range of properties, including low energy bulk phases, liquid structure, as well as point, line, and plane defects in the diamond structure.

CMB-lensing beyond the Born approximation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Marozzi, Giovanni; Fanizza, Giuseppe; Durrer, Ruth

2016-09-01

We investigate the weak lensing corrections to the cosmic microwave background temperature anisotropies considering effects beyond the Born approximation. To this aim, we use the small deflection angle approximation, to connect the lensed and unlensed power spectra, via expressions for the deflection angles up to third order in the gravitational potential. While the small deflection angle approximation has the drawback to be reliable only for multipoles ℓ ∼< 2500, it allows us to consistently take into account the non-Gaussian nature of cosmological perturbation theory beyond the linear level. The contribution to the lensed temperature power spectrum coming from the non-Gaussianmore » nature of the deflection angle at higher order is a new effect which has not been taken into account in the literature so far. It turns out to be the leading contribution among the post-Born lensing corrections. On the other hand, the effect is smaller than corrections coming from non-linearities in the matter power spectrum, and its imprint on CMB lensing is too small to be seen in present experiments.« less

New Hardness Results for Diophantine Approximation

NASA Astrophysics Data System (ADS)

Eisenbrand, Friedrich; Rothvoß, Thomas

We revisit simultaneous Diophantine approximation, a classical problem from the geometry of numbers which has many applications in algorithms and complexity. The input to the decision version of this problem consists of a rational vector α ∈ ℚ n , an error bound ɛ and a denominator bound N ∈ ℕ + . One has to decide whether there exists an integer, called the denominator Q with 1 ≤ Q ≤ N such that the distance of each number Q ·α i to its nearest integer is bounded by ɛ. Lagarias has shown that this problem is NP-complete and optimization versions have been shown to be hard to approximate within a factor n c/ loglogn for some constant c > 0. We strengthen the existing hardness results and show that the optimization problem of finding the smallest denominator Q ∈ ℕ + such that the distances of Q·α i to the nearest integer are bounded by ɛ is hard to approximate within a factor 2 n unless {textrm{P}} = NP.

Local approximation of a metapopulation's equilibrium.

PubMed

Barbour, A D; McVinish, R; Pollett, P K

2018-04-18

We consider the approximation of the equilibrium of a metapopulation model, in which a finite number of patches are randomly distributed over a bounded subset [Formula: see text] of Euclidean space. The approximation is good when a large number of patches contribute to the colonization pressure on any given unoccupied patch, and when the quality of the patches varies little over the length scale determined by the colonization radius. If this is the case, the equilibrium probability of a patch at z being occupied is shown to be close to [Formula: see text], the equilibrium occupation probability in Levins's model, at any point [Formula: see text] not too close to the boundary, if the local colonization pressure and extinction rates appropriate to z are assumed. The approximation is justified by giving explicit upper and lower bounds for the occupation probabilities, expressed in terms of the model parameters. Since the patches are distributed randomly, the occupation probabilities are also random, and we complement our bounds with explicit bounds on the probability that they are satisfied at all patches simultaneously.

BORN CROSS SECTIONS FOR INELASTIC SCATTERING OF ELECTRONS BY HYDROGEN ATOMS. III. 5s, 5p, 5d, 5f, 5g STATES

DOE Office of Scientific and Technical Information (OSTI.GOV)

Milford, S.N.; Morrissey, J.J.; Scanlon, J.H.

1960-12-01

Born total cross sections were computed for the strong optically allowed transitions from n = 5 to n' = 6, at incident energies between 0.2 and 1361 ev. Thirty energy values were considered for the 5s to 6p and 5g to 6h cases, and nine for the other transitions. The cross sections obtained were larger than those of comparable transitions for lower n. The Bethe (dipole) approximation was also used, and was found to give good agreement with the Born results down to relatively low energies ( approx equal 3 ev). (auth)

Fostering Formal Commutativity Knowledge with Approximate Arithmetic

PubMed Central

Hansen, Sonja Maria; Haider, Hilde; Eichler, Alexandra; Godau, Claudia; Frensch, Peter A.; Gaschler, Robert

2015-01-01

How can we enhance the understanding of abstract mathematical principles in elementary school? Different studies found out that nonsymbolic estimation could foster subsequent exact number processing and simple arithmetic. Taking the commutativity principle as a test case, we investigated if the approximate calculation of symbolic commutative quantities can also alter the access to procedural and conceptual knowledge of a more abstract arithmetic principle. Experiment 1 tested first graders who had not been instructed about commutativity in school yet. Approximate calculation with symbolic quantities positively influenced the use of commutativity-based shortcuts in formal arithmetic. We replicated this finding with older first graders (Experiment 2) and third graders (Experiment 3). Despite the positive effect of approximation on the spontaneous application of commutativity-based shortcuts in arithmetic problems, we found no comparable impact on the application of conceptual knowledge of the commutativity principle. Overall, our results show that the usage of a specific arithmetic principle can benefit from approximation. However, the findings also suggest that the correct use of certain procedures does not always imply conceptual understanding. Rather, the conceptual understanding of commutativity seems to lag behind procedural proficiency during elementary school. PMID:26560311

Mott physics beyond the Brinkman-Rice scenario

NASA Astrophysics Data System (ADS)

Wysokiński, Marcin M.; Fabrizio, Michele

2017-04-01

The main flaw of the well-known Brinkman-Rice description, obtained through the Gutzwiller approximation, of the paramagnetic Mott transition in the Hubbard model is in neglecting high-energy virtual processes that generate, for instance, the antiferromagnetic exchange J ˜t2/U . Here, we propose a way to capture those processes by combining the Brinkman-Rice approach with a variational Schrieffer-Wolff transformation, and apply this method to study the single-band metal-to-insulator transition in a Bethe lattice with infinite coordination number, where the Gutzwiller approximation becomes exact. We indeed find for the Mott transition a description very close to the real one provided by the dynamical mean-field theory, an encouraging result in view of possible applications to more involved models.

A Discrete Approximation Framework for Hereditary Systems.

DTIC Science & Technology

1980-05-01

schemes which are included in the general framework and which may be implemented directly on high-speed computing machines are developed. A numerical...an appropriately chosen Hilbert space. We then proceed to develop general approximation schemes for the solutions to the homogeneous AEE which in turn...rich classes of these schemes . In addition, two particular families of approximation schemes included in the general framework are developed and

Best uniform approximation to a class of rational functions

NASA Astrophysics Data System (ADS)

Zheng, Zhitong; Yong, Jun-Hai

2007-10-01

We explicitly determine the best uniform polynomial approximation to a class of rational functions of the form 1/(x-c)2+K(a,b,c,n)/(x-c) on [a,b] represented by their Chebyshev expansion, where a, b, and c are real numbers, n-1 denotes the degree of the best approximating polynomial, and K is a constant determined by a, b, c, and n. Our result is based on the explicit determination of a phase angle [eta] in the representation of the approximation error by a trigonometric function. Moreover, we formulate an ansatz which offers a heuristic strategies to determine the best approximating polynomial to a function represented by its Chebyshev expansion. Combined with the phase angle method, this ansatz can be used to find the best uniform approximation to some more functions.

Approximating the Helium Wavefunction in Positronium-Helium Scattering

NASA Technical Reports Server (NTRS)

DiRienzi, Joseph; Drachman, Richard J.

2003-01-01

In the Kohn variational treatment of the positronium- hydrogen scattering problem the scattering wave function is approximated by an expansion in some appropriate basis set, but the target and projectile wave functions are known exactly. In the positronium-helium case, however, a difficulty immediately arises in that the wave function of the helium target atom is not known exactly, and there are several ways to deal with the associated eigenvalue in formulating the variational scattering equations to be solved. In this work we will use the Kohn variational principle in the static exchange approximation to d e t e e the zero-energy scattering length for the Ps-He system, using a suite of approximate target functions. The results we obtain will be compared with each other and with corresponding values found by other approximation techniques.

Minimax rational approximation of the Fermi-Dirac distribution.

PubMed

Moussa, Jonathan E

2016-10-28

Accurate rational approximations of the Fermi-Dirac distribution are a useful component in many numerical algorithms for electronic structure calculations. The best known approximations use O(log(βΔ)log(ϵ -1 )) poles to achieve an error tolerance ϵ at temperature β -1 over an energy interval Δ. We apply minimax approximation to reduce the number of poles by a factor of four and replace Δ with Δ occ , the occupied energy interval. This is particularly beneficial when Δ ≫ Δ occ , such as in electronic structure calculations that use a large basis set.

Minimax rational approximation of the Fermi-Dirac distribution

NASA Astrophysics Data System (ADS)

Moussa, Jonathan E.

2016-10-01

Accurate rational approximations of the Fermi-Dirac distribution are a useful component in many numerical algorithms for electronic structure calculations. The best known approximations use O(log(βΔ)log(ɛ-1)) poles to achieve an error tolerance ɛ at temperature β-1 over an energy interval Δ. We apply minimax approximation to reduce the number of poles by a factor of four and replace Δ with Δocc, the occupied energy interval. This is particularly beneficial when Δ ≫ Δocc, such as in electronic structure calculations that use a large basis set.

On direct theorems for best polynomial approximation

NASA Astrophysics Data System (ADS)

Auad, A. A.; AbdulJabbar, R. S.

2018-05-01

This paper is to obtain similarity for the best approximation degree of functions, which are unbounded in L p,α (A = [0,1]), which called weighted space by algebraic polynomials. {E}nH{(f)}p,α and the best approximation degree in the same space on the interval [0,2π] by trigonometric polynomials {E}nT{(f)}p,α of direct wellknown theorems in forms the average modules.

Background magnetic spectra - Approximately 10 to the -5th to approximately 10 to the 5th Hz

NASA Astrophysics Data System (ADS)

Lanzerotti, L. J.; Maclennan, C. G.; Fraser-Smith, A. C.

1990-09-01

The determination of the amplitude and functional form of the geomagnetic fluctuations measured at the Arrival Heights area of the Hut Point Peninsula on Ross Island in June 1986 is presented. The frequency range covered is from approximately 10 to the -5th to approximately 10 to the 5th Hz, with a gap between 0.1 and 10 Hz due to instrumentation limitations. In spite of this gap, it is thought that these magnetic fluctuation spectra, obtained from data acquired simultaneously with two instruments, cover the broadest frequency range to date. Schematic spectra derived from the data obtained are provided.

Compression of strings with approximate repeats.

PubMed

Allison, L; Edgoose, T; Dix, T I

1998-01-01

We describe a model for strings of characters that is loosely based on the Lempel Ziv model with the addition that a repeated substring can be an approximate match to the original substring; this is close to the situation of DNA, for example. Typically there are many explanations for a given string under the model, some optimal and many suboptimal. Rather than commit to one optimal explanation, we sum the probabilities over all explanations under the model because this gives the probability of the data under the model. The model has a small number of parameters and these can be estimated from the given string by an expectation-maximization (EM) algorithm. Each iteration of the EM algorithm takes O(n2) time and a few iterations are typically sufficient. O(n2) complexity is impractical for strings of more than a few tens of thousands of characters and a faster approximation algorithm is also given. The model is further extended to include approximate reverse complementary repeats when analyzing DNA strings. Tests include the recovery of parameter estimates from known sources and applications to real DNA strings.

Environmental projects. Volume 5, part 1: Study of subsurface contamination. Part 2: Guide to implement environmental compliance programs

NASA Technical Reports Server (NTRS)

Bengelsdorf, I.

1988-01-01

In support of the national goal for the preservation of the environment and the protection of human health and safety, NASA, the Jet Propulsion Laboratory, and the Goldstone Deep Space Communications Complex have adopted the position that their operating installations shall maintain a high level of compliance in regard to regulations concerning environmental hazards. An investigation carried out by Engineering Science, Inc. focused on possible underground contamination that may have resulted from leaks and/or spills from storage facilities at the Goldstone Communications Complex. It also involved the cleanup of a non-hazardous waste dumpsite at the Mojave Base Site at the Goldstone complex. The report also includes details of the management duties and responsibilities needed to maintain compliance with environmental laws and regulations.

Approximating smooth functions using algebraic-trigonometric polynomials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sharapudinov, Idris I

2011-01-14

The problem under consideration is that of approximating classes of smooth functions by algebraic-trigonometric polynomials of the form p{sub n}(t)+{tau}{sub m}(t), where p{sub n}(t) is an algebraic polynomial of degree n and {tau}{sub m}(t)=a{sub 0}+{Sigma}{sub k=1}{sup m}a{sub k} cos k{pi}t + b{sub k} sin k{pi}t is a trigonometric polynomial of order m. The precise order of approximation by such polynomials in the classes W{sup r}{sub {infinity}(}M) and an upper bound for similar approximations in the class W{sup r}{sub p}(M) with 4/3

Minimax rational approximation of the Fermi-Dirac distribution

DOE PAGES

Moussa, Jonathan E.

2016-10-27

Accurate rational approximations of the Fermi-Dirac distribution are a useful component in many numerical algorithms for electronic structure calculations. The best known approximations use O(log(βΔ)log(ϵ –1)) poles to achieve an error tolerance ϵ at temperature β –1 over an energy interval Δ. We apply minimax approximation to reduce the number of poles by a factor of four and replace Δ with Δ occ, the occupied energy interval. Furthermore, this is particularly beneficial when Δ >> Δ occ, such as in electronic structure calculations that use a large basis set.

Incorporating approximation error in surrogate based Bayesian inversion

NASA Astrophysics Data System (ADS)

Zhang, J.; Zeng, L.; Li, W.; Wu, L.

2015-12-01

There are increasing interests in applying surrogates for inverse Bayesian modeling to reduce repetitive evaluations of original model. In this way, the computational cost is expected to be saved. However, the approximation error of surrogate model is usually overlooked. This is partly because that it is difficult to evaluate the approximation error for many surrogates. Previous studies have shown that, the direct combination of surrogates and Bayesian methods (e.g., Markov Chain Monte Carlo, MCMC) may lead to biased estimations when the surrogate cannot emulate the highly nonlinear original system. This problem can be alleviated by implementing MCMC in a two-stage manner. However, the computational cost is still high since a relatively large number of original model simulations are required. In this study, we illustrate the importance of incorporating approximation error in inverse Bayesian modeling. Gaussian process (GP) is chosen to construct the surrogate for its convenience in approximation error evaluation. Numerical cases of Bayesian experimental design and parameter estimation for contaminant source identification are used to illustrate this idea. It is shown that, once the surrogate approximation error is well incorporated into Bayesian framework, promising results can be obtained even when the surrogate is directly used, and no further original model simulations are required.

The closure approximation in the hierarchy equations.

NASA Technical Reports Server (NTRS)

Adomian, G.

1971-01-01

The expectation of the solution process in a stochastic operator equation can be obtained from averaged equations only under very special circumstances. Conditions for validity are given and the significance and validity of the approximation in widely used hierarchy methods and the ?self-consistent field' approximation in nonequilibrium statistical mechanics are clarified. The error at any level of the hierarchy can be given and can be avoided by the use of the iterative method.

Adequacy of selected evapotranspiration approximations for hydrologic simulation

USGS Publications Warehouse

Sumner, D.M.

2006-01-01

Evapotranspiration (ET) approximations, usually based on computed potential ET (PET) and diverse PET-to-ET conceptualizations, are routinely used in hydrologic analyses. This study presents an approach to incorporate measured (actual) ET data, increasingly available using micrometeorological methods, to define the adequacy of ET approximations for hydrologic simulation. The approach is demonstrated at a site where eddy correlation-measured ET values were available. A baseline hydrologic model incorporating measured ET values was used to evaluate the sensitivity of simulated water levels, subsurface recharge, and surface runoff to error in four ET approximations. An annually invariant pattern of mean monthly vegetation coefficients was shown to be most effective, despite the substantial year-to-year variation in measured vegetation coefficients. The temporal variability of available water (precipitation minus ET) at the humid, subtropical site was largely controlled by the relatively high temporal variability of precipitation, benefiting the effectiveness of coarse ET approximations, a result that is likely to prevail at other humid sites.

Dynamics of bright-bright solitons in Bose-Einstein condensate with Raman-induced one-dimensional spin-orbit coupling

NASA Astrophysics Data System (ADS)

Wen, Lin; Zhang, Xiao-Fei; Hu, Ai-Yuan; Zhou, Jing; Yu, Peng; Xia, Lei; Sun, Qing; Ji, An-Chun

2018-03-01

We investigate the dynamics of bright-bright solitons in one-dimensional two-component Bose-Einstein condensates with Raman-induced spin-orbit coupling, via the variational approximation and the numerical simulation of Gross-Pitaevskii equations. For the uniform system without trapping potential, we obtain two population balanced stationary solitons. By performing the linear stability analysis, we find a Goldstone eigenmode and an oscillation eigenmode around these stationary solitons. Moreover, we derive a general dynamical solution to describe the center-of-mass motion and spin evolution of the solitons under the action of spin-orbit coupling. The effects of a harmonic trap have also been discussed.

Approximate analytic expression for the Skyrmions crystal

NASA Astrophysics Data System (ADS)

Grandi, Nicolás; Sturla, Mauricio

2018-01-01

We find approximate solutions for the two-dimensional nonlinear Σ-model with Dzyalioshinkii-Moriya term, representing magnetic Skyrmions. They are built in an analytic form, by pasting different approximate solutions found in different regions of space. We verify that our construction reproduces the phenomenology known from numerical solutions and Monte Carlo simulations, giving rise to a Skyrmion lattice at an intermediate range of magnetic field, flanked by spiral and spin-polarized phases for low and high magnetic fields, respectively.

On Born approximation in black hole scattering

NASA Astrophysics Data System (ADS)

Batic, D.; Kelkar, N. G.; Nowakowski, M.

2011-12-01

A massless field propagating on spherically symmetric black hole metrics such as the Schwarzschild, Reissner-Nordström and Reissner-Nordström-de Sitter backgrounds is considered. In particular, explicit formulae in terms of transcendental functions for the scattering of massless scalar particles off black holes are derived within a Born approximation. It is shown that the conditions on the existence of the Born integral forbid a straightforward extraction of the quasi normal modes using the Born approximation for the scattering amplitude. Such a method has been used in literature. We suggest a novel, well defined method, to extract the large imaginary part of quasinormal modes via the Coulomb-like phase shift. Furthermore, we compare the numerically evaluated exact scattering amplitude with the Born one to find that the approximation is not very useful for the scattering of massless scalar, electromagnetic as well as gravitational waves from black holes.

Efficient solution of parabolic equations by Krylov approximation methods

NASA Technical Reports Server (NTRS)

Gallopoulos, E.; Saad, Y.

1990-01-01

Numerical techniques for solving parabolic equations by the method of lines is addressed. The main motivation for the proposed approach is the possibility of exploiting a high degree of parallelism in a simple manner. The basic idea of the method is to approximate the action of the evolution operator on a given state vector by means of a projection process onto a Krylov subspace. Thus, the resulting approximation consists of applying an evolution operator of a very small dimension to a known vector which is, in turn, computed accurately by exploiting well-known rational approximations to the exponential. Because the rational approximation is only applied to a small matrix, the only operations required with the original large matrix are matrix-by-vector multiplications, and as a result the algorithm can easily be parallelized and vectorized. Some relevant approximation and stability issues are discussed. We present some numerical experiments with the method and compare its performance with a few explicit and implicit algorithms.

Precise analytic approximations for the Bessel function J1 (x)

NASA Astrophysics Data System (ADS)

Maass, Fernando; Martin, Pablo

2018-03-01

Precise and straightforward analytic approximations for the Bessel function J1 (x) have been found. Power series and asymptotic expansions have been used to determine the parameters of the approximation, which is as a bridge between both expansions, and it is a combination of rational and trigonometric functions multiplied with fractional powers of x. Here, several improvements with respect to the so called Multipoint Quasirational Approximation technique have been performed. Two procedures have been used to determine the parameters of the approximations. The maximum absolute errors are in both cases smaller than 0.01. The zeros of the approximation are also very precise with less than 0.04 per cent for the first one. A second approximation has been also determined using two more parameters, and in this way the accuracy has been increased to less than 0.001.

An approximation method for configuration optimization of trusses

NASA Technical Reports Server (NTRS)

Hansen, Scott R.; Vanderplaats, Garret N.

1988-01-01

Two- and three-dimensional elastic trusses are designed for minimum weight by varying the areas of the members and the location of the joints. Constraints on member stresses and Euler buckling are imposed and multiple static loading conditions are considered. The method presented here utilizes an approximate structural analysis based on first order Taylor series expansions of the member forces. A numerical optimizer minimizes the weight of the truss using information from the approximate structural analysis. Comparisons with results from other methods are made. It is shown that the method of forming an approximate structural analysis based on linearized member forces leads to a highly efficient method of truss configuration optimization.

Geometrical-optics approximation of forward scattering by coated particles.

PubMed

Xu, Feng; Cai, Xiaoshu; Ren, Kuanfang

2004-03-20

By means of geometrical optics we present an approximation algorithm with which to accelerate the computation of scattering intensity distribution within a forward angular range (0 degrees-60 degrees) for coated particles illuminated by a collimated incident beam. Phases of emerging rays are exactly calculated to improve the approximation precision. This method proves effective for transparent and tiny absorbent particles with size parameters larger than 75 but fails to give good approximation results at scattering angles at which refractive rays are absent. When the absorption coefficient of a particle is greater than 0.01, the geometrical optics approximation is effective only for forward small angles, typically less than 10 degrees or so.

Revised Thomas-Fermi approximation for singular potentials

NASA Astrophysics Data System (ADS)

Dufty, James W.; Trickey, S. B.

2016-08-01

Approximations for the many-fermion free-energy density functional that include the Thomas-Fermi (TF) form for the noninteracting part lead to singular densities for singular external potentials (e.g., attractive Coulomb). This limitation of the TF approximation is addressed here by a formal map of the exact Euler equation for the density onto an equivalent TF form characterized by a modified Kohn-Sham potential. It is shown to be a "regularized" version of the Kohn-Sham potential, tempered by convolution with a finite-temperature response function. The resulting density is nonsingular, with the equilibrium properties obtained from the total free-energy functional evaluated at this density. This new representation is formally exact. Approximate expressions for the regularized potential are given to leading order in a nonlocality parameter, and the limiting behavior at high and low temperatures is described. The noninteracting part of the free energy in this approximation is the usual Thomas-Fermi functional. These results generalize and extend to finite temperatures the ground-state regularization by R. G. Parr and S. Ghosh [Proc. Natl. Acad. Sci. U.S.A. 83, 3577 (1986), 10.1073/pnas.83.11.3577] and by L. R. Pratt, G. G. Hoffman, and R. A. Harris [J. Chem. Phys. 88, 1818 (1988), 10.1063/1.454105] and formally systematize the finite-temperature regularization given by the latter authors.

Double power series method for approximating cosmological perturbations

NASA Astrophysics Data System (ADS)

Wren, Andrew J.; Malik, Karim A.

2017-04-01

We introduce a double power series method for finding approximate analytical solutions for systems of differential equations commonly found in cosmological perturbation theory. The method was set out, in a noncosmological context, by Feshchenko, Shkil' and Nikolenko (FSN) in 1966, and is applicable to cases where perturbations are on subhorizon scales. The FSN method is essentially an extension of the well known Wentzel-Kramers-Brillouin (WKB) method for finding approximate analytical solutions for ordinary differential equations. The FSN method we use is applicable well beyond perturbation theory to solve systems of ordinary differential equations, linear in the derivatives, that also depend on a small parameter, which here we take to be related to the inverse wave-number. We use the FSN method to find new approximate oscillating solutions in linear order cosmological perturbation theory for a flat radiation-matter universe. Together with this model's well-known growing and decaying Mészáros solutions, these oscillating modes provide a complete set of subhorizon approximations for the metric potential, radiation and matter perturbations. Comparison with numerical solutions of the perturbation equations shows that our approximations can be made accurate to within a typical error of 1%, or better. We also set out a heuristic method for error estimation. A Mathematica notebook which implements the double power series method is made available online.

Approximation abilities of neuro-fuzzy networks

NASA Astrophysics Data System (ADS)

Mrówczyńska, Maria

2010-01-01

The paper presents the operation of two neuro-fuzzy systems of an adaptive type, intended for solving problems of the approximation of multi-variable functions in the domain of real numbers. Neuro-fuzzy systems being a combination of the methodology of artificial neural networks and fuzzy sets operate on the basis of a set of fuzzy rules "if-then", generated by means of the self-organization of data grouping and the estimation of relations between fuzzy experiment results. The article includes a description of neuro-fuzzy systems by Takaga-Sugeno-Kang (TSK) and Wang-Mendel (WM), and in order to complement the problem in question, a hierarchical structural self-organizing method of teaching a fuzzy network. A multi-layer structure of the systems is a structure analogous to the structure of "classic" neural networks. In its final part the article presents selected areas of application of neuro-fuzzy systems in the field of geodesy and surveying engineering. Numerical examples showing how the systems work concerned: the approximation of functions of several variables to be used as algorithms in the Geographic Information Systems (the approximation of a terrain model), the transformation of coordinates, and the prediction of a time series. The accuracy characteristics of the results obtained have been taken into consideration.

Approximating Exponential and Logarithmic Functions Using Polynomial Interpolation

ERIC Educational Resources Information Center

Gordon, Sheldon P.; Yang, Yajun

2017-01-01

This article takes a closer look at the problem of approximating the exponential and logarithmic functions using polynomials. Either as an alternative to or a precursor to Taylor polynomial approximations at the precalculus level, interpolating polynomials are considered. A measure of error is given and the behaviour of the error function is…

Finding the Best Quadratic Approximation of a Function

ERIC Educational Resources Information Center

Yang, Yajun; Gordon, Sheldon P.

2011-01-01

This article examines the question of finding the best quadratic function to approximate a given function on an interval. The prototypical function considered is f(x) = e[superscript x]. Two approaches are considered, one based on Taylor polynomial approximations at various points in the interval under consideration, the other based on the fact…

Dynamic Analyses of Result Quality in Energy-Aware Approximate Programs

NASA Astrophysics Data System (ADS)

RIngenburg, Michael F.

Energy efficiency is a key concern in the design of modern computer systems. One promising approach to energy-efficient computation, approximate computing, trades off output precision for energy efficiency. However, this tradeoff can have unexpected effects on computation quality. This thesis presents dynamic analysis tools to study, debug, and monitor the quality and energy efficiency of approximate computations. We propose three styles of tools: prototyping tools that allow developers to experiment with approximation in their applications, online tools that instrument code to determine the key sources of error, and online tools that monitor the quality of deployed applications in real time. Our prototyping tool is based on an extension to the functional language OCaml. We add approximation constructs to the language, an approximation simulator to the runtime, and profiling and auto-tuning tools for studying and experimenting with energy-quality tradeoffs. We also present two online debugging tools and three online monitoring tools. The first online tool identifies correlations between output quality and the total number of executions of, and errors in, individual approximate operations. The second tracks the number of approximate operations that flow into a particular value. Our online tools comprise three low-cost approaches to dynamic quality monitoring. They are designed to monitor quality in deployed applications without spending more energy than is saved by approximation. Online monitors can be used to perform real time adjustments to energy usage in order to meet specific quality goals. We present prototype implementations of all of these tools and describe their usage with several applications. Our prototyping, profiling, and autotuning tools allow us to experiment with approximation strategies and identify new strategies, our online tools succeed in providing new insights into the effects of approximation on output quality, and our monitors succeed in

Comparison of dynamical approximation schemes for non-linear gravitational clustering

NASA Technical Reports Server (NTRS)

Melott, Adrian L.

1994-01-01

We have recently conducted a controlled comparison of a number of approximations for gravitational clustering against the same n-body simulations. These include ordinary linear perturbation theory (Eulerian), the adhesion approximation, the frozen-flow approximation, the Zel'dovich approximation (describable as first-order Lagrangian perturbation theory), and its second-order generalization. In the last two cases we also created new versions of approximation by truncation, i.e., smoothing the initial conditions by various smoothing window shapes and varying their sizes. The primary tool for comparing simulations to approximation schemes was crosscorrelation of the evolved mass density fields, testing the extent to which mass was moved to the right place. The Zel'dovich approximation, with initial convolution with a Gaussian e(exp -k(exp 2)/k(exp 2, sub G)) where k(sub G) is adjusted to be just into the nonlinear regime of the evolved model (details in text) worked extremely well. Its second-order generalization worked slightly better. All other schemes, including those proposed as generalizations of the Zel'dovich approximation created by adding forces, were in fact generally worse by this measure. By explicitly checking, we verified that the success of our best-choice was a result of the best treatment of the phases of nonlinear Fourier components. Of all schemes tested, the adhesion approximation produced the most accurate nonlinear power spectrum and density distribution, but its phase errors suggest mass condensations were moved to slightly the wrong location. Due to its better reproduction of the mass density distribution function and power spectrum, it might be preferred for some uses. We recommend either n-body simulations or our modified versions of the Zel'dovich approximation, depending upon the purpose. The theoretical implication is that pancaking is implicit in all cosmological gravitational clustering, at least from Gaussian initial conditions, even

Application of Approximate Unsteady Aerodynamics for Flutter Analysis

NASA Technical Reports Server (NTRS)

Pak, Chan-gi; Li, Wesley W.

2010-01-01

A technique for approximating the modal aerodynamic influence coefficient (AIC) matrices by using basis functions has been developed. A process for using the resulting approximated modal AIC matrix in aeroelastic analysis has also been developed. The method requires the unsteady aerodynamics in frequency domain, and this methodology can be applied to the unsteady subsonic, transonic, and supersonic aerodynamics. The flutter solution can be found by the classic methods, such as rational function approximation, k, p-k, p, root locus et cetera. The unsteady aeroelastic analysis using unsteady subsonic aerodynamic approximation is demonstrated herein. The technique presented is shown to offer consistent flutter speed prediction on an aerostructures test wing (ATW) 2 and a hybrid wing body (HWB) type of vehicle configuration with negligible loss in precision. This method computes AICs that are functions of the changing parameters being studied and are generated within minutes of CPU time instead of hours. These results may have practical application in parametric flutter analyses as well as more efficient multidisciplinary design and optimization studies.

Singularly Perturbed Lie Bracket Approximation

DOE PAGES

Durr, Hans-Bernd; Krstic, Miroslav; Scheinker, Alexander; ...

2015-03-27

Here, we consider the interconnection of two dynamical systems where one has an input-affine vector field. We show that by employing a singular perturbation analysis and the Lie bracket approximation technique, the stability of the overall system can be analyzed by regarding the stability properties of two reduced, uncoupled systems.

Computational aspects of pseudospectral Laguerre approximations

NASA Technical Reports Server (NTRS)

Funaro, Daniele

1989-01-01

Pseudospectral approximations in unbounded domains by Laguerre polynomials lead to ill-conditioned algorithms. Introduced are a scaling function and appropriate numerical procedures in order to limit these unpleasant phenomena.

Explicitly solvable complex Chebyshev approximation problems related to sine polynomials

NASA Technical Reports Server (NTRS)

Freund, Roland

1989-01-01

Explicitly solvable real Chebyshev approximation problems on the unit interval are typically characterized by simple error curves. A similar principle is presented for complex approximation problems with error curves induced by sine polynomials. As an application, some new explicit formulae for complex best approximations are derived.

Approximate convective heating equations for hypersonic flows

NASA Technical Reports Server (NTRS)

Zoby, E. V.; Moss, J. N.; Sutton, K.

1979-01-01

Laminar and turbulent heating-rate equations appropriate for engineering predictions of the convective heating rates about blunt reentry spacecraft at hypersonic conditions are developed. The approximate methods are applicable to both nonreacting and reacting gas mixtures for either constant or variable-entropy edge conditions. A procedure which accounts for variable-entropy effects and is not based on mass balancing is presented. Results of the approximate heating methods are in good agreement with existing experimental results as well as boundary-layer and viscous-shock-layer solutions.

Kernel K-Means Sampling for Nyström Approximation.

PubMed

He, Li; Zhang, Hong

2018-05-01

A fundamental problem in Nyström-based kernel matrix approximation is the sampling method by which training set is built. In this paper, we suggest to use kernel -means sampling, which is shown in our works to minimize the upper bound of a matrix approximation error. We first propose a unified kernel matrix approximation framework, which is able to describe most existing Nyström approximations under many popular kernels, including Gaussian kernel and polynomial kernel. We then show that, the matrix approximation error upper bound, in terms of the Frobenius norm, is equal to the -means error of data points in kernel space plus a constant. Thus, the -means centers of data in kernel space, or the kernel -means centers, are the optimal representative points with respect to the Frobenius norm error upper bound. Experimental results, with both Gaussian kernel and polynomial kernel, on real-world data sets and image segmentation tasks show the superiority of the proposed method over the state-of-the-art methods.

Low-lying 1/2- hidden strange pentaquark states in the constituent quark model

NASA Astrophysics Data System (ADS)

Li, Hui; Wu, Zong-Xiu; An, Chun-Sheng; Chen, Hong

2017-12-01

We investigate the spectrum of the low-lying 1/2- hidden strange pentaquark states, employing the constituent quark model, and looking at two ways within that model of mediating the hyperfine interaction between quarks - Goldstone boson exchange and one gluon exchange. Numerical results show that the lowest 1/2- hidden strange pentaquark state in the Goldstone boson exchange model lies at ˜1570 MeV, so this pentaquark configuration may form a notable component in S 11(1535) if the Goldstone boson exchange model is applied. This is consistent with the prediction that S 11(1535) couples very strongly to strangeness channels. Supported by National Natural Science Foundation of China (11675131, 11645002), Chongqing Natural Science Foundation (cstc2015jcyjA00032) and Fundamental Research Funds for the Central Universities (SWU115020)

Dipole Approximation to Predict the Resonances of Dimers Composed of Dielectric Resonators for Directional Emission: Dielectric Dimers Dipole Approximation

DOE PAGES

Campione, Salvatore; Warne, Larry K.; Basilio, Lorena I.

2017-09-29

In this paper we develop a fully-retarded, dipole approximation model to estimate the effective polarizabilities of a dimer made of dielectric resonators. They are computed from the polarizabilities of the two resonators composing the dimer. We analyze the situation of full-cubes as well as split-cubes, which have been shown to exhibit overlapping electric and magnetic resonances. We compare the effective dimer polarizabilities to ones retrieved via full-wave simulations as well as ones computed via a quasi-static, dipole approximation. We observe good agreement between the fully-retarded solution and the full-wave results, whereas the quasi-static approximation is less accurate for the problemmore » at hand. The developed model can be used to predict the electric and magnetic resonances of a dimer under parallel or orthogonal (to the dimer axis) excitation. This is particularly helpful when interested in locating frequencies at which the dimer will emit directional radiation.« less

Resumming the large-N approximation for time evolving quantum systems

NASA Astrophysics Data System (ADS)

Mihaila, Bogdan; Dawson, John F.; Cooper, Fred

2001-05-01

In this paper we discuss two methods of resumming the leading and next to leading order in 1/N diagrams for the quartic O(N) model. These two approaches have the property that they preserve both boundedness and positivity for expectation values of operators in our numerical simulations. These approximations can be understood either in terms of a truncation to the infinitely coupled Schwinger-Dyson hierarchy of equations, or by choosing a particular two-particle irreducible vacuum energy graph in the effective action of the Cornwall-Jackiw-Tomboulis formalism. We confine our discussion to the case of quantum mechanics where the Lagrangian is L(x,ẋ)=(12)∑Ni=1x˙2i-(g/8N)[∑Ni=1x2i- r20]2. The key to these approximations is to treat both the x propagator and the x2 propagator on similar footing which leads to a theory whose graphs have the same topology as QED with the x2 propagator playing the role of the photon. The bare vertex approximation is obtained by replacing the exact vertex function by the bare one in the exact Schwinger-Dyson equations for the one and two point functions. The second approximation, which we call the dynamic Debye screening approximation, makes the further approximation of replacing the exact x2 propagator by its value at leading order in the 1/N expansion. These two approximations are compared with exact numerical simulations for the quantum roll problem. The bare vertex approximation captures the physics at large and modest N better than the dynamic Debye screening approximation.

An approximate classical unimolecular reaction rate theory

NASA Astrophysics Data System (ADS)

Zhao, Meishan; Rice, Stuart A.

1992-05-01

We describe a classical theory of unimolecular reaction rate which is derived from the analysis of Davis and Gray by use of simplifying approximations. These approximations concern the calculation of the locations of, and the fluxes of phase points across, the bottlenecks to fragmentation and to intramolecular energy transfer. The bottleneck to fragment separation is represented as a vibration-rotation state dependent separatrix, which approximation is similar to but extends and improves the approximations for the separatrix introduced by Gray, Rice, and Davis and by Zhao and Rice. The novel feature in our analysis is the representation of the bottlenecks to intramolecular energy transfer as dividing surfaces in phase space; the locations of these dividing surfaces are determined by the same conditions as locate the remnants of robust tori with frequency ratios related to the golden mean (in a two degree of freedom system these are the cantori). The flux of phase points across each dividing surface is calculated with an analytic representation instead of a stroboscopic mapping. The rate of unimolecular reaction is identified with the net rate at which phase points escape from the region of quasiperiodic bounded motion to the region of free fragment motion by consecutively crossing the dividing surfaces for intramolecular energy exchange and the separatrix. This new theory generates predictions of the rates of predissociation of the van der Waals molecules HeI2, NeI2 and ArI2 which are in very good agreement with available experimental data.

Representation of Ice Geometry by Parametric Functions: Construction of Approximating NURBS Curves and Quantification of Ice Roughness--Year 1: Approximating NURBS Curves

NASA Technical Reports Server (NTRS)

Dill, Loren H.; Choo, Yung K. (Technical Monitor)

2004-01-01

Software was developed to construct approximating NURBS curves for iced airfoil geometries. Users specify a tolerance that determines the extent to which the approximating curve follows the rough ice. The user can therefore smooth the ice geometry in a controlled manner, thereby enabling the generation of grids suitable for numerical aerodynamic simulations. Ultimately, this ability to smooth the ice geometry will permit studies of the effects of smoothing upon the aerodynamics of iced airfoils. The software was applied to several different types of iced airfoil data collected in the Icing Research Tunnel at NASA Glenn Research Center, and in all cases was found to efficiently generate suitable approximating NURBS curves. This method is an improvement over the current "control point formulation" of Smaggice (v.1.2). In this report, we present the relevant theory of approximating NURBS curves and discuss typical results of the software.

Approximations to the exact exchange potential: KLI versus semilocal

NASA Astrophysics Data System (ADS)

Tran, Fabien; Blaha, Peter; Betzinger, Markus; Blügel, Stefan

2016-10-01

In the search for an accurate and computationally efficient approximation to the exact exchange potential of Kohn-Sham density functional theory, we recently compared various semilocal exchange potentials to the exact one [F. Tran et al., Phys. Rev. B 91, 165121 (2015), 10.1103/PhysRevB.91.165121]. It was concluded that the Becke-Johnson (BJ) potential is a very good starting point, but requires the use of empirical parameters to obtain good agreement with the exact exchange potential. In this work, we extend the comparison by considering the Krieger-Li-Iafrate (KLI) approximation, which is a beyond-semilocal approximation. It is shown that overall the KLI- and BJ-based potentials are the most reliable approximations to the exact exchange potential, however, sizable differences, especially for the antiferromagnetic transition-metal oxides, can be obtained.

Coherent-Anomaly Method in Critical Phenomena. III. Mean-Field Transfer-Matrix Method in the 2D Ising Model

NASA Astrophysics Data System (ADS)

Hu, Xiao; Katori, Makoto; Suzuki, Masuo

1987-11-01

Two kinds of systematic mean-field transfer-matrix methods are formulated in the 2-dimensional Ising spin system, by introducing Weiss-like and Bethe-like approximations. All the critical exponents as well as the true critical point can be estimated in these methods following the CAM procedure. The numerical results of the above system are Tc*≃2.271 (J/kB), γ{=}γ'≃1.749, β≃0.131 and δ≃15.1. The specific heat is confirmd to be continuous and to have a logarithmic divergence at the true critical point, i.e., α{=}α'{=}0. Thus, the finite-degree-of-approximation scaling ansatz is shown to be correct and very powerful in practical estimations of the critical exponents as well as the true critical point.

Coherent-Anomaly Method in Critical Phenomena. III.

NASA Astrophysics Data System (ADS)

Hu, Xiao; Katori, Makoto; Suzuki, Masuo

Two kinds of systematic mean-field transfer-matrix methods are formulated in the 2-dimensional Ising spin system, by introducing Weiss-like and Bethe-like approximations. All the critical exponents as well as the true critical point can be estimated in these methods following the CAM procedure. The numerical results of the above system are Tc* = 2.271 (J/kB), γ=γ' ≃ 1.749, β≃0.131 and δ ≃ 15.1. The specific heat is confirmed to be continuous and to have a logarithmic divergence at the true critical point, i.e., α=α'=0. Thus, the finite-degree-of-approximation scaling ansatz is shown to be correct and very powerful in practical estimations of the critical exponents as well as the true critical point.

On the dipole approximation with error estimates

NASA Astrophysics Data System (ADS)

Boßmann, Lea; Grummt, Robert; Kolb, Martin

2018-01-01

The dipole approximation is employed to describe interactions between atoms and radiation. It essentially consists of neglecting the spatial variation of the external field over the atom. Heuristically, this is justified by arguing that the wavelength is considerably larger than the atomic length scale, which holds under usual experimental conditions. We prove the dipole approximation in the limit of infinite wavelengths compared to the atomic length scale and estimate the rate of convergence. Our results include N-body Coulomb potentials and experimentally relevant electromagnetic fields such as plane waves and laser pulses.

Rational-spline approximation with automatic tension adjustment

NASA Technical Reports Server (NTRS)

Schiess, J. R.; Kerr, P. A.

1984-01-01

An algorithm for weighted least-squares approximation with rational splines is presented. A rational spline is a cubic function containing a distinct tension parameter for each interval defined by two consecutive knots. For zero tension, the rational spline is identical to a cubic spline; for very large tension, the rational spline is a linear function. The approximation algorithm incorporates an algorithm which automatically adjusts the tension on each interval to fulfill a user-specified criterion. Finally, an example is presented comparing results of the rational spline with those of the cubic spline.

Short-Path Statistics and the Diffusion Approximation

NASA Astrophysics Data System (ADS)

Blanco, Stéphane; Fournier, Richard

2006-12-01

In the field of first return time statistics in bounded domains, short paths may be defined as those paths for which the diffusion approximation is inappropriate. This is at the origin of numerous open questions concerning the characterization of residence time distributions. We show here how general integral constraints can be derived that make it possible to address short-path statistics indirectly by application of the diffusion approximation to long paths. Application to the moments of the distribution at the low-Knudsen limit leads to simple practical results and novel physical pictures.

Cosmological collapse and the improved Zel'dovich approximation.

NASA Astrophysics Data System (ADS)

Salopek, D. S.; Stewart, J. M.; Croudace, K. M.; Parry, J.

Using a general relativistic formulation, the authors show how to compute the higher order terms in the Zel'dovich approximation which describes cosmological collapse. They evolve the 3-metric in a spatial gradient expansion. Their method is an advance over earlier work because it is local at each order. Using the improved Zel'dovich approximation, they compute the epoch of collapse.

Robustness of controllers designed using Galerkin type approximations

NASA Technical Reports Server (NTRS)

Morris, K. A.

1990-01-01

One of the difficulties in designing controllers for infinite-dimensional systems arises from attempting to calculate a state for the system. It is shown that Galerkin type approximations can be used to design controllers which will perform as designed when implemented on the original infinite-dimensional system. No assumptions, other than those typically employed in numerical analysis, are made on the approximating scheme.

Analytic Interatomic Forces in the Random Phase Approximation

NASA Astrophysics Data System (ADS)

Ramberger, Benjamin; Schäfer, Tobias; Kresse, Georg

2017-03-01

We discuss that in the random phase approximation (RPA) the first derivative of the energy with respect to the Green's function is the self-energy in the G W approximation. This relationship allows us to derive compact equations for the RPA interatomic forces. We also show that position dependent overlap operators are elegantly incorporated in the present framework. The RPA force equations have been implemented in the projector augmented wave formalism, and we present illustrative applications, including ab initio molecular dynamics simulations, the calculation of phonon dispersion relations for diamond and graphite, as well as structural relaxations for water on boron nitride. The present derivation establishes a concise framework for forces within perturbative approaches and is also applicable to more involved approximations for the correlation energy.

Polynomial approximation of the Lense-Thirring rigid precession frequency

NASA Astrophysics Data System (ADS)

De Falco, Vittorio; Motta, Sara

2018-05-01

We propose a polynomial approximation of the global Lense-Thirring rigid precession frequency to study low-frequency quasi-periodic oscillations around spinning black holes. This high-performing approximation allows to determine the expected frequencies of a precessing thick accretion disc with fixed inner radius and variable outer radius around a black hole with given mass and spin. We discuss the accuracy and the applicability regions of our polynomial approximation, showing that the computational times are reduced by a factor of ≈70 in the range of minutes.

Flexible Approximation Model Approach for Bi-Level Integrated System Synthesis

NASA Technical Reports Server (NTRS)

Sobieszczanski-Sobieski, Jaroslaw; Kim, Hongman; Ragon, Scott; Soremekun, Grant; Malone, Brett

2004-01-01

Bi-Level Integrated System Synthesis (BLISS) is an approach that allows design problems to be naturally decomposed into a set of subsystem optimizations and a single system optimization. In the BLISS approach, approximate mathematical models are used to transfer information from the subsystem optimizations to the system optimization. Accurate approximation models are therefore critical to the success of the BLISS procedure. In this paper, new capabilities that are being developed to generate accurate approximation models for BLISS procedure will be described. The benefits of using flexible approximation models such as Kriging will be demonstrated in terms of convergence characteristics and computational cost. An approach of dealing with cases where subsystem optimization cannot find a feasible design will be investigated by using the new flexible approximation models for the violated local constraints.

The complex variable boundary element method: Applications in determining approximative boundaries

USGS Publications Warehouse

Hromadka, T.V.

1984-01-01

The complex variable boundary element method (CVBEM) is used to determine approximation functions for boundary value problems of the Laplace equation such as occurs in potential theory. By determining an approximative boundary upon which the CVBEM approximator matches the desired constant (level curves) boundary conditions, the CVBEM is found to provide the exact solution throughout the interior of the transformed problem domain. Thus, the acceptability of the CVBEM approximation is determined by the closeness-of-fit of the approximative boundary to the study problem boundary. ?? 1984.

Approximation methods for stochastic petri nets

NASA Technical Reports Server (NTRS)

Jungnitz, Hauke Joerg

1992-01-01

Stochastic Marked Graphs are a concurrent decision free formalism provided with a powerful synchronization mechanism generalizing conventional Fork Join Queueing Networks. In some particular cases the analysis of the throughput can be done analytically. Otherwise the analysis suffers from the classical state explosion problem. Embedded in the divide and conquer paradigm, approximation techniques are introduced for the analysis of stochastic marked graphs and Macroplace/Macrotransition-nets (MPMT-nets), a new subclass introduced herein. MPMT-nets are a subclass of Petri nets that allow limited choice, concurrency and sharing of resources. The modeling power of MPMT is much larger than that of marked graphs, e.g., MPMT-nets can model manufacturing flow lines with unreliable machines and dataflow graphs where choice and synchronization occur. The basic idea leads to the notion of a cut to split the original net system into two subnets. The cuts lead to two aggregated net systems where one of the subnets is reduced to a single transition. A further reduction leads to a basic skeleton. The generalization of the idea leads to multiple cuts, where single cuts can be applied recursively leading to a hierarchical decomposition. Based on the decomposition, a response time approximation technique for the performance analysis is introduced. Also, delay equivalence, which has previously been introduced in the context of marked graphs by Woodside et al., Marie's method and flow equivalent aggregation are applied to the aggregated net systems. The experimental results show that response time approximation converges quickly and shows reasonable accuracy in most cases. The convergence of Marie's method and flow equivalent aggregation are applied to the aggregated net systems. The experimental results show that response time approximation converges quickly and shows reasonable accuracy in most cases. The convergence of Marie's is slower, but the accuracy is generally better. Delay

A Subsonic Aircraft Design Optimization With Neural Network and Regression Approximators

NASA Technical Reports Server (NTRS)

Patnaik, Surya N.; Coroneos, Rula M.; Guptill, James D.; Hopkins, Dale A.; Haller, William J.

2004-01-01

The Flight-Optimization-System (FLOPS) code encountered difficulty in analyzing a subsonic aircraft. The limitation made the design optimization problematic. The deficiencies have been alleviated through use of neural network and regression approximations. The insight gained from using the approximators is discussed in this paper. The FLOPS code is reviewed. Analysis models are developed and validated for each approximator. The regression method appears to hug the data points, while the neural network approximation follows a mean path. For an analysis cycle, the approximate model required milliseconds of central processing unit (CPU) time versus seconds by the FLOPS code. Performance of the approximators was satisfactory for aircraft analysis. A design optimization capability has been created by coupling the derived analyzers to the optimization test bed CometBoards. The approximators were efficient reanalysis tools in the aircraft design optimization. Instability encountered in the FLOPS analyzer was eliminated. The convergence characteristics were improved for the design optimization. The CPU time required to calculate the optimum solution, measured in hours with the FLOPS code was reduced to minutes with the neural network approximation and to seconds with the regression method. Generation of the approximators required the manipulation of a very large quantity of data. Design sensitivity with respect to the bounds of aircraft constraints is easily generated.

An approximation function for frequency constrained structural optimization

NASA Technical Reports Server (NTRS)

Canfield, R. A.

1989-01-01

The purpose is to examine a function for approximating natural frequency constraints during structural optimization. The nonlinearity of frequencies has posed a barrier to constructing approximations for frequency constraints of high enough quality to facilitate efficient solutions. A new function to represent frequency constraints, called the Rayleigh Quotient Approximation (RQA), is presented. Its ability to represent the actual frequency constraint results in stable convergence with effectively no move limits. The objective of the optimization problem is to minimize structural weight subject to some minimum (or maximum) allowable frequency and perhaps subject to other constraints such as stress, displacement, and gage size, as well. A reason for constraining natural frequencies during design might be to avoid potential resonant frequencies due to machinery or actuators on the structure. Another reason might be to satisy requirements of an aircraft or spacecraft's control law. Whatever the structure supports may be sensitive to a frequency band that must be avoided. Any of these situations or others may require the designer to insure the satisfaction of frequency constraints. A further motivation for considering accurate approximations of natural frequencies is that they are fundamental to dynamic response constraints.

Meta-regression approximations to reduce publication selection bias.

PubMed

Stanley, T D; Doucouliagos, Hristos

2014-03-01

Publication selection bias is a serious challenge to the integrity of all empirical sciences. We derive meta-regression approximations to reduce this bias. Our approach employs Taylor polynomial approximations to the conditional mean of a truncated distribution. A quadratic approximation without a linear term, precision-effect estimate with standard error (PEESE), is shown to have the smallest bias and mean squared error in most cases and to outperform conventional meta-analysis estimators, often by a great deal. Monte Carlo simulations also demonstrate how a new hybrid estimator that conditionally combines PEESE and the Egger regression intercept can provide a practical solution to publication selection bias. PEESE is easily expanded to accommodate systematic heterogeneity along with complex and differential publication selection bias that is related to moderator variables. By providing an intuitive reason for these approximations, we can also explain why the Egger regression works so well and when it does not. These meta-regression methods are applied to several policy-relevant areas of research including antidepressant effectiveness, the value of a statistical life, the minimum wage, and nicotine replacement therapy. Copyright © 2013 John Wiley & Sons, Ltd.

Low rank approximation in G 0W 0 calculations

DOE PAGES

Shao, MeiYue; Lin, Lin; Yang, Chao; ...

2016-06-04

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 tr ansport, 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 techniquemore » in which the self energy is expressed as the convolution of a noninteracting 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 cost of G 0W 0 calculation can be reduced by constructing a low rank approximation to the frequency dependent part of W 0 . In particular, we examine the effect of such a low rank approximation on the accuracy of the G 0W 0 approximation. We also discuss how the numerical convolution of G 0 and W 0 can be evaluated efficiently and accurately by using a contour deformation technique with an appropriate choice of the contour.« less

Pythagorean Approximations and Continued Fractions

ERIC Educational Resources Information Center

Peralta, Javier

2008-01-01

In this article, we will show that the Pythagorean approximations of [the square root of] 2 coincide with those achieved in the 16th century by means of continued fractions. Assuming this fact and the known relation that connects the Fibonacci sequence with the golden section, we shall establish a procedure to obtain sequences of rational numbers…

Approximate strip exchanging.

PubMed

Roy, Swapnoneel; Thakur, Ashok Kumar

2008-01-01

Genome rearrangements have been modelled by a variety of primitives such as reversals, transpositions, block moves and block interchanges. We consider such a genome rearrangement primitive Strip Exchanges. Given a permutation, the challenge is to sort it by using minimum number of strip exchanges. A strip exchanging move interchanges the positions of two chosen strips so that they merge with other strips. The strip exchange problem is to sort a permutation using minimum number of strip exchanges. We present here the first non-trivial 2-approximation algorithm to this problem. We also observe that sorting by strip-exchanges is fixed-parameter-tractable. Lastly we discuss the application of strip exchanges in a different area Optical Character Recognition (OCR) with an example.

Asteroid 1999 JD6

NASA Image and Video Library

2015-07-31

This collage of radar images of near-Earth asteroid 1999 JD6 was collected by NASA scientists on July 25, 2015. The images show the rotation of the asteroid, which made its closest approach on July 24 at 9:55 p.m. PDT (12:55 a.m. EDT on July 25) at a distance of about 4.5 million miles (7.2 million kilometers, or about 19 times the distance from Earth to the moon). The asteroid appears to be a contact binary -- an asteroid with two lobes that are stuck together. These views, which are radar echoes, were obtained by pairing NASA's 230-foot-wide (70-meter) Deep Space Network antenna at Goldstone, California, with the 330-foot (100-meter) National Science Foundation Green Bank Telescope in West Virginia. Using this approach, the Goldstone antenna beams a radar signal at an asteroid and Green Bank receives the reflections. The technique, referred to as a bistatic observation, dramatically improves the amount of detail that can be seen in radar images. The new views obtained with the technique show features as small as about 25 feet (7.5 meters) wide. The images show the asteroid is highly elongated, with a length of approximately 1.2 miles (2 kilometers) on its long axis. http://photojournal.jpl.nasa.gov/catalog/PIA19647

The unitary convolution approximation for heavy ions

NASA Astrophysics Data System (ADS)

Grande, P. L.; Schiwietz, G.

2002-10-01

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-equilibrium stopping force as a function of the projectile charge as well as with the equilibrium energy loss under non-aligned and channeling conditions.

An Origami Approximation to the Cosmic Web

NASA Astrophysics Data System (ADS)

Neyrinck, Mark C.

2016-10-01

The powerful Lagrangian view of structure formation was essentially introduced to cosmology by Zel'dovich. In the current cosmological paradigm, a dark-matter-sheet 3D manifold, inhabiting 6D position-velocity phase space, was flat (with vanishing velocity) at the big bang. Afterward, gravity stretched and bunched the sheet together in different places, forming a cosmic web when projected to the position coordinates. Here, I explain some properties of an origami approximation, in which the sheet does not stretch or contract (an assumption that is false in general), but is allowed to fold. Even without stretching, the sheet can form an idealized cosmic web, with convex polyhedral voids separated by straight walls and filaments, joined by convex polyhedral nodes. The nodes form in `polygonal' or `polyhedral' collapse, somewhat like spherical/ellipsoidal collapse, except incorporating simultaneous filament and wall formation. The origami approximation allows phase-space geometries of nodes, filaments, and walls to be more easily understood, and may aid in understanding spin correlations between nearby galaxies. This contribution explores kinematic origami-approximation models giving velocity fields for the first time.

Comparison of universal approximators incorporating partial monotonicity by structure.

PubMed

Minin, Alexey; Velikova, Marina; Lang, Bernhard; Daniels, Hennie

2010-05-01

Neural networks applied in control loops and safety-critical domains have to meet more requirements than just the overall best function approximation. On the one hand, a small approximation error is required; on the other hand, the smoothness and the monotonicity of selected input-output relations have to be guaranteed. Otherwise, the stability of most of the control laws is lost. In this article we compare two neural network-based approaches incorporating partial monotonicity by structure, namely the Monotonic Multi-Layer Perceptron (MONMLP) network and the Monotonic MIN-MAX (MONMM) network. We show the universal approximation capabilities of both types of network for partially monotone functions. On a number of datasets, we investigate the advantages and disadvantages of these approaches related to approximation performance, training of the model and convergence. 2009 Elsevier Ltd. All rights reserved.

Integral approximations to classical diffusion and smoothed particle hydrodynamics

DOE PAGES

Du, Qiang; Lehoucq, R. B.; Tartakovsky, A. M.

2014-12-31

The contribution of the paper is the approximation of a classical diffusion operator by an integral equation with a volume constraint. A particular focus is on classical diffusion problems associated with Neumann boundary conditions. By exploiting this approximation, we can also approximate other quantities such as the flux out of a domain. Our analysis of the model equation on the continuum level is closely related to the recent work on nonlocal diffusion and peridynamic mechanics. In particular, we elucidate the role of a volumetric constraint as an approximation to a classical Neumann boundary condition in the presence of physical boundary.more » The volume-constrained integral equation then provides the basis for accurate and robust discretization methods. As a result, an immediate application is to the understanding and improvement of the Smoothed Particle Hydrodynamics (SPH) method.« less

A Varifold Approach to Surface Approximation

NASA Astrophysics Data System (ADS)

Buet, Blanche; Leonardi, Gian Paolo; Masnou, Simon

2017-11-01

We show that the theory of varifolds can be suitably enriched to open the way to applications in the field of discrete and computational geometry. Using appropriate regularizations of the mass and of the first variation of a varifold we introduce the notion of approximate mean curvature and show various convergence results that hold, in particular, for sequences of discrete varifolds associated with point clouds or pixel/voxel-type discretizations of d-surfaces in the Euclidean n-space, without restrictions on dimension and codimension. The variational nature of the approach also allows us to consider surfaces with singularities, and in that case the approximate mean curvature is consistent with the generalized mean curvature of the limit surface. A series of numerical tests are provided in order to illustrate the effectiveness and generality of the method.

Relativistic bound states in three space-time dimensions in Minkowski space

NASA Astrophysics Data System (ADS)

Gutierrez, C.; Gigante, V.; Frederico, T.; Tomio, Lauro

2016-01-01

With the aim to derive a workable framework for bound states in Minkowski space, we have investigated the Nakanishi perturbative integral representation of the Bethe-Salpeter (BS) amplitude in two-dimensions (2D) in space and time (2+1). The homogeneous BS amplitude, projected onto the light-front plane, is used to derive an equation for the Nakanishi weight function. The formal development is illustrated in detail and applied to the bound system composed by two scalar particles interacting through the exchange of a massive scalar. The explicit forms of the integral equations are obtained in ladder approximation.

Approximating exponential and logarithmic functions using polynomial interpolation

NASA Astrophysics Data System (ADS)

Gordon, Sheldon P.; Yang, Yajun

2017-04-01

This article takes a closer look at the problem of approximating the exponential and logarithmic functions using polynomials. Either as an alternative to or a precursor to Taylor polynomial approximations at the precalculus level, interpolating polynomials are considered. A measure of error is given and the behaviour of the error function is analysed. The results of interpolating polynomials are compared with those of Taylor polynomials.

Solving the infeasible trust-region problem using approximations.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Renaud, John E.; Perez, Victor M.; Eldred, Michael Scott

2004-07-01

The use of optimization in engineering design has fueled the development of algorithms for specific engineering needs. When the simulations are expensive to evaluate or the outputs present some noise, the direct use of nonlinear optimizers is not advisable, since the optimization process will be expensive and may result in premature convergence. The use of approximations for both cases is an alternative investigated by many researchers including the authors. When approximations are present, a model management is required for proper convergence of the algorithm. In nonlinear programming, the use of trust-regions for globalization of a local algorithm has been provenmore » effective. The same approach has been used to manage the local move limits in sequential approximate optimization frameworks as in Alexandrov et al., Giunta and Eldred, Perez et al. , Rodriguez et al., etc. The experience in the mathematical community has shown that more effective algorithms can be obtained by the specific inclusion of the constraints (SQP type of algorithms) rather than by using a penalty function as in the augmented Lagrangian formulation. The presence of explicit constraints in the local problem bounded by the trust region, however, may have no feasible solution. In order to remedy this problem the mathematical community has developed different versions of a composite steps approach. This approach consists of a normal step to reduce the amount of constraint violation and a tangential step to minimize the objective function maintaining the level of constraint violation attained at the normal step. Two of the authors have developed a different approach for a sequential approximate optimization framework using homotopy ideas to relax the constraints. This algorithm called interior-point trust-region sequential approximate optimization (IPTRSAO) presents some similarities to the two normal-tangential steps algorithms. In this paper, a description of the similarities is presented

Lognormal Approximations of Fault Tree Uncertainty Distributions.

PubMed

El-Shanawany, Ashraf Ben; Ardron, Keith H; Walker, Simon P

2018-01-26

Fault trees are used in reliability modeling to create logical models of fault combinations that can lead to undesirable events. The output of a fault tree analysis (the top event probability) is expressed in terms of the failure probabilities of basic events that are input to the model. Typically, the basic event probabilities are not known exactly, but are modeled as probability distributions: therefore, the top event probability is also represented as an uncertainty distribution. Monte Carlo methods are generally used for evaluating the uncertainty distribution, but such calculations are computationally intensive and do not readily reveal the dominant contributors to the uncertainty. In this article, a closed-form approximation for the fault tree top event uncertainty distribution is developed, which is applicable when the uncertainties in the basic events of the model are lognormally distributed. The results of the approximate method are compared with results from two sampling-based methods: namely, the Monte Carlo method and the Wilks method based on order statistics. It is shown that the closed-form expression can provide a reasonable approximation to results obtained by Monte Carlo sampling, without incurring the computational expense. The Wilks method is found to be a useful means of providing an upper bound for the percentiles of the uncertainty distribution while being computationally inexpensive compared with full Monte Carlo sampling. The lognormal approximation method and Wilks's method appear attractive, practical alternatives for the evaluation of uncertainty in the output of fault trees and similar multilinear models. © 2018 Society for Risk Analysis.

Direct application of Padé approximant for solving nonlinear differential equations.

PubMed

Vazquez-Leal, Hector; Benhammouda, Brahim; Filobello-Nino, Uriel; Sarmiento-Reyes, Arturo; Jimenez-Fernandez, Victor Manuel; Garcia-Gervacio, Jose Luis; Huerta-Chua, Jesus; Morales-Mendoza, Luis Javier; Gonzalez-Lee, Mario

2014-01-01

This work presents a direct procedure to apply Padé method to find approximate solutions for nonlinear differential equations. Moreover, we present some cases study showing the strength of the method to generate highly accurate rational approximate solutions compared to other semi-analytical methods. The type of tested nonlinear equations are: a highly nonlinear boundary value problem, a differential-algebraic oscillator problem, and an asymptotic problem. The high accurate handy approximations obtained by the direct application of Padé method shows the high potential if the proposed scheme to approximate a wide variety of problems. What is more, the direct application of the Padé approximant aids to avoid the previous application of an approximative method like Taylor series method, homotopy perturbation method, Adomian Decomposition method, homotopy analysis method, variational iteration method, among others, as tools to obtain a power series solutions to post-treat with the Padé approximant. 34L30.

Dual methods and approximation concepts in structural synthesis

NASA Technical Reports Server (NTRS)

Fleury, C.; Schmit, L. A., Jr.

1980-01-01

Approximation concepts and dual method algorithms are combined to create a method for minimum weight design of structural systems. Approximation concepts convert the basic mathematical programming statement of the structural synthesis problem into a sequence of explicit primal problems of separable form. These problems are solved by constructing explicit dual functions, which are maximized subject to nonnegativity constraints on the dual variables. It is shown that the joining together of approximation concepts and dual methods can be viewed as a generalized optimality criteria approach. The dual method is successfully extended to deal with pure discrete and mixed continuous-discrete design variable problems. The power of the method presented is illustrated with numerical results for example problems, including a metallic swept wing and a thin delta wing with fiber composite skins.

Comparison of approximate solutions to the phonon Boltzmann transport equation with the relaxation time approximation: Spherical harmonics expansions and the discrete ordinates method

NASA Astrophysics Data System (ADS)

Christenson, J. G.; Austin, R. A.; Phillips, R. J.

2018-05-01

The phonon Boltzmann transport equation is used to analyze model problems in one and two spatial dimensions, under transient and steady-state conditions. New, explicit solutions are obtained by using the P1 and P3 approximations, based on expansions in spherical harmonics, and are compared with solutions from the discrete ordinates method. For steady-state energy transfer, it is shown that analytic expressions derived using the P1 and P3 approximations agree quantitatively with the discrete ordinates method, in some cases for large Knudsen numbers, and always for Knudsen numbers less than unity. However, for time-dependent energy transfer, the PN solutions differ qualitatively from converged solutions obtained by the discrete ordinates method. Although they correctly capture the wave-like behavior of energy transfer at short times, the P1 and P3 approximations rely on one or two wave velocities, respectively, yielding abrupt, step-changes in temperature profiles that are absent when the angular dependence of the phonon velocities is captured more completely. It is shown that, with the gray approximation, the P1 approximation is formally equivalent to the so-called "hyperbolic heat equation." Overall, these results support the use of the PN approximation to find solutions to the phonon Boltzmann transport equation for steady-state conditions. Such solutions can be useful in the design and analysis of devices that involve heat transfer at nanometer length scales, where continuum-scale approaches become inaccurate.

Test particle propagation in magnetostatic turbulence. 2: The local approximation method

NASA Technical Reports Server (NTRS)

Klimas, A. J.; Sandri, G.; Scudder, J. D.; Howell, D. R.

1976-01-01

An approximation method for statistical mechanics is presented and applied to a class of problems which contains a test particle propagation problem. All of the available basic equations used in statistical mechanics are cast in the form of a single equation which is integrodifferential in time and which is then used as the starting point for the construction of the local approximation method. Simplification of the integrodifferential equation is achieved through approximation to the Laplace transform of its kernel. The approximation is valid near the origin in the Laplace space and is based on the assumption of small Laplace variable. No other small parameter is necessary for the construction of this approximation method. The n'th level of approximation is constructed formally, and the first five levels of approximation are calculated explicitly. It is shown that each level of approximation is governed by an inhomogeneous partial differential equation in time with time independent operator coefficients. The order in time of these partial differential equations is found to increase as n does. At n = 0 the most local first order partial differential equation which governs the Markovian limit is regained.

Blocking performance approximation in flexi-grid networks

NASA Astrophysics Data System (ADS)

Ge, Fei; Tan, Liansheng

2016-12-01

The blocking probability to the path requests is an important issue in flexible bandwidth optical communications. In this paper, we propose a blocking probability approximation method of path requests in flexi-grid networks. It models the bundled neighboring carrier allocation with a group of birth-death processes and provides a theoretical analysis to the blocking probability under variable bandwidth traffic. The numerical results show the effect of traffic parameters to the blocking probability of path requests. We use the first fit algorithm in network nodes to allocate neighboring carriers to path requests in simulations, and verify approximation results.

Congruence Approximations for Entrophy Endowed Hyperbolic Systems

NASA Technical Reports Server (NTRS)

Barth, Timothy J.; Saini, Subhash (Technical Monitor)

1998-01-01

Building upon the standard symmetrization theory for hyperbolic systems of conservation laws, congruence properties of the symmetrized system are explored. These congruence properties suggest variants of several stabilized numerical discretization procedures for hyperbolic equations (upwind finite-volume, Galerkin least-squares, discontinuous Galerkin) that benefit computationally from congruence approximation. Specifically, it becomes straightforward to construct the spatial discretization and Jacobian linearization for these schemes (given a small amount of derivative information) for possible use in Newton's method, discrete optimization, homotopy algorithms, etc. Some examples will be given for the compressible Euler equations and the nonrelativistic MHD equations using linear and quadratic spatial approximation.

Bethe, Hans Albrecht (1906-)

NASA Astrophysics Data System (ADS)

Murdin, P.

2000-11-01

Physicist, born in Strasburg, Germany (present-day France), Nobel prizewinner (1967). As professor of physics at Cornell University he worked out the nuclear reactions occurring in the Sun. He worked on the development of the atomic bomb in the Manhatten project, and, after the second World War, pursued again research on stellar nuclear energy sources and the origin of the chemical elements in th...

Theory and applications of a deterministic approximation to the coalescent model

PubMed Central

Jewett, Ethan M.; Rosenberg, Noah A.

2014-01-01

Under the coalescent model, the random number nt of lineages ancestral to a sample is nearly deterministic as a function of time when nt is moderate to large in value, and it is well approximated by its expectation E[nt]. In turn, this expectation is well approximated by simple deterministic functions that are easy to compute. Such deterministic functions have been applied to estimate allele age, effective population size, and genetic diversity, and they have been used to study properties of models of infectious disease dynamics. Although a number of simple approximations of E[nt] have been derived and applied to problems of population-genetic inference, the theoretical accuracy of the formulas and the inferences obtained using these approximations is not known, and the range of problems to which they can be applied is not well understood. Here, we demonstrate general procedures by which the approximation nt ≈ E[nt] can be used to reduce the computational complexity of coalescent formulas, and we show that the resulting approximations converge to their true values under simple assumptions. Such approximations provide alternatives to exact formulas that are computationally intractable or numerically unstable when the number of sampled lineages is moderate or large. We also extend an existing class of approximations of E[nt] to the case of multiple populations of time-varying size with migration among them. Our results facilitate the use of the deterministic approximation nt ≈ E[nt] for deriving functionally simple, computationally efficient, and numerically stable approximations of coalescent formulas under complicated demographic scenarios. PMID:24412419

Front dynamics and entanglement in the XXZ chain with a gradient

NASA Astrophysics Data System (ADS)

Eisler, Viktor; Bauernfeind, Daniel

2017-11-01

We consider the XXZ spin chain with a magnetic field gradient and study the profiles of the magnetization as well as the entanglement entropy. For a slowly varying field, it is shown that, by means of a local density approximation, the ground-state magnetization profile can be obtained with standard Bethe ansatz techniques. Furthermore, it is argued that the low-energy description of the theory is given by a Luttinger liquid with slowly varying parameters. This allows us to obtain a very good approximation of the entanglement profile using a recently introduced technique of conformal field theory in curved spacetime. Finally, the front dynamics is also studied after the gradient field has been switched off, following arguments of generalized hydrodynamics for integrable systems. While for the XX chain the hydrodynamic solution can be found analytically, the XXZ case appears to be more complicated and the magnetization profiles are recovered only around the edge of the front via an approximate numerical solution.

Discussion of CoSA: Clustering of Sparse Approximations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Armstrong, Derek Elswick

2017-03-07

The purpose of this talk is to discuss the possible applications of CoSA (Clustering of Sparse Approximations) to the exploitation of HSI (HyperSpectral Imagery) data. CoSA is presented by Moody et al. in the Journal of Applied Remote Sensing (“Land cover classification in multispectral imagery using clustering of sparse approximations over learned feature dictionaries”, Vol. 8, 2014) and is based on machine learning techniques.

Quantum group symmetries and completeness for \\boldsymbol {A}_{\\boldsymbol {2n}}^{\\boldsymbol{(2)}} open spin chains

NASA Astrophysics Data System (ADS)

Ahmed, Ibrahim; Nepomechie, Rafael I.; Wang, Chunguang

2017-07-01

We argue that the Hamiltonians for A(2)2n open quantum spin chains corresponding to two choices of integrable boundary conditions have the symmetries Uq(Bn) and Uq(Cn) , respectively. We find a formula for the Dynkin labels of the Bethe states (which determine the degeneracies of the corresponding eigenvalues) in terms of the numbers of Bethe roots of each type. With the help of this formula, we verify numerically (for a generic value of the anisotropy parameter) that the degeneracies and multiplicities of the spectra implied by the quantum group symmetries are completely described by the Bethe ansatz.

Green-Ampt approximations: A comprehensive analysis

NASA Astrophysics Data System (ADS)

Ali, Shakir; Islam, Adlul; Mishra, P. K.; Sikka, Alok K.

2016-04-01

Green-Ampt (GA) model and its modifications are widely used for simulating infiltration process. Several explicit approximate solutions to the implicit GA model have been developed with varying degree of accuracy. In this study, performance of nine explicit approximations to the GA model is compared with the implicit GA model using the published data for broad range of soil classes and infiltration time. The explicit GA models considered are Li et al. (1976) (LI), Stone et al. (1994) (ST), Salvucci and Entekhabi (1994) (SE), Parlange et al. (2002) (PA), Barry et al. (2005) (BA), Swamee et al. (2012) (SW), Ali et al. (2013) (AL), Almedeij and Esen (2014) (AE), and Vatankhah (2015) (VA). Six statistical indicators (e.g., percent relative error, maximum absolute percent relative error, average absolute percent relative errors, percent bias, index of agreement, and Nash-Sutcliffe efficiency) and relative computer computation time are used for assessing the model performance. Models are ranked based on the overall performance index (OPI). The BA model is found to be the most accurate followed by the PA and VA models for variety of soil classes and infiltration periods. The AE, SW, SE, and LI model also performed comparatively better. Based on the overall performance index, the explicit models are ranked as BA > PA > VA > LI > AE > SE > SW > ST > AL. Results of this study will be helpful in selection of accurate and simple explicit approximate GA models for solving variety of hydrological problems.

Strong washout approximation to resonant leptogenesis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Garbrecht, Björn; Gautier, Florian; Klaric, Juraj, E-mail: garbrecht@tum.de, E-mail: florian.gautier@tum.de, E-mail: juraj.klaric@tum.de

We show that the effective decay asymmetry for resonant Leptogenesis in the strong washout regime with two sterile neutrinos and a single active flavour can in wide regions of parameter space be approximated by its late-time limit ε=Xsin(2φ)/(X{sup 2}+sin{sup 2}φ), where X=8πΔ/(|Y{sub 1}|{sup 2}+|Y{sub 2}|{sup 2}), Δ=4(M{sub 1}-M{sub 2})/(M{sub 1}+M{sub 2}), φ=arg(Y{sub 2}/Y{sub 1}), and M{sub 1,2}, Y{sub 1,2} are the masses and Yukawa couplings of the sterile neutrinos. This approximation in particular extends to parametric regions where |Y{sub 1,2}|{sup 2}>> Δ, i.e. where the width dominates the mass splitting. We generalise the formula for the effective decay asymmetry to themore » case of several flavours of active leptons and demonstrate how this quantity can be used to calculate the lepton asymmetry for phenomenological scenarios that are in agreement with the observed neutrino oscillations. We establish analytic criteria for the validity of the late-time approximation for the decay asymmetry and compare these with numerical results that are obtained by solving for the mixing and the oscillations of the sterile neutrinos. For phenomenologically viable models with two sterile neutrinos, we find that the flavoured effective late-time decay asymmetry can be applied throughout parameter space.« less

An approximation theory for the identification of linear thermoelastic systems

NASA Technical Reports Server (NTRS)

Rosen, I. G.; Su, Chien-Hua Frank

1990-01-01

An abstract approximation framework and convergence theory for the identification of thermoelastic systems is developed. Starting from an abstract operator formulation consisting of a coupled second order hyperbolic equation of elasticity and first order parabolic equation for heat conduction, well-posedness is established using linear semigroup theory in Hilbert space, and a class of parameter estimation problems is then defined involving mild solutions. The approximation framework is based upon generic Galerkin approximation of the mild solutions, and convergence of solutions of the resulting sequence of approximating finite dimensional parameter identification problems to a solution of the original infinite dimensional inverse problem is established using approximation results for operator semigroups. An example involving the basic equations of one dimensional linear thermoelasticity and a linear spline based scheme are discussed. Numerical results indicate how the approach might be used in a study of damping mechanisms in flexible structures.

Reply to Steele & Ferrer: Modeling Oscillation, Approximately or Exactly?

ERIC Educational Resources Information Center

Oud, Johan H. L.; Folmer, Henk

2011-01-01

This article addresses modeling oscillation in continuous time. It criticizes Steele and Ferrer's article "Latent Differential Equation Modeling of Self-Regulatory and Coregulatory Affective Processes" (2011), particularly the approximate estimation procedure applied. This procedure is the latent version of the local linear approximation procedure…

Boson expansions based on the random phase approximation representation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pedrocchi, V.G.; Tamura, T.

1984-04-01

A new boson expansion theory based on the random phase approximation is presented. The boson expansions are derived here directly in the random phase approximation representation with the help of a technique that combines the use of the Usui operator with that of a new bosonization procedure, called the term-by-term bosonization method. The present boson expansion theory is constructed by retaining a single collective quadrupole random phase approximation component, a truncation that allows for a perturbative treatment of the whole problem. Both Hermitian, as well as non-Hermitian boson expansions, valid for even nuclei, are obtained.

Dissociation between exact and approximate addition in developmental dyslexia.

PubMed

Yang, Xiujie; Meng, Xiangzhi

2016-09-01

Previous research has suggested that number sense and language are involved in number representation and calculation, in which number sense supports approximate arithmetic, and language permits exact enumeration and calculation. Meanwhile, individuals with dyslexia have a core deficit in phonological processing. Based on these findings, we thus hypothesized that children with dyslexia may exhibit exact calculation impairment while doing mental arithmetic. The reaction time and accuracy while doing exact and approximate addition with symbolic Arabic digits and non-symbolic visual arrays of dots were compared between typically developing children and children with dyslexia. Reaction time analyses did not reveal any differences across two groups of children, the accuracies, interestingly, revealed a distinction of approximation and exact addition across two groups of children. Specifically, two groups of children had no differences in approximation. Children with dyslexia, however, had significantly lower accuracy in exact addition in both symbolic and non-symbolic tasks than that of typically developing children. Moreover, linguistic performances were selectively associated with exact calculation across individuals. These results suggested that children with dyslexia have a mental arithmetic deficit specifically in the realm of exact calculation, while their approximation ability is relatively intact. Copyright © 2016 Elsevier Ltd. All rights reserved.

A quantum relaxation-time approximation for finite fermion systems

NASA Astrophysics Data System (ADS)

Reinhard, P.-G.; Suraud, E.

2015-03-01

We propose a relaxation time approximation for the description of the dynamics of strongly excited fermion systems. Our approach is based on time-dependent density functional theory at the level of the local density approximation. This mean-field picture is augmented by collisional correlations handled in relaxation time approximation which is inspired from the corresponding semi-classical picture. The method involves the estimate of microscopic relaxation rates/times which is presently taken from the well established semi-classical experience. The relaxation time approximation implies evaluation of the instantaneous equilibrium state towards which the dynamical state is progressively driven at the pace of the microscopic relaxation time. As test case, we consider Na clusters of various sizes excited either by a swift ion projectile or by a short and intense laser pulse, driven in various dynamical regimes ranging from linear to strongly non-linear reactions. We observe a strong effect of dissipation on sensitive observables such as net ionization and angular distributions of emitted electrons. The effect is especially large for moderate excitations where typical relaxation/dissipation time scales efficiently compete with ionization for dissipating the available excitation energy. Technical details on the actual procedure to implement a working recipe of such a quantum relaxation approximation are given in appendices for completeness.

RATIONAL APPROXIMATIONS TO GENERALIZED HYPERGEOMETRIC FUNCTIONS.

DTIC Science & Technology

Under weak restrictions on the various free parameters, general theorems for rational representations of the generalized hypergeometric functions...and certain Meijer G-functions are developed. Upon specialization, these theorems yield a sequency of rational approximations which converge to the

Plasma Physics Approximations in Ares

DOE Office of Scientific and Technical Information (OSTI.GOV)

Managan, R. A.

Lee & More derived analytic forms for the transport properties of a plasma. Many hydro-codes use their formulae for electrical and thermal conductivity. The coefficients are complex functions of Fermi-Dirac integrals, F n( μ/θ ), the chemical potential, μ or ζ = ln(1+e μ/θ ), and the temperature, θ = kT. Since these formulae are expensive to compute, rational function approximations were fit to them. Approximations are also used to find the chemical potential, either μ or ζ . The fits use ζ as the independent variable instead of μ/θ . New fits are provided for A α (ζmore » ),A β (ζ ), ζ, f(ζ ) = (1 + e -μ/θ)F 1/2(μ/θ), F 1/2'/F 1/2, F c α, and F c β. In each case the relative error of the fit is minimized since the functions can vary by many orders of magnitude. The new fits are designed to exactly preserve the limiting values in the non-degenerate and highly degenerate limits or as ζ→ 0 or ∞. The original fits due to Lee & More and George Zimmerman are presented for comparison.« less

36 CFR 254.11 - Exchanges at approximately equal value.

Code of Federal Regulations, 2010 CFR

2010-07-01

... equal value. 254.11 Section 254.11 Parks, Forests, and Public Property FOREST SERVICE, DEPARTMENT OF AGRICULTURE LANDOWNERSHIP ADJUSTMENTS Land Exchanges § 254.11 Exchanges at approximately equal value. (a) The authorized officer may exchange lands which are of approximately equal value upon a determination that: (1...

Discrete geometric analysis of message passing algorithm on graphs

NASA Astrophysics Data System (ADS)

Watanabe, Yusuke

2010-04-01

We often encounter probability distributions given as unnormalized products of non-negative functions. The factorization structures are represented by hypergraphs called factor graphs. Such distributions appear in various fields, including statistics, artificial intelligence, statistical physics, error correcting codes, etc. Given such a distribution, computations of marginal distributions and the normalization constant are often required. However, they are computationally intractable because of their computational costs. One successful approximation method is Loopy Belief Propagation (LBP) algorithm. The focus of this thesis is an analysis of the LBP algorithm. If the factor graph is a tree, i.e. having no cycle, the algorithm gives the exact quantities. If the factor graph has cycles, however, the LBP algorithm does not give exact results and possibly exhibits oscillatory and non-convergent behaviors. The thematic question of this thesis is "How the behaviors of the LBP algorithm are affected by the discrete geometry of the factor graph?" The primary contribution of this thesis is the discovery of a formula that establishes the relation between the LBP, the Bethe free energy and the graph zeta function. This formula provides new techniques for analysis of the LBP algorithm, connecting properties of the graph and of the LBP and the Bethe free energy. We demonstrate applications of the techniques to several problems including (non) convexity of the Bethe free energy, the uniqueness and stability of the LBP fixed point. We also discuss the loop series initiated by Chertkov and Chernyak. The loop series is a subgraph expansion of the normalization constant, or partition function, and reflects the graph geometry. We investigate theoretical natures of the series. Moreover, we show a partial connection between the loop series and the graph zeta function.

Basis Function Approximation of Transonic Aerodynamic Influence Coefficient Matrix

NASA Technical Reports Server (NTRS)

Li, Wesley Waisang; Pak, Chan-Gi

2010-01-01

A technique for approximating the modal aerodynamic influence coefficients [AIC] matrices by using basis functions has been developed and validated. An application of the resulting approximated modal AIC matrix for a flutter analysis in transonic speed regime has been demonstrated. This methodology can be applied to the unsteady subsonic, transonic and supersonic aerodynamics. The method requires the unsteady aerodynamics in frequency-domain. The flutter solution can be found by the classic methods, such as rational function approximation, k, p-k, p, root-locus et cetera. The unsteady aeroelastic analysis for design optimization using unsteady transonic aerodynamic approximation is being demonstrated using the ZAERO(TradeMark) flutter solver (ZONA Technology Incorporated, Scottsdale, Arizona). The technique presented has been shown to offer consistent flutter speed prediction on an aerostructures test wing [ATW] 2 configuration with negligible loss in precision in transonic speed regime. These results may have practical significance in the analysis of aircraft aeroelastic calculation and could lead to a more efficient design optimization cycle

Basis Function Approximation of Transonic Aerodynamic Influence Coefficient Matrix

NASA Technical Reports Server (NTRS)

Li, Wesley W.; Pak, Chan-gi

2011-01-01

A technique for approximating the modal aerodynamic influence coefficients matrices by using basis functions has been developed and validated. An application of the resulting approximated modal aerodynamic influence coefficients matrix for a flutter analysis in transonic speed regime has been demonstrated. This methodology can be applied to the unsteady subsonic, transonic, and supersonic aerodynamics. The method requires the unsteady aerodynamics in frequency-domain. The flutter solution can be found by the classic methods, such as rational function approximation, k, p-k, p, root-locus et cetera. The unsteady aeroelastic analysis for design optimization using unsteady transonic aerodynamic approximation is being demonstrated using the ZAERO flutter solver (ZONA Technology Incorporated, Scottsdale, Arizona). The technique presented has been shown to offer consistent flutter speed prediction on an aerostructures test wing 2 configuration with negligible loss in precision in transonic speed regime. These results may have practical significance in the analysis of aircraft aeroelastic calculation and could lead to a more efficient design optimization cycle.

Approximation methods in relativistic eigenvalue perturbation theory

NASA Astrophysics Data System (ADS)

Noble, Jonathan Howard

In this dissertation, three questions, concerning approximation methods for the eigenvalues of quantum mechanical systems, are investigated: (i) What is a pseudo--Hermitian Hamiltonian, and how can its eigenvalues be approximated via numerical calculations? This is a fairly broad topic, and the scope of the investigation is narrowed by focusing on a subgroup of pseudo--Hermitian operators, namely, PT--symmetric operators. Within a numerical approach, one projects a PT--symmetric Hamiltonian onto an appropriate basis, and uses a straightforward two--step algorithm to diagonalize the resulting matrix, leading to numerically approximated eigenvalues. (ii) Within an analytic ansatz, how can a relativistic Dirac Hamiltonian be decoupled into particle and antiparticle degrees of freedom, in appropriate kinematic limits? One possible answer is the Foldy--Wouthuysen transform; however, there are alter- native methods which seem to have some advantages over the time--tested approach. One such method is investigated by applying both the traditional Foldy--Wouthuysen transform and the "chiral" Foldy--Wouthuysen transform to a number of Dirac Hamiltonians, including the central-field Hamiltonian for a gravitationally bound system; namely, the Dirac-(Einstein-)Schwarzschild Hamiltonian, which requires the formal- ism of general relativity. (iii) Are there are pseudo--Hermitian variants of Dirac Hamiltonians that can be approximated using a decoupling transformation? The tachyonic Dirac Hamiltonian, which describes faster-than-light spin-1/2 particles, is gamma5--Hermitian, i.e., pseudo-Hermitian. Superluminal particles remain faster than light upon a Lorentz transformation, and hence, the Foldy--Wouthuysen program is unsuited for this case. Thus, inspired by the Foldy--Wouthuysen program, a decoupling transform in the ultrarelativistic limit is proposed, which is applicable to both sub- and superluminal particles.

A non-perturbative argument for the non-abelian Higgs mechanism

DOE Office of Scientific and Technical Information (OSTI.GOV)

De Palma, G.; INFN, Sezione di Pisa, Pisa; Strocchi, F., E-mail: franco.strocchi@sns.it

2013-09-15

The evasion of massless Goldstone bosons by the non-abelian Higgs mechanism is proved by a non-perturbative argument in the local BRST gauge. -- Highlights: •The perturbative explanation of the Higgs mechanism (HM) is not under mathematical control. •We offer a non-perturbative proof of the absence of Goldstone bosons from the non-abelian HM. •Our non-perturbative proof in the BRST gauge avoids a mean field ansatz and expansion.

Propagation Effects of Importance to the NASA/JPL Deep Space Network (DSN)

NASA Technical Reports Server (NTRS)

Slobin, Steve

1999-01-01

This paper presents Propagation Effects of Importance To The NASA/JPL Deep Space Network (DSN). The topics include: 1) DSN Antennas; 2) Deep Space Telecom Link Basics; 3) DSN Propagation Region of Interest; 4) Ka-Band Weather Effects Models and Examples; 5) Existing Goldstone Ka-Band Atmosphere Attenuation Model; 6) Existing Goldstone Atmosphere Noise Temperature Model; and 7) Ka-Band delta (G/T) Relative to Vacuum Condition. This paper summarizes the topics above.

Comparison of the Radiative Two-Flux and Diffusion Approximations

NASA Technical Reports Server (NTRS)

Spuckler, Charles M.

2006-01-01

Approximate solutions are sometimes used to determine the heat transfer and temperatures in a semitransparent material in which conduction and thermal radiation are acting. A comparison of the Milne-Eddington two-flux approximation and the diffusion approximation for combined conduction and radiation heat transfer in a ceramic material was preformed to determine the accuracy of the diffusion solution. A plane gray semitransparent layer without a substrate and a non-gray semitransparent plane layer on an opaque substrate were considered. For the plane gray layer the material is semitransparent for all wavelengths and the scattering and absorption coefficients do not vary with wavelength. For the non-gray plane layer the material is semitransparent with constant absorption and scattering coefficients up to a specified wavelength. At higher wavelengths the non-gray plane layer is assumed to be opaque. The layers are heated on one side and cooled on the other by diffuse radiation and convection. The scattering and absorption coefficients were varied. The error in the diffusion approximation compared to the Milne-Eddington two flux approximation was obtained as a function of scattering coefficient and absorption coefficient. The percent difference in interface temperatures and heat flux through the layer obtained using the Milne-Eddington two-flux and diffusion approximations are presented as a function of scattering coefficient and absorption coefficient. The largest errors occur for high scattering and low absorption except for the back surface temperature of the plane gray layer where the error is also larger at low scattering and low absorption. It is shown that the accuracy of the diffusion approximation can be improved for some scattering and absorption conditions if a reflectance obtained from a Kubelka-Munk type two flux theory is used instead of a reflection obtained from the Fresnel equation. The Kubelka-Munk reflectance accounts for surface reflection and

Ranking Support Vector Machine with Kernel Approximation

PubMed Central

Dou, Yong

2017-01-01

Learning to rank algorithm has become important in recent years due to its successful application in information retrieval, recommender system, and computational biology, and so forth. Ranking support vector machine (RankSVM) is one of the state-of-art ranking models and has been favorably used. Nonlinear RankSVM (RankSVM with nonlinear kernels) can give higher accuracy than linear RankSVM (RankSVM with a linear kernel) for complex nonlinear ranking problem. However, the learning methods for nonlinear RankSVM are still time-consuming because of the calculation of kernel matrix. In this paper, we propose a fast ranking algorithm based on kernel approximation to avoid computing the kernel matrix. We explore two types of kernel approximation methods, namely, the Nyström method and random Fourier features. Primal truncated Newton method is used to optimize the pairwise L2-loss (squared Hinge-loss) objective function of the ranking model after the nonlinear kernel approximation. Experimental results demonstrate that our proposed method gets a much faster training speed than kernel RankSVM and achieves comparable or better performance over state-of-the-art ranking algorithms. PMID:28293256

Ranking Support Vector Machine with Kernel Approximation.

PubMed

Chen, Kai; Li, Rongchun; Dou, Yong; Liang, Zhengfa; Lv, Qi

2017-01-01

Learning to rank algorithm has become important in recent years due to its successful application in information retrieval, recommender system, and computational biology, and so forth. Ranking support vector machine (RankSVM) is one of the state-of-art ranking models and has been favorably used. Nonlinear RankSVM (RankSVM with nonlinear kernels) can give higher accuracy than linear RankSVM (RankSVM with a linear kernel) for complex nonlinear ranking problem. However, the learning methods for nonlinear RankSVM are still time-consuming because of the calculation of kernel matrix. In this paper, we propose a fast ranking algorithm based on kernel approximation to avoid computing the kernel matrix. We explore two types of kernel approximation methods, namely, the Nyström method and random Fourier features. Primal truncated Newton method is used to optimize the pairwise L2-loss (squared Hinge-loss) objective function of the ranking model after the nonlinear kernel approximation. Experimental results demonstrate that our proposed method gets a much faster training speed than kernel RankSVM and achieves comparable or better performance over state-of-the-art ranking algorithms.

Traveling-cluster approximation for uncorrelated amorphous systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sen, A.K.; Mills, R.; Kaplan, T.

1984-11-15

We have developed a formalism for including cluster effects in the one-electron Green's function for a positionally disordered (liquid or amorphous) system without any correlation among the scattering sites. This method is an extension of the technique known as the traveling-cluster approximation (TCA) originally obtained and applied to a substitutional alloy by Mills and Ratanavararaksa. We have also proved the appropriate fixed-point theorem, which guarantees, for a bounded local potential, that the self-consistent equations always converge upon iteration to a unique, Herglotz solution. To our knowledge, this is the only analytic theory for considering cluster effects. Furthermore, we have performedmore » some computer calculations in the pair TCA, for the model case of delta-function potentials on a one-dimensional random chain. These results have been compared with ''exact calculations'' (which, in principle, take into account all cluster effects) and with the coherent-potential approximation (CPA), which is the single-site TCA. The density of states for the pair TCA clearly shows some improvement over the CPA and yet, apparently, the pair approximation distorts some of the features of the exact results.« less

Approximate Locality for Quantum Systems on Graphs

NASA Astrophysics Data System (ADS)

Osborne, Tobias J.

2008-10-01

In this Letter we make progress on a long-standing open problem of Aaronson and Ambainis [Theory Comput. 1, 47 (2005)1557-2862]: we show that if U is a sparse unitary operator with a gap Δ in its spectrum, then there exists an approximate logarithm H of U which is also sparse. The sparsity pattern of H gets more dense as 1/Δ increases. This result can be interpreted as a way to convert between local continuous-time and local discrete-time quantum processes. As an example we show that the discrete-time coined quantum walk can be realized stroboscopically from an approximately local continuous-time quantum walk.

Mean-field approximation for spacing distribution functions in classical systems

NASA Astrophysics Data System (ADS)

González, Diego Luis; Pimpinelli, Alberto; Einstein, T. L.

2012-01-01

We propose a mean-field method to calculate approximately the spacing distribution functions p(n)(s) in one-dimensional classical many-particle systems. We compare our method with two other commonly used methods, the independent interval approximation and the extended Wigner surmise. In our mean-field approach, p(n)(s) is calculated from a set of Langevin equations, which are decoupled by using a mean-field approximation. We find that in spite of its simplicity, the mean-field approximation provides good results in several systems. We offer many examples illustrating that the three previously mentioned methods give a reasonable description of the statistical behavior of the system. The physical interpretation of each method is also discussed.

Facial approximation-from facial reconstruction synonym to face prediction paradigm.

PubMed

Stephan, Carl N

2015-05-01

Facial approximation was first proposed as a synonym for facial reconstruction in 1987 due to dissatisfaction with the connotations the latter label held. Since its debut, facial approximation's identity has morphed as anomalies in face prediction have accumulated. Now underpinned by differences in what problems are thought to count as legitimate, facial approximation can no longer be considered a synonym for, or subclass of, facial reconstruction. Instead, two competing paradigms of face prediction have emerged, namely: facial approximation and facial reconstruction. This paper shines a Kuhnian lens across the discipline of face prediction to comprehensively review these developments and outlines the distinguishing features between the two paradigms. © 2015 American Academy of Forensic Sciences.

An analysis and demonstration of clock synchronization by VLBI. [Very Long Baseline Interferometry for Deep Space Net

NASA Technical Reports Server (NTRS)

Hurd, W. J.

1974-01-01

A prototype of a semi-real time system for synchronizing the Deep Space Net station clocks by radio interferometry was successfully demonstrated on August 30, 1972. The system utilized an approximate maximum likelihood estimation procedure for processing the data, thereby achieving essentially optimum time sync estimates for a given amount of data, or equivalently, minimizing the amount of data required for reliable estimation. Synchronization accuracies as good as 100 ns rms were achieved between Deep Space Stations 11 and 12, both at Goldstone, Calif. The accuracy can be improved by increasing the system bandwidth until the fundamental limitations due to baseline and source position uncertainties and atmospheric effects are reached. These limitations are under 10 ns for transcontinental baselines.

An analysis and demonstration of clock synchronization by VLBI

NASA Technical Reports Server (NTRS)

Hurd, W. J.

1972-01-01

A prototype of a semireal-time system for synchronizing the DSN station clocks by radio interferometry was successfully demonstrated. The system utilized an approximate maximum likelihood estimation procedure for processing the data, thereby achieving essentially optimum time synchronization estimates for a given amount of data, or equivalently, minimizing the amount of data required for reliable estimation. Synchronization accuracies as good as 100 nsec rms were achieved between DSS 11 and DSS 12, both at Goldstone, California. The accuracy can be improved by increasing the system bandwidth until the fundamental limitations due to position uncertainties of baseline and source and atmospheric effects are reached. These limitations are under ten nsec for transcontinental baselines.

Discrete-Time Stable Generalized Self-Learning Optimal Control With Approximation Errors.

PubMed

Wei, Qinglai; Li, Benkai; Song, Ruizhuo

2018-04-01

In this paper, a generalized policy iteration (GPI) algorithm with approximation errors is developed for solving infinite horizon optimal control problems for nonlinear systems. The developed stable GPI algorithm provides a general structure of discrete-time iterative adaptive dynamic programming algorithms, by which most of the discrete-time reinforcement learning algorithms can be described using the GPI structure. It is for the first time that approximation errors are explicitly considered in the GPI algorithm. The properties of the stable GPI algorithm with approximation errors are analyzed. The admissibility of the approximate iterative control law can be guaranteed if the approximation errors satisfy the admissibility criteria. The convergence of the developed algorithm is established, which shows that the iterative value function is convergent to a finite neighborhood of the optimal performance index function, if the approximate errors satisfy the convergence criterion. Finally, numerical examples and comparisons are presented.

Approximate Arithmetic Training Improves Informal Math Performance in Low Achieving Preschoolers

PubMed Central

Szkudlarek, Emily; Brannon, Elizabeth M.

2018-01-01

Recent studies suggest that practice with approximate and non-symbolic arithmetic problems improves the math performance of adults, school aged children, and preschoolers. However, the relative effectiveness of approximate arithmetic training compared to available educational games, and the type of math skills that approximate arithmetic targets are unknown. The present study was designed to (1) compare the effectiveness of approximate arithmetic training to two commercially available numeral and letter identification tablet applications and (2) to examine the specific type of math skills that benefit from approximate arithmetic training. Preschool children (n = 158) were pseudo-randomly assigned to one of three conditions: approximate arithmetic, letter identification, or numeral identification. All children were trained for 10 short sessions and given pre and post tests of informal and formal math, executive function, short term memory, vocabulary, alphabet knowledge, and number word knowledge. We found a significant interaction between initial math performance and training condition, such that children with low pretest math performance benefited from approximate arithmetic training, and children with high pretest math performance benefited from symbol identification training. This effect was restricted to informal, and not formal, math problems. There were also effects of gender, socio-economic status, and age on post-test informal math score after intervention. A median split on pretest math ability indicated that children in the low half of math scores in the approximate arithmetic training condition performed significantly better than children in the letter identification training condition on post-test informal math problems when controlling for pretest, age, gender, and socio-economic status. Our results support the conclusion that approximate arithmetic training may be especially effective for children with low math skills, and that approximate arithmetic

Approximate Arithmetic Training Improves Informal Math Performance in Low Achieving Preschoolers.

PubMed

Szkudlarek, Emily; Brannon, Elizabeth M

2018-01-01

Recent studies suggest that practice with approximate and non-symbolic arithmetic problems improves the math performance of adults, school aged children, and preschoolers. However, the relative effectiveness of approximate arithmetic training compared to available educational games, and the type of math skills that approximate arithmetic targets are unknown. The present study was designed to (1) compare the effectiveness of approximate arithmetic training to two commercially available numeral and letter identification tablet applications and (2) to examine the specific type of math skills that benefit from approximate arithmetic training. Preschool children ( n = 158) were pseudo-randomly assigned to one of three conditions: approximate arithmetic, letter identification, or numeral identification. All children were trained for 10 short sessions and given pre and post tests of informal and formal math, executive function, short term memory, vocabulary, alphabet knowledge, and number word knowledge. We found a significant interaction between initial math performance and training condition, such that children with low pretest math performance benefited from approximate arithmetic training, and children with high pretest math performance benefited from symbol identification training. This effect was restricted to informal, and not formal, math problems. There were also effects of gender, socio-economic status, and age on post-test informal math score after intervention. A median split on pretest math ability indicated that children in the low half of math scores in the approximate arithmetic training condition performed significantly better than children in the letter identification training condition on post-test informal math problems when controlling for pretest, age, gender, and socio-economic status. Our results support the conclusion that approximate arithmetic training may be especially effective for children with low math skills, and that approximate arithmetic

Analytic approximations to the modon dispersion relation. [in oceanography

NASA Technical Reports Server (NTRS)

Boyd, J. P.

1981-01-01

Three explicit analytic approximations are given to the modon dispersion relation developed by Flierl et al. (1980) to describe Gulf Stream rings and related phenomena in the oceans and atmosphere. The solutions are in the form of k(q), and are developed in the form of a power series in q for small q, an inverse power series in 1/q for large q, and a two-point Pade approximant. The low order Pade approximant is shown to yield a solution for the dispersion relation with a maximum relative error for the lowest branch of the function equal to one in 700 in the q interval zero to infinity.

Approximate Dispersion Relations for Waves on Arbitrary Shear Flows

NASA Astrophysics Data System (ADS)

Ellingsen, S. À.; Li, Y.

2017-12-01

An approximate dispersion relation is derived and presented for linear surface waves atop a shear current whose magnitude and direction can vary arbitrarily with depth. The approximation, derived to first order of deviation from potential flow, is shown to produce good approximations at all wavelengths for a wide range of naturally occuring shear flows as well as widely used model flows. The relation reduces in many cases to a 3-D generalization of the much used approximation by Skop (1987), developed further by Kirby and Chen (1989), but is shown to be more robust, succeeding in situations where the Kirby and Chen model fails. The two approximations incur the same numerical cost and difficulty. While the Kirby and Chen approximation is excellent for a wide range of currents, the exact criteria for its applicability have not been known. We explain the apparently serendipitous success of the latter and derive proper conditions of applicability for both approximate dispersion relations. Our new model has a greater range of applicability. A second order approximation is also derived. It greatly improves accuracy, which is shown to be important in difficult cases. It has an advantage over the corresponding second-order expression proposed by Kirby and Chen that its criterion of accuracy is explicitly known, which is not currently the case for the latter to our knowledge. Our second-order term is also arguably significantly simpler to implement, and more physically transparent, than its sibling due to Kirby and Chen.