Evolution of nonlinear waves in a blood-filled artery with an aneurysm

NASA Astrophysics Data System (ADS)

Nikolova, E. V.; Jordanov, I. P.; Dimitrova, Z. I.; Vitanov, N. K.

2017-10-01

We discuss propagation of traveling waves in a blood-filled hyper-elastic artery with a local dilatation (an aneurysm). The processes in the injured artery are modeled by an equation of the motion of the arterial wall and by equations of the motion of the fluid (the blood). Taking into account the specific arterial geometry and applying the reductive perturbation method in long-wave approximation we reduce the model equations to a version of the perturbed Korteweg-de Vries kind equation with variable coefficients. Exact traveling-wave solutions of this equation are obtained by the modified method of simplest equation where the differential equation of Abel is used as a simplest equation. A particular case of the obtained exact solution is numerically simulated and discussed from the point of view of arterial disease mechanics.

The Noble-Abel Stiffened-Gas equation of state

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

Le Métayer, Olivier, E-mail: olivier.lemetayer@univ-amu.fr; Saurel, Richard, E-mail: richard.saurel@univ-amu.fr; RS2N, 371 Chemin de Gaumin, 83640 Saint-Zacharie

2016-04-15

Hyperbolic two-phase flow models have shown excellent ability for the resolution of a wide range of applications ranging from interfacial flows to fluid mixtures with several velocities. These models account for waves propagation (acoustic and convective) and consist in hyperbolic systems of partial differential equations. In this context, each phase is compressible and needs an appropriate convex equation of state (EOS). The EOS must be simple enough for intensive computations as well as boundary conditions treatment. It must also be accurate, this being challenging with respect to simplicity. In the present approach, each fluid is governed by a novel EOSmore » named “Noble Abel stiffened gas,” this formulation being a significant improvement of the popular “Stiffened Gas (SG)” EOS. It is a combination of the so-called “Noble-Abel” and “stiffened gas” equations of state that adds repulsive effects to the SG formulation. The determination of the various thermodynamic functions and associated coefficients is the aim of this article. We first use thermodynamic considerations to determine the different state functions such as the specific internal energy, enthalpy, and entropy. Then we propose to determine the associated coefficients for a liquid in the presence of its vapor. The EOS parameters are determined from experimental saturation curves. Some examples of liquid-vapor fluids are examined and associated parameters are computed with the help of the present method. Comparisons between analytical and experimental saturation curves show very good agreement for wide ranges of temperature for both liquid and vapor.« less

Recovery of refractivity profiles and pressure and temperature distributions in the lower atmosphere from satellite-to-satellite radio occultation data

NASA Technical Reports Server (NTRS)

Murray, C. W., Jr.

1977-01-01

The feasibility of recovering parameters from one-way range rate between two earth orbiting spacecraft during occultation of the tracking signal by the earth's lower atmosphere. The tracking data is inverted by an integral transformation (Abel transform) to obtain a vertical refractivity profile above the point of closest approach of the ray connecting the satellites. Pressure and temperature distributions can be obtained from values of dry refractivity using the hydrostatic equation and perfect gas law. Two methods are investigated for recovering pressure and temperature parameters. Results show that recovery is much more sensitive to satellite velocity errors than to satellite position errors. An error analysis is performed. An example is given demonstrating recovery of parameters from radio occultation data obtained during satellite-to-satellite tracking of Nimbus 6 by the ATS 6 satellite.

VizieR Online Data Catalog: Ultradiffuse galaxies found in deep HST images of HFF (Lee+, 2017)

NASA Astrophysics Data System (ADS)

Lee, M. G.; Kang, J.; Lee, J. H.; Jang in, S.

2018-03-01

Abell S1063 and Abell 2744 are located at redshift z=0.348 and z=0.308, respectively, so their HST fields cover a relatively large fraction of each cluster. They are part of the target galaxy clusters in the Hubble Frontier Fields (HFF) Program, for which deep Hubble Space Telescope (HST) images are available (Lotz+ 2017ApJ...837...97L). We used ACS/F814W(I) and WFC3/F105W(Y) images for Abell S1063 and Abell 2744 in the HFF. The effective wavelengths of the F814W and F105W filters for the redshifts of Abell S1063 and Abell 2744 (6220 and 8030Å) correspond approximately to SDSS r' and Cousins I (or SDSS i') in the rest frame, respectively. Figure 1 display color images of the HST fields for Abell S1063 and Abell 2744. In this study we adopt the cosmological parameters H0=73km/s/Mpc, ΩM=0.27, and ΩΛ=0.73. For these parameters, luminosity distance moduli of Abell S1063 and Abell 2744 are (m-M)0=41.25 (d=1775Mpc) and 40.94 (d=1540Mpc), and angular diameter distances are 978 and 901Mpc, respectively. (5 data files).

The GenABEL Project for statistical genomics.

PubMed

Karssen, Lennart C; van Duijn, Cornelia M; Aulchenko, Yurii S

2016-01-01

Development of free/libre open source software is usually done by a community of people with an interest in the tool. For scientific software, however, this is less often the case. Most scientific software is written by only a few authors, often a student working on a thesis. Once the paper describing the tool has been published, the tool is no longer developed further and is left to its own device. Here we describe the broad, multidisciplinary community we formed around a set of tools for statistical genomics. The GenABEL project for statistical omics actively promotes open interdisciplinary development of statistical methodology and its implementation in efficient and user-friendly software under an open source licence. The software tools developed withing the project collectively make up the GenABEL suite, which currently consists of eleven tools. The open framework of the project actively encourages involvement of the community in all stages, from formulation of methodological ideas to application of software to specific data sets. A web forum is used to channel user questions and discussions, further promoting the use of the GenABEL suite. Developer discussions take place on a dedicated mailing list, and development is further supported by robust development practices including use of public version control, code review and continuous integration. Use of this open science model attracts contributions from users and developers outside the "core team", facilitating agile statistical omics methodology development and fast dissemination.

Finite-band solutions of the coupled dispersionless hierarchy

NASA Astrophysics Data System (ADS)

Li, Zhu

2016-08-01

The coupled dispersionless hierarchy is derived with the help of the zero curvature equation. Based on the Lax matrix, we introduce an algebraic curve {{ K }}n of arithmetic genus n, from which we establish the corresponding meromorphic function ϕ, the Baker-Akhiezer function {\\varphi }1, and Dubrovin-type equations. The straightening out of all the flows is given under the Abel-Jacobi coordinates. Using the asymptotic properties of ϕ and {\\varphi }1, we obtain the explicit theta function representations of the meromorphic function ϕ, the Baker-Akhiezer function {\\varphi }1 and of solutions for the whole hierarchy.

Dark matter dynamics in Abell 3827: new data consistent with standard cold dark matter

NASA Astrophysics Data System (ADS)

Massey, Richard; Harvey, David; Liesenborgs, Jori; Richard, Johan; Stach, Stuart; Swinbank, Mark; Taylor, Peter; Williams, Liliya; Clowe, Douglas; Courbin, Frédéric; Edge, Alastair; Israel, Holger; Jauzac, Mathilde; Joseph, Rémy; Jullo, Eric; Kitching, Thomas D.; Leonard, Adrienne; Merten, Julian; Nagai, Daisuke; Nightingale, James; Robertson, Andrew; Romualdez, Luis Javier; Saha, Prasenjit; Smit, Renske; Tam, Sut-Ieng; Tittley, Eric

2018-06-01

We present integral field spectroscopy of galaxy cluster Abell 3827, using Atacama Large Millimetre Array (ALMA) and Very Large Telescope/Multi-Unit Spectroscopic Explorer. It reveals an unusual configuration of strong gravitational lensing in the cluster core, with at least seven lensed images of a single background spiral galaxy. Lens modelling based on Hubble Space Telescope imaging had suggested that the dark matter associated with one of the cluster's central galaxies may be offset. The new spectroscopic data enable better subtraction of foreground light, and better identification of multiple background images. The inferred distribution of dark matter is consistent with being centred on the galaxies, as expected by Λ cold dark matter. Each galaxy's dark matter also appears to be symmetric. Whilst, we do not find an offset between mass and light (suggestive of self-interacting dark matter) as previously reported, the numerical simulations that have been performed to calibrate Abell 3827 indicate that offsets and asymmetry are still worth looking for in collisions with particular geometries. Meanwhile, ALMA proves exceptionally useful for strong lens image identifications.

Tomography and the Herglotz-Wiechert inverse formulation

NASA Astrophysics Data System (ADS)

Nowack, Robert L.

1990-04-01

In this paper, linearized tomography and the Herglotz-Wiechert inverse formulation are compared. Tomographic inversions for 2-D or 3-D velocity structure use line integrals along rays and can be written in terms of Radon transforms. For radially concentric structures, Radon transforms are shown to reduce to Abel transforms. Therefore, for straight ray paths, the Abel transform of travel-time is a tomographic algorithm specialized to a one-dimensional radially concentric medium. The Herglotz-Wiechert formulation uses seismic travel-time data to invert for one-dimensional earth structure and is derived using exact ray trajectories by applying an Abel transform. This is of historical interest since it would imply that a specialized tomographic-like algorithm has been used in seismology since the early part of the century (see Herglotz, 1907; Wiechert, 1910). Numerical examples are performed comparing the Herglotz-Wiechert algorithm and linearized tomography along straight rays. Since the Herglotz-Wiechert algorithm is applicable under specific conditions, (the absence of low velocity zones) to non-straight ray paths, the association with tomography may prove to be useful in assessing the uniqueness of tomographic results generalized to curved ray geometries.

The GenABEL Project for statistical genomics

PubMed Central

Karssen, Lennart C.; van Duijn, Cornelia M.; Aulchenko, Yurii S.

2016-01-01

Development of free/libre open source software is usually done by a community of people with an interest in the tool. For scientific software, however, this is less often the case. Most scientific software is written by only a few authors, often a student working on a thesis. Once the paper describing the tool has been published, the tool is no longer developed further and is left to its own device. Here we describe the broad, multidisciplinary community we formed around a set of tools for statistical genomics. The GenABEL project for statistical omics actively promotes open interdisciplinary development of statistical methodology and its implementation in efficient and user-friendly software under an open source licence. The software tools developed withing the project collectively make up the GenABEL suite, which currently consists of eleven tools. The open framework of the project actively encourages involvement of the community in all stages, from formulation of methodological ideas to application of software to specific data sets. A web forum is used to channel user questions and discussions, further promoting the use of the GenABEL suite. Developer discussions take place on a dedicated mailing list, and development is further supported by robust development practices including use of public version control, code review and continuous integration. Use of this open science model attracts contributions from users and developers outside the “core team”, facilitating agile statistical omics methodology development and fast dissemination. PMID:27347381

Chandra and XMM-Newton Observations of the Abell 3395/Abell 3391 Intercluster Filament

NASA Astrophysics Data System (ADS)

Alvarez, Gabriella E.; Randall, Scott W.; Bourdin, Hervé; Jones, Christine; Holley-Bockelmann, Kelly

2018-05-01

We present Chandra and XMM-Newton X-ray observations of the Abell 3391/Abell 3395 intercluster filament. It has been suggested that the galaxy clusters Abell 3395, Abell 3391, and the galaxy group ESO-161 -IG 006 located between the two clusters, are in alignment along a large-scale intercluster filament. We find that the filament is aligned close to the plane of the sky, in contrast to previous results. We find a global projected filament temperature kT = {4.45}-0.55+0.89 keV, electron density {n}e={1.08}-0.05+0.06× {10}-4 cm‑3, and {M}gas}={2.7}-0.1+0.2 × {10}13 M ⊙. The thermodynamic properties of the filament are consistent with that of the intracluster medium (ICM) of Abell 3395 and Abell 3391, suggesting that the filament emission is dominated by ICM gas that has been tidally disrupted during an early stage merger between these two clusters. We present temperature, density, entropy, and abundance profiles across the filament. We find that the galaxy group ESO-161 may be undergoing ram-pressure-stripping in the low-density environment at or near the virial radius of both clusters, due to its rapid motion through the filament.

Hubble Frontier Field Abell 2744

NASA Image and Video Library

2014-01-07

This long-exposure image from NASA Hubble Space Telescope of massive galaxy cluster Abell 2744 is the deepest ever made of any cluster of galaxies. Shown in the foreground is Abell 2744, located in the constellation Sculptor.

The X-ray luminosity functions of Abell clusters from the Einstein Cluster Survey

NASA Technical Reports Server (NTRS)

Burg, R.; Giacconi, R.; Forman, W.; Jones, C.

1994-01-01

We have derived the present epoch X-ray luminosity function of northern Abell clusters using luminosities from the Einstein Cluster Survey. The sample is sufficiently large that we can determine the luminosity function for each richness class separately with sufficient precision to study and compare the different luminosity functions. We find that, within each richness class, the range of X-ray luminosity is quite large and spans nearly a factor of 25. Characterizing the luminosity function for each richness class with a Schechter function, we find that the characteristic X-ray luminosity, L(sub *), scales with richness class as (L(sub *) varies as N(sub*)(exp gamma), where N(sub *) is the corrected, mean number of galaxies in a richness class, and the best-fitting exponent is gamma = 1.3 +/- 0.4. Finally, our analysis suggests that there is a lower limit to the X-ray luminosity of clusters which is determined by the integrated emission of the cluster member galaxies, and this also scales with richness class. The present sample forms a baseline for testing cosmological evolution of Abell-like clusters when an appropriate high-redshift cluster sample becomes available.

Compilation of Abstracts of Theses Submitted by Candidates for Degrees: October 1990 to September 1991

DTIC Science & Technology

1991-09-30

Tool (ASSET) COMPUTER SCIENCE Vicki Sue Abel VIEWER - A User Interface for Failure 49 Lieutenant Commander, U.S. Navy Region Analysis and Medio Monti...California Current System using a Primitive Equation Model Charles C. McGlothin, Jr. Ambient Sound in the Ocean Induced by 257 Lieutenant, U.S. Navy Heavy...parameters,, and ambient flow/oscillating flow combinations using VAX-3520 and NASA’s Supercomputers. Extensive sensitivity analysis has been performed

Is there substructure around M87?

NASA Astrophysics Data System (ADS)

Oldham, L. J.; Evans, N. W.

2016-10-01

We present a general method to identify infalling substructure in discrete data sets with position and line-of-sight velocity data. We exploit the fact that galaxies falling on to a brightest cluster galaxy (BCG) in a virialized cluster, or dwarf satellites falling on to a central galaxy like the Milky Way, follow nearly radial orbits. If the orbits are exactly radial, we show how to find the probability distribution for a satellite's energy, given a tracer density for the satellite population, by solving an Abel integral equation. This is an extension of Eddington's classical formula for the isotropic distribution function. When applied to a system of galaxies, clustering in energy space can then be quantified using the Kullback-Leibler divergence, and groups of objects can be identified which, though separated in the sky, may be falling in on the same orbit. This method is tested using mock data and applied to the satellite galaxy population around M87, the BCG in Virgo, and a number of associations that are found, which may represent infalling galaxy groups.

Abel's theorem in the noncommutative case

NASA Astrophysics Data System (ADS)

Leitenberger, Frank

2004-03-01

We define noncommutative binary forms. Using the typical representation of Hermite we prove the fundamental theorem of algebra and we derive a noncommutative Cardano formula for cubic forms. We define quantized elliptic and hyperelliptic differentials of the first kind. Following Abel we prove Abel's theorem.

Existence and stability of dispersive solutions to the Kadomtsev-Petviashvili equation in the presence of dispersion effect

NASA Astrophysics Data System (ADS)

Das, Amiya; Ganguly, Asish

2017-07-01

The paper deals with Kadomtsev-Petviashvili (KP) equation in presence of a small dispersion effect. The nature of solutions are examined under the dispersion effect by using Lyapunov function and dynamical system theory. We prove that when dispersion is added to the KP equation, in certain regions, yet there exist bounded traveling wave solutions in the form of solitary waves, periodic and elliptic functions. The general solution of the equation with or without the dispersion effect are obtained in terms of Weirstrass ℘ functions and Jacobi elliptic functions. New form of kink-type solutions are established by exploring a new technique based on factorization method, use of functional transformation and the Abel's first order nonlinear equation. Furthermore, the stability analysis of the dispersive solutions are examined which shows that the traveling wave velocity is a bifurcation parameter which governs between different classes of waves. We use the phase plane analysis and show that at a critical velocity, the solution has a transcritical bifurcation.

Electric and magnetic polarization saturations for a thermally loaded penny-shaped crack in a magneto-electro-thermo-elastic medium

NASA Astrophysics Data System (ADS)

Li, P.-D.; Li, X.-Y.; Kang, G.-Z.; Müller, R.

2017-09-01

This paper is devoted to investigating the thermal-induced electric and magnetic polarization saturations (PS) at the tip of a penny-shaped crack embedded in an infinite space of magneto-electro-thermo-elastic medium. In view of the symmetry with respect to the cracked plane, this crack problem is formulated by a mixed boundary value problem. By virtue of the solution to the Abel type integral equation, the governing equations corresponding to the present problem are analytically solved and the generalized crack surface displacement and field intensity factors are obtained in closed-forms. Applying the hypothesis of the electric and magnetic PS model to the analytical results, the sizes of the electric and magnetic yielding zones are determined. Numerical calculations are carried out to reveal the influences of the thermal load and the electric and magnetic yielding strengths on the results, and to show the distributions of the electric and magnetic potentials on the crack surfaces. It is found that the sizes of electric and magnetic yielding zones are mainly dependent on the electric and magnetic yielding strengths, respectively. Since the multi-ferroic media are widely used in various complex thermal environments, the present work could serve as a reference for the designs of various magneto-electric composite structures.

Tauberian theorems for Abel summability of sequences of fuzzy numbers

NASA Astrophysics Data System (ADS)

Yavuz, Enes; ćoşkun, Hüsamettin

2015-09-01

We give some conditions under which Abel summable sequences of fuzzy numbers are convergent. As corollaries we obtain the results given in [E. Yavuz, Ö. Talo, Abel summability of sequences of fuzzy numbers, Soft computing 2014, doi: 10.1007/s00500-014-1563-7].

75 FR 62424 - EDS, an HP Company (Re-Branded as HP-Enterprise Services) Including On-Site Workers From: Abel...

Federal Register 2010, 2011, 2012, 2013, 2014

2010-10-08

... Floyd and Company, Trinity Government SYS a Private Co, Verizon Network Integration Corp, Vision... Provider Inc., Teksystems, The Experts Inc., TM Floyd and Company, Trinity Government SYS a Private Co... Compuware Corp Comsys Information Technology SVC, Diversified Systems Inc., E- Corn LLC, Farrington...

A variational regularization of Abel transform for GPS radio occultation

NASA Astrophysics Data System (ADS)

Wee, Tae-Kwon

2018-04-01

In the Global Positioning System (GPS) radio occultation (RO) technique, the inverse Abel transform of measured bending angle (Abel inversion, hereafter AI) is the standard means of deriving the refractivity. While concise and straightforward to apply, the AI accumulates and propagates the measurement error downward. The measurement error propagation is detrimental to the refractivity in lower altitudes. In particular, it builds up negative refractivity bias in the tropical lower troposphere. An alternative to AI is the numerical inversion of the forward Abel transform, which does not incur the integration of error-possessing measurement and thus precludes the error propagation. The variational regularization (VR) proposed in this study approximates the inversion of the forward Abel transform by an optimization problem in which the regularized solution describes the measurement as closely as possible within the measurement's considered accuracy. The optimization problem is then solved iteratively by means of the adjoint technique. VR is formulated with error covariance matrices, which permit a rigorous incorporation of prior information on measurement error characteristics and the solution's desired behavior into the regularization. VR holds the control variable in the measurement space to take advantage of the posterior height determination and to negate the measurement error due to the mismodeling of the refractional radius. The advantages of having the solution and the measurement in the same space are elaborated using a purposely corrupted synthetic sounding with a known true solution. The competency of VR relative to AI is validated with a large number of actual RO soundings. The comparison to nearby radiosonde observations shows that VR attains considerably smaller random and systematic errors compared to AI. A noteworthy finding is that in the heights and areas that the measurement bias is supposedly small, VR follows AI very closely in the mean refractivity deserting the first guess. In the lowest few kilometers that AI produces large negative refractivity bias, VR reduces the refractivity bias substantially with the aid of the background, which in this study is the operational forecasts of the European Centre for Medium-Range Weather Forecasts (ECMWF). It is concluded based on the results presented in this study that VR offers a definite advantage over AI in the quality of refractivity.

ROSAT HRI images of Abell 85 and Abell 496: Evidence for inhomogeneities in cooling flows

NASA Technical Reports Server (NTRS)

Prestwich, Andrea H.; Guimond, Stephen J.; Luginbuhl, Christian B.; Joy, Marshall

1995-01-01

We present ROSAT high-resolution images of two clusters of galaxies with cooling flows, Abell 496 and Abell 85. In these clusters, X-ray emission on small scales above the general cluster emission is significant at the 3 sigma level. There is no evidence for optical counterparts. If real, the enhancements may be associated with clumps of gas at a lower temperature and higher density than the ambient medium, or hotter, denser gas perhaps compressed by magnetic fields. These observations can be used to test models of how thermal instabilities form and evolve in cooling flows.

ROSAT HRI images of Abell 85 and Abell 496: Evidence for inhomogeneities in cooling flows

NASA Technical Reports Server (NTRS)

Prestwich, Andrea H.; Guimond, Stephen J.; Luginbuhl, Christian; Joy, Marshall

1994-01-01

We present ROSAT HRI images of two clusters of galaxies with cooling flows, Abell 496 and Abell 85. In these clusters, x-ray emission on small scales above the general cluster emission is significant at the 3 sigma level. There is no evidence for optical counterparts. The enhancements may be associated with lumps of gas at a lower temperature and higher density than the ambient medium, or hotter, denser gas perhaps compressed by magnetic fields. These observations can be used to test models of how thermal instabilities form and evolve in cooling flows.

The wonderful apparatus of John Jacob Abel called the "artificial kidney".

PubMed

Eknoyan, Garabed

2009-01-01

Hemodialysis, which now provides life-saving therapy to millions of individuals, began as an exploratory attempt to sustain the lives of selected patients in the 1950s. That was a century after the formulation of the concept and determination of the laws governing dialysis. The first step in the translation of the laboratory principles of dialysis to living animals was the "vividiffusion" apparatus developed by John Jacob Abel (1859-1938), dubbed the "artificial kidney" in the August 11, 1913 issue of The Times of London reporting the demonstration of vividiffusion by Abel at University College. The detailed article in the January 18, 1914 of the New York Times, reproduced here, is based on the subsequent medical reports published by Abel et al. Tentative attempts of human dialysis in the decade that followed based on the vividiffusion apparatus of Abel and his materials (collodion, hirudin, and glass) met with failure and had to be abandoned. Practical dialysis became possible in the 1940s and thereafter after cellophane, heparin, and teflon became available. Abel worked in an age of great progress and experimental work in the basic sciences that laid the foundations of science-driven medicine. It was a "Heroic Age of Medicine," when medical discoveries and communicating them to the public were assuming increasing importance. This article provides the cultural, social, scientific, and medical background in which Abel worked, developed and reported his wonderful apparatus called the "artificial kidney."

ParallABEL: an R library for generalized parallelization of genome-wide association studies.

PubMed

Sangket, Unitsa; Mahasirimongkol, Surakameth; Chantratita, Wasun; Tandayya, Pichaya; Aulchenko, Yurii S

2010-04-29

Genome-Wide Association (GWA) analysis is a powerful method for identifying loci associated with complex traits and drug response. Parts of GWA analyses, especially those involving thousands of individuals and consuming hours to months, will benefit from parallel computation. It is arduous acquiring the necessary programming skills to correctly partition and distribute data, control and monitor tasks on clustered computers, and merge output files. Most components of GWA analysis can be divided into four groups based on the types of input data and statistical outputs. The first group contains statistics computed for a particular Single Nucleotide Polymorphism (SNP), or trait, such as SNP characterization statistics or association test statistics. The input data of this group includes the SNPs/traits. The second group concerns statistics characterizing an individual in a study, for example, the summary statistics of genotype quality for each sample. The input data of this group includes individuals. The third group consists of pair-wise statistics derived from analyses between each pair of individuals in the study, for example genome-wide identity-by-state or genomic kinship analyses. The input data of this group includes pairs of SNPs/traits. The final group concerns pair-wise statistics derived for pairs of SNPs, such as the linkage disequilibrium characterisation. The input data of this group includes pairs of individuals. We developed the ParallABEL library, which utilizes the Rmpi library, to parallelize these four types of computations. ParallABEL library is not only aimed at GenABEL, but may also be employed to parallelize various GWA packages in R. The data set from the North American Rheumatoid Arthritis Consortium (NARAC) includes 2,062 individuals with 545,080, SNPs' genotyping, was used to measure ParallABEL performance. Almost perfect speed-up was achieved for many types of analyses. For example, the computing time for the identity-by-state matrix was linearly reduced from approximately eight hours to one hour when ParallABEL employed eight processors. Executing genome-wide association analysis using the ParallABEL library on a computer cluster is an effective way to boost performance, and simplify the parallelization of GWA studies. ParallABEL is a user-friendly parallelization of GenABEL.

Measurement of electron density profiles on HT-6M tokamak by 7-channel FIR HCN laser interferometer

NASA Astrophysics Data System (ADS)

Xiang, Gao; Qiliang, Guo

1990-12-01

Electron density measurements are periormed on HT-6M tokamak using a 7 channel Far-Infrared HCN laser interferometer. From the measured line integrals--7 channel phase shifts the electron density profile is reconstructed by a fit procedure. Results were tested by comparison to Abel inverted. Some recent interesting experimental results were reported.

Modeling & Testing of Inflatable Structures for Rapidly Deployable Port Infrastructures

DTIC Science & Technology

2010-07-01

Rapidly Deployable Port Infrastructures By: Andrew Bloxom Abel Medellin Chris Vince Dr. Solomon Yim N SW C C D -C IS D -2 01...Andrew Bloxom, Abel Medellin , Chris Vince, Dr. Solomon Yim 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING...Andrew Bloxom Abel Medellin Chris Vince Dr. Solomon Yim A special thanks to: • Ben Testerman and Dr. Pat

ParallABEL: an R library for generalized parallelization of genome-wide association studies

PubMed Central

2010-01-01

Background Genome-Wide Association (GWA) analysis is a powerful method for identifying loci associated with complex traits and drug response. Parts of GWA analyses, especially those involving thousands of individuals and consuming hours to months, will benefit from parallel computation. It is arduous acquiring the necessary programming skills to correctly partition and distribute data, control and monitor tasks on clustered computers, and merge output files. Results Most components of GWA analysis can be divided into four groups based on the types of input data and statistical outputs. The first group contains statistics computed for a particular Single Nucleotide Polymorphism (SNP), or trait, such as SNP characterization statistics or association test statistics. The input data of this group includes the SNPs/traits. The second group concerns statistics characterizing an individual in a study, for example, the summary statistics of genotype quality for each sample. The input data of this group includes individuals. The third group consists of pair-wise statistics derived from analyses between each pair of individuals in the study, for example genome-wide identity-by-state or genomic kinship analyses. The input data of this group includes pairs of SNPs/traits. The final group concerns pair-wise statistics derived for pairs of SNPs, such as the linkage disequilibrium characterisation. The input data of this group includes pairs of individuals. We developed the ParallABEL library, which utilizes the Rmpi library, to parallelize these four types of computations. ParallABEL library is not only aimed at GenABEL, but may also be employed to parallelize various GWA packages in R. The data set from the North American Rheumatoid Arthritis Consortium (NARAC) includes 2,062 individuals with 545,080, SNPs' genotyping, was used to measure ParallABEL performance. Almost perfect speed-up was achieved for many types of analyses. For example, the computing time for the identity-by-state matrix was linearly reduced from approximately eight hours to one hour when ParallABEL employed eight processors. Conclusions Executing genome-wide association analysis using the ParallABEL library on a computer cluster is an effective way to boost performance, and simplify the parallelization of GWA studies. ParallABEL is a user-friendly parallelization of GenABEL. PMID:20429914

The HST Frontier Fields

NASA Astrophysics Data System (ADS)

Lotz, Jennifer; Mountain, M.; Grogin, N. A.; Koekemoer, A. M.; Capak, P. L.; Mack, J.; Coe, D. A.; Barker, E. A.; Adler, D. S.; Avila, R. J.; Anderson, J.; Casertano, S.; Christian, C. A.; Gonzaga, S.; Ferguson, H. C.; Fruchter, A. S.; Jenkner, H.; Jordan, I. J.; Hammer, D.; Hilbert, B.; Lawton, B. L.; Lee, J. C.; Lucas, R. A.; MacKenty, J. W.; Mutchler, M. J.; Ogaz, S.; Reid, I. N.; Royle, P.; Robberto, M.; Sembach, K.; Smith, L. J.; Sokol, J.; Surace, J. A.; Taylor, D.; Tumlinson, J.; Viana, A.; Williams, R. E.; Workman, W.

2014-01-01

Using Director's Discretionary observing time, HST is undertaking a revolutionary deep field observing program to peer deeper into the Universe than ever before. The Frontier Fields will combine the power of HST with the natural gravitational telescopes of high-magnification clusters of galaxies to produce the deepest observations of clusters and their lensed galaxies and the second-deepest observations of blank fields ever obtained. Up to six strong-lensing clusters (Abell 2744, MACSJ0416.1-2403, MACSJ0717.5+3745, MACSJ1149.5+2223, AbellS1063, and Abell 370) will be targeted with coordinated parallels of adjacent blank fields with ACS/WFC and WFC3/IR cameras to ~29th ABmag depths in seven bandpasses over the next three years. These observations will reveal distant galaxy populations ~10-100 times fainter than any previously observed, and improve our statistical understanding of galaxies during the epoch of reionization. Here we present Hubble Space Telescope observations of the first set of the Frontier Fields, Abell 2744, and describe the HST Frontier Fields observing strategy and schedule. All data for this observing program is nonproprietary and available immediately upon entry into the Mikulski Archive for Space Telescopes.

Anti-inflammatory and antioxidative effects of Camellia oleifera Abel components.

PubMed

Xiao, Xiaomei; He, Liangmei; Chen, Yayun; Wu, Longhuo; Wang, Lin; Liu, Zhiping

2017-11-01

Camellia oleifera Abel is a member of Camellia, and its seeds are used to extract Camellia oil, which is generally used as cooking oil in the south of China. Camellia oil consists of unsaturated fatty acids, tea polyphenol, squalene, saponin, carrot element and vitamins, etc. The seed remains after oil extraction of C. oleifera Abel are by-products of oil production, named as Camellia oil cake. Its extracts contain bioactive compounds including sasanquasaponin, flavonoid and tannin. Major components from Camellia oil and its cake have been shown to have anti-inflammatory, antioxidative, antimicrobial and antitumor activities. In this review, we will summarize the latest advance in the studies on anti-inflammatory or antioxidative effects of C. oleifera products, thus providing valuable reference for the future research and development of C. oleifera Abel.

Scattering General Analysis; ANALISIS GENERAL DE LA DISPERSION

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

Tixaire, A.G.

1962-01-01

A definition of scattering states is given. It is shown that such states must belong to the absolutely continuous part of the spectrum of the total hamiltonian whenever scattering systems are considered. Such embedding may be proper unless the quantum system is physically admissible. The Moller wave operators are analyzed using Abel- and Cesaro-limit theoretical arguments. Von Neumann s ergodic theorem is partially generalized. A rigorous derivation of the Gell-Mann and Goldberger and Lippmann and Schwinger equations is obtained by making use of results on spectral theory, wave function, and eigendifferential concepts contained. (auth)

The application of trigonal curve to the Mikhailov-Shabat-Sokolov flows

NASA Astrophysics Data System (ADS)

He, Guoliang; Geng, Xianguo; Wu, Lihua

2016-08-01

Resorting to the characteristic polynomial of Lax matrix for the Mikhailov-Shabat-Sokolov hierarchy associated with a {3 × 3} matrix spectral problem, we introduce a trigonal curve, from which we deduce the associated Baker-Akhiezer function, meromorphic functions and Dubrovin-type equations. The straightening out of the Mikhailov-Shabat-Sokolov flows is exactly given through the Abel map. On the basis of these results and the theory of trigonal curve, we obtain the explicit theta function representations of the Baker-Akhiezer function, the meromorphic functions, and in particular, that of solutions for the entire Mikhailov-Shabat-Sokolov hierarchy.

Digital holographic interferometry employing Fresnel transform reconstruction for the study of flow shear stabilized Z-pinch plasmas.

PubMed

Ross, M P; Shumlak, U

2016-10-01

The ZaP-HD flow Z-pinch project provides a platform to explore how shear flow stabilized Z-pinches could scale to high-energy-density plasma (plasma with pressures exceeding 1 Mbar) and fusion reactor conditions. The Z-pinch is a linear plasma confinement geometry in which the plasma carries axial electric current and is confined by its self-induced magnetic field. ZaP-HD generates shear stabilized, axisymmetric Z-pinches with stable lifetimes approaching 60 μs. The goal of the project is to increase the plasma density and temperature compared to the previous ZaP project by compressing the plasma to smaller radii (≈1 mm). Radial and axial plasma electron density structure is measured using digital holographic interferometry (DHI), which provides the necessary fine spatial resolution. ZaP-HD's DHI system uses a 2 ns Nd:YAG laser pulse with a second harmonic generator (λ = 532 nm) to produce holograms recorded by a Nikon D3200 digital camera. The holograms are numerically reconstructed with the Fresnel transform reconstruction method to obtain the phase shift caused by the interaction of the laser beam with the plasma. This provides a two-dimensional map of line-integrated electron density, which can be Abel inverted to determine the local number density. The DHI resolves line-integrated densities down to 3 × 10 20 m -2 with spatial resolution near 10 μm. This paper presents the first application of Fresnel transform reconstruction as an analysis technique for a plasma diagnostic, and it analyzes the method's accuracy through study of synthetic data. It then presents an Abel inversion procedure that utilizes data on both sides of a Z-pinch local number density profile to maximize profile symmetry. Error estimation and Abel inversion are applied to the measured data.

Ultra-deep K S-band Imaging of the Hubble Frontier Fields

NASA Astrophysics Data System (ADS)

Brammer, Gabriel B.; Marchesini, Danilo; Labbé, Ivo; Spitler, Lee; Lange-Vagle, Daniel; Barker, Elizbeth A.; Tanaka, Masayuki; Fontana, Adriano; Galametz, Audrey; Ferré-Mateu, Anna; Kodama, Tadayuki; Lundgren, Britt; Martis, Nicholas; Muzzin, Adam; Stefanon, Mauro; Toft, Sune; van der Wel, Arjen; Vulcani, Benedetta; Whitaker, Katherine E.

2016-09-01

We present an overview of the “KIFF” project, which provides ultra-deep K s -band imaging of all six of the Hubble Frontier Fields clusters, Abell 2744, MACS-0416, Abell S1063, Abell 370, MACS-0717, and MACS-1149. All of these fields have recently been observed with large allocations of Directors’ Discretionary Time with the Hubble and Spitzer telescopes, covering 0.4\\lt λ \\lt 1.6 μ {{m}} and 3.6-4.5 μ {{m}}, respectively. VLT/HAWK-I integrations of the first four fields reach 5σ limiting depths of {K}s˜ 26.0 (AB, point sources) and have excellent image quality (FWHM ˜ 0.″4). The MACS-0717 and MACS-1149 fields are observable from the northern hemisphere, and shorter Keck/MOSFIRE integrations on those fields reach limiting depths of K s = 25.5 and 25.1, with a seeing FWHM of ˜ 0.″4 and 0\\buildrel{\\prime\\prime}\\over{.} 5. In all cases the K s -band mosaics cover the primary cluster and parallel HST/ACS+WFC3 fields. The total area of the K s -band coverage is 490 arcmin2. The K s -band at 2.2 μ {{m}} crucially fills the gap between the reddest HST filter (1.6 μ {{m}} ˜ H band) and the IRAC 3.6 μ {{m}} passband. While reaching the full depths of the space-based imaging is not currently feasible from the ground, the deep K s -band images provide important constraints on both the redshifts and the stellar population properties of galaxies extending well below the characteristic stellar mass across most of the age of the universe, down to and including the redshifts of the targeted galaxy clusters (z≲ 0.5). Reduced, aligned mosaics of all six survey fields are provided.

Cosmological constraints from strong gravitational lensing in clusters of galaxies.

PubMed

Jullo, Eric; Natarajan, Priyamvada; Kneib, Jean-Paul; D'Aloisio, Anson; Limousin, Marceau; Richard, Johan; Schimd, Carlo

2010-08-20

Current efforts in observational cosmology are focused on characterizing the mass-energy content of the universe. We present results from a geometric test based on strong lensing in galaxy clusters. Based on Hubble Space Telescope images and extensive ground-based spectroscopic follow-up of the massive galaxy cluster Abell 1689, we used a parametric model to simultaneously constrain the cluster mass distribution and dark energy equation of state. Combining our cosmological constraints with those from x-ray clusters and the Wilkinson Microwave Anisotropy Probe 5-year data gives Omega(m) = 0.25 +/- 0.05 and w(x) = -0.97 +/- 0.07, which are consistent with results from other methods. Inclusion of our method with all other available techniques brings down the current 2sigma contours on the dark energy equation-of-state parameter w(x) by approximately 30%.

Redshifts in the Southern Abell Redshift Survey Clusters. I. The Data

NASA Astrophysics Data System (ADS)

Way, M. J.; Quintana, H.; Infante, L.; Lambas, D. G.; Muriel, H.

2005-11-01

The Southern Abell Redshift Survey (SARS) contains 39 clusters of galaxies with redshifts in the range 0.021h (while avoiding the LMC and SMC), with |b|>40°. Cluster locations were chosen from the Abell and Abell-Corwin-Olowin catalogs, while galaxy positions were selected from the Automatic Plate Measuring Facility galaxy catalog with extinction-corrected magnitudes in the range 15<=bJ<19. SARS used the Las Campanas 2.5 m du Pont telescope, observing either 65 or 128 objects concurrently over a 1.5 deg2 field. New redshifts for 3440 galaxies are reported in the fields of these 39 clusters of galaxies.

Resolution of the apparent discrepancy between the number of massive subhaloes in Abell 2744 and ΛCDM

NASA Astrophysics Data System (ADS)

Mao, Tian-Xiang; Wang, Jie; Frenk, Carlos S.; Gao, Liang; Li, Ran; Wang, Qiao; Cao, Xiaoyue; Li, Ming

2018-07-01

Schwinn et al. have recently compared the abundance and distribution of massive substructures identified in a gravitational lensing analysis of Abell 2744 by Jauzac et al. and N-body simulation, and found no cluster in Lambda cold dark matter (ΛCDM) simulation that is similar to Abell 2744. Schwinn et al. identified the measured projected aperture masses with the actual masses associated with subhaloes in the Millenium XXL N-body simulation. We have used the high-resolution Phoenix cluster simulations to show that such an identification is incorrect: the aperture mass is dominated by mass in the body of the cluster that happens to be projected along the line of sight to the subhalo. This enhancement varies from factors of a few to factors of more than 100, particularly for subhaloes projected near the centre of the cluster. We calculate aperture masses for subhaloes in our simulation and compare them to the measurements for Abell 2744. We find that the data for Abell 2744 are in excellent agreement with the matched predictions from ΛCDM. We provide further predictions for aperture mass functions of subhaloes in idealized surveys with varying mass detection thresholds.

Nonminimal coupling for the gravitational and electromagnetic fields: Black hole solutions and solitons

NASA Astrophysics Data System (ADS)

Balakin, Alexander B.; Bochkarev, Vladimir V.; Lemos, José P. S.

2008-04-01

Using a Lagrangian formalism, a three-parameter nonminimal Einstein-Maxwell theory is established. The three parameters q1, q2, and q3 characterize the cross-terms in the Lagrangian, between the Maxwell field and terms linear in the Ricci scalar, Ricci tensor, and Riemann tensor, respectively. Static spherically symmetric equations are set up, and the three parameters are interrelated and chosen so that effectively the system reduces to a one parameter only, q. Specific black hole and other type of one-parameter solutions are studied. First, as a preparation, the Reissner-Nordström solution, with q1=q2=q3=0, is displayed. Then, we search for solutions in which the electric field is regular everywhere as well as asymptotically Coulombian, and the metric potentials are regular at the center as well as asymptotically flat. In this context, the one-parameter model with q1≡-q, q2=2q, q3=-q, called the Gauss-Bonnet model, is analyzed in detail. The study is done through the solution of the Abel equation (the key equation), and the dynamical system associated with the model. There is extra focus on an exact solution of the model and its critical properties. Finally, an exactly integrable one-parameter model, with q1≡-q, q2=q, q3=0, is considered also in detail. A special submodel, in which the Fibonacci number appears naturally, of this one-parameter model is shown, and the corresponding exact solution is presented. Interestingly enough, it is a soliton of the theory, the Fibonacci soliton, without horizons and with a mild conical singularity at the center.

Astrometry With the Hubble Space Telescope: Trigonometric Parallaxes of Planetary Nebula Nuclei NGC 6853, NGC 7293, ABELL 31, and DeHt 5

DTIC Science & Technology

2009-12-01

reserved. Printed in the U.S.A. ASTROMETRY WITH THE HUBBLE SPACE TELESCOPE: TRIGONOMETRIC PARALLAXES OF PLANETARY NEBULA NUCLEI NGC 6853, NGC 7293, ABELL 31...present absolute parallaxes and relative proper motions for the central stars of the planetary nebulae NGC 6853 (The Dumbbell), NGC 7293 (The Helix...Abell 31, and DeHt 5. This paper details our reduction and analysis using DeHt 5 as an example. We obtain these planetary nebula nuclei (PNNi

A 1400-MHz survey of 1478 Abell clusters of galaxies

NASA Technical Reports Server (NTRS)

Owen, F. N.; White, R. A.; Hilldrup, K. C.; Hanisch, R. J.

1982-01-01

Observations of 1478 Abell clusters of galaxies with the NRAO 91-m telescope at 1400 MHz are reported. The measured beam shape was deconvolved from the measured source Gaussian fits in order to estimate the source size and position angle. All detected sources within 0.5 corrected Abell cluster radii are listed, including the cluster number, richness class, distance class, magnitude of the tenth brightest galaxy, redshift estimate, corrected cluster radius in arcmin, right ascension and error, declination and error, total flux density and error, and angular structure for each source.

Quasi-periodic Solutions of the Kaup-Kupershmidt Hierarchy

NASA Astrophysics Data System (ADS)

Geng, Xianguo; Wu, Lihua; He, Guoliang

2013-08-01

Based on solving the Lenard recursion equations and the zero-curvature equation, we derive the Kaup-Kupershmidt hierarchy associated with a 3×3 matrix spectral problem. Resorting to the characteristic polynomial of the Lax matrix for the Kaup-Kupershmidt hierarchy, we introduce a trigonal curve {K}_{m-1} and present the corresponding Baker-Akhiezer function and meromorphic function on it. The Abel map is introduced to straighten out the Kaup-Kupershmidt flows. With the aid of the properties of the Baker-Akhiezer function and the meromorphic function and their asymptotic expansions, we arrive at their explicit Riemann theta function representations. The Riemann-Jacobi inversion problem is achieved by comparing the asymptotic expansion of the Baker-Akhiezer function and its Riemann theta function representation, from which quasi-periodic solutions of the entire Kaup-Kupershmidt hierarchy are obtained in terms of the Riemann theta functions.

VizieR Online Data Catalog: Abell 315 spectroscopic dataset (Biviano+, 2017)

NASA Astrophysics Data System (ADS)

Biviano, A.; Popesso, P.; Dietrich, J. P.; Zhang, Y.-Y.; Erfanianfar, G.; Romaniello, M.; Sartoris, B.

2017-03-01

Abell 315 was observed at the European Southern Observatory (ESO) Very Large Telescope (VLT) with the VIsible MultiObject Spectrograph (VIMOS). The VIMOS data were acquired using 8 separate pointings, plus 2 additional pointings required to provide the needed redundancy within the central region and to cover the gaps between the VIMOS quadrants. Catalog of galaxies with redshifts in the region of the cluster Abell 315, with flags indicating whether these galaxies are members of the cluster, members of substructures within the cluster, and with probabilities for the cluster members to belong to the main cluster structure. (1 data file).

Health reform and technology--what does it mean for us?

PubMed

Abele, J

1995-01-01

John Abele, Founder Chairman of Boston Scientific Corporation, spoke at AAMI's 30th Annual Meeting on 22 May in Anaheim, CA. His speech was part of AAMI's plenary session, "The Impact of a Reformed Health System on New Technology." After his speech, Abele joined three of AAMI's experts in a roundtable discussion on the topics he raised. See the BI&T Forum page 479 for their discussion. As a business entrepreneur and scientist, Abele is well versed in the topic of health reform and scientific advancements. He began his career with a degree in physics and philosophy, then moved into the health care field because of his fascination with medical devices and technologies. He has spent years working as an engineer, a salesperson, a general manager, and a partner in a research and development company. He was a cofounder of AAMI in 1965. Boston Scientific's roots trace back to 1969, when Abele joined with Itzhak Bentov to build a company around a steerable catheter. The associated technology became a platform for many types of tools that could be used as alternatives to surgery in most organs of the body. Today, with over 5,000 employees, 4,000 products, and a worldwide presence, the original objective of developing products and procedures that reduce risk, trauma, cost, and time still applies. Abele is the author of many papers and book chapters, and he has lectured extensively on the technology of various medical devices and technical, social, economic, and political trends affecting health care. His major interests are science education and the process by which new technology is invented, developed, and introduced to society. The following article is based on Abele's presentation.

Abyssal BEnthic Laboratory (ABEL): a novel approach for long-term investigation at abyssal depths

NASA Astrophysics Data System (ADS)

Berta, M.; Gasparoni, F.; Capobianco, M.

1995-03-01

This study assesses the feasibility of a configuration for a benthic underwater system, called ABEL (Abyssal BEnthic Laboratory), capable of operating both under controlled and autonomous modes for periods of several months to over one year at abyssal depths up to 6000 m. A network of stations, capable of different configurations, has been identified as satisfying the widest range of scientific expectations, and at the same time to address the technological challenge to increase the feasibility of scientific investigations, even when the need is not yet well specified. The overall system consists of a central Benthic Investigation Laboratory, devoted to the execution of the most complex scientific activities, with fixed Satellite Stations acting as nodes of a measuring network and a Mobile Station extending ABEL capabilities with the possibility to carry out surveys over the investigation area and interventions on the fixed stations. ABEL architecture also includes a dedicated deployment and recovery module, as well as sea-surface and land-based facilities. Such an installation constitutes the sea-floor equivalent of a meteorological or geophysical laboratory. Attention has been paid to selecting investigation tools supporting the ABEL system to carry out its mission with high operativity and minimal risk and environmental impact. This demands technologies to enable presence and operation at abyssal depths for the required period of time. Presence can be guaranteed by proper choice of power supply and communication systems. Operations require visual and manipulative capabilities, as well as deployment and retrieval capabilities. Advanced control system architectures must be considered, along with knowledge based approaches, to comply with the requirements for autonomous control. The results of this investigation demonstrate the feasibility of the ABEL concept and the pre-dimensioning of its main components.

A Strong Merger Shock in Abell 665

NASA Technical Reports Server (NTRS)

Dasadia, S.; Sun, M.; Sarazin, C.; Morandi, A.; Markevitch, M.; Wik, D.; Feretti, L.; Giovannini, G.; Govoni, F.

2016-01-01

Deep (103 ks) Chandra observations of Abell 665 have revealed rich structures in this merging galaxy cluster, including a strong shock and two cold fronts. The newly discovered shock has a Mach number of M =?3.0 +/- 0.6, propagating in front of a cold disrupted cloud. This makes Abell 665 the second cluster, after the Bullet cluster, where a strong merger shock of M is approximately 3 has been detected. The shock velocity from jump conditions is consistent with (2.7 +/- 0.7) × 10(exp 3) km s(exp -1). The new data also reveal a prominent southern cold front with potentially heated gas ahead of it. Abell 665 also hosts a giant radio halo. There is a hint of diffuse radio emission extending to the shock at the north, which needs to be examined with better radio data. This new strong shock provides a great opportunity to study the reacceleration model with the X-ray and radio data combined.

The X-ray cluster Abell 744

NASA Technical Reports Server (NTRS)

Kurtz, M. J.; Huchra, J. P.; Beers, T. C.; Geller, M. J.; Gioia, I. M.

1985-01-01

X-ray and optical observations of the cluster of galaxies Abell 744 are presented. The X-ray flux (assuming H(0) = 100 km/s per Mpc) is about 9 x 10 to the 42nd erg/s. The X-ray source is extended, but shows no other structure. Photographic photometry (in Kron-Cousins R), calibrated by deep CCD frames, is presented for all galaxies brighter than 19th magnitude within 0.75 Mpc of the cluster center. The luminosity function is normal, and the isopleths show little evidence of substructure near the cluster center. The cluster has a dominant central galaxy, which is classified as a normal brightest-cluster elliptical on the basis of its luminosity profile. New redshifts were obtained for 26 galaxies in the vicinity of the cluster center; 20 appear to be cluster members. The spatial distribution of redshifts is peculiar; the dispersion within the 150 kpc core radius is much greater than outside. Abell 744 is similar to the nearby cluster Abell 1060.

Uncertainties in the cluster-cluster correlation function

NASA Astrophysics Data System (ADS)

Ling, E. N.; Frenk, C. S.; Barrow, J. D.

1986-12-01

The bootstrap resampling technique is applied to estimate sampling errors and significance levels of the two-point correlation functions determined for a subset of the CfA redshift survey of galaxies and a redshift sample of 104 Abell clusters. The angular correlation function for a sample of 1664 Abell clusters is also calculated. The standard errors in xi(r) for the Abell data are found to be considerably larger than quoted 'Poisson errors'. The best estimate for the ratio of the correlation length of Abell clusters (richness class R greater than or equal to 1, distance class D less than or equal to 4) to that of CfA galaxies is 4.2 + 1.4 or - 1.0 (68 percentile error). The enhancement of cluster clustering over galaxy clustering is statistically significant in the presence of resampling errors. The uncertainties found do not include the effects of possible systematic biases in the galaxy and cluster catalogs and could be regarded as lower bounds on the true uncertainty range.

Revisiting the monster: the mass profile of the galaxy cluster Abell 3827 using dynamical and strong lensing constrains

NASA Astrophysics Data System (ADS)

Rodrigo Carrasco Damele, Eleazar; Verdugo, Tomas

2018-01-01

The galaxy cluster Abell 3827 is one of the most massive clusters know at z ≦ 0.1 (Richness class 2, BM typeI, X-ray LX = 2.4 x 1044 erg s-1). The Brightest Cluster Galaxy (BCG) in Abell 3827 is perhaps the most extreme example of ongoing galaxy cannibalism. The multi-component BCG hosts the stellar remnants nuclei of at least four bright elliptical galaxies embedded in a common assymetric halo extended up to 15 kpc. The most notorious characteristic of the BCG is the existence of a unique strong gravitational lens system located within the inner 15 kpc region. A mass estimation of the galaxy based on strong lensing model was presented in Carrasco et al (2010, ApJL, 715, 160). Moreover, the exceptional strong lensing lens system in Abell 3827 and the location of the four bright galaxies has been used to measure for the first time small physical separations between dark and ordinary matter (Williams et al. 2011, MNRAS, 415, 448, Massey et al. 2015, MNRAS, 449, 3393). In this contribution, we present a detailed strong lensing and dynamical analysis of the cluster Abell 3827 based on spectroscopic redshift of the lensed features and from ~70 spectroscopically confirmed member galaxies inside 0.5 x 0.5 Mpc from the cluster center.

Improved Abel transform inversion: First application to COSMIC/FORMOSAT-3

NASA Astrophysics Data System (ADS)

Aragon-Angel, A.; Hernandez-Pajares, M.; Juan, J.; Sanz, J.

2007-05-01

In this paper the first results of Ionospheric Tomographic inversion are presented, using the Improved Abel Transform on the COSMIC/FORMOSAT-3 constellation of 6 LEO satellites, carrying on-board GPS receivers.[- 4mm] The Abel transform inversion is a wide used technique which in the ionospheric context makes it possible to retrieve electron densities as a function of height based of STEC (Slant Total Electron Content) data gathered from GPS receivers on board of LEO (Low Earth Orbit) satellites. Within this precise use, the classical approach of the Abel inversion is based on the assumption of spherical symmetry of the electron density in the vicinity of an occultation, meaning that the electron content varies in height but not horizontally. In particular, one implication of this assumption is that the VTEC (Vertical Total Electron Content) is a constant value for the occultation region. This assumption may not always be valid since horizontal ionospheric gradients (a very frequent feature in some ionosphere problematic areas such as the Equatorial region) could significantly affect the electron profiles. [- 4mm] In order to overcome this limitation/problem of the classical Abel inversion, a studied improvement of this technique can be obtained by assuming separability in the electron density (see Hernández-Pajares et al. 2000). This means that the electron density can be expressed by the multiplication of VTEC data and a shape function which assumes all the height dependency in it while the VTEC data keeps the horizontal dependency. Actually, it is more realistic to assume that this shape fuction depends only on the height and to use VTEC information to take into account the horizontal variation rather than considering spherical symmetry in the electron density function as it has been carried out in the classical approach of the Abel inversion.[-4mm] Since the above mentioned improved Abel inversion technique has already been tested and proven to be a useful tool to obtain a vertical description of the ionospheric electron density (see García-Fernández et al. 2003), a natural following step would be to extend the use of this technique to the recently available COSMIC data. The COSMIC satellite constellation, formed by 6 micro-satellites, is being deployed since April 2006 in circular orbit around the Earth, with a final altitude of about 700-800 kilometers. Its global and almost uniform coverage will overcome one of the main limitations of this technique which is the sparcity of data, related to lack of GPS receivers in some regions. This can significantly stimulate the development of radio occultation techniques with the use of the huge volume of data provided by the COSMIC constellation to be processed and analysed updating the current knowledge of the Ionospheres nature and behaviour. In this context a summary of the Improvel Abel transform inversion technique and the first results based on COSMIC constellation data will be presented. Moreover, future improvements, taking into account the higher temporal and global spatial coverage, will be discussed. [-4mm] References:M. Hernández-Pajares, J. M. Juan and J. Sanz, Improving the Abel inversion by adding ground GPS data to LEO radio occultations in ionospheric sounding, GEOPHYSICAL RESEARCH LETTERS, VOL. 27, NO. 16, PAGES 2473-2476, AUGUST 15, 2000.M. Garcia-Fernández, M. Hernández-Pajares, M. Juan, and J. Sanz, Improvement of ionospheric electron density estimation with GPSMET occultations using Abel inversion and VTEC Information, JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. A9, 1338, doi:10.1029/2003JA009952, 2003

Editorial

NASA Astrophysics Data System (ADS)

Li, C. P.; Mainardi, F.

2011-03-01

Fractional calculus, in allowing integrals and derivatives of any positive real order (the term "fractional" is kept only for historical reasons), can be considered a branch of mathematical analysis which deals with integro-differential equations where the integrals are of convolution type and exhibit (weakly singular) kernels of power-law type. It has a history of at least three hundred years because it can be dated back to the letter from G.W. Leibniz to G.A. de L'Hôpital and J. Wallis, dated 30 September 1695, in which the meaning of the one-half order derivative was first discussed and were made some remarks about its possibility. Subsequent mention of fractional derivatives was made, in some context or the other by L. Euler (1730), J.L. Lagrange (1772), P.S. Laplace (1812), S.F. Lacroix (1819), J.B.J. Fourier (1822), N.H. Abel (1823), J. Liouville (1832), B. Riemann (1847), H.L. Greer (1859), H. Holmgren (1865), A.K. Grünwald (1867), A.V. Letnikov (1868), N.Ya. Sonin (1869), H. Laurent (1884), P.A. Nekrassov (1888), A. Krug (1890), O. Heaviside (1892), S. Pincherle (1902), H. Weyl (1919), P. Lévy (1923), A. Marchaud (1927), H.T. Davis (1936), A. Zygmund (1945), M. Riesz (1949), W. Feller (1952), just to cite some relevant contributors up the mid of the last century, see e.g. [1,2]. Recently, a poster illustrating the major contributors during the period 1695-1970 has been published [3].

Quasi-periodic solutions of the Belov-Chaltikian lattice hierarchy

NASA Astrophysics Data System (ADS)

Geng, Xianguo; Zeng, Xin

Utilizing the characteristic polynomial of Lax matrix for the Belov-Chaltikian (BC) lattice hierarchy associated with a 3 × 3 discrete matrix spectral problem, we introduce a trigonal curve with three infinite points, from which we establish the associated Dubrovin-type equations. The essential properties of the Baker-Akhiezer function and the meromorphic function are discussed, that include their asymptotic behavior near three infinite points on the trigonal curve and the divisor of the meromorphic function. The Abel map is introduced to straighten out the continuous flow and the discrete flow in the Jacobian variety, from which the quasi-periodic solutions of the entire BC lattice hierarchy are obtained in terms of the Riemann theta function.

The Power of Woman-Positive Literacy Work. Program-Based Action Research.

ERIC Educational Resources Information Center

Lloyd, Betty-Ann; And Others

The experiences of Canadian women in adult basic education and literacy (ABEL) were examined in a national research project during which 2 contact women from each of 12 ABEL programs across Canada spend one-half day each week "researching" their program's "woman-positive" activities and the consequences of those activities for…

Abel inversion using fast Fourier transforms.

PubMed

Kalal, M; Nugent, K A

1988-05-15

A fast Fourier transform based Abel inversion technique is proposed. The method is faster than previously used techniques, potentially very accurate (even for a relatively small number of points), and capable of handling large data sets. The technique is discussed in the context of its use with 2-D digital interferogram analysis algorithms. Several examples are given.

Retrieval Performance and Indexing Differences in ABELL and MLAIB

ERIC Educational Resources Information Center

Graziano, Vince

2012-01-01

Searches for 117 British authors are compared in the Annual Bibliography of English Language and Literature (ABELL) and the Modern Language Association International Bibliography (MLAIB). Authors are organized by period and genre within the early modern era. The number of records for each author was subdivided by format, language of publication,…

ABEL model: Evaluates corporations` claims of inability to afford penalties and compliance costs (version 3.0.16). Model-simulation

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

NONE

1998-11-01

The easy-to-use ABEL software evaluates for-profit company claims of inability to afford penalties, clean-up costs, or compliance costs. Violators raise the issue of inability to pay in most of EPA`s enforcement actions regardless of whether there is any hard evidence supporting those claims. The program enables Federal, State and local enforcement professionals to quickly determine if there was any validity to those claims. ABEL is a tool that promotes quick settlements by performing screening analyses of defendants and potentially responsible parties (PRP`s) to determine their financial capacity. After analyzing some basic financial ratios that reflect a company`s solvency, ABEL assessesmore » the firm`s ability to pay by focusing on projected cash flows. The model explicitly calculates the value of projected, internally generated cash flows from historical tax information, and compares these cash flows to the proposed environmental expenditure(s). The software is extremely easy to use. Version 3.0.16 updates the standard values for inflation and discount rate.« less

PredictABEL: an R package for the assessment of risk prediction models.

PubMed

Kundu, Suman; Aulchenko, Yurii S; van Duijn, Cornelia M; Janssens, A Cecile J W

2011-04-01

The rapid identification of genetic markers for multifactorial diseases from genome-wide association studies is fuelling interest in investigating the predictive ability and health care utility of genetic risk models. Various measures are available for the assessment of risk prediction models, each addressing a different aspect of performance and utility. We developed PredictABEL, a package in R that covers descriptive tables, measures and figures that are used in the analysis of risk prediction studies such as measures of model fit, predictive ability and clinical utility, and risk distributions, calibration plot and the receiver operating characteristic plot. Tables and figures are saved as separate files in a user-specified format, which include publication-quality EPS and TIFF formats. All figures are available in a ready-made layout, but they can be customized to the preferences of the user. The package has been developed for the analysis of genetic risk prediction studies, but can also be used for studies that only include non-genetic risk factors. PredictABEL is freely available at the websites of GenABEL ( http://www.genabel.org ) and CRAN ( http://cran.r-project.org/).

Evidence for an extensive intracluster medium from radio observations of distant Abell clusters

NASA Technical Reports Server (NTRS)

Hanisch, R. J.; Ulmer, M. P.

1985-01-01

Observations have been made of 18 distance class 5 and 6 Abell clusters of galaxies using the VLA in its 'C' configuration at a frequency of 1460 MHz. Half of the clusters in the sample are confirmed or probable sources of X-ray emission. All the detected radio sources with flux densities above 10 mJy are reported, and information is provided concerning the angular extent of the sources, as well as the most likely optical identification. The existence of an extensive intracluster medium is inferred by identifying extended/distorted radio sources with galaxies whose apparent magnitudes are consistent with their being cluster members and that are at projected distances of 3-4 Abell radii (6-8 Mpc) from the nearest cluster center. By requiring that the radio sources are confined by the ambient medium, the ambient density is calculated and the total cluster mass is estimated. As a sample calculation, a wide-angle-tail radio source some 5 Mpc from the center of Abell 348 is used to estimate these quantities.

High-Performance Mixed Models Based Genome-Wide Association Analysis with omicABEL software

PubMed Central

Fabregat-Traver, Diego; Sharapov, Sodbo Zh.; Hayward, Caroline; Rudan, Igor; Campbell, Harry; Aulchenko, Yurii; Bientinesi, Paolo

2014-01-01

To raise the power of genome-wide association studies (GWAS) and avoid false-positive results in structured populations, one can rely on mixed model based tests. When large samples are used, and when multiple traits are to be studied in the ’omics’ context, this approach becomes computationally challenging. Here we consider the problem of mixed-model based GWAS for arbitrary number of traits, and demonstrate that for the analysis of single-trait and multiple-trait scenarios different computational algorithms are optimal. We implement these optimal algorithms in a high-performance computing framework that uses state-of-the-art linear algebra kernels, incorporates optimizations, and avoids redundant computations, increasing throughput while reducing memory usage and energy consumption. We show that, compared to existing libraries, our algorithms and software achieve considerable speed-ups. The OmicABEL software described in this manuscript is available under the GNU GPL v. 3 license as part of the GenABEL project for statistical genomics at http: //www.genabel.org/packages/OmicABEL. PMID:25717363

High-Performance Mixed Models Based Genome-Wide Association Analysis with omicABEL software.

PubMed

Fabregat-Traver, Diego; Sharapov, Sodbo Zh; Hayward, Caroline; Rudan, Igor; Campbell, Harry; Aulchenko, Yurii; Bientinesi, Paolo

2014-01-01

To raise the power of genome-wide association studies (GWAS) and avoid false-positive results in structured populations, one can rely on mixed model based tests. When large samples are used, and when multiple traits are to be studied in the 'omics' context, this approach becomes computationally challenging. Here we consider the problem of mixed-model based GWAS for arbitrary number of traits, and demonstrate that for the analysis of single-trait and multiple-trait scenarios different computational algorithms are optimal. We implement these optimal algorithms in a high-performance computing framework that uses state-of-the-art linear algebra kernels, incorporates optimizations, and avoids redundant computations, increasing throughput while reducing memory usage and energy consumption. We show that, compared to existing libraries, our algorithms and software achieve considerable speed-ups. The OmicABEL software described in this manuscript is available under the GNU GPL v. 3 license as part of the GenABEL project for statistical genomics at http: //www.genabel.org/packages/OmicABEL.

Rapid Inversion of Angular Deflection Data for Certain Axisymmetric Refractive Index Distributions

NASA Technical Reports Server (NTRS)

Rubinstein, R.; Greenberg, P. S.

1994-01-01

Certain functions useful for representing axisymmetric refractive-index distributions are shown to have exact solutions for Abel transformation of the resulting angular deflection data. An advantage of this procedure over direct numerical Abel inversion is that least-squares curve fitting is a smoothing process that reduces the noise sensitivity of the computation

Vitamins and Violence: Can Micronutrients Make Students Behave, Schools Safer and Test Scores Better? The Abell Report. Volume 23, No.6

ERIC Educational Resources Information Center

Rodgers, Joann Ellison

2010-01-01

The notion that vitamins, minerals, and other "supplemental" nutrients profoundly change behavior, mood, and intellect has origins as old as recorded history. Research has indeed suggested connections between nutrient deficiencies and behavior problems, but correlations are not the same as causality. This "Abell Report" is an…

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

Suganuma, Hideo; Sakumichi, Naoyuki

In the context of the dual superconductor picture for the confinement mechanism, we study maximally Abelian (MA) projection of quark confinement in SU(3) quenched lattice QCD with 32{sup 4} at β=6.4 (i.e., a ≃ 0.058 fm). We investigate the static quark-antiquark potential V(r), its Abelian part V{sub Abel}(r) and its off-diagonal part V{sub off}(r), respectively, from the on-axis lattice data. As a remarkable fact, we find almost perfect Abelian dominance for quark confinement, i.e., σ{sub Abel} ≃ σ for the string tension, on the fine and large-volume lattice. We find also a nontrivial summation relation of V (r) ≃ V{submore » Abel}(r)+V{sub off}(r)« less

Computational-hydrodynamic studies of the Noh compressible flow problem using non-ideal equations of state

NASA Astrophysics Data System (ADS)

Honnell, Kevin; Burnett, Sarah; Yorke, Chloe'; Howard, April; Ramsey, Scott

2017-06-01

The Noh problem is classic verification problem in the field of compressible flows. Simple to conceptualize, it is nonetheless difficult for numerical codes to predict correctly, making it an ideal code-verification test bed. In its original incarnation, the fluid is a simple ideal gas; once validated, however, these codes are often used to study highly non-ideal fluids and solids. In this work the classic Noh problem is extended beyond the commonly-studied polytropic ideal gas to more realistic equations of state (EOS) including the stiff gas, the Nobel-Abel gas, and the Carnahan-Starling hard-sphere fluid, thus enabling verification studies to be performed on more physically-realistic fluids. Exact solutions are compared with numerical results obtained from the Lagrangian hydrocode FLAG, developed at Los Alamos. For these more realistic EOSs, the simulation errors decreased in magnitude both at the origin and at the shock, but also spread more broadly about these points compared to the ideal EOS. The overall spatial convergence rate remained first order.

Probing the Curious Case of a Galaxy Cluster Merger in Abell 115 with High-fidelity Chandra X-Ray Temperature and Radio Maps

NASA Astrophysics Data System (ADS)

Hallman, Eric J.; Alden, Brian; Rapetti, David; Datta, Abhirup; Burns, Jack O.

2018-05-01

We present results from an X-ray and radio study of the merging galaxy cluster Abell 115. We use the full set of five Chandra observations taken of A115 to date (360 ks total integration) to construct high-fidelity temperature and surface brightness maps. We also examine radio data from the Very Large Array at 1.5 GHz and the Giant Metrewave Radio Telescope at 0.6 GHz. We propose that the high X-ray spectral temperature between the subclusters results from the interaction of the bow shocks driven into the intracluster medium by the motion of the subclusters relative to one another. We have identified morphologically similar scenarios in Enzo numerical N-body/hydrodynamic simulations of galaxy clusters in a cosmological context. In addition, the giant radio relic feature in A115, with an arc-like structure and a relatively flat spectral index, is likely consistent with other shock-associated giant radio relics seen in other massive galaxy clusters. We suggest a dynamical scenario that is consistent with the structure of the X-ray gas, the hot region between the clusters, and the radio relic feature.

Deep Chandra Observations of Abell 586: A Remarkably Relaxed Non-Cool-Core Cluster

NASA Astrophysics Data System (ADS)

Richstein, Hannah; Su, Yuanyuan

2018-01-01

The dichotomy between cool-core and non-cool-core clusters has been a lasting perplexity in extragalactic astronomy. Nascent cores in non-cool-core clusters may have been disrupted by major mergers, yet the dichotomy cannot be reproduced in cosmology simulations. We present deep Chandra observations of the massive galaxy cluster Abell 586, which resides at z=0.17, thus allowing its gas properties to be measured out to its virial radius. Abell 586 appears remarkably relaxed with a nearly spherical X-ray surface brightness distribution and without any offset between its X-ray and optical centroids. We measure that its temperature profile does not decrease towards the cluster center and its central entropy stays above 100 keV cm2. A non-cool-core emerges in Abell 586 in the absence of any disruptions on the large scale. Our study demonstrates that non-cool-core clusters can be formed without major mergers. The origins of some non-cool-core clusters may be related to conduction, AGN feedback, or preheating.The SAO REU program is funded by the National Science Foundation REU and Department of Defense ASSURE programs under NSF Grant AST-1659473, and by the Smithsonian Institution.

Oleiferoside W from the roots of Camellia oleifera C. Abel, inducing cell cycle arrest and apoptosis in A549 cells.

PubMed

Wu, Jiang-Ping; Kang, Nai-Xin; Zhang, Mi-Ya; Gao, Hong-Wei; Li, Xiao-Ran; Liu, Yan-Li; Xu, Qiong-Ming; Yang, Shi-Lin

2017-07-06

Camellia oleifera C. Abel has been widely cultivated in China, and a group of bioactive constituents such as triterpeniod saponin have been isolated from C. oleifera C. Abel. In the current study, a new triterpeniod saponin was isolated from the EtOH extract of the roots of C. oleifera C. Abel, named as oleiferoside W, and the cytotoxic properties of oleiferoside W were evaluated in non-small cell lung cancer A549 cells. At the same time the inducing apoptosis, the depolarization of mitochondrial membrane potential (Δψ), the up-regulation of related pro-apoptotic proteins, such as cleaved-PARP, cleaved-caspase-3, and the down-regulation of anti-apoptotic marker Bcl-2/Bax were measured on oleiferoside W. Furthermore, the function, inducing the generation of reactive oxygen species (ROS) and apoptosis, of oleiferoside W could be reversed by N-acetylcysteine (NAC). In conclusion, our findings showed that oleiferoside W induced apoptosis involving mitochondrial pathway and increasing intracellular ROS production in the A549 cells, suggesting that oleiferoside W may have the possibility to be a useful anticancer agent for therapy in lung cancer.

Serre duality, Abel's theorem, and Jacobi inversion for supercurves over a thick superpoint

NASA Astrophysics Data System (ADS)

Rothstein, Mitchell J.; Rabin, Jeffrey M.

2015-04-01

The principal aim of this paper is to extend Abel's theorem to the setting of complex supermanifolds of dimension 1 | q over a finite-dimensional local supercommutative C-algebra. The theorem is proved by establishing a compatibility of Serre duality for the supercurve with Poincaré duality on the reduced curve. We include an elementary algebraic proof of the requisite form of Serre duality, closely based on the account of the reduced case given by Serre in Algebraic groups and class fields, combined with an invariance result for the topology on the dual of the space of répartitions. Our Abel map, taking Cartier divisors of degree zero to the dual of the space of sections of the Berezinian sheaf, modulo periods, is defined via Penkov's characterization of the Berezinian sheaf as the cohomology of the de Rham complex of the sheaf D of differential operators. We discuss the Jacobi inversion problem for the Abel map and give an example demonstrating that if n is an integer sufficiently large that the generic divisor of degree n is linearly equivalent to an effective divisor, this need not be the case for all divisors of degree n.

Abell 48 - a rare WN-type central star of a planetary nebula

NASA Astrophysics Data System (ADS)

Todt, H.; Kniazev, A. Y.; Gvaramadze, V. V.; Hamann, W.-R.; Buckley, D.; Crause, L.; Crawford, S. M.; Gulbis, A. A. S.; Hettlage, C.; Hooper, E.; Husser, T.-O.; Kotze, P.; Loaring, N.; Nordsieck, K. H.; O'Donoghue, D.; Pickering, T.; Potter, S.; Romero-Colmenero, E.; Vaisanen, P.; Williams, T.; Wolf, M.

2013-04-01

A considerable fraction of the central stars of planetary nebulae (CSPNe) are hydrogen-deficient. Almost all of these H-deficient central stars (CSs) display spectra with strong carbon and helium lines. Most of them exhibit emission-line spectra resembling those of massive WC stars. Therefore these stars are classed as CSPNe of spectral type [WC]. Recently, quantitative spectral analysis of two emission-line CSs, PB 8 and IC 4663, revealed that these stars do not belong to the [WC] class. Instead PB 8 has been classified as [WN/WC] type and IC 4663 as [WN] type. In this work we report the spectroscopic identification of another rare [WN] star, the CS of Abell 48. We performed a spectral analysis of Abell 48 with the Potsdam Wolf-Rayet (PoWR) models for expanding atmospheres. We find that the expanding atmosphere of Abell 48 is mainly composed of helium (85 per cent by mass), hydrogen (10 per cent) and nitrogen (5 per cent). The residual hydrogen and the enhanced nitrogen abundance make this object different from the other [WN] star IC 4663. We discuss the possible origin of this atmospheric composition.

Chandra Catches Early Phase of Cosmic Assembly

NASA Astrophysics Data System (ADS)

2004-08-01

A NASA Chandra X-ray Observatory image has revealed a complex of several intergalactic hot gas clouds in the process of merging. The superb Chandra spatial resolution made it possible to distinguish individual galaxies from the massive clouds of hot gas. One of the clouds, which that envelops hundreds of galaxies, has an extraordinarily low concentration of iron atoms, indicating that it is in the very early stages of cluster evolution. "We may be seeing hot intergalactic gas in a relatively pristine state before it has been polluted by gas from galaxies," said Q. Daniel Wang of the University of Massachusetts in Amherst, and lead author on an upcoming Astrophysical Journal article describing the study. "This discovery should provide valuable insight into how the most massive structures in the universe are assembled." 3-Panel Image of Abell 2125, Its Core & Galaxy C153 3-Panel Image of Abell 2125, Its Core & Galaxy C153 The complex, known as Abell 2125,is about 3 billion light years from Earth, and is seen at a time about 11 billion years after the Big Bang, when many galaxy clusters are believed to have formed. The Chandra Abell 2125 image shows several huge elongated clouds of multimillion degree gas coming together from different directions. These hot gas clouds, each of which contains hundreds of galaxies, appear to be in the process of merging to form a single massive galaxy cluster. Chandra, Hubble Space Telescope, and Very Large Array radio telescope data show that several galaxies in the Abell 2125 core cluster are being stripped of their gas as they fall through surrounding high-pressure hot gas. This stripping process has enriched the core cluster's gas in heavy elements such as iron. Abell 2125's Core & Galaxy C153 Abell 2125's Core & Galaxy C153 The gas in the pristine cloud, which is still several million light years away from the core cluster, is conspicuous for its lack of iron atoms. This anemic cloud must be in a very early evolutionary stage. The iron atoms produced by supernovas in the embedded galaxies must still be contained in and around the galaxies, perhaps in grains of dust not well mixed with the observed X-ray-emitting gas. Over time, as the cluster merges with the other clusters and the hot gas pressure increases, the dust grains will be driven from the galaxies, mixed with the hot gas, and destroyed, liberating the iron atoms. Building a massive galaxy cluster is a step-by-step enterprise that takes billions of years. Exactly how long it takes for such a cluster to form depends on many factors, such as the density of subclusters in the vicinity, the rate of the expansion of the universe, and the relative amounts of dark energy and dark matter. Chandra X-ray Image of Abell 2125, Low Energy Chandra X-ray Image of Abell 2125, Low Energy Cluster formation also involves complex interactions between the galaxies and the hot gas that may determine how large the galaxies in the cluster can ultimately become. These interactions determine how the galaxies maintain their gas content, the fuel for star formation. The observations of Abell 2125 provide a rare glimpse into the early steps in this process. NASA's Marshall Space Flight Center, Huntsville, Ala., manages the Chandra program for NASA's Office of Space Science, Washington. Northrop Grumman of Redondo Beach, Calif., formerly TRW, Inc., was the prime development contractor for the observatory. The Smithsonian Astrophysical Observatory controls science and flight operations from the Chandra X-ray Center in Cambridge, Mass. Additional information and images are available at: http://chandra.harvard.edu and http://chandra.nasa.gov

VizieR Online Data Catalog: Halpha measurements in Abell 2465 (Wegner+, 2015)

NASA Astrophysics Data System (ADS)

Wegner, G. A.; Chu, D. S.; Hwang, H. S.

2015-07-01

The wavelength of the Hα line at the redshift of Abell 2465 is near 817nm in a clear spectral region between the many telluric emission lines. A custom narrow-band filter for observing Hα was obtained from the Andover Corp. It has a peak transmission at 817.7nm (m817) and a full width at half-maximum (FWHM) of 8.77nm. The wide filter was a Gunn i (ig) filter with nearly the same central wavelength of 820nm and a FWHM of 185nm, and was manufactured by Custom Scientific. Hα observations of Abell 2465 were obtained 2012 September 19-23 using the 2.4m Hiltner telescope at the MDM Observatory on Kitt Peak. The 'Nellie' CCD was used. (1 data file).

The nature of the driving mechanism in the pulsating hybrid PG 1159 star Abell 43

NASA Astrophysics Data System (ADS)

Quirion, P.-O.; Fontaine, G.; Brassard, P.

2005-10-01

We extend our previous pulsational stability analyses of PG 1159 stars by modeling the hybrid PG 1159 type star Abell 43. We show that the standard κ-mechanism due to the ionization of C and O in the envelope of this H-rich PG 1159 star is perfectly able to drive g-mode pulsations. Thus, contrary to a recent suggestion, there is no need to invoke any new or exotic mechanism to explain the pulsational instabilities observed in this particular star. Our expected instability band for l=1 modes extends in period from ~2604 s to ~5529 s, which is consistent with the available photometric observations of Abell 43. We also suggest that efforts to detect luminosity variations in its sibling NGC 7094 be pursued.

Abell 1763: A Giant Gas Sloshing Spiral But No Cool Core

NASA Astrophysics Data System (ADS)

Douglass, Edmund

2017-09-01

We propose a 76 ksec observation of the z=0.23 galaxy cluster Abell 1763. Previous Chandra data reveals the system as host to a large 950 kpc gas sloshing spiral. Atypical of spiral-hosting clusters, an intact cool core is not detected. Its absence suggests the interaction has led to significant disruption since the onset of core sloshing. The primary cluster is accompanied by two X-ray emitting subsystems. Given the orientation of the spiral, both systems are strong candidates for being the perturber responsible for its formation. Abell 1763 provides us with the rare opportunity to examine an infall event (primary + perturber) resulting in sloshing to the point of core disintegration. Detailed analysis will be performed on the disrupted core, the spiral, and the perturber candidates.

Multicolour CCD surface photometry for E and S0 galaxies in 10 clusters

NASA Astrophysics Data System (ADS)

Jorgensen, Inger; Franx, Marijn; Kjaergaard, Per

1995-04-01

CCD surface photometry for 232 E and S0 galaxies is presented. The galaxies are observed in Gunn r and Johnson B, or Gunn r and g. For 48 of the galaxies surface photometry in Johnson U is also presented. Aperture magnitudes in Gunn nu are derived for half of the galaxies. Galaxies in the following clusters have been observed: Abell 194, Abell 539, Abell 3381, Abell 3574, Abell S639, Abell S753, HydraI (Abell 1060), DC2345-28, Doradus and Grm15. The data are part of our ongoing study of the large-scale motions in the Universe and the physical background for the fundamental plane. We use a full model fitting technique for analysing the CCD images. This gives radial profiles of local surface brightness, colour, ellipticity and position angle. The residuals relative to the elliptical isophotes are described quantitatively by Fourier expansions. Effective radius, mean surface brightness and total magnitude are derived by fitting a de Vaucouleurs r^¼ growth curve. We have derived a characteristic radius r_n similar to the diameter D_n introduced by Dressler et al. The derivation of the effective parameters and of r_n takes the seeing into account. We confirm the results by Saglia et al. that the effects of the seeing can be substantial. Seeing-corrected values of the effective parameters and r_n are also presented for 147 E and S0 galaxies in the Coma cluster. Colours, colour gradients and geometrical parameters are derived. The photometry is internally consistent within 0.016 mag. Comparison with the photoelectric aperture photometry from Burstein et al. shows a mean offset of 0.010 mag with an rms scatter of 0.034 mag. The global photometric parameters are compared with data from Faber et al., Lucey et al. and Lucey & Carter. These comparisons imply that the typical rms errors are as follows - log r_n:+/-0.015 log r_e:+/-0.045 m_T:+/-0.09 mag; _e:+/-0.16 mag. The rms error on the combination log r_e-0.35_e which enters the fundamental plane is +/-0.020. Also, comparisons with data from Saglia et al. are presented. The accuracy of the absolute photometry, as well as the derived parameters, makes the data suitable for our investigations of the fundamental plane and of the large-scale motions in the Universe.

An Analysis of Rich Cluster Redshift Survey Data for Large Scale Structure Studies

NASA Astrophysics Data System (ADS)

Slinglend, K.; Batuski, D.; Haase, S.; Hill, J.

1994-12-01

The results from the COBE satellite show the existence of structure on scales on the order of 10% or more of the horizon scale of the universe. Rich clusters of galaxies from Abell's catalog show evidence of structure on scales of 100 Mpc and may hold the promise of confirming structure on the scale of the COBE result. However, many Abell clusters have zero or only one measured redshift, so present knowledge of their three dimensional distribution has quite large uncertainties. The shortage of measured redshifts for these clusters may also mask a problem of projection effects corrupting the membership counts for the clusters. Our approach in this effort has been to use the MX multifiber spectrometer on the Steward 2.3m to measure redshifts of at least ten galaxies in each of 80 Abell cluster fields with richness class R>= 1 and mag10 <= 16.8 (estimated z<= 0.12) and zero or one measured redshifts. This work will result in a deeper, more complete (and reliable) sample of positions of rich clusters. Our primary intent for the sample is for two-point correlation and other studies of the large scale structure traced by these clusters in an effort to constrain theoretical models for structure formation. We are also obtaining enough redshifts per cluster so that a much better sample of reliable cluster velocity dispersions will be available for other studies of cluster properties. To date, we have collected such data for 64 clusters, and for most of them, we have seven or more cluster members with redshifts, allowing for reliable velocity dispersion calculations. Velocity histograms and stripe density plots for several interesting cluster fields are presented, along with summary tables of cluster redshift results. Also, with 10 or more redshifts in most of our cluster fields (30({') } square, just about an `Abell diameter' at z ~ 0.1) we have investigated the extent of projection effects within the Abell catalog in an effort to quantify and understand how this may effect the Abell sample.

Tracing Large Scale Structure with a Redshift Survey of Rich Clusters of Galaxies

NASA Astrophysics Data System (ADS)

Batuski, D.; Slinglend, K.; Haase, S.; Hill, J. M.

1993-12-01

Rich clusters of galaxies from Abell's catalog show evidence of structure on scales of 100 Mpc and hold promise of confirming the existence of structure in the more immediate universe on scales corresponding to COBE results (i.e., on the order of 10% or more of the horizon size of the universe). However, most Abell clusters do not as yet have measured redshifts (or, in the case of most low redshift clusters, have only one or two galaxies measured), so present knowledge of their three dimensional distribution has quite large uncertainties. The shortage of measured redshifts for these clusters may also mask a problem of projection effects corrupting the membership counts for the clusters, perhaps even to the point of spurious identifications of some of the clusters themselves. Our approach in this effort has been to use the MX multifiber spectrometer to measure redshifts of at least ten galaxies in each of about 80 Abell cluster fields with richness class R>= 1 and mag10 <= 16.8. This work will result in a somewhat deeper, much more complete (and reliable) sample of positions of rich clusters. Our primary use for the sample is for two-point correlation and other studies of the large scale structure traced by these clusters. We are also obtaining enough redshifts per cluster so that a much better sample of reliable cluster velocity dispersions will be available for other studies of cluster properties. To date, we have collected such data for 40 clusters, and for most of them, we have seven or more cluster members with redshifts, allowing for reliable velocity dispersion calculations. Velocity histograms for several interesting cluster fields are presented, along with summary tables of cluster redshift results. Also, with 10 or more redshifts in most of our cluster fields (30({') } square, just about an `Abell diameter' at z ~ 0.1) we have investigated the extent of projection effects within the Abell catalog in an effort to quantify and understand how this may effect the Abell sample.

X-ray emission from a complete sample of Abell clusters of galaxies

NASA Astrophysics Data System (ADS)

Briel, Ulrich G.; Henry, J. Patrick

1993-11-01

The ROSAT All-Sky Survey (RASS) is used to investigate the X-ray properties of a complete sample of Abell clusters with measured redshifts and accurate positions. The sample comprises the 145 clusters within a 561 square degree region at high galactic latitude. The mean redshift is 0.17. This sample is especially well suited to be studied within the RASS since the mean exposure time is higher than average and the mean galactic column density is very low. These together produce a flux limit of about 4.2 x 10-13 erg/sq cm/s in the 0.5 to 2.5 keV energy band. Sixty-six (46%) individual clusters are detected at a significance level higher than 99.7% of which 7 could be chance coincidences of background or foreground sources. At redshifts greater than 0.3 six clusters out of seven (86%) are detected at the same significance level. The detected objects show a clear X-ray luminosity -- galaxy count relation with a dispersion consistent with other external estimates of the error in the counts. By analyzing the excess of positive fluctuations of the X-ray flux at the cluster positions, compared with the fluctuations of randomly drawn background fields, it is possible to extend these results below the nominal flux limit. We find 80% of richness R greater than or = 0 and 86% of R greater than or = 1 clusters are X-ray emitters with fluxes above 1 x 10-13 erg/sq cm/s. Nearly 90% of the clusters meeting the requirements to be in Abell's statistical sample emit above the same level. We therefore conclude that almost all Abell clusters are real clusters and the Abell catalog is not strongly contaminated by projection effects. We use the Kaplan-Meier product limit estimator to calculate the cumulative X-ray luminosity function. We show that the shape of the luminosity functions are similiar for different richness classes, but the characteristic luminosities of richness 2 clusters are about twice those of richness 1 clusters which are in turn about twice those of richness 0 clusters. This result is another manifestation of the luminosity -- richness elation for Abell clusters.

Environmental Effects on Galaxy Evolution. II. Quantifying the Tidal Features in NIR Images of the Cluster Abell 85

NASA Astrophysics Data System (ADS)

Venkatapathy, Y.; Bravo-Alfaro, H.; Mayya, Y. D.; Lobo, C.; Durret, F.; Gamez, V.; Valerdi, M.; Granados-Contreras, A. P.; Navarro-Poupard, F.

2017-12-01

This work is part of a series of papers devoted to investigating the evolution of cluster galaxies during their infall. In the present article, we image in NIR a selected sample of galaxies throughout the massive cluster Abell 85 (z = 0.055). We obtain (JHK‧) photometry for 68 objects, reaching ˜1 mag arcsec-2 deeper than 2MASS. We use these images to unveil asymmetries in the outskirts of a sample of bright galaxies and develop a new asymmetry index, {α }{An}, which allows us to quantify the degree of disruption by the relative area occupied by the tidal features on the plane of the sky. We measure the asymmetries for a subsample of 41 large-area objects, finding clear asymmetries in 10 galaxies; most of these are in groups and pairs projected at different clustercentric distances, and some of them are located beyond R 500. Combining information on the H I gas content of blue galaxies and the distribution of substructures across Abell 85 with the present NIR asymmetry analysis, we obtain a very powerful tool to confirm that tidal mechanisms are indeed present and are currently affecting a fraction of galaxies in Abell 85. However, when comparing our deep NIR images with UV blue images of two very disrupted (jellyfish) galaxies in this cluster, we discard the presence of tidal interactions down to our detection limit. Our results suggest that ram-pressure stripping is at the origin of such spectacular disruptions. We conclude that across a complex cluster like Abell 85, environmental mechanisms, both gravitational and hydrodynamical, are playing an active role in driving galaxy evolution.

A Fiber Interferometer for the Magnetized Shock Experiment

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

Yoo, Christian

2012-08-30

The Magnetized Shock Experiment (MSX) at Los Alamos National Laboratory requires remote diagnostics of plasma density. Laser interferometry can be used to determine the line-integrated density of the plasma. A multi-chord heterodyne fiber optic Mach-Zehnder interferometer is being assembled and integrated into the experiment. The advantage of the fiber coupling is that many different view chords can be easily obtained by simply moving transmit and receive fiber couplers. Several such fiber sets will be implemented to provide a time history of line-averaged density for several chords at once. The multiple chord data can then be Abel inverted to provide radiallymore » resolved spatial profiles of density. We describe the design and execution of this multiple fiber interferometer.« less

A Fiber Interferometer for the Magnetized Shock Experiment

NASA Astrophysics Data System (ADS)

Yoo, C. B.; Gao, K. W.; Weber, T. E.; Intrator, T. P.

2012-10-01

The Magnetized Shock Experiment (MSX) at Los Alamos National Laboratory requires remote diagnostics of plasma density. Laser interferometry can be used to determine the line-integrated density of the plasma. A multi-chord heterodyne fiber optic Mach-Zehnder interferometer is being assembled and integrated into the experiment. The advantage of the fiber coupling is that many different view chords can be easily obtained by simply moving transmit and receive fiber couplers. Several such fiber sets will be implemented to provide a time history of line-averaged density for several chords at once. The multiple chord data can then be Abel inverted to provide radially resolved spatial profiles of density. We describe the design and execution of this multiple fiber interferometer.

Topology in two dimensions. II - The Abell and ACO cluster catalogues

NASA Astrophysics Data System (ADS)

Plionis, Manolis; Valdarnini, Riccardo; Coles, Peter

1992-09-01

We apply a method for quantifying the topology of projected galaxy clustering to the Abell and ACO catalogues of rich clusters. We use numerical simulations to quantify the statistical bias involved in using high peaks to define the large-scale structure, and we use the results obtained to correct our observational determinations for this known selection effect and also for possible errors introduced by boundary effects. We find that the Abell cluster sample is consistent with clusters being identified with high peaks of a Gaussian random field, but that the ACO shows a slight meatball shift away from the Gaussian behavior over and above that expected purely from the high-peak selection. The most conservative explanation of this effect is that it is caused by some artefact of the procedure used to select the clusters in the two samples.

Cluster redshifts in five suspected superclusters

NASA Technical Reports Server (NTRS)

Ciardullo, R.; Ford, H.; Harms, R.

1985-01-01

Redshift surveys for rich superclusters were carried out in five regions of the sky containing surface-density enhancements of Abell clusters. While several superclusters are identified, projection effects dominate each field, and no system contains more than five rich clusters. Two systems are found to be especially interesting. The first, field 0136 10, is shown to contain a superposition of at least four distinct superclusters, with the richest system possessing a small velocity dispersion. The second system, 2206 - 22, though a region of exceedingly high Abell cluster surface density, appears to be a remarkable superposition of 23 rich clusters almost uniformly distributed in redshift space between 0.08 and 0.24. The new redshifts significantly increase the three-dimensional information available for the distance class 5 and 6 Abell clusters and allow the spatial correlation function around rich superclusters to be estimated.

Anti-Brownian ELectrokinetic (ABEL) Trapping of Single High Density Lipoprotein (HDL) Particles

NASA Astrophysics Data System (ADS)

Bockenhauer, Samuel; Furstenberg, Alexandre; Wang, Quan; Devree, Brian; Jie Yao, Xiao; Bokoch, Michael; Kobilka, Brian; Sunahara, Roger; Moerner, W. E.

2010-03-01

The ABEL trap is a novel device for trapping single biomolecules in solution for extended observation. The trap estimates the position of a fluorescently-labeled object as small as ˜10 nm in solution and then applies a feedback electrokinetic drift every 20 us to trap the object by canceling its Brownian motion. We use the ABEL trap to study HDL particles at the single-copy level. HDL particles, essential in regulation of ``good'' cholesterol in humans, comprise a small (˜10 nm) lipid bilayer disc bounded by a belt of apolipoproteins. By engineering HDL particles with single fluorescent donor/acceptor probes and varying lipid compositions, we are working to study lipid diffusion on small length scales. We also use HDL particles as hosts for single transmembrane receptors, which should enable study of receptor conformational dynamics on long timescales.

RELICS Discovery of a Probable Lens-magnified SN behind Galaxy Cluster Abell 1763

NASA Astrophysics Data System (ADS)

Rodney, S.; Coe, D.; Bradley, L.; Strolger, L.; Brammer, G.; Avila, R.; Ryan, R.; Ogaz, S.; Riess, A.; Sharon, K.; Johnson, T.; Paterno-Mahler, R.; Molino, A.; Graham, M.; Kelly, P.; Filippenko, A.; Frye, B.; Foley, R.; Schmidt, K.; Umetsu, K.; Czakon, N.; Weiner, B.; Stark, D.; Mainali, R.; Zitrin, A.; Sendra, I.; Graur, O.; Grillo, C.; Hjorth, J.; Selsing, J.; Christensen, L.; Rosati, P.; Nonino, M.; Balestra, I.; Vulcani, B.; McCully, C.; Dawson, W.; Bouwens, R.; Lam, D.; Trenti, M.; Nunez, D. Carrasco; Matheson, T.; Merten, J.; Jha, S.; Jones, C.; Andrade-Santos, F.; Salmon, B.; Bradac, M.; Hoag, A.; Huang, K.; Wang, X.; Oesch, P.

2016-07-01

We report the discovery of a likely supernova (SN) in the background field of the galaxy cluster Abell 1763 (a.k.a. RXC J1335.3+4059, ZwCl 1333.7+4117). The SN candidate was detected in Hubble Space Telescope (HST) observations collected on June 17, 2016 as part of the Reionization Lensing Cluster Survey (RELICS, HST program ID: 14096, PI: D.Coe).

GNSS-Based Space Weather Systems Including COSMIC Ionospheric Measurements

NASA Technical Reports Server (NTRS)

Komjathy, Attila; Mandrake, Lukas; Wilson, Brian; Iijima, Byron; Pi, Xiaoqing; Hajj, George; Mannucci, Anthony J.

2006-01-01

The presentation outline includes University Corporation for Atmospheric Research (UCAR) and Jet Propulsion Laboratory (JPL) product comparisons, assimilating ground-based global positioning satellites (GPS) and COSMIC into JPL/University of Southern California (USC) Global Assimilative Ionospheric Model (GAIM), and JPL/USC GAIM validation. The discussion of comparisons examines Abel profiles and calibrated TEC. The JPL/USC GAIM validation uses Arecibo ISR, Jason-2 VTEC, and Abel profiles.

Anti-Brownian ELectrokinetic (ABEL) trapping of single β2-adrenergic receptors in the absence and presence of agonist

NASA Astrophysics Data System (ADS)

Bockenhauer, Samuel; Fuerstenberg, Alexandre; Yao, Xiao Jie; Kobilka, Brian K.; Moerner, W. E.

2012-02-01

The ABEL trap allows trapping of single biomolecules in solution for extended observation without immobilization. The essential idea combines fluorescence-based position estimation with fast electrokinetic feedback in a microfluidic geometry to counter the Brownian motion of a single nanoscale object, hence maintaining its position in the field of view for hundreds of milliseconds to seconds. Such prolonged observation of single proteins allows access to slow dynamics, as probed by any available photophysical observables. We have used the ABEL trap to study conformational dynamics of the β2-adrenergic receptor, a key G-protein coupled receptor and drug target, in the absence and presence of agonist. A single environment-sensitive dye reports on the receptor microenvironment, providing a real-time readout of conformational change for each trapped receptor. The focus of this paper will be a quantitative comparison of the ligandfree and agonist-bound receptor data from our ABEL trap experiments. We observe a small but clearly detectable shift in conformational equilibria and a lengthening of fluctuation timescales upon binding of agonist. In order to quantify the shift in state distributions and timescales, we apply nonparametric statistical tests to place error bounds on the resulting single-molecule distributions.

Remote Sensing of the Ionosphere and Plasmasphere from Space Using Radiowaves

NASA Technical Reports Server (NTRS)

Mannucci, Anthony J.

2008-01-01

Topics include the scientific context, trans-ionospheric and sounding, small-scale structure, plasmasphere, fast and slow tomography, and pseudo-imaging. Individual slides focus on where geospace science stands today, variability in inner magnetosphere electric fields, Appleton-Hartree formula, phase and range ionospheric observables, examples of leveling, large ionization changes during storms, new mid-latitude phenomena, ionospheric sounding, COSMIC CERTO/Tri-band beacon, LEO-ground radio tomography, irregularity measurements, COSMIC, critical sensor data from COSMIC GPS limb sounding, occultation geometry, comparison of calibrated slant TEC measurements for 26 June 2006, historic examples of Abel electron density profiles, comparison of UCAR and JPL Able profiles of 26 June 2006, validating UCAR and JPL Abel profiles using Arecibo ISR measurements for 26 June 2006, E-region from GPS/MET 1995, Abel versus gradient assisted retrieval, 3000 profiles/day, plasmasphere, JASON TEC above satellite, GPS equatorial plasmasphere measurements, April 2002 geomagnetic storm, and space-based GPS tomography.

A Statistical Study of Multiply Imaged Systems in the Lensing Cluster Abell 68

NASA Astrophysics Data System (ADS)

Richard, Johan; Kneib, Jean-Paul; Jullo, Eric; Covone, Giovanni; Limousin, Marceau; Ellis, Richard; Stark, Daniel; Bundy, Kevin; Czoske, Oliver; Ebeling, Harald; Soucail, Geneviève

2007-06-01

We have carried out an extensive spectroscopic survey with the Keck and VLT telescopes, targeting lensed galaxies in the background of the massive cluster Abell 68. Spectroscopic measurements are obtained for 26 lensed images, including a distant galaxy at z=5.4. Redshifts have been determined for 5 out of 7 multiple-image systems. Through a careful modeling of the mass distribution in the strongly lensed regime, we derive a mass estimate of 5.3×1014 Msolar within 500 kpc. Our mass model is then used to constrain the redshift distribution of the remaining multiply imaged and singly imaged sources. This enables us to examine the physical properties for a subsample of 7 Lyα emitters at 1.7<~z<~5.5, whose unlensed luminosities of ~=1041 ergs s-1 are fainter than similar objects found in blank fields. Of particular interest is an extended Lyα emission region surrounding a highly magnified source at z=2.6, detected in VIMOS integral field spectroscopy data. The physical scale of the most distant lensed source at z=5.4 is very small (<300 pc), similar to the lensed z~5.6 emitter reported by Ellis et al. in Abell 2218. New photometric data available for Abell 2218 allow for a direct comparison between these two unique objects. Our survey illustrates the practicality of using lensing clusters to probe the faint end of the z~2-5 Lyα luminosity function in a manner that is complementary to blank-field narrowband surveys. Data presented herein were obtained at the W. M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation. Also based on observations collected at the Very Large Telescope (Antu/UT1 and Melipal/UT3), European Southern Observatory, Paranal, Chile (ESO programs 070.A-0643 and 073.A-0774), the NASA/ESA Hubble Space Telescope (program 8249) obtained at the Space Telescope Science Institute, which is operated by AURA under NASA contract NAS5-26555, and the Canada-France-Hawaii Telescope (CFHT), which is operated by the National Research Council of Canada, the Institut National des Sciences de l'Univers of the Centre National de la Recherche Scientifique of France, and the University of Hawaii.

VizieR Online Data Catalog: Strong lensing mass modeling of 4 HFF clusters (Kawamata+, 2016)

NASA Astrophysics Data System (ADS)

Kawamata, R.; Oguri, M.; Ishigaki, M.; Shimasaku, K.; Ouchi, M.

2018-02-01

We use the public HFF data (http://www.stsci.edu/hst/campaigns/frontier-fields/) for our analysis. The HFF targets six massive clusters, Abell 2744 (z=0.308), MACS J0416.1-2403 (z=0.397), MACS J0717.5+3745 (z=0.545), MACS J1149.6+2223 (z=0.541), Abell S1063 (z=0.348), and Abell 370 (z=0.375), which have been chosen according to their lensing strength and also their accessibility from major ground-based telescopes. The cluster core and parallel field region of each cluster are observed deeply with the IR channel of Wide Field Camera 3 (WFC3/IR) and the Advanced Camera for Surveys (ACS). As of 2015 October, HST observations for the first four clusters, Abell 2744, MACS J0416.1-2403, MACS J0717.5+3745, and MACS J1149.6+2223, are completed. In this study, we use the Version 1.0 data products of drizzled images with a pixel scale of 0.03"/pixel provided by the Space Telescope Science Institute (STScI). The images for each cluster consist of F435W (B435), F606W (V606), and F814W (i814) images from ACS, and F105W (Y105), F125W (J125), F140W (JH140), and F160W (H160) images from WFC3/IR. (7 data files).

Analysis of the optical emission of the young precataclysmic variables HS 1857+5144 and ABELL 65

NASA Astrophysics Data System (ADS)

Shimansky, V. V.; Pozdnyakova, S. A.; Borisov, N. V.; Bikmaev, I. F.; Vlasyuk, V. V.; Spiridonova, O. I.; Galeev, A. I.; Mel'Nikov, S. S.

2009-10-01

We analyze the physical state and the properties of the close binary systems HS 1857+5144 and Abell 65. We took the spectra of both systems over a wide range of orbital phases with the 6-m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences (SAO RAS) and obtained their multicolor light curves with the RTT150 and Zeiss-1000 telescopes of the SAO RAS. We demonstrate that both Abell 65 and HS 1857+5144 are young precataclysmic variables (PV) with orbital periods of P orb = 1. d 003729 and P orb = 0. d 26633331, respectively. The observed brightness and spectral variations during the orbital period are due to the radiation of the cold component, which absorbs the short-wave radiation of the hot component and reemits it in the visual part of the spectrum. A joint analysis of the brightness and radial velocity curves allowed us to find the possible and optimum sets of their fundamental parameters. We found the luminosity excesses of the secondary components of HS 1857+5144 and Abell 65 with respect to the corresponding Main Sequence stars to be typical for such objects. The excess luminosities of the secondary components of all young PVs are indicative of their faster relaxation rate towards the quiescent state compared to the rates estimated in earlier studies.

Development of 1RM Prediction Equations for Bench Press in Moderately Trained Men.

PubMed

Macht, Jordan W; Abel, Mark G; Mullineaux, David R; Yates, James W

2016-10-01

Macht, JW, Abel, MG, Mullineaux, DR, and Yates, JW. Development of 1RM prediction equations for bench press in moderately trained men. J Strength Cond Res 30(10): 2901-2906, 2016-There are a variety of established 1 repetition maximum (1RM) prediction equations, however, very few prediction equations use anthropometric characteristics exclusively or in part, to estimate 1RM strength. Therefore, the purpose of this study was to develop an original 1RM prediction equation for bench press using anthropometric and performance characteristics in moderately trained male subjects. Sixty male subjects (21.2 ± 2.4 years) completed a 1RM bench press and were randomly assigned a load to complete as many repetitions as possible. In addition, body composition, upper-body anthropometric characteristics, and handgrip strength were assessed. Regression analysis was used to develop a performance-based 1RM prediction equation: 1RM = 1.20 repetition weight + 2.19 repetitions to fatigue - 0.56 biacromial width (cm) + 9.6 (R = 0.99, standard error of estimate [SEE] = 3.5 kg). Regression analysis to develop a nonperformance-based 1RM prediction equation yielded: 1RM (kg) = 0.997 cross-sectional area (CSA) (cm) + 0.401 chest circumference (cm) - 0.385%fat - 0.185 arm length (cm) + 36.7 (R = 0.81, SEE = 13.0 kg). The performance prediction equations developed in this study had high validity coefficients, minimal mean bias, and small limits of agreement. The anthropometric equations had moderately high validity coefficient but larger limits of agreement. The practical applications of this study indicate that the inclusion of anthropometric characteristics and performance variables produce a valid prediction equation for 1RM strength. In addition, the CSA of the arm uses a simple nonperformance method of estimating the lifter's 1RM. This information may be used to predict the starting load for a lifter performing a 1RM prediction protocol or a 1RM testing protocol.

Statistical analysis of catalogs of extragalactic objects. II - The Abell catalog of rich clusters

NASA Technical Reports Server (NTRS)

Hauser, M. G.; Peebles, P. J. E.

1973-01-01

The results of a power-spectrum analysis are presented for the distribution of clusters in the Abell catalog. Clear and direct evidence is found for superclusters with small angular scale, in agreement with the recent study of Bogart and Wagoner (1973). It is also found that the degree and angular scale of the apparent superclustering varies with distance in the manner expected if the clustering is intrinsic to the spatial distribution rather than a consequence of patchy local obscuration.

UV spectroscopy including ISM line absorption: of the exciting star of Abell 35

NASA Astrophysics Data System (ADS)

Ziegler, M.; Rauch, T.; Werner, K.; Kruk, J. W.

Reliable spectral analysis that is based on high-resolution UV observations requires an adequate, simultaneous modeling of the interstellar line absorption and reddening. In the case of the central star of the planetary nebula Abell 35, BD-22 3467, we demonstrate our current standard spectral-analysis method that is based on the Tübingen NLTE Model-Atmosphere Package (TMAP). We present an on- going spectral analysis of FUSE and HST/STIS observations of BD-22 3467.

Weak Gravitational Lensing by the Nearby Cluster Abell 3667.

PubMed

Joffre; Fischer; Frieman; McKay; Mohr; Nichol; Johnston; Sheldon; Bernstein

2000-05-10

We present two weak lensing reconstructions of the nearby (zcl=0.055) merging cluster Abell 3667, based on observations taken approximately 1 yr apart under different seeing conditions. This is the lowest redshift cluster with a weak lensing mass reconstruction to date. The reproducibility of features in the two mass maps demonstrates that weak lensing studies of low-redshift clusters are feasible. These data constitute the first results from an X-ray luminosity-selected weak lensing survey of 19 low-redshift (z<0.1) southern clusters.

A compilation of redshifts and velocity dispersions for Abell clusters (Struble and Rood 1987): Documentation for the machine-readable version

NASA Technical Reports Server (NTRS)

Warren, Wayne H., Jr.

1989-01-01

The machine readable version of the compilation, as it is currently being distributed from the Astronomical Data Center, is described. The catalog contains redshifts and velocity dispersions for all Abell clusters for which these data had been published up to 1986 July. Also included are 1950 equatorial coordinates for the centers of the listed clusters, numbers of observations used to determine the redshifts, and bibliographical references citing the data sources.

Controlling Brownian motion of single protein molecules and single fluorophores in aqueous buffer.

PubMed

Cohen, Adam E; Moerner, W E

2008-05-12

We present an Anti-Brownian Electrokinetic trap (ABEL trap) capable of trapping individual fluorescently labeled protein molecules in aqueous buffer. The ABEL trap operates by tracking the Brownian motion of a single fluorescent particle in solution, and applying a time-dependent electric field designed to induce an electrokinetic drift that cancels the Brownian motion. The trapping strength of the ABEL trap is limited by the latency of the feedback loop. In previous versions of the trap, this latency was set by the finite frame rate of the camera used for video-tracking. In the present system, the motion of the particle is tracked entirely in hardware (without a camera or image-processing software) using a rapidly rotating laser focus and lock-in detection. The feedback latency is set by the finite rate of arrival of photons. We demonstrate trapping of individual molecules of the protein GroEL in buffer, and we show confinement of single fluorophores of the dye Cy3 in water.

UV Observations of the Galaxy Cluster Abell 1795 with the Optical Monitor on XMM-Newton

NASA Technical Reports Server (NTRS)

Mittaz, J. P. D.; Kaastra, J. S.; Tamura, T.; Fabian, A. C.; Mushotzky, F.; Peterson, J. R.; Ikebe, Y.; Lumb, D. H.; Paerels, F.; Stewart, G.

2000-01-01

We present the results of an analysis of broad band UV observations of the central regions of Abell 1795 observed with the optical monitor on XMM-Newton. As have been found with other UV observations of the central regions of clusters of galaxies, we find evidence for star formation. However, we also find evidence for absorption in the cD galaxy on a more extended scale than has been seen with optical imaging. We also report the first UV observation of part of the filamentary structure seen in H-alpha, X-rays and very deep U band imaging. The part of the filament we see is very blue with UV colours consistent with a very early (O/B) stellar population. This is the first direct evidence of a dominant population of early type stars at the centre of Abell 1795 and implies very recent star formation. The relationship of this emission to emission at other wavebands is discussed.

The kinematics of dense clusters of galaxies. II - The distribution of velocity dispersions

NASA Technical Reports Server (NTRS)

Zabludoff, Ann I.; Geller, Margaret J.; Huchra, John P.; Ramella, Massimo

1993-01-01

From the survey of 31 Abell R above 1 cluster fields within z of 0.02-0.05, we extract 25 dense clusters with velocity dispersions omicron above 300 km/s and with number densities exceeding the mean for the Great Wall of galaxies by one deviation. From the CfA Redshift Survey (in preparation), we obtain an approximately volume-limited catalog of 31 groups with velocity dispersions above 100 km/s and with the same number density limit. We combine these well-defined samples to obtain the distribution of cluster velocity dispersions. The group sample enables us to correct for incompleteness in the Abell catalog at low velocity dispersions. The clusters from the Abell cluster fields populate the high dispersion tail. For systems with velocity dispersions above 700 km/s, approximately the median for R = 1 clusters, the group and cluster abundances are consistent. The combined distribution is consistent with cluster X-ray temperature functions.

The cluster-cluster correlation function. [of galaxies

NASA Technical Reports Server (NTRS)

Postman, M.; Geller, M. J.; Huchra, J. P.

1986-01-01

The clustering properties of the Abell and Zwicky cluster catalogs are studied using the two-point angular and spatial correlation functions. The catalogs are divided into eight subsamples to determine the dependence of the correlation function on distance, richness, and the method of cluster identification. It is found that the Corona Borealis supercluster contributes significant power to the spatial correlation function to the Abell cluster sample with distance class of four or less. The distance-limited catalog of 152 Abell clusters, which is not greatly affected by a single system, has a spatial correlation function consistent with the power law Xi(r) = 300r exp -1.8. In both the distance class four or less and distance-limited samples the signal in the spatial correlation function is a power law detectable out to 60/h Mpc. The amplitude of Xi(r) for clusters of richness class two is about three times that for richness class one clusters. The two-point spatial correlation function is sensitive to the use of estimated redshifts.

Watching Single Enzymes and Fluorescent Proteins in Action in Solution Using a Microfluidic Trap

NASA Astrophysics Data System (ADS)

Goldsmith, Randall

2012-02-01

Observation of dynamics of single biomolecules over a prolonged time without altering the biomolecule via immobilization is achieved with a specialized microfluidic device. This device, the Anti-Brownian ELectrokinetic (ABEL) Trap, uses real-time electrokinetic feedback to cancel Brownian motion of single objects in solution. First, we use the ABEL Trap to study Allophycocyanin (APC), a photosynthetic antenna-protein and popular fluorescent probe. A complex relationship between fluorescence intensity and lifetime is observed, suggesting light-induced conformational changes and radiative and non-radiative rate fluctuations. Second, we apply the ABEL Trap to single molecules of the multi-copper enzyme blue Nitrite Reductase where a fluorescent label reports on the oxidation state of the Type I Copper. Redox cycling is observed and kinetic analysis allows extraction of the microscopic rate constants in the kinetic scheme. Evidence of a substrate-induced shift of the intramolecular electron transfer rate is seen. Taken together, these observations provide windows of unprecedented detail into the dynamics of solution-phase biomolecules.

On the multiple zeros of a real analytic function with applications to the averaging theory of differential equations

NASA Astrophysics Data System (ADS)

García, Isaac A.; Llibre, Jaume; Maza, Susanna

2018-06-01

In this work we consider real analytic functions , where , Ω is a bounded open subset of , is an interval containing the origin, are parameters, and ε is a small parameter. We study the branching of the zero-set of at multiple points when the parameter ε varies. We apply the obtained results to improve the classical averaging theory for computing T-periodic solutions of λ-families of analytic T-periodic ordinary differential equations defined on , using the displacement functions defined by these equations. We call the coefficients in the Taylor expansion of in powers of ε the averaged functions. The main contribution consists in analyzing the role that have the multiple zeros of the first non-zero averaged function. The outcome is that these multiple zeros can be of two different classes depending on whether the zeros belong or not to the analytic set defined by the real variety associated to the ideal generated by the averaged functions in the Noetheriang ring of all the real analytic functions at . We bound the maximum number of branches of isolated zeros that can bifurcate from each multiple zero z 0. Sometimes these bounds depend on the cardinalities of minimal bases of the former ideal. Several examples illustrate our results and they are compared with the classical theory, branching theory and also under the light of singularity theory of smooth maps. The examples range from polynomial vector fields to Abel differential equations and perturbed linear centers.

Non-thermal pressure in the outskirts of Abell 2142

NASA Astrophysics Data System (ADS)

Fusco-Femiano, Roberto; Lapi, Andrea

2018-03-01

Clumping and turbulence are expected to affect the matter accreted on to the outskirts of galaxy clusters. To determine their impact on the thermodynamic properties of Abell 2142, we perform an analysis of the X-ray temperature data from XMM-Newton via our SuperModel, a state-of-the-art tool for investigating the astrophysics of the intracluster medium already tested on many individual clusters (since Cavaliere, Lapi & Fusco-Femiano 2009). Using the gas density profile corrected for clumpiness derived by Tchernin et al. (2016), we find evidence for the presence of a non-thermal pressure component required to sustain gravity in the cluster outskirts of Abell 2142, that amounts to about 30 per cent of the total pressure at the virial radius. The presence of the non-thermal component implies the gas fraction to be consistent with the universal value at the virial radius and the electron thermal pressure profile to be in good agreement with that inferred from the SZ data. Our results indicate that the presence of gas clumping and of a non-thermal pressure component are both necessary to recover the observed physical properties in the cluster outskirts. Moreover, we stress that an alternative method often exploited in the literature (included Abell 2142) to determine the temperature profile kBT = Pe/ne basing on a combination of the Sunyaev-Zel'dovich (SZ) pressure Pe and of the X-ray electron density ne does not allow us to highlight the presence of non-thermal pressure support in the cluster outskirts.

UVIT view of ram-pressure stripping in action: Star formation in the stripped gas of the GASP jellyfish galaxy JO201 in Abell 85

NASA Astrophysics Data System (ADS)

George, K.; Poggianti, B. M.; Gullieuszik, M.; Fasano, G.; Bellhouse, C.; Postma, J.; Moretti, A.; Jaffé, Y.; Vulcani, B.; Bettoni, D.; Fritz, J.; Côté, P.; Ghosh, S. K.; Hutchings, J. B.; Mohan, R.; Sreekumar, P.; Stalin, C. S.; Subramaniam, A.; Tandon, S. N.

2018-06-01

Jellyfish are cluster galaxies that experience strong ram-pressure effects that strip their gas. Their Hα images reveal ionized gas tails up to 100 kpc, which could be hosting ongoing star formation. Here we report the ultraviolet (UV) imaging observation of the jellyfish galaxy JO201 obtained at a spatial resolution ˜ 1.3 kpc. The intense burst of star formation happening in the tentacles is the focus of the present study. JO201 is the "UV-brightest cluster galaxy" in Abell 85 (z ˜ 0.056) with knots and streams of star formation in the ultraviolet. We identify star forming knots both in the stripped gas and in the galaxy disk and compare the UV features with the ones traced by Hα emission. Overall, the two emissions remarkably correlate, both in the main body and along the tentacles. Similarly, also the star formation rates of individual knots derived from the extinction-corrected FUV emission agree with those derived from the Hα emission and range from ˜ 0.01 -to- 2.07 M⊙ yr-1. The integrated star formation rate from FUV flux is ˜ 15 M⊙ yr-1. The unprecedented deep UV imaging study of the jellyfish galaxy JO201 shows clear signs of extraplanar star-formation activity due to a recent/ongoing gas stripping event.

GASP. V. Ram-pressure stripping of a ring Hoag's-like galaxy in a massive cluster

NASA Astrophysics Data System (ADS)

Moretti, A.; Poggianti, B. M.; Gullieuszik, M.; Mapelli, M.; Jaffé, Y. L.; Fritz, J.; Biviano, A.; Fasano, G.; Bettoni, D.; Vulcani, B.; D'Onofrio, M.

2018-04-01

Through an ongoing MUSE program dedicated to study gas removal processes in galaxies (GAs Stripping Phenomena in galaxies with MUSE, GASP), we have obtained deep and wide integral field spectroscopy of the galaxy JO171. This galaxy resembles the Hoag's galaxy, one of the most spectacular examples of ring galaxies, characterized by a completely detached ring of young stars surrounding a central old spheroid. At odds with the isolated Hoag's galaxy, JO171 is part of a dense environment, the cluster Abell 3667, which is causing gas stripping along tentacles. Moreover, its ring counter-rotates with respect to the central spheroid. The joint analysis of the stellar populations and the gas/stellar kinematics shows that the origin of the ring was not due to an internal mechanism, but was related to a gas accretion event that happened in the distant past, prior to accretion on to Abell 3667, most probably within a filament. More recently, since infall in the cluster, the gas in the ring has been stripped by ram pressure, causing the quenching of star formation in the stripped half of the ring. This is the first observed case of ram-pressure stripping in action in a ring galaxy, and MUSE observations are able to reveal both of the events (accretion and stripping) that caused dramatic transformations in this galaxy.

Shocks and Bubbles in a Deep Chandra Observation of the Cooling Flow Cluster Abell 2052

DTIC Science & Technology

2009-01-01

the bubble rims related to radio source outbursts have been found in a few clusters including M87/ Virgo (Forman et al. 2005), Hydra A (Nulsen et al...Printed in the U.S.A. SHOCKS AND BUBBLES IN A DEEP CHANDRA OBSERVATION OF THE COOLING FLOW CLUSTER ABELL 2052 E. L. Blanton1, S. W. Randall2, E. M...Douglass1, C. L. Sarazin3, T. E. Clarke4,5, and B. R. McNamara2,6,7 1 Institute for Astrophysical Research , Boston University, 725 Commonwealth Avenue

Abell 2069 - An X-ray cluster of galaxies with multiple subcondensations

NASA Technical Reports Server (NTRS)

Gioia, I. M.; Maccacaro, T.; Geller, M. J.; Huchra, J. P.; Stocke, J.; Steiner, J. E.

1982-01-01

X-ray and optical observations of the cluster Abell 2069 are presented. The cluster is at a mean redshift of 0.116. The cluster shows multiple condensations in both the X-ray emission and in the galaxy surface density and, thus, does not appear to be relaxed. There is a close correspondence between the gas and galaxy distributions which indicates that the galaxies in this system do map the mass distribution, contrary to what might be expected if low-mass neutrinos dominate the cluster mass.

Towards an understanding of dark matter: Precise gravitational lensing analysis complemented by robust photometric redshifts

NASA Astrophysics Data System (ADS)

Coe, Daniel Aaron

The goal of thesis is to help scientists resolve one of the great mysteries of our time: the nature of Dark Matter. Dark Matter is currently believed to make up over 80% of the material in our universe, yet we have so far inferred but a few of its basic properties. Here we study the Dark Matter surrounding a galaxy cluster, Abell 1689, via the most direct method currently available--gravitational lensing. Abell 1689 is a "strong" gravitational lens, meaning it produces multiple images of more distant galaxies. The observed positions of these images can be measured very precisely and act as a blueprint allowing us to reconstruct the Dark Matter distribution of the lens. Until now, such mass models of Abell 1689 have reproduced the observed multiple images well but with significant positional offsets. Using a new method we develop here, we obtain a new mass model which perfectly reproduces the observed positions of 168 knots identified within 135 multiple images of 42 galaxies. An important ingredient to our mass model is the accurate measurement of distances to the lensed galaxies via their photometric redshifts. Here we develop tools which improve the accuracy of these measurements based on our study of the Hubble Ultra Deep Field, the only image yet taken to comparable depth as the magnified regions of Abell 1689. We present results both for objects in the Hubble Ultra Deep Field and for galaxies gravitationally lensed by Abell 1689. As part of this thesis, we also provide reviews of Dark Matter and Gravitational Lensing, including a chapter devoted to the mass profiles of Dark Matter halos realized in simulations. The original work presented here was performed primarily by myself under the guidance of Narciso Benítez and Holland Ford as a member of the Advanced Camera for Surveys GTO Science Team at Johns Hopkins University and the Instituto de Astrofisica de Andalucfa. My advisors served on my thesis committee along with Rick White, Gabor Domokos, and Steve Zelditch.

Bayesian Abel Inversion in Quantitative X-Ray Radiography

DOE PAGES

Howard, Marylesa; Fowler, Michael; Luttman, Aaron; ...

2016-05-19

A common image formation process in high-energy X-ray radiography is to have a pulsed power source that emits X-rays through a scene, a scintillator that absorbs X-rays and uoresces in the visible spectrum in response to the absorbed photons, and a CCD camera that images the visible light emitted from the scintillator. The intensity image is related to areal density, and, for an object that is radially symmetric about a central axis, the Abel transform then gives the object's volumetric density. Two of the primary drawbacks to classical variational methods for Abel inversion are their sensitivity to the type andmore » scale of regularization chosen and the lack of natural methods for quantifying the uncertainties associated with the reconstructions. In this work we cast the Abel inversion problem within a statistical framework in order to compute volumetric object densities from X-ray radiographs and to quantify uncertainties in the reconstruction. A hierarchical Bayesian model is developed with a likelihood based on a Gaussian noise model and with priors placed on the unknown density pro le, the data precision matrix, and two scale parameters. This allows the data to drive the localization of features in the reconstruction and results in a joint posterior distribution for the unknown density pro le, the prior parameters, and the spatial structure of the precision matrix. Results of the density reconstructions and pointwise uncertainty estimates are presented for both synthetic signals and real data from a U.S. Department of Energy X-ray imaging facility.« less

Applications for edge detection techniques using Chandra and XMM-Newton data: galaxy clusters and beyond

NASA Astrophysics Data System (ADS)

Walker, S. A.; Sanders, J. S.; Fabian, A. C.

2016-09-01

The unrivalled spatial resolution of the Chandra X-ray observatory has allowed many breakthroughs to be made in high-energy astrophysics. Here we explore applications of Gaussian gradient magnitude (GGM) filtering to X-ray data, which dramatically improves the clarity of surface brightness edges in X-ray observations, and maps gradients in X-ray surface brightness over a range of spatial scales. In galaxy clusters, we find that this method is able to reveal remarkable substructure behind the cold fronts in Abell 2142 and Abell 496, possibly the result of Kelvin-Helmholtz instabilities. In Abell 2319 and Abell 3667, we demonstrate that the GGM filter can provide a straightforward way of mapping variations in the widths and jump ratios along the lengths of cold fronts. We present results from our ongoing programme of analysing the Chandra and XMM-Newton archives with the GGM filter. In the Perseus cluster, we identify a previously unseen edge around 850 kpc from the core to the east, lying outside a known large-scale cold front, which is possibly a bow shock. In MKW 3s we find an unusual `V' shape surface brightness enhancement starting at the cluster core, which may be linked to the AGN jet. In the Crab nebula a new, moving feature in the outer part of the torus is identified which moves across the plane of the sky at a speed of ˜0.1c, and lies much further from the central pulsar than the previous motions seen by Chandra.

Embedded spiral patterns in the massive galaxy cluster Abell 1835

NASA Astrophysics Data System (ADS)

Ueda, S.; Kitayama, T.; Dotani, T.

2017-10-01

We report on the properties of the intracluster medium (ICM) in the central region of the massive galaxy cluster, Abell 1835, obtained with the data from the Chandra X-ray Observatory. We find distinctive spiral patterns in the cool core in the residual image of the X-ray surface brightness after its nominal profile is subtracted. The spiral patterns consist of two arms. One of them appears as positive, and the other appears as negative excesses in the residual image. Their sizes are ˜ 70 kpc and their morphologies are consistent with each other. We find that the spiral patterns extend from the cool core out to the hotter surrounding ICM. We analyze the X-ray spectra extracted from both regions. We obtain that the ICM properties are similar to those expected by gas sloshing. We also find that the ICM in the two regions of spiral patterns is near or is in pressure equilibrium. Abell 1835 may now be experiencing gas sloshing induced by an off-axis minor merger. These results have been already published (Ueda, Kitayama, & Dotani 2017, ApJ, 837, 34).

The XMM Cluster Outskirts Project (X-COP)

NASA Astrophysics Data System (ADS)

Eckert, D.

2017-10-01

The outskirts of galaxy clusters (typically the regions located beyond R500) are the regions where the transition between the virialized ICM and the infalling material from the large-scale structure takes place. As such, they play a central role in our understanding of the processes leading to the virialization of the accreting gas within the central dark-matter halo. I will give an overview of the XMM cluster outskirts project (X-COP), a very large program on XMM to study the virial region of galaxy clusters with unprecedented details. I will show how X-ray observations can be combined with the Sunyaev-Zeldovich signal to recover the thermodynamic properties and hydrostatic mass of the ICM, bypassing the need for expensive X-ray spectroscopic observations. I will discuss the results obtained using this technique on Abell 2142 and Abell 2319 and give prospects for the results expected using the full X-COP sample. I will also present recent results on the search for warm-hot baryons in the filaments connected to clusters, emphasizing on the discovery of 3 filaments of 10-million-degree gas connected to the massive cluster Abell 2744.

Hierarchical Velocity Structure in the Core of Abell 2597

NASA Technical Reports Server (NTRS)

Still, Martin; Mushotzky, Richard

2004-01-01

We present XMM-Newton RGS and EPIC data of the putative cooling flow cluster Abell 2597. Velocities of the low-ionization emission lines in the spectrum are blue shifted with respect to the high-ionization lines by 1320 (sup +660) (sub -210) kilometers per second, which is consistent with the difference in the two peaks of the galaxy velocity distribution and may be the signature of bulk turbulence, infall, rotation or damped oscillation in the cluster. A hierarchical velocity structure such as this could be the direct result of galaxy mergers in the cluster core, or the injection of power into the cluster gas from a central engine. The uniform X-ray morphology of the cluster, the absence of fine scale temperature structure and the random distribution of the the galaxy positions, independent of velocity, suggests that our line of sight is close to the direction of motion. These results have strong implications for cooling flow models of the cluster Abell 2597. They give impetus to those models which account for the observed temperature structure of some clusters using mergers instead of cooling flows.

Implications for gravitational lensing and the dark matter content in clusters of galaxies from spatially resolved x-ray spectra

NASA Technical Reports Server (NTRS)

Loewenstein, M.

1994-01-01

A simple method for deriving well-behaved temperature solutions to the equation of hydrostatic equilibrium for intracluster media with X-ray imaging observations is presented and applied to a series of generalized models as well as to observations of the Perseus cluster and Abell 2256. In these applications the allowed range in the ratio of nonbaryons to baryons as a function of radius is derived, taking into account the uncertainties and crude spatial resolution of the X-ray spectra and considering a range of physically reasonable mass models with various scale heights. Particular attention is paid to the central regions of the cluster, and it is found that the dark matter can be sufficiently concentrated to be consistent with the high central mass surface densities for moderate-redshift clusters from their gravitational lensing properties.

Analysis of LAC Observations of Clusters of Galaxies and Supernova Remnants

NASA Technical Reports Server (NTRS)

Hughes, J.

1996-01-01

The following publications are included and serve as the final report: The X-ray Spectrum of Abell 665; Clusters of Galaxies; Ginga Observation of an Oxygen-rich Supernova Remnant; Ginga Observations of the Coma Cluster and Studies of the Spatial Distribution of Iron; A Measurement of the Hubble Constant from the X-ray Properties and the Sunyaev-Zel'dovich Effect of Abell 2218; Non-polytropic Model for the Coma Cluster; and Abundance Gradients in Cooling Flow Clusters: Ginga LAC (Large Area Counter) and Einstein SSS (Solid State Spectrometer) Spectra of A496, A1795, A2142, and A2199.

HUBBLE AND KECK DISCOVER GALAXY BUILDING BLOCK

NASA Technical Reports Server (NTRS)

2002-01-01

This NASA Hubble Space Telescope image shows a very small, faint galaxy 'building block' newly discovered by a unique collaboration between ground- and space-based telescopes. Hubble and the 10-meter Keck Telescopes in Hawaii joined forces, using a galaxy cluster which acts as gravitational lens to detect what scientists believe is one of the smallest very distant objects ever found. The galaxy cluster Abell 2218 was used by a team of European and American astronomers led by Richard Ellis (Caltech) in their systematic search for intrinsically faint distant star-forming systems. Without help from Abell 2218's exceptional magnifying power to make objects appear about 30 times brighter, the galaxy building block would have been undetectable. In the image to the right, the object is seen distorted into two nearly identical, very red 'images' by the gravitational lens. The image pair represents the magnified result of a single background object gravitationally lensed by Abell 2218 and viewed at a distance of 13.4 billion light-years. The intriguing object contains only one million stars, far fewer than a mature galaxy, and scientists believe it is very young. Such young star-forming systems of low mass at early cosmic times are likely to be the objects from which present-day galaxies have formed. In the image to the left, the full overview of the galaxy cluster Abell 2218 is seen. This image was taken by Hubble in 1999 at the completion of Hubble Servicing Mission 3A. Credit: NASA, ESA, Richard Ellis (Caltech) and Jean-Paul Kneib (Observatoire Midi-Pyrenees, France) Acknowledgment: NASA, A. Fruchter and the ERO Team (STScI and ST-ECF)

Suzaku observations of the outskirts of the galaxy cluster Abell 3395, including a filament toward Abell 3391

NASA Astrophysics Data System (ADS)

Sugawara, Yuuki; Takizawa, Motokazu; Itahana, Madoka; Akamatsu, Hiroki; Fujita, Yutaka; Ohashi, Takaya; Ishisaki, Yoshitaka

2017-12-01

The results of Suzaku observations of the outskirts of Abell 3395, including a large-scale structure filament toward Abell 3391, are presented. We measured temperature and abundance distributions from the southern outskirt of A 3395 to the north at the virial radius, where a filament structure has been found in the former X-ray and Sunyaev-Zel'dovich (SZ) effect observations between A 3391 and A 3395. The overall temperature structure is consistent with the universal profile proposed by Okabe, N., et al. 2014, PASJ, 66, 99 for relaxed clusters, except for the filament region. A hint of intracluster medium heating is found between the two clusters, which might be due to their interaction in the early phase of a cluster merger. Although we obtained a relatively low metal abundance of Z=0.169^{+0.164+0.009+0.018}_{-0.150-0.004-0.015} solar, where the first, second, and third errors are statistical, cosmic X-ray background systematic, and non-X-ray background systematic, respectively, at the virial radius in the filament, our results are still consistent with previous results for other clusters (Z ˜ 0.3 solar) within errors. Therefore, our results are also consistent with the early enrichment scenario. We estimated Compton y parameters only from X-ray results in the region between A 3391 and A 3395 assuming a simple geometry. They are smaller than the previous SZ results with the Planck satellite. The difference could be attributed to a more elaborate geometry such as a filament inclined to the line-of-sight direction, or underestimation of the X-ray temperature because of the unresolved multi-temperature structures or undetected hot X-ray emission of the shock-heated gas.

Mystery solved: discovery of extended radio emission in the merging galaxy cluster Abell 2146

NASA Astrophysics Data System (ADS)

Hlavacek-Larrondo, J.; Gendron-Marsolais, M.-L.; Fecteau-Beaucage, D.; van Weeren, R. J.; Russell, H. R.; Edge, A.; Olamaie, M.; Rumsey, C.; King, L.; Fabian, A. C.; McNamara, B.; Hogan, M.; Mezcua, M.; Taylor, G.

2018-04-01

Abell 2146 (z = 0.232) is a massive galaxy cluster currently undergoing a spectacular merger in the plane of the sky with a bullet-like morphology. It was the first system in which both the bow and upstream shock fronts were detected at X-ray wavelengths (Mach ˜2), yet deep Giant MetreWave Telescope 325 MHz observations failed to detect extended radio emission associated with the cluster as is typically seen in such systems. We present new, multiconfiguration 1-2 GHz Karl G. Jansky Very Large Array (VLA) observations of Abell 2146 totalling 16 h of observations. These data reveal for the first time the presence of an extended (≈850 kpc), faint radio structure associated with Abell 2146. The structure appears to harbour multiple components, one associated with the upstream shock that we classify as a radio relic and one associated with the subcluster core that is consisted as being a radio halo bounded by the bow shock. The newly detected structures have some of the lowest radio powers detected thus far in any cluster (P1.4 GHz, halo = 2.4 ± 0.2 × 1023 W Hz-1 and P1.4 GHz, relic = 2.2 ± 0.2 × 1023 W Hz-1). The flux measurement of the halo, as well as its morphology, also suggests that the halo was recently created (≈0.3 Gyr after core passage), consistent with the dynamical state of the cluster. These observations demonstrate the capacity of the upgraded VLA to detect extremely faint and extended radio structures. Based on these observations, we predict that many more radio relics and radio haloes in merging clusters should be detected by future radio facilities such as the Square Kilometre Array.

Method of mechanical quadratures for solving singular integral equations of various types

NASA Astrophysics Data System (ADS)

Sahakyan, A. V.; Amirjanyan, H. A.

2018-04-01

The method of mechanical quadratures is proposed as a common approach intended for solving the integral equations defined on finite intervals and containing Cauchy-type singular integrals. This method can be used to solve singular integral equations of the first and second kind, equations with generalized kernel, weakly singular equations, and integro-differential equations. The quadrature rules for several different integrals represented through the same coefficients are presented. This allows one to reduce the integral equations containing integrals of different types to a system of linear algebraic equations.

Single-molecule dynamics in nanofabricated traps

NASA Astrophysics Data System (ADS)

Cohen, Adam

2009-03-01

The Anti-Brownian Electrokinetic trap (ABEL trap) provides a means to immobilize a single fluorescent molecule in solution, without surface attachment chemistry. The ABEL trap works by tracking the Brownian motion of a single molecule, and applying feedback electric fields to induce an electrokinetic motion that approximately cancels the Brownian motion. We present a new design for the ABEL trap that allows smaller molecules to be trapped and more information to be extracted from the dynamics of a single molecule than was previously possible. In particular, we present strategies for extracting dynamically fluctuating mobilities and diffusion coefficients, as a means to probe dynamic changes in molecular charge and shape. If one trapped molecule is good, many trapped molecules are better. An array of single molecules in solution, each immobilized without surface attachment chemistry, provides an ideal test-bed for single-molecule analyses of intramolecular dynamics and intermolecular interactions. We present a technology for creating such an array, using a fused silica plate with nanofabricated dimples and a removable cover for sealing single molecules within the dimples. With this device one can watch the shape fluctuations of single molecules of DNA or study cooperative interactions in weakly associating protein complexes.

HUBBLE VIEWS DISTANT GALAXIES THROUGH A COSMIC LENS

NASA Technical Reports Server (NTRS)

2002-01-01

This NASA Hubble Space Telescope image of the rich galaxy cluster, Abell 2218, is a spectacular example of gravitational lensing. The arc-like pattern spread across the picture like a spider web is an illusion caused by the gravitational field of the cluster. The cluster is so massive and compact that light rays passing through it are deflected by its enormous gravitational field, much as an optical lens bends light to form an image. The process magnifies, brightens and distorts images of objects that lie far beyond the cluster. This provides a powerful 'zoom lens' for viewing galaxies that are so far away they could not normally be observed with the largest available telescopes. Hubble's high resolution reveals numerous arcs which are difficult to detect with ground-based telescopes because they appear to be so thin. The arcs are the distorted images of a very distant galaxy population extending 5-10 times farther than the lensing cluster. This population existed when the universe was just one quarter of its present age. The arcs provide a direct glimpse of how star forming regions are distributed in remote galaxies, and other clues to the early evoution of galaxies. Hubble also reveals multiple imaging, a rarer lensing event that happens when the distortion is large enough to produce more than one image of the same galaxy. Abell 2218 has an unprecedented total of seven multiple systems. The abundance of lensing features in Abell 2218 has been used to make a detailed map of the distribution of matter in the cluster's center. From this, distances can be calculated for a sample of 120 faint arclets found on the Hubble image. These arclets represent galaxies that are 50 times fainter than objects that can be seen with ground-based telescopes. Studies of remote galaxies viewed through well-studied lenses like Abell 2218 promise to reveal the nature of normal galaxies at much earlier epochs than was previously possible. The technique is a powerful combination of Hubble's superlative capabilities and the 'natural' focusing properties of massive clusters like Abell 2218. The image was taken with the Wide Field Planetary Camera 2. Credits: W.Couch (University of New South Wales), R. Ellis (Cambridge University), and NASA

Computation of Collision-Induced Absorption by Simple Molecular Complexes, for Astrophysical Applications

NASA Astrophysics Data System (ADS)

Abel, Martin; Frommhold, Lothar; Li, Xiaoping; Hunt, Katharine L. C.

2012-06-01

The interaction-induced absorption by collisional pairs of H{_2} molecules is an important opacity source in the atmospheres of various types of planets and cool stars, such as late stars, low-mass stars, brown dwarfs, cool white dwarf stars, the ambers of the smaller, burnt out main sequence stars, exoplanets, etc., and therefore of special astronomical interest The emission spectra of cool white dwarf stars differ significantly in the infrared from the expected blackbody spectra of their cores, which is largely due to absorption by collisional H{_2}-H{_2}, H{_2}-He, and H{_2}-H complexes in the stellar atmospheres. Using quantum-chemical methods we compute the atmospheric absorption from hundreds to thousands of kelvin. Laboratory measurements of interaction-induced absorption spectra by H{_2} pairs exist only at room temperature and below. We show that our results reproduce these measurements closely, so that our computational data permit reliable modeling of stellar atmosphere opacities even for the higher temperatures. First results for H_2-He complexes have already been applied to astrophysical models have shown great improvements in these models. L. Frommhold, Collision-Induced Absorption in Gases, Cambridge University Press, Cambridge, New York, 1993 and 2006 X. Li, K. L. C. Hunt, F. Wang, M. Abel, and L. Frommhold, Collision-Induced Infrared Absorption by Molecular Hydrogen Pairs at Thousands of Kelvin, Int. J. of Spect., vol. 2010, Article ID 371201, 11 pages, 2010. doi: 10.1155/2010/371201 M. Abel, L. Frommhold, X. Li, and K. L. C. Hunt, Collision-induced absorption by H{_2} pairs: From hundreds to thousands of Kelvin, J. Phys. Chem. A, 115, 6805-6812, 2011} L. Frommhold, M. Abel, F. Wang, M. Gustafsson, X. Li, and K. L. C. Hunt, "Infrared atmospheric emission and absorption by simple molecular complexes, from first principles", Mol. Phys. 108, 2265, 2010 M. Abel, L. Frommhold, X. Li, and K. L. C. Hunt, Infrared absorption by collisional H_2-He complexes at temperatures up to 9000 K and frequencies from 0 to 20000 cm-1, J. Chem. Phys., 136, 044319, 2012 D. Saumon, M. S. Marley, M. Abel, L. Frommhold, and R. S. Freedman, New H_2 collision-induced absorption and NH_3 opacity and the spectra of the coolest brown dwarfs, Astrophysical Journal, 2012

The Distance and Mass of the Galaxy Cluster Abell 1995 Derived from Sunyaev-Zeldovich Effect and X-Ray Measurements

NASA Technical Reports Server (NTRS)

Patel, Sandeep K.; Joy, Marshall; Carlstrom, John E.; Holder, Gilbert P.; Reese, Erik D.; Gomez, Percy L.; Hughes, John P.; Grego, Laura; Holzapfel, William L.

2000-01-01

We present multiwavelength observations of the Abell 1995 galaxy cluster. From an analysis of X-ray spectroscopy and imaging data, we derive the electron temperature, cluster core radius, and central electron number density. Using optical spectroscopy of 15 cluster members, we derive an accurate cluster redshift and velocity dispersion. Finally, the interferometric imaging of the Sunyaev-Zeldovich effect toward Abell 1995 at 28.5 GHz provides a measure of the integrated pressure through the cluster. The X-ray and Sunyaev-Zeldovich effect observations are combined to determine the angular diameter distance to the cluster of D(sub A) = 1294(sup +294 +438, sub -283 -458) Mpc (Statistical followed by systematic uncertainty), implying a Hubble constant of H(sub 0) = 52.2(sup +11.4 +18.5, sub -11.9 -17.7) km/s.Mpc for Omega(sub M) = 0.3 and Omega(sub lambda) = 0.7. We find a best-fit H(sub 0) of 46 km/s.Mpc for the Omega(sub M) = 1 and Omega(sub lambda) = 0 cosmology, and 48 km/s.Mpc for Omega(sub M) = 0.3 and Omega(sub lambda) = 0.0. The X-ray data are also used to derive a total cluster mass of M(sup HSE, sub tot)(r(sub 500)) = 5.18(sup +0.62, sub -0.48) x 10(exp 14)/h solar mass; the optical velocity dispersion yields an independent and consistent estimate of M(sup virial, sub tot)(r(sub 500)) = 6.35(sup +1.51, sub -1.19) X 10(exp 14) /h solar mass. Both of the total mass estimates are evaluated at a fiducial radius, r(sub 500) = 830 /h kpc, where the overdensity is 500 times the critical density. The total cluster mass is then combined with gas mass measurements to determine a cluster gas mass fraction of F(sub g) = 0.056(sup +0.010, sub -0.013) /h(sup 3/2) in combination with recent baryon density constraints, the measured gas mass fraction yields an upper limit on the mass density parameter of Omega(sub M) h(sup 1/2) <= 0.34(sup +/0.06, sub 0.05.

The genus curve of the Abell clusters

NASA Technical Reports Server (NTRS)

Rhoads, James E.; Gott, J. Richard, III; Postman, Marc

1994-01-01

We study the topology of large-scale structure through a genus curve measurement of the recent Abell catalog redshift survey of Postman, Huchra, and Geller (1992). The structure is found to be spongelike near median density and to exhibit isolated superclusters and voids at high and low densities, respectively. The genus curve shows a slight shift toward 'meatball' topology, but remains consistent with the hypothesis of Gaussian random phase initial conditions. The amplitude of the genus curve corresponds to a power-law spectrum with index n = 0.21(sub -0.47 sup +0.43) on scales of 48/h Mpc or to a cold dark matter power spectrum with omega h = 0.36(sub -0.17 sup +0.46).

The genus curve of the Abell clusters

NASA Astrophysics Data System (ADS)

Rhoads, James E.; Gott, J. Richard, III; Postman, Marc

1994-01-01

We study the topology of large-scale structure through a genus curve measurement of the recent Abell catalog redshift survey of Postman, Huchra, and Geller (1992). The structure is found to be spongelike near median density and to exhibit isolated superclusters and voids at high and low densities, respectively. The genus curve shows a slight shift toward 'meatball' topology, but remains consistent with the hypothesis of Gaussian random phase initial conditions. The amplitude of the genus curve corresponds to a power-law spectrum with index n = 0.21-0.47+0.43 on scales of 48/h Mpc or to a cold dark matter power spectrum with omega h = 0.36-0.17+0.46.

Galaxy Cluster Abell 1689

NASA Image and Video Library

2017-12-08

Release Date: March 10, 2010 - Distant galaxy clusters mysteriously stream at a million miles per hour along a path roughly centered on the southern constellations Centaurus and Hydra. A new study led by Alexander Kashlinsky at NASA's Goddard Space Flight Center in Greenbelt, Md., tracks this collective motion -- dubbed the "dark flow" -- to twice the distance originally reported, out to more than 2.5 billion light-years. Abell 1689, redshift 0.181. Credit: NASA/Goddard Space Flight Center/Scientific Visualization Studio/ESA/L. Bradley/JHU To learn more go to: www.nasa.gov/centers/goddard/news/releases/2010/10-023.html To see other visualizations related to this story go to: svs.gsfc.nasa.gov/goto?10580

VizieR Online Data Catalog: Magellan/M2FS spectroscopy of Abell 267 (Tucker+, 2017)

NASA Astrophysics Data System (ADS)

Tucker, E.; Walker, M. G.; Mateo, M.; Olszewski, E. W.; Bailey, J. I.; Crane, J. D.; Shectman, S. A.

2018-02-01

We select targets for Michigan/Magellan Fiber System (M2FS) observations by identifying galaxies detected in SDSS images (Data Release 12; Alam et al.2015, Cat. V/147) that are projected along the line of sight to Abell 267 and are likely to be quiescent cluster members. We observed 223 individual galaxy spectra on 2013 November 30 on the Clay Magellan Telescope using M2FS. We used the low-resolution grating on M2FS and chose a coverage range of 4600-6400Å with a resolution of R~2000. The detector used with M2FS consists of two 4096*4112 pixel CCDs. (1 data file).

The Kormendy relation of galaxies in the Frontier Fields clusters: Abell S1063 and MACS J1149.5+2223

NASA Astrophysics Data System (ADS)

Tortorelli, Luca; Mercurio, Amata; Paolillo, Maurizio; Rosati, Piero; Gargiulo, Adriana; Gobat, Raphael; Balestra, Italo; Caminha, G. B.; Annunziatella, Marianna; Grillo, Claudio; Lombardi, Marco; Nonino, Mario; Rettura, Alessandro; Sartoris, Barbara; Strazzullo, Veronica

2018-06-01

We analyse the Kormendy relations (KRs) of the two Frontier Fields clusters, Abell S1063, at z = 0.348, and MACS J1149.5+2223, at z = 0.542, exploiting very deep Hubble Space Telescope photometry and Very Large Telescope (VLT)/Multi Unit Spectroscopic Explorer (MUSE) integral field spectroscopy. With this novel data set, we are able to investigate how the KR parameters depend on the cluster galaxy sample selection and how this affects studies of galaxy evolution based on the KR. We define and compare four different galaxy samples according to (a) Sérsic indices: early-type (`ETG'), (b) visual inspection: `ellipticals', (c) colours: `red', (d) spectral properties: `passive'. The classification is performed for a complete sample of galaxies with mF814W ≤ 22.5 ABmag (M* ≳ 1010.0 M⊙). To derive robust galaxy structural parameters, we use two methods: (1) an iterative estimate of structural parameters using images of increasing size, in order to deal with closely separated galaxies and (2) different background estimations, to deal with the intracluster light contamination. The comparison between the KRs obtained from the different samples suggests that the sample selection could affect the estimate of the best-fitting KR parameters. The KR built with ETGs is fully consistent with the one obtained for ellipticals and passive. On the other hand, the KR slope built on the red sample is only marginally consistent with those obtained with the other samples. We also release the photometric catalogue with structural parameters for the galaxies included in the present analysis.

Revisiting Abell 2744: a powerful synergy of GLASS spectroscopy and HFF photometry

NASA Astrophysics Data System (ADS)

Wang, Xin; Wang

We present new emission line identifications and improve the lensing reconstruction of the mass distribution of galaxy cluster Abell 2744 using the Grism Lens-Amplified Survey from Space (GLASS) spectroscopy and the Hubble Frontier Fields (HFF) imaging. We performed blind and targeted searches for faint line emitters on all objects, including the arc sample, within the field of view (FoV) of GLASS prime pointings. We report 55 high quality spectroscopic redshifts, 5 of which are for arc images. We also present an extensive analysis based on the HFF photometry, measuring the colors and photometric redshifts of all objects within the FoV, and comparing the spectroscopic and photometric redshift estimates. In order to improve the lens model of Abell 2744, we develop a rigorous algorithm to screen arc images, based on their colors and morphology, and selecting the most reliable ones to use. As a result, 25 systems (corresponding to 72 images) pass the screening process and are used to reconstruct the gravitational potential of the cluster pixellated on an adaptive mesh. The resulting total mass distribution is compared with a stellar mass map obtained from the Spitzer Frontier Fields data in order to study the relative distribution of stars and dark matter in the cluster.

Characterizing the Small Scale Structure in Clusters of Galaxies

NASA Technical Reports Server (NTRS)

Forman, William R.

2001-01-01

We studied galaxy clusters Abell 119, Abell 754, and Abell 1750, using data from the ASCA and ROSAT satellites. In addition, we completed the paper "Merging Binary Clusters". In this paper we study three prominent bi-modal X-ray clusters: A3528, A1750 and A3395. Since the sub-clusters in these systems have projected separations of 0.93, 1.00 and 0.67 Mpc respectively, we examine their X-ray and optical observations to investigate the dynamics and possible merging of these sub-clusters. Using data taken with ROSAT and ASCA, we analyze the temperature and surface brightness distributions. We also analyze the velocity distributions of the three clusters using new measurements supplemented with previously published data. We examined both the overall cluster properties as well as the two sub-cluster elements in each. These results were then applied to the determination of the overall cluster masses, that demonstrate excellent consistency between the various methods used. While the characteristic parameters of the sub-clusters are typical of isolated objects, our temperature results for the regions between the two sub-clusters clearly confirm the presence of merger activity that is suggested by the surface brightness distributions. These three clusters represent a progression of equal-sized sub-cluster mergers, starting from initial contact to immediately before first core passage.

A photometric analysis of Abell 1689: two-dimensional multistructure decomposition, morphological classification and the Fundamental Plane

NASA Astrophysics Data System (ADS)

Dalla Bontà, E.; Davies, R. L.; Houghton, R. C. W.; D'Eugenio, F.; Méndez-Abreu, J.

2018-02-01

We present a photometric analysis of 65 galaxies in the rich cluster Abell 1689 at z = 0.183, using the Hubble Space Telescope Advanced Camera for Surveys archive images in the rest-frame V band. We perform two-dimensional multicomponent photometric decomposition of each galaxy adopting different models of the surface-brightness distribution. We present an accurate morphological classification for each of the sample galaxies. For 50 early-type galaxies, we fit both a de Vaucouleurs law and a Sérsic law; S0s are modelled by also including a disc component described by an exponential law. Bars of SB0s are described by the profile of a Ferrers ellipsoid. For the 15 spirals, we model a Sérsic bulge, exponential disc and, when required, a Ferrers bar component. We derive the Fundamental Plane (FP) by fitting 40 early-type galaxies in the sample, using different surface-brightness distributions. We find that the tightest plane is that derived by Sérsic bulges. We find that bulges of spirals lie on the same relation. The FP is better defined by the bulges alone rather than the entire galaxies. Comparison with local samples shows both an offset and rotation in the FP of Abell 1689.

Inverting ion images without Abel inversion: maximum entropy reconstruction of velocity maps.

PubMed

Dick, Bernhard

2014-01-14

A new method for the reconstruction of velocity maps from ion images is presented, which is based on the maximum entropy concept. In contrast to other methods used for Abel inversion the new method never applies an inversion or smoothing to the data. Instead, it iteratively finds the map which is the most likely cause for the observed data, using the correct likelihood criterion for data sampled from a Poissonian distribution. The entropy criterion minimizes the information content in this map, which hence contains no information for which there is no evidence in the data. Two implementations are proposed, and their performance is demonstrated with simulated and experimental data: Maximum Entropy Velocity Image Reconstruction (MEVIR) obtains a two-dimensional slice through the velocity distribution and can be compared directly to Abel inversion. Maximum Entropy Velocity Legendre Reconstruction (MEVELER) finds one-dimensional distribution functions Q(l)(v) in an expansion of the velocity distribution in Legendre polynomials P((cos θ) for the angular dependence. Both MEVIR and MEVELER can be used for the analysis of ion images with intensities as low as 0.01 counts per pixel, with MEVELER performing significantly better than MEVIR for images with low intensity. Both methods perform better than pBASEX, in particular for images with less than one average count per pixel.

Search For Cosmic-Ray-Induced Gamma-Ray Emission In Galaxy Clusters

DOE PAGES

Ackermann, M.

2014-04-30

Current theories predict relativistic hadronic particle populations in clusters of galaxies in addition to the already observed relativistic leptons. In these scenarios hadronic interactions give rise to neutral pions which decay into rays that are potentially observable with the Large Area Telescope (LAT) on board the Fermi space telescope. We present a joint likelihood analysis searching for spatially extended γ-ray emission at the locations of 50 galaxy clusters in 4 years of Fermi-LAT data under the assumption of the universal cosmic-ray model proposed by Pinzke & Pfrommer (2010). We find an excess at a significance of 2.7 σ which uponmore » closer inspection is however correlated to individual excess emission towards three galaxy clusters: Abell 400, Abell 1367 and Abell 3112. We discuss these cases in detail and conservatively attribute the emission to unmodeled background (for example, radio galaxies within the clusters). Through the combined analysis of 50 clusters we exclude hadronic injection efficiencies in simple hadronic models above 21% and establish limits on the cosmic-ray to thermal pressure ratio within the virial radius, R200, to be below 1.2-1.4% depending on the morphological classification. In addition we derive new limits on the γ-ray flux from individual clusters in our sample.« less

Chandra Observation of the WAT Radio Source/ICM Interaction in Abell 623

NASA Astrophysics Data System (ADS)

Anand, Gagandeep; Blanton, Elizabeth L.; Randall, Scott W.; Paterno-Mahler, Rachel; Douglass, Edmund

2017-01-01

Galaxy clusters are important objects for studying the physics of the intracluster medium (ICM), galaxy formation and evolution, and cosmological parameters. Clusters containing wide-angle tail (WAT) radio sources are particularly valuable for studies of the interaction between these sources and the surrounding ICM. These sources are thought to form when the ram pressure from the ICM caused by the relative motion between the host radio galaxy and the cluster bends the radio lobes into a distinct wide-angle morphology. We present our results from the analysis of a Chandra observation of the nearby WAT hosting galaxy cluster Abell 623. A clear decrement in X-ray emission is coincident with the southern radio lobe, consistent with being a cavity carved out by the radio source. We present profiles of surface brightness, temperature, density, and pressure and find evidence for a possible shock. Based on the X-ray pressure in the vicinity of the radio lobes and assumptions about the content of the lobes, we estimate the relative ICM velocity required to bend the lobes into the observed angle. We also present spectral model fits to the overall diffuse cluster emission and see no strong signature for a cool core. The sum of the evidence indicates that Abell 623 may be undergoing a large scale cluster-cluster merger.

Color Dispersion as an Indicator of Stellar Population Complexity: Insights from the Pixel Color–Magnitude Diagrams of 32 Bright Galaxies in Abell 1139 and Abell 2589

NASA Astrophysics Data System (ADS)

Lee, Joon Hyeop; Pak, Mina; Lee, Hye-Ran; Oh, Sree

2018-04-01

We investigate the properties of bright galaxies of various morphological types in Abell 1139 and Abell 2589, using pixel color–magnitude diagram (pCMD) analysis. The sample contains 32 galaxies brighter than M r = ‑21.3 mag with spectroscopic redshifts, which are deeply imaged in the g and r bands using the MegaCam mounted on the Canada–France–Hawaii Telescope. After masking contaminants with two-step procedures, we examine how the detailed properties in the pCMDs depend on galaxy morphology and infrared color. The mean g ‑ r color as a function of surface brightness (μ r ) in the pCMD of a galaxy shows good performance in distinguishing between early- and late-type galaxies, but it is not perfect because of the similarity between elliptical galaxies and bulge-dominated spiral galaxies. On the other hand, the g ‑ r color dispersion as a function of μ r works better. We find that the best set of parameters for galaxy classification is a combination of the minimum color dispersion at μ r ≤ 21.2 mag arcsec‑2 and the maximum color dispersion at 20.0 ≤ μ r ≤ 21.0 mag arcsec‑2 the latter reflects the complexity of stellar populations at the disk component in a typical spiral galaxy. Finally, the color dispersion measurements of an elliptical galaxy appear to be correlated with the Wide-field Infrared Survey Explorer infrared color ([4.6]–[12]). This indicates that the complexity of stellar populations in an elliptical galaxy is related to its recent star formation activities. From this observational evidence, we infer that gas-rich minor mergers or gas interactions may have usually occurred during the recent growth of massive elliptical galaxies.

Pixel Color–Magnitude Diagram Analysis of the Brightest Cluster Galaxies in Dynamically Young and Old Clusters Abell 1139 and Abell 2589

NASA Astrophysics Data System (ADS)

Lee, Joon Hyeop; Oh, Sree; Jeong, Hyunjin; Yi, Sukyoung K.; Kyeong, Jaemann; Park, Byeong-Gon

2017-07-01

As a case study to understand the coevolution of Brightest Cluster Galaxies (BCGs) and their host clusters, we investigate the BCGs in dynamically young and old clusters Abell 1139 (A1139) and Abell 2589 (A2589). We analyze the pixel color–magnitude diagrams (pCMDs) using deep g- and r-band images, obtained from the Canada–France–Hawaii Telescope observations. After masking foreground/background objects and smoothing pixels in consideration of the observational seeing size, detailed pCMD features are compared between the two BCGs. (1) Although the overall shapes of the pCMDs are similar to those of typical early-type galaxies, the A2589-BCG tends to have redder mean pixel color and smaller pixel color deviation at given surface brightness than the A1139-BCG. (2) The mean pixel color distribution as a function of pixel surface brightness (pCMD backbone) indicates that the A2589-BCG formed a larger central body (∼2.0 kpc in radius) via major dry mergers at an early epoch than the A1139-BCG (a central body ∼1.3 kpc in radius), whereas they have grown commonly in subsequent minor mergers. (3) The spatial distributions of the pCMD outliers reveal that the A1139-BCG experienced considerable tidal events more recently than the A2589-BCG, whereas the A2589-BCG has an asymmetric compact core, possibly resulting from a major dry merger at an early epoch. (4) The A2589-BCG shows a very large faint-to-bright pixel number ratio, compared to early-type non-BCGs, whereas the ratio for the A1139-BCG is not distinctively large. These results are consistent with the idea that the BCG in the dynamically older cluster (A2589) formed earlier and is better relaxed.

Deformation analysis of polymers composites: rheological model involving time-based fractional derivative

NASA Astrophysics Data System (ADS)

Zhou, H. W.; Yi, H. Y.; Mishnaevsky, L.; Wang, R.; Duan, Z. Q.; Chen, Q.

2017-05-01

A modeling approach to time-dependent property of Glass Fiber Reinforced Polymers (GFRP) composites is of special interest for quantitative description of long-term behavior. An electronic creep machine is employed to investigate the time-dependent deformation of four specimens of dog-bond-shaped GFRP composites at various stress level. A negative exponent function based on structural changes is introduced to describe the damage evolution of material properties in the process of creep test. Accordingly, a new creep constitutive equation, referred to fractional derivative Maxwell model, is suggested to characterize the time-dependent behavior of GFRP composites by replacing Newtonian dashpot with the Abel dashpot in the classical Maxwell model. The analytic solution for the fractional derivative Maxwell model is given and the relative parameters are determined. The results estimated by the fractional derivative Maxwell model proposed in the paper are in a good agreement with the experimental data. It is shown that the new creep constitutive model proposed in the paper needs few parameters to represent various time-dependent behaviors.

Dynamical Effects of the Scale Invariance of the Empty Space: The Fall of Dark Matter?

NASA Astrophysics Data System (ADS)

Maeder, Andre

2017-11-01

The hypothesis of the scale invariance of the macroscopic empty space, which intervenes through the cosmological constant, has led to new cosmological models. They show an accelerated cosmic expansion after the initial stages and satisfy several major cosmological tests. No unknown particles are needed. Developing the weak-field approximation, we find that the here-derived equation of motion corresponding to Newton’s equation also contains a small outward acceleration term. Its order of magnitude is about \\sqrt{{\\varrho }{{c}}/\\varrho } × Newton’s gravity (ϱ being the mean density of the system and {\\varrho }{{c}} the usual critical density). The new term is thus particularly significant for very low density systems. A modified virial theorem is derived and applied to clusters of galaxies. For the Coma Cluster and Abell 2029, the dynamical masses are about a factor of 5-10 smaller than in the standard case. This tends to leave no room for dark matter in these clusters. Then, the two-body problem is studied and an equation corresponding to the Binet equation is obtained. It implies some secular variations of the orbital parameters. The results are applied to the rotation curve of the outer layers of the Milky Way. Starting backward from the present rotation curve, we calculate the past evolution of the Galactic rotation and find that, in the early stages, it was steep and Keplerian. Thus, the flat rotation curves of galaxies appear as an age effect, a result consistent with recent observations of distant galaxies by Genzel et al. and Lang et al. Finally, in an appendix we also study the long-standing problem of the increase with age of the vertical velocity dispersion in the Galaxy. The observed increase appears to result from the new small acceleration term in the equation of the harmonic oscillator describing stellar motions around the Galactic plane. Thus, we tend to conclude that neither dark energy nor dark matter seems to be needed in the proposed theoretical context.

A comparison of techniques for inversion of radio-ray phase data in presence of ray bending

NASA Technical Reports Server (NTRS)

Wallio, H. A.; Grossi, M. D.

1972-01-01

Derivations are presented of the straight-line Abel transform and the seismological Herglotz-Wiechert transform (which takes ray bending into account) that are used in the reconstruction of refractivity profiles from radio-wave phase data. Profile inversion utilizing these approaches, performed in computer-simulated experiments, are compared for cases of positive, zero, and negative ray bending. For thin atmospheres and ionospheres, such as the Martian atmosphere and ionosphere, radio wave signals are shown to be inverted accurately with both methods. For dense media, such as the solar corona or the lower Venus atmosphere, the refractive recovered by the seismological Herglotz-Wiechert transform provide a significant improvement compared with the straight-line Abel transform.

Study of the technique of stellar occultation

NASA Technical Reports Server (NTRS)

Hays, P. B.; Graves, M. E.; Roble, R. G.; Shah, A. N.

1973-01-01

The results are reported of a study of the stellar occultation technique for measuring the composition of the atmosphere. The intensity of starlight was monitored during the occultation using the Wisconsin stellar ultraviolet photometers aboard the Orbiting Astronomical Observatory (OAO-A2). A schematic diagram of an occultation is shown where the change in intensity at a given wavelength is illustrated. The vertical projection of the attenuation region is typically 60 km deep for molecular oxygen and 30 km deep for ozone. Intensity profiles obtained during various occultations were analyzed by first determining the tangential columm density of the absorbing gases, and then Abel inverting the column densities to obtain the number density profile. Errors are associated with each step in the inversion scheme and have been considered as an integral part of this study.

A new integrable equation combining the modified KdV equation with the negative-order modified KdV equation: multiple soliton solutions and a variety of solitonic solutions

NASA Astrophysics Data System (ADS)

Wazwaz, Abdul-Majid

2018-07-01

A new third-order integrable equation is constructed via combining the recursion operator of the modified KdV equation (MKdV) and its inverse recursion operator. The developed equation will be termed the modified KdV-negative order modified KdV equation (MKdV-nMKdV). The complete integrability of this equation is confirmed by showing that it nicely possesses the Painlevé property. We obtain multiple soliton solutions for the newly developed integrable equation. Moreover, this equation enjoys a variety of solutions which include solitons, peakons, cuspons, negaton, positon, complexiton and other solutions.

On integrability of the Killing equation

NASA Astrophysics Data System (ADS)

Houri, Tsuyoshi; Tomoda, Kentaro; Yasui, Yukinori

2018-04-01

Killing tensor fields have been thought of as describing the hidden symmetry of space(-time) since they are in one-to-one correspondence with polynomial first integrals of geodesic equations. Since many problems in classical mechanics can be formulated as geodesic problems in curved space and spacetime, solving the defining equation for Killing tensor fields (the Killing equation) is a powerful way to integrate equations of motion. Thus it has been desirable to formulate the integrability conditions of the Killing equation, which serve to determine the number of linearly independent solutions and also to restrict the possible forms of solutions tightly. In this paper, we show the prolongation for the Killing equation in a manner that uses Young symmetrizers. Using the prolonged equations, we provide the integrability conditions explicitly.

Cosmogenic nuclide dating of Sahelanthropus tchadensis and Australopithecus bahrelghazali: Mio-Pliocene hominids from Chad

PubMed Central

Lebatard, Anne-Elisabeth; Bourlès, Didier L.; Duringer, Philippe; Jolivet, Marc; Braucher, Régis; Carcaillet, Julien; Schuster, Mathieu; Arnaud, Nicolas; Monié, Patrick; Lihoreau, Fabrice; Likius, Andossa; Mackaye, Hassan Taisso; Vignaud, Patrick; Brunet, Michel

2008-01-01

Ages were determined at two hominid localities from the Chad Basin in the Djurab Desert (Northern Chad). In the Koro Toro fossiliferous area, KT 12 locality (16°00′N, 18°53′E) was the site of discovery of Australopithecus bahrelghazali (Abel) and in the Toros-Menalla fossiliferous area, TM 266 locality (16°15′N, 17°29′E) was the site of discovery of Sahelanthropus tchadensis (Toumaï). At both localities, the evolutive degree of the associated fossil mammal assemblages allowed a biochronological estimation of the hominid remains: early Pliocene (3–3.5 Ma) at KT 12 and late Miocene (≈7 Ma) at TM 266. Atmospheric 10Be, a cosmogenic nuclide, was used to quasicontinuously date these sedimentary units. The authigenic 10Be/9Be dating of a pelite relic within the sedimentary level containing Abel yields an age of 3.58 ± 0.27 Ma that points to the contemporaneity of Australopithecus bahrelghazali (Abel) with Australopithecus afarensis (Lucy). The 28 10Be/9Be ages obtained within the anthracotheriid unit containing Toumaï bracket, by absolute dating, the age of Sahelanthropus tchadensis to lie between 6.8 and 7.2 Ma. This chronological constraint is an important cornerstone both for establishing the earliest stages of hominid evolution and for new calibrations of the molecular clock. PMID:18305174

Quantum integrability and functional equations

NASA Astrophysics Data System (ADS)

Volin, Dmytro

2010-03-01

In this thesis a general procedure to represent the integral Bethe Ansatz equations in the form of the Reimann-Hilbert problem is given. This allows us to study in simple way integrable spin chains in the thermodynamic limit. Based on the functional equations we give the procedure that allows finding the subleading orders in the solution of various integral equations solved to the leading order by the Wiener-Hopf technics. The integral equations are studied in the context of the AdS/CFT correspondence, where their solution allows verification of the integrability conjecture up to two loops of the strong coupling expansion. In the context of the two-dimensional sigma models we analyze the large-order behavior of the asymptotic perturbative expansion. Obtained experience with the functional representation of the integral equations allowed us also to solve explicitly the crossing equations that appear in the AdS/CFT spectral problem.

Abell 1367: a high fraction of late-type galaxies displaying H I morphological and kinematic perturbations

NASA Astrophysics Data System (ADS)

Scott, T. C.; Brinks, E.; Cortese, L.; Boselli, A.; Bravo-Alfaro, H.

2018-04-01

To investigate the effects the cluster environment has on late-type galaxies (LTGs), we studied H I perturbation signatures for all Abell 1367 LTGs with H I detections. We used new Very Large Array H I observations combined with AGES single-dish blind survey data. Our study indicates that the asymmetry between the high- and low-velocity wings of the characteristic double-horn-integrated H I spectrum as measured by the asymmetry parameter, A_{flux}, can be a useful diagnostic for ongoing and/or recent H I stripping. 26 per cent of A1367 LTGs have an A_{flux} ratio, more asymmetrical than 3 times the 1σ spread in the A_{flux} ratio distribution of an undisturbed sample of isolated galaxies (2 per cent) and samples from other denser environments (10 per cent-20 per cent). Over half of the A1367 LTGs, which are members of groups or pairs, have an A_{flux} ratio larger than twice the 1σ spread found in the isolated sample. This suggests intergroup/pair interactions could be making a significant contribution to the LTGs displaying such A_{flux} ratios. The study also demonstrates that the definition of the H I offset from the optical centre of LTGs is resolution dependent, suggesting that unresolved AGES H I offsets that are significantly larger than the pointing uncertainties (>2σ), reflect interactions which have asymmetrically displaced, significant masses of lower density H I, while having minimal impact on the location of the highest density H I in resolved maps. The distribution of A_{flux} from a comparable sample of Virgo galaxies provides a clear indication that the frequency of H I profile perturbations is lower than in A1367.

VLA Radio Observations of the HST Frontier Fields Cluster Abell 2744: The Discovery of New Radio Relics

NASA Astrophysics Data System (ADS)

Pearce, C. J. J.; van Weeren, R. J.; Andrade-Santos, F.; Jones, C.; Forman, W. R.; Brüggen, M.; Bulbul, E.; Clarke, T. E.; Kraft, R. P.; Medezinski, E.; Mroczkowski, T.; Nonino, M.; Nulsen, P. E. J.; Randall, S. W.; Umetsu, K.

2017-08-01

Cluster mergers leave distinct signatures in the intracluster medium (ICM) in the form of shocks and diffuse cluster radio sources that provide evidence for the acceleration of relativistic particles. However, the physics of particle acceleration in the ICM is still not fully understood. Here we present new 1-4 GHz Jansky Very Large Array (VLA) and archival Chandra observations of the HST Frontier Fields Cluster Abell 2744. In our new VLA images, we detect the previously known ˜2.1 Mpc radio halo and ˜1.5 Mpc radio relic. We carry out a radio spectral analysis from which we determine the relic’s injection spectral index to be {α }{inj}=-1.12+/- 0.19. This corresponds to a shock Mach number of { M }={2.05}-0.19+0.31 under the assumption of diffusive shock acceleration. We also find evidence for spectral steepening in the post-shock region. We do not find evidence for a significant correlation between the radio halo’s spectral index and ICM temperature. In addition, we observe three new polarized diffuse sources and determine two of these to be newly discovered giant radio relics. These two relics are located in the southeastern and northwestern outskirts of the cluster. The corresponding integrated spectral indices measure -1.81 ± 0.26 and -0.63 ± 0.21 for the SE and NW relics, respectively. From an X-ray surface brightness profile we also detect a possible density jump of R={1.39}-0.22+0.34 co-located with the newly discovered SE relic. This density jump would correspond to a shock front Mach number of { M }={1.26}-0.15+0.25.

Television documentary, history and memory. An analysis of Sergio Zavoli's The Gardens of Abel.

PubMed

Foot, John

2014-10-20

This article examines a celebrated documentary made for Italian state TV in 1968 and transmitted in 1969 to an audience of millions. The programme - The Gardens of Abel - looked at changes introduced by the radical psychiatrist Franco Basaglia in an asylum in the north-east of Italy (Gorizia). The article examines the content of this programme for the first time, questions some of the claims that have been made for it, and outlines the sources used by the director, Sergio Zavoli. The article argues that the film was as much an expression of Zavoli's vision and ideas as it was linked to those of Franco Basaglia himself. Finally, the article highlights the way that this programme has become part of historical discourse and popular memory.

The cD galaxy in Abell cluster 1775

NASA Technical Reports Server (NTRS)

Hayes, J. J. E.; Bhattacharya, B.

1990-01-01

Over the last 20 years, a number of workers have studied the multiple nuclei cD galaxy in the rich Abell cluster 1775, trying to discover its nature. In all the cases though, very little has been published concerning its morphology. The majority of arguments about the nature of this object have been based on the relative radial velocities of the 2 components with each other and with the other galaxies in the cluster, or its radio morphology. Very little work has been done on the optical morphology. To rectify that lack of data, the authors have obtained charge coupled device (CCD) images of the cD. The authors find from the CCD data that the cD is unlikely to be a bound object and that there is strong evidence for a collision.

Evolution of the UV upturn in cluster galaxies: Abell 1689

NASA Astrophysics Data System (ADS)

Ali, S. S.; Bremer, M. N.; Phillipps, S.; De Propris, R.

2018-05-01

We have measured the strength of the UV upturn for red sequence galaxies in the Abell 1689 cluster at z = 0.18, reaching to or below the L* level and therefore probing the general evolution of the upturn phenomenon. We find that the range of UV upturn strengths in the population as a whole has not declined over the past 2.2 Gyrs. This is consistent with a model where hot horizontal branch stars, produced by a Helium-enriched population, provide the required UV flux. Based on local counterparts, this interpretation of the result implies Helium abundances of at least 1.5 times the primordial value for this HB population, along with high formation and assembly redshifts for the galaxies and at least a subset of their stellar populations.

Inhibition of α-glucosidase by polysaccharides from the fruit hull of Camellia oleifera Abel.

PubMed

Zhang, Sheng; Li, Xiang-Zhou

2015-01-22

We isolated and purified polysaccharides from the Camellia oleifera Abel. fruit hull and studied its hypoglycemic potential. Our results revealed six polysaccharides (CFPA-1-5 & CFPB) from the aqueous extract from the defatted C. oleifera fruit hull. Purified polysaccharides (purity >90%) were investigated for the inhibition of α-glucosidase activity in vitro. Two polysaccharides, CFPB and CFPA-3 were present in high concentration in the fruit hull and showed a dose-dependent inhibition of α-glucosidase activity, with IC50 concentrations of 11.80 and 10.95 μg/mL, respectively. This result suggests that polysaccharides (CFP) extracted from the fruit hull of C. oleifera may have potential as functional foods with featuring a hypoglycemic effect. Copyright © 2014 Elsevier Ltd. All rights reserved.

Television documentary, history and memory. An analysis of Sergio Zavoli's The Gardens of Abel

PubMed Central

Foot, John

2014-01-01

This article examines a celebrated documentary made for Italian state TV in 1968 and transmitted in 1969 to an audience of millions. The programme – The Gardens of Abel – looked at changes introduced by the radical psychiatrist Franco Basaglia in an asylum in the north-east of Italy (Gorizia). The article examines the content of this programme for the first time, questions some of the claims that have been made for it, and outlines the sources used by the director, Sergio Zavoli. The article argues that the film was as much an expression of Zavoli's vision and ideas as it was linked to those of Franco Basaglia himself. Finally, the article highlights the way that this programme has become part of historical discourse and popular memory. PMID:25937804

Profile inversion in presence of ray bending

NASA Technical Reports Server (NTRS)

Wallio, H. A.; Grossi, M. D.

1972-01-01

Inversion of radio occultation data for planetary atmospheres and ionospheres has been performed using the seismological Herglotz-Wiechert method, as adapted by Phinney and Anderson to the radio-occultation case. Profile reconstruction performed in computer simulated experiments with this approach have been compared with the ones obtained with the straight-ray Abel transform. For a thin atmosphere and ionosphere, like the ones encountered on Mars, microwave occultation data can be inverted accurately with both methods. For a dense ionosphere like the sun's corona, ray bending of microwaves is severe, and recovered refractivity by the Herglotz-Wiechert method provides significant improvement over the straight-ray Abel transform: the error reduces from more than 60% to less than 20% at a height of 60,000 km above the base of the corona.

Explicit solution of integrated 1 - exp equation for predicting accumulation and decline of concentrations for drugs obeying nonlinear saturation kinetics.

PubMed

Keller, Frieder; Hartmann, Bertram; Czock, David

2009-12-01

To describe nonlinear, saturable pharmacokinetics, the Michaelis-Menten equation is frequently used. However, the Michaelis-Menten equation has no integrated solution for concentrations but only for the time factor. Application of the Lambert W function was proposed recently to obtain an integrated solution of the Michaelis-Menten equation. As an alternative to the Michaelis-Menten equation, a 1 - exp equation has been used to describe saturable kinetics, with the advantage that the integrated 1 - exp equation has an explicit solution for concentrations. We used the integrated 1 - exp equation to predict the accumulation kinetics and the nonlinear concentration decline for a proposed fictive drug. In agreement with the recently proposed method, we found that for the integrated 1 - exp equation no steady state is obtained if the maximum rate of change in concentrations (Vmax) within interval (Tau) is less than the difference between peak and trough concentrations (Vmax x Tau < C peak - C trough).

RADIO AND DEEP CHANDRA OBSERVATIONS OF THE DISTURBED COOL CORE CLUSTER ABELL 133

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

Randall, S. W.; Nulsen, P. E. J.; Forman, W. R.

2010-10-10

We present results based on new Chandra and multi-frequency radio observations of the disturbed cool core cluster Abell 133. The diffuse gas has a complex bird-like morphology, with a plume of emission extending from two symmetric wing-like features. The plume is capped with a filamentary radio structure that has been previously classified as a radio relic. X-ray spectral fits in the region of the relic indicate the presence of either high-temperature gas or non-thermal emission, although the measured photon index is flatter than would be expected if the non-thermal emission is from inverse Compton scattering of the cosmic microwave backgroundmore » by the radio-emitting particles. We find evidence for a weak elliptical X-ray surface brightness edge surrounding the core, which we show is consistent with a sloshing cold front. The plume is consistent with having formed due to uplift by a buoyantly rising radio bubble, now seen as the radio relic, and has properties consistent with buoyantly lifted plumes seen in other systems (e.g., M87). Alternatively, the plume may be a gas sloshing spiral viewed edge-on. Results from spectral analysis of the wing-like features are inconsistent with the previous suggestion that the wings formed due to the passage of a weak shock through the cool core. We instead conclude that the wings are due to X-ray cavities formed by displacement of X-ray gas by the radio relic. The central cD galaxy contains two small-scale cold gas clumps that are slightly offset from their optical and UV counterparts, suggestive of a galaxy-galaxy merger event. On larger scales, there is evidence for cluster substructure in both optical observations and the X-ray temperature map. We suggest that the Abell 133 cluster has recently undergone a merger event with an interloping subgroup, initialing gas sloshing in the core. The torus of sloshed gas is seen close to edge-on, leading to the somewhat ragged appearance of the elliptical surface brightness edge. We show that the additional buoyant force from a passing subcluster can have a significant effect on the rise trajectories of buoyant bubbles, although this effect alone cannot fully explain the morphology of Abell 133. The radio observations reveal a large-scale double-lobed structure not previously identified in the literature. We conclude that this structure represents a previously unreported background giant radio galaxy at z = 0.293, the northern lobe of which overlies the radio relic in the core of Abell 133. A rough estimate indicates that the contribution of this background lobe to the total radio emission in the region of the relic is modest (<13%).« less

On the integration of a class of nonlinear systems of ordinary differential equations

NASA Astrophysics Data System (ADS)

Talyshev, Aleksandr A.

2017-11-01

For each associative, commutative, and unitary algebra over the field of real or complex numbers and an integrable nonlinear ordinary differential equation we can to construct integrable systems of ordinary differential equations and integrable systems of partial differential equations. In this paper we consider in some sense the inverse problem. Determine the conditions under which a given system of ordinary differential equations can be represented as a differential equation in some associative, commutative and unitary algebra. It is also shown that associativity is not a necessary condition.

Large Scale Structure Studies: Final Results from a Rich Cluster Redshift Survey

NASA Astrophysics Data System (ADS)

Slinglend, K.; Batuski, D.; Haase, S.; Hill, J.

1995-12-01

The results from the COBE satellite show the existence of structure on scales on the order of 10% or more of the horizon scale of the universe. Rich clusters of galaxies from the Abell-ACO catalogs show evidence of structure on scales of 100 Mpc and hold the promise of confirming structure on the scale of the COBE result. Unfortunately, until now, redshift information has been unavailable for a large percentage of these clusters, so present knowledge of their three dimensional distribution has quite large uncertainties. Our approach in this effort has been to use the MX multifiber spectrometer on the Steward 2.3m to measure redshifts of at least ten galaxies in each of 88 Abell cluster fields with richness class R>= 1 and mag10 <= 16.8 (estimated z<= 0.12) and zero or one measured redshifts. This work has resulted in a deeper, 95% complete and more reliable sample of 3-D positions of rich clusters. The primary intent of this survey has been to constrain theoretical models for the formation of the structure we see in the universe today through 2-pt. spatial correlation function and other analyses of the large scale structures traced by these clusters. In addition, we have obtained enough redshifts per cluster to greatly improve the quality and size of the sample of reliable cluster velocity dispersions available for use in other studies of cluster properties. This new data has also allowed the construction of an updated and more reliable supercluster candidate catalog. Our efforts have resulted in effectively doubling the volume traced by these clusters. Presented here is the resulting 2-pt. spatial correlation function, as well as density plots and several other figures quantifying the large scale structure from this much deeper and complete sample. Also, with 10 or more redshifts in most of our cluster fields, we have investigated the extent of projection effects within the Abell catalog in an effort to quantify and understand how this may effect the Abell sample.

The cluster Abell 780: an optical view

NASA Astrophysics Data System (ADS)

Durret, F.; Slezak, E.; Adami, C.

2009-11-01

Context: The Abell 780 cluster, better known as the Hydra A cluster, has been thouroughly analyzed in X-rays. However, little is known about its optical properties. Aims: We propose to derive the galaxy luminosity function (GLF) in this apparently relaxed cluster and to search for possible environmental effects by comparing the GLFs in various regions and by looking at the galaxy distribution at large scale around Abell 780. Methods: Our study is based on optical images obtained with the ESO 2.2m telescope and WFI camera in the B and R bands, covering a total region of 67.22 × 32.94 arcmin^2, or 4.235 × 2.075 Mpc2 for a cluster redshift of 0.0539. Results: In a region of 500 kpc radius around the cluster center, the GLF in the R band shows a double structure, with a broad and flat bright part and a flat faint end that can be fit by a power law with an index α ~ - 0.85 ± 0.12 in the 20.25 ≤ R ≤ 21.75 interval. If we divide this 500 kpc radius region in north+south or east+west halves, we find no clear difference between the GLFs in these smaller regions. No obvious large-scale structure is apparent within 5 Mpc from the cluster, based on galaxy redshifts and magnitudes collected from the NED database in a much larger region than that covered by our data, suggesting that there is no major infall of material in any preferential direction. However, the Serna-Gerbal method reveals a gravitationally bound structure of 27 galaxies, which includes the cD, and of a more strongly gravitationally bound structure of 14 galaxies. Conclusions: These optical results agree with the overall relaxed structure of Abell 780 previously derived from X-ray analyses. Based on observations obtained at the European Southern Observatory, program ESO 68.A-0084(A), P. I. E. Slezak. This research has made use of the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.

Dynamics of a differential-difference integrable (2+1)-dimensional system.

PubMed

Yu, Guo-Fu; Xu, Zong-Wei

2015-06-01

A Kadomtsev-Petviashvili- (KP-) type equation appears in fluid mechanics, plasma physics, and gas dynamics. In this paper, we propose an integrable semidiscrete analog of a coupled (2+1)-dimensional system which is related to the KP equation and the Zakharov equation. N-soliton solutions of the discrete equation are presented. Some interesting examples of soliton resonance related to the two-soliton and three-soliton solutions are investigated. Numerical computations using the integrable semidiscrete equation are performed. It is shown that the integrable semidiscrete equation gives very accurate numerical results in the cases of one-soliton evolution and soliton interactions.

Determination of elementary first integrals of a generalized Raychaudhuri equation by the Darboux integrability method

NASA Astrophysics Data System (ADS)

Choudhury, A. Ghose; Guha, Partha; Khanra, Barun

2009-10-01

The Darboux integrability method is particularly useful to determine first integrals of nonplanar autonomous systems of ordinary differential equations, whose associated vector fields are polynomials. In particular, we obtain first integrals for a variant of the generalized Raychaudhuri equation, which has appeared in string inspired modern cosmology.

Two-dimensional integrating matrices on rectangular grids. [solving differential equations associated with rotating structures

NASA Technical Reports Server (NTRS)

Lakin, W. D.

1981-01-01

The use of integrating matrices in solving differential equations associated with rotating beam configurations is examined. In vibration problems, by expressing the equations of motion of the beam in matrix notation, utilizing the integrating matrix as an operator, and applying the boundary conditions, the spatial dependence is removed from the governing partial differential equations and the resulting ordinary differential equations can be cast into standard eigenvalue form. Integrating matrices are derived based on two dimensional rectangular grids with arbitrary grid spacings allowed in one direction. The derivation of higher dimensional integrating matrices is the initial step in the generalization of the integrating matrix methodology to vibration and stability problems involving plates and shells.

X-ray constraints on the shape of the dark matter in five Abell clusters

NASA Technical Reports Server (NTRS)

Buote, David A.; Canizares, Claude R.

1992-01-01

X-ray observations obtained with the Einstein Observatory are used to constrain the shape of the dark matter in the inner regions of Abell clusters A401, A426, A1656, A2029, and A2199, each of which exhibits highly flattened optical isopleths. The dark matter is modeled as an ellipsoid with a mass density of about r exp -2. The possible shapes of the dark matter is constrained by comparing these model isophotes to the image isophotes. The X-ray isophotes, and therefore the gravitational potentials, have ellipticities of about 0.1-0.2. The dark matter within the central 1 Mpc is found to be substantially rounder for all the clusters. It is concluded that the shape of the galaxy distributions in these clusters traces neither the gravitational potential nor the gravitating matter.

Application of a XMM-Newton EPIC Monte Carlo to Analysis And Interpretation of Data for Abell 1689, RXJ0658-55 And the Centaurus Clusters of Galaxies

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

Andersson, Karl E.; /Stockholm U. /SLAC; Peterson, J.R.

2007-04-17

We propose a new Monte Carlo method to study extended X-ray sources with the European Photon Imaging Camera (EPIC) aboard XMM Newton. The Smoothed Particle Inference (SPI) technique, described in a companion paper, is applied here to the EPIC data for the clusters of galaxies Abell 1689, Centaurus and RXJ 0658-55 (the ''bullet cluster''). We aim to show the advantages of this method of simultaneous spectral-spatial modeling over traditional X-ray spectral analysis. In Abell 1689 we confirm our earlier findings about structure in temperature distribution and produce a high resolution temperature map. We also confirm our findings about velocity structuremore » within the gas. In the bullet cluster, RXJ 0658-55, we produce the highest resolution temperature map ever to be published of this cluster allowing us to trace what looks like the motion of the bullet in the cluster. We even detect a south to north temperature gradient within the bullet itself. In the Centaurus cluster we detect, by dividing up the luminosity of the cluster in bands of gas temperatures, a striking feature to the north-east of the cluster core. We hypothesize that this feature is caused by a subcluster left over from a substantial merger that slightly displaced the core. We conclude that our method is very powerful in determining the spatial distributions of plasma temperatures and very useful for systematic studies in cluster structure.« less

Illuminating a Dark Lens : A Type Ia Supernova Magnified by the Frontier Fields Galaxy Cluster Abell 2744

NASA Astrophysics Data System (ADS)

Rodney, Steven A.; Patel, Brandon; Scolnic, Daniel; Foley, Ryan J.; Molino, Alberto; Brammer, Gabriel; Jauzac, Mathilde; Bradač, Maruša; Broadhurst, Tom; Coe, Dan; Diego, Jose M.; Graur, Or; Hjorth, Jens; Hoag, Austin; Jha, Saurabh W.; Johnson, Traci L.; Kelly, Patrick; Lam, Daniel; McCully, Curtis; Medezinski, Elinor; Meneghetti, Massimo; Merten, Julian; Richard, Johan; Riess, Adam; Sharon, Keren; Strolger, Louis-Gregory; Treu, Tommaso; Wang, Xin; Williams, Liliya L. R.; Zitrin, Adi

2015-09-01

SN HFF14Tom is a Type Ia SN discovered at z=1.3457+/- 0.0001 behind the galaxy cluster Abell 2744 (z = 0.308). In a cosmology-independent analysis, we find that HFF14Tom is 0.77 ± 0.15 mag brighter than unlensed Type Ia SNe at similar redshift, implying a lensing magnification of {μ }{obs}=2.03+/- 0.29. This observed magnification provides a rare opportunity for a direct empirical test of galaxy cluster lens models. Here we test 17 lens models, 13 of which were generated before the SN magnification was known, qualifying as pure “blind tests.” The models are collectively fairly accurate: 8 of the models deliver median magnifications that are consistent with the measured μ to within 1σ. However, there is a subtle systematic bias: the significant disagreements all involve models overpredicting the magnification. We evaluate possible causes for this mild bias, and find no single physical or methodological explanation to account for it. We do find that model accuracy can be improved to some extent with stringent quality cuts on multiply imaged systems, such as requiring that a large fraction have spectroscopic redshifts. In addition to testing model accuracies as we have done here, Type Ia SN magnifications could also be used as inputs for future lens models of Abell 2744 and other clusters, providing valuable constraints in regions where traditional strong- and weak-lensing information is unavailable.

The near-infrared Tully-Fisher relation - A preliminary study of the Coma and Abell 400 clusters

NASA Technical Reports Server (NTRS)

Guhathakurta, Puragra; Bernstein, Gary; Raychaudhury, Somak; Haynes, Martha; Giovanelli, Riccardo; Herter, Terry; Vogt, Nicole

1993-01-01

We have started a large project to study the NIR Tully-Fisher (TF) relation using H- and I-band surface photometry of spiral galaxies. A preliminary study of 20 spirals in the Coma and Abell 400 clusters is presented. The NIR images have been used to derive accurate inclinations and total magnitudes, and rotational linewidths are measured from high-quality 21-cm Arecibo data. The scatter in the Coma TF plot is found to be 0.19 mag in the H band and 0.20 mag in the I band for a set of 13 galaxies, if we assume that they are all at the same distance. The deviation of the Coma galaxies from the best-fit Tully-Fisher relation is correlated with their redshift, indicating that some of the galaxies are not bound to the cluster. Indeed, if we treat all the galaxies in the Coma sample as undergoing free Hubble expansion, the TF scatter drops to 0.12 and 0.13 mag for the H- and I-band datasets, respectively. The Abell 400 sample is best fit by a common distance model, yielding a scatter of 0.12 mag for seven galaxies in H using a fixed TF slope. We are in the process of studying cluster and field spirals out to about 10,000 km/s in order to calibrate the NIR TF relation and will apply it to more nearby galaxies to measure the peculiar velocity field in the local universe.

Accurate D-bar Reconstructions of Conductivity Images Based on a Method of Moment with Sinc Basis.

PubMed

Abbasi, Mahdi

2014-01-01

Planar D-bar integral equation is one of the inverse scattering solution methods for complex problems including inverse conductivity considered in applications such as Electrical impedance tomography (EIT). Recently two different methodologies are considered for the numerical solution of D-bar integrals equation, namely product integrals and multigrid. The first one involves high computational burden and the other one suffers from low convergence rate (CR). In this paper, a novel high speed moment method based using the sinc basis is introduced to solve the two-dimensional D-bar integral equation. In this method, all functions within D-bar integral equation are first expanded using the sinc basis functions. Then, the orthogonal properties of their products dissolve the integral operator of the D-bar equation and results a discrete convolution equation. That is, the new moment method leads to the equation solution without direct computation of the D-bar integral. The resulted discrete convolution equation maybe adapted to a suitable structure to be solved using fast Fourier transform. This allows us to reduce the order of computational complexity to as low as O (N (2)log N). Simulation results on solving D-bar equations arising in EIT problem show that the proposed method is accurate with an ultra-linear CR.

Geometry, Heat Equation and Path Integrals on the Poincaré Upper Half-Plane

NASA Astrophysics Data System (ADS)

Kubo, R.

1988-01-01

Geometry, heat equation and Feynman's path integrals are studied on the Poincaré upper half-plane. The fundamental solution to the heat equation partial f/partial t = Delta_{H} f is expressed in terms of a path integral defined on the upper half-plane. It is shown that Kac's statement that Feynman's path integral satisfies the Schrödinger equation is also valid for our case.

A model of axonal transport drug delivery

NASA Astrophysics Data System (ADS)

Kuznetsov, Andrey V.

2012-04-01

In this paper a model of targeted drug delivery by means of active (motor-driven) axonal transport is developed. The model is motivated by recent experimental research by Filler et al. (A.G. Filler, G.T. Whiteside, M. Bacon, M. Frederickson, F.A. Howe, M.D. Rabinowitz, A.J. Sokoloff, T.W. Deacon, C. Abell, R. Munglani, J.R. Griffiths, B.A. Bell, A.M.L. Lever, Tri-partite complex for axonal transport drug delivery achieves pharmacological effect, Bmc Neuroscience 11 (2010) 8) that reported synthesis and pharmacological efficiency tests of a tri-partite complex designed for axonal transport drug delivery. The developed model accounts for two populations of pharmaceutical agent complexes (PACs): PACs that are transported retrogradely by dynein motors and PACs that are accumulated in the axon at the Nodes of Ranvier. The transitions between these two populations of PACs are described by first-order reactions. An analytical solution of the coupled system of transient equations describing conservations of these two populations of PACs is obtained by using Laplace transform. Numerical results for various combinations of parameter values are presented and their physical significance is discussed.

Squared eigenfunctions for the Sasa-Satsuma equation

NASA Astrophysics Data System (ADS)

Yang, Jianke; Kaup, D. J.

2009-02-01

Squared eigenfunctions are quadratic combinations of Jost functions and adjoint Jost functions which satisfy the linearized equation of an integrable equation. They are needed for various studies related to integrable equations, such as the development of its soliton perturbation theory. In this article, squared eigenfunctions are derived for the Sasa-Satsuma equation whose spectral operator is a 3×3 system, while its linearized operator is a 2×2 system. It is shown that these squared eigenfunctions are sums of two terms, where each term is a product of a Jost function and an adjoint Jost function. The procedure of this derivation consists of two steps: First is to calculate the variations of the potentials via variations of the scattering data by the Riemann-Hilbert method. The second one is to calculate the variations of the scattering data via the variations of the potentials through elementary calculations. While this procedure has been used before on other integrable equations, it is shown here, for the first time, that for a general integrable equation, the functions appearing in these variation relations are precisely the squared eigenfunctions and adjoint squared eigenfunctions satisfying, respectively, the linearized equation and the adjoint linearized equation of the integrable system. This proof clarifies this procedure and provides a unified explanation for previous results of squared eigenfunctions on individual integrable equations. This procedure uses primarily the spectral operator of the Lax pair. Thus two equations in the same integrable hierarchy will share the same squared eigenfunctions (except for a time-dependent factor). In the Appendix, the squared eigenfunctions are presented for the Manakov equations whose spectral operator is closely related to that of the Sasa-Satsuma equation.

Mathematical Methods for Physics and Engineering Third Edition Paperback Set

NASA Astrophysics Data System (ADS)

Riley, Ken F.; Hobson, Mike P.; Bence, Stephen J.

2006-06-01

Prefaces; 1. Preliminary algebra; 2. Preliminary calculus; 3. Complex numbers and hyperbolic functions; 4. Series and limits; 5. Partial differentiation; 6. Multiple integrals; 7. Vector algebra; 8. Matrices and vector spaces; 9. Normal modes; 10. Vector calculus; 11. Line, surface and volume integrals; 12. Fourier series; 13. Integral transforms; 14. First-order ordinary differential equations; 15. Higher-order ordinary differential equations; 16. Series solutions of ordinary differential equations; 17. Eigenfunction methods for differential equations; 18. Special functions; 19. Quantum operators; 20. Partial differential equations: general and particular; 21. Partial differential equations: separation of variables; 22. Calculus of variations; 23. Integral equations; 24. Complex variables; 25. Application of complex variables; 26. Tensors; 27. Numerical methods; 28. Group theory; 29. Representation theory; 30. Probability; 31. Statistics; Index.

Integrability: mathematical methods for studying solitary waves theory

NASA Astrophysics Data System (ADS)

Wazwaz, Abdul-Majid

2014-03-01

In recent decades, substantial experimental research efforts have been devoted to linear and nonlinear physical phenomena. In particular, studies of integrable nonlinear equations in solitary waves theory have attracted intensive interest from mathematicians, with the principal goal of fostering the development of new methods, and physicists, who are seeking solutions that represent physical phenomena and to form a bridge between mathematical results and scientific structures. The aim for both groups is to build up our current understanding and facilitate future developments, develop more creative results and create new trends in the rapidly developing field of solitary waves. The notion of the integrability of certain partial differential equations occupies an important role in current and future trends, but a unified rigorous definition of the integrability of differential equations still does not exist. For example, an integrable model in the Painlevé sense may not be integrable in the Lax sense. The Painlevé sense indicates that the solution can be represented as a Laurent series in powers of some function that vanishes on an arbitrary surface with the possibility of truncating the Laurent series at finite powers of this function. The concept of Lax pairs introduces another meaning of the notion of integrability. The Lax pair formulates the integrability of nonlinear equation as the compatibility condition of two linear equations. However, it was shown by many researchers that the necessary integrability conditions are the existence of an infinite series of generalized symmetries or conservation laws for the given equation. The existence of multiple soliton solutions often indicates the integrability of the equation but other tests, such as the Painlevé test or the Lax pair, are necessary to confirm the integrability for any equation. In the context of completely integrable equations, studies are flourishing because these equations are able to describe the real features in a variety of vital areas in science, technology and engineering. In recognition of the importance of solitary waves theory and the underlying concept of integrable equations, a variety of powerful methods have been developed to carry out the required analysis. Examples of such methods which have been advanced are the inverse scattering method, the Hirota bilinear method, the simplified Hirota method, the Bäcklund transformation method, the Darboux transformation, the Pfaffian technique, the Painlevé analysis, the generalized symmetry method, the subsidiary ordinary differential equation method, the coupled amplitude-phase formulation, the sine-cosine method, the sech-tanh method, the mapping and deformation approach and many new other methods. The inverse scattering method, viewed as a nonlinear analogue of the Fourier transform method, is a powerful approach that demonstrates the existence of soliton solutions through intensive computations. At the center of the theory of integrable equations lies the bilinear forms and Hirota's direct method, which can be used to obtain soliton solutions by using exponentials. The Bäcklund transformation method is a useful invariant transformation that transforms one solution into another of a differential equation. The Darboux transformation method is a well known tool in the theory of integrable systems. It is believed that there is a connection between the Bäcklund transformation and the Darboux transformation, but it is as yet not known. Archetypes of integrable equations are the Korteweg-de Vries (KdV) equation, the modified KdV equation, the sine-Gordon equation, the Schrödinger equation, the Vakhnenko equation, the KdV6 equation, the Burgers equation, the fifth-order Lax equation and many others. These equations yield soliton solutions, multiple soliton solutions, breather solutions, quasi-periodic solutions, kink solutions, homo-clinic solutions and other solutions as well. The couplings of linear and nonlinear equations were recently discovered and subsequently received considerable attention. The concept of couplings forms a new direction for developing innovative construction methods. The recently obtained results in solitary waves theory highlight new approaches for additional creative ideas, promising further achievements and increased progress in this field. We are grateful to all of the authors who accepted our invitation to contribute to this comment section.

Coprimeness-preserving non-integrable extension to the two-dimensional discrete Toda lattice equation

NASA Astrophysics Data System (ADS)

Kamiya, Ryo; Kanki, Masataka; Mase, Takafumi; Tokihiro, Tetsuji

2017-01-01

We introduce a so-called coprimeness-preserving non-integrable extension to the two-dimensional Toda lattice equation. We believe that this equation is the first example of such discrete equations defined over a three-dimensional lattice. We prove that all the iterates of the equation are irreducible Laurent polynomials of the initial data and that every pair of two iterates is co-prime, which indicate confined singularities of the equation. By reducing the equation to two- or one-dimensional lattices, we obtain coprimeness-preserving non-integrable extensions to the one-dimensional Toda lattice equation and the Somos-4 recurrence.

Evolution of Planetary Nebulae with WR-type Central Stars

NASA Astrophysics Data System (ADS)

Danehkar, Ashkbiz

2014-04-01

This thesis presents a study of the kinematics, physical conditions and chemical abundances for a sample of Galactic planetary nebulae (PNe) with Wolf-Rayet (WR) and weak emission-line stars (wels), based on optical integral field unit (IFU) spectroscopy obtained with the Wide Field Spectrograph (WiFeS) on the Australian National University 2.3 telescope at Siding Spring Observatory, and complemented by spectra from the literature. PNe surrounding WR-type stars constitute a particular study class for this study. A considerable fraction of currently well-identified central stars of PNe exhibit 'hydrogen-deficient' fast expanding atmospheres characterized by a large mass-loss rate. Most of them were classified as the carbon-sequence and a few of them as the nitrogen-sequence of the WR-type stars. What are less clear are the physical mechanisms and evolutionary paths that remove the hydrogen-rich outer layer from these degenerate cores, and transform it into a fast stellar wind. The aim of this thesis is to determine kinematic structure, density distribution, thermal structure and elemental abundances for a sample of PNe with different hydrogen-deficient central stars, which might provide clues about the origin and formation of their hydrogen-deficient stellar atmospheres. Hα and [N II] emission features have been used to determine kinematic structures. Based on spatially resolved observations of these emission lines, combined with archival Hubble Space Telescope imaging for compact PNe, morphological structures of these PNe have been determined. Comparing the velocity maps from the IFU spectrograph with those provided by morpho-kinematic models allowed disentangling of the different morphological components of most PNe, apart from the compact objects. The results indicate that these PNe have axisymmetric morphologies, either bipolar or elliptical. In many cases, the associated kinematic maps for PNe around hot WR-type stars also show the presence of so-called fast low-ionization emission regions (FLIERs). The WiFeS observations, complemented with archival spectra from the literature, have been used to carry out plasma diagnostics and abundance analysis using both collisionally excited lines (CELs) and optical recombination lines (ORLs). ORL abundances for carbon, nitrogen and oxygen have been derived where adequate recombination lines were available. The weak physical dependence of ORLs has also been used to determine the physical properties. It is found that the ORL abundances are several times higher than the CEL abundances, whereas the temperatures derived from the He I recombination lines are typically lower than those measured from the collisionally excited nebular-to-auroral forbidden line ratios. The abundance discrepancy factors (ADFs) for doubly-ionized nitrogen and oxygen are within a range from 2 to 49, which are closely correlated with the dichotomy between temperatures derived from forbidden lines and those from He I recombination lines. The results show that the ADF and temperature dichotomy are correlated with the intrinsic nebular Hβ surface brightness, suggesting that the abundance discrepancy problem must be related to the nebular evolution. Three-dimensional photoionization models of a carefully selected sample of Galactic PNe have been constructed, constrained by the WiFeS observations (Abell 48 and SuWt 2) and the double echelle MIKE spectroscopy from the literature (Hb 4 and PB 8). The WiFeS observations have been used to perform the empirical analysis of Abell 48 and SuWt 2. The spatially resolved velocity distributions were used to determine the kinematic structures of Hb 4 and Abell 48. The previously identified non-LTE model atmospheres of Abell 48 and PB 8 have been used as ionizing fluxes in their photoionization models. It is found that the enhancement of the [N II] emission in the FLIERs of Hb 4 is more attributed to the geometry and density distribution, while the ionization correction factor method and electron temperature used for the empirical analysis are mostly responsible for apparent inhomogeneity of nitrogen abundance. However, the results indicate that the chemically inhomogeneous models, containing a small fraction of metal-rich inclusions (around 5 percent), provide acceptable matches to the observed ORLs in Hb 4 and PB 8. The observed nebular spectrum of Abell 48 was best produced by using a nitrogen-sequence non-LTE model atmosphere of a low-mass progenitor star rather than a massive Pop I star. For Abell 48, the helium temperature predicted by the photoionization model is higher than those empirically derived, suggesting the presence of a fraction of cold metal-rich structures inside the nebula. It is found that a dual-dust chemistry with different grain species and discrete grain sizes likely produces the nebular Spitzer mid-infrared continuum of PB 8. The photoionization models of SuWt 2 suggest the presence of a hot hydrogen-deficient degenerate core, compatible with what is known as a PG 1159-type star, while the nebula's age is consistent with a born-again scenario.

Calculation of transonic flows using an extended integral equation method

NASA Technical Reports Server (NTRS)

Nixon, D.

1976-01-01

An extended integral equation method for transonic flows is developed. In the extended integral equation method velocities in the flow field are calculated in addition to values on the aerofoil surface, in contrast with the less accurate 'standard' integral equation method in which only surface velocities are calculated. The results obtained for aerofoils in subcritical flow and in supercritical flow when shock waves are present compare satisfactorily with the results of recent finite difference methods.

Fredholm-Volterra Integral Equation with a Generalized Singular Kernel and its Numerical Solutions

NASA Astrophysics Data System (ADS)

El-Kalla, I. L.; Al-Bugami, A. M.

2010-11-01

In this paper, the existence and uniqueness of solution of the Fredholm-Volterra integral equation (F-VIE), with a generalized singular kernel, are discussed and proved in the spaceL2(Ω)×C(0,T). The Fredholm integral term (FIT) is considered in position while the Volterra integral term (VIT) is considered in time. Using a numerical technique we have a system of Fredholm integral equations (SFIEs). This system of integral equations can be reduced to a linear algebraic system (LAS) of equations by using two different methods. These methods are: Toeplitz matrix method and Product Nyström method. A numerical examples are considered when the generalized kernel takes the following forms: Carleman function, logarithmic form, Cauchy kernel, and Hilbert kernel.

Student Solution Manual for Mathematical Methods for Physics and Engineering Third Edition

NASA Astrophysics Data System (ADS)

Riley, K. F.; Hobson, M. P.

2006-03-01

Preface; 1. Preliminary algebra; 2. Preliminary calculus; 3. Complex numbers and hyperbolic functions; 4. Series and limits; 5. Partial differentiation; 6. Multiple integrals; 7. Vector algebra; 8. Matrices and vector spaces; 9. Normal modes; 10. Vector calculus; 11. Line, surface and volume integrals; 12. Fourier series; 13. Integral transforms; 14. First-order ordinary differential equations; 15. Higher-order ordinary differential equations; 16. Series solutions of ordinary differential equations; 17. Eigenfunction methods for differential equations; 18. Special functions; 19. Quantum operators; 20. Partial differential equations: general and particular; 21. Partial differential equations: separation of variables; 22. Calculus of variations; 23. Integral equations; 24. Complex variables; 25. Application of complex variables; 26. Tensors; 27. Numerical methods; 28. Group theory; 29. Representation theory; 30. Probability; 31. Statistics.

Fun House Mirror in Space

NASA Image and Video Library

2010-08-19

NASA Hubble Space Telescope shows the inner region of Abell 1689, an immense cluster of galaxies located 2.2 billion light-years away. The cluster gravitational field is warping light from background galaxies, causing them to appear as arcs.

Celestial Cities and the Roads That Connect Them

NASA Image and Video Library

2008-01-25

Observations from NASA Spitzer Space Telescope show that filamentary galaxies form stars at twice the rate of their densely clustered counterparts. This is a representation of galaxies in and surrounding a galaxy cluster called Abell 1763.

Shocking Tails in the Major Merger Abell 2744

NASA Astrophysics Data System (ADS)

Owers, Matt S.; Couch, Warrick J.; Nulsen, Paul E. J.; Randall, Scott W.

2012-05-01

We identify four rare "jellyfish" galaxies in Hubble Space Telescope imagery of the major merger cluster Abell 2744. These galaxies harbor trails of star-forming knots and filaments which have formed in situ in gas tails stripped from the parent galaxies, indicating they are in the process of being transformed by the environment. Further evidence for rapid transformation in these galaxies comes from their optical spectra, which reveal starburst, poststarburst, and active galactic nucleus features. Most intriguingly, three of the jellyfish galaxies lie near intracluster medium features associated with a merging "Bullet-like" subcluster and its shock front detected in Chandra X-ray images. We suggest that the high-pressure merger environment may be responsible for the star formation in the gaseous tails. This provides observational evidence for the rapid transformation of galaxies during the violent core passage phase of a major cluster merger.

X-ray lines and self-interacting dark matter.

PubMed

Mambrini, Yann; Toma, Takashi

We study the correlation between a monochromatic signal from annihilating dark matter and its self-interacting cross section. We apply our argument to a complex scalar dark sector, where the pseudo-scalar plays the role of a warm dark matter candidate while the scalar mediates its interaction with the Standard Model. We combine the recent observation of the cluster Abell 3827 for self-interacting dark matter and the constraints on the annihilation cross section for monochromatic X-ray lines. We also confront our model to a set of recent experimental analyses and find that such an extension can naturally produce a monochromatic keV signal corresponding to recent observations of Perseus or Andromeda, while in the meantime it predicts a self-interacting cross section of the order of [Formula: see text], as recently claimed in the observation of the cluster Abell 3827. We also propose a way to distinguish such models by future direct detection techniques.

On the X-ray spectrum of the volume emissivity arising from Abell clusters

NASA Technical Reports Server (NTRS)

Stottlemyer, A. R.; Boldt, E. A.

1984-01-01

HEAO 1 A-2 X-ray spectra (2-15 keV) for an optically selected sample of Abell clusters of galaxies with z less than 0.1 have been analyzed to determine the energy dependence of the cosmological X-ray volume emissivity arising from such clusters. This spectrum is well fitted by an isothermal-bremsstrahlung model with kT = 7.4 + or - 1.5 KeV. This result is a test of the isothermal-volume-emissivity spectrum to be inferred from the conjecture that all contributing clusters may be characterized by kT = 7 keV, as assumed by McKee et al. (1980) in estimating the underlying luminosity function for the same sample. Although satisfied at the statistical level indicated, the analysis of a low-luminosity subsample suggests that this assumption of identical isothermal spectra would lead to a systematic error for a more statistically precise determination of the luminosity function's form.

SHOCKING TAILS IN THE MAJOR MERGER ABELL 2744

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

Owers, Matt S.; Couch, Warrick J.; Nulsen, Paul E. J.

We identify four rare 'jellyfish' galaxies in Hubble Space Telescope imagery of the major merger cluster Abell 2744. These galaxies harbor trails of star-forming knots and filaments which have formed in situ in gas tails stripped from the parent galaxies, indicating they are in the process of being transformed by the environment. Further evidence for rapid transformation in these galaxies comes from their optical spectra, which reveal starburst, poststarburst, and active galactic nucleus features. Most intriguingly, three of the jellyfish galaxies lie near intracluster medium features associated with a merging 'Bullet-like' subcluster and its shock front detected in Chandra X-raymore » images. We suggest that the high-pressure merger environment may be responsible for the star formation in the gaseous tails. This provides observational evidence for the rapid transformation of galaxies during the violent core passage phase of a major cluster merger.« less

A new solution procedure for a nonlinear infinite beam equation of motion

NASA Astrophysics Data System (ADS)

Jang, T. S.

2016-10-01

Our goal of this paper is of a purely theoretical question, however which would be fundamental in computational partial differential equations: Can a linear solution-structure for the equation of motion for an infinite nonlinear beam be directly manipulated for constructing its nonlinear solution? Here, the equation of motion is modeled as mathematically a fourth-order nonlinear partial differential equation. To answer the question, a pseudo-parameter is firstly introduced to modify the equation of motion. And then, an integral formalism for the modified equation is found here, being taken as a linear solution-structure. It enables us to formulate a nonlinear integral equation of second kind, equivalent to the original equation of motion. The fixed point approach, applied to the integral equation, results in proposing a new iterative solution procedure for constructing the nonlinear solution of the original beam equation of motion, which consists luckily of just the simple regular numerical integration for its iterative process; i.e., it appears to be fairly simple as well as straightforward to apply. A mathematical analysis is carried out on both natures of convergence and uniqueness of the iterative procedure by proving a contractive character of a nonlinear operator. It follows conclusively,therefore, that it would be one of the useful nonlinear strategies for integrating the equation of motion for a nonlinear infinite beam, whereby the preceding question may be answered. In addition, it may be worth noticing that the pseudo-parameter introduced here has double roles; firstly, it connects the original beam equation of motion with the integral equation, second, it is related with the convergence of the iterative method proposed here.

A new (2+1) dimensional integrable evolution equation for an ion acoustic wave in a magnetized plasma

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

Mukherjee, Abhik, E-mail: abhik.mukherjee@saha.ac.in; Janaki, M. S., E-mail: ms.janaki@saha.ac.in; Kundu, Anjan, E-mail: anjan.kundu@saha.ac.in

2015-07-15

A new, completely integrable, two dimensional evolution equation is derived for an ion acoustic wave propagating in a magnetized, collisionless plasma. The equation is a multidimensional generalization of a modulated wavepacket with weak transverse propagation, which has resemblance to nonlinear Schrödinger (NLS) equation and has a connection to Kadomtsev-Petviashvili equation through a constraint relation. Higher soliton solutions of the equation are derived through Hirota bilinearization procedure, and an exact lump solution is calculated exhibiting 2D structure. Some mathematical properties demonstrating the completely integrable nature of this equation are described. Modulational instability using nonlinear frequency correction is derived, and the correspondingmore » growth rate is calculated, which shows the directional asymmetry of the system. The discovery of this novel (2+1) dimensional integrable NLS type equation for a magnetized plasma should pave a new direction of research in the field.« less

Algorithms for the computation of solutions of the Ornstein-Zernike equation.

PubMed

Peplow, A T; Beardmore, R E; Bresme, F

2006-10-01

We introduce a robust and efficient methodology to solve the Ornstein-Zernike integral equation using the pseudoarc length (PAL) continuation method that reformulates the integral equation in an equivalent but nonstandard form. This enables the computation of solutions in regions where the compressibility experiences large changes or where the existence of multiple solutions and so-called branch points prevents Newton's method from converging. We illustrate the use of the algorithm with a difficult problem that arises in the numerical solution of integral equations, namely the evaluation of the so-called no-solution line of the Ornstein-Zernike hypernetted chain (HNC) integral equation for the Lennard-Jones potential. We are able to use the PAL algorithm to solve the integral equation along this line and to connect physical and nonphysical solution branches (both isotherms and isochores) where appropriate. We also show that PAL continuation can compute solutions within the no-solution region that cannot be computed when Newton and Picard methods are applied directly to the integral equation. While many solutions that we find are new, some correspond to states with negative compressibility and consequently are not physical.

Integral equations in the study of polar and ionic interaction site fluids

PubMed Central

Howard, Jesse J.

2011-01-01

In this review article we consider some of the current integral equation approaches and application to model polar liquid mixtures. We consider the use of multidimensional integral equations and in particular progress on the theory and applications of three dimensional integral equations. The IEs we consider may be derived from equilibrium statistical mechanical expressions incorporating a classical Hamiltonian description of the system. We give example including salt solutions, inhomogeneous solutions and systems including proteins and nucleic acids. PMID:22383857

Revisiting Abell 2744: a powerful synergy of the GLASS spectroscopy and the HFF photometry.

NASA Astrophysics Data System (ADS)

Wang, Xin; Borello Schmidt, Kasper; Treu, Tommaso

2015-08-01

We present new emission line identifications and improve the strong lensing reconstruction of the massive cluster Abell 2744 using the Grism Lens-Amplified Survey from Space (GLASS) observations and the full depth of the Hubble Frontier Fields (HFF) imaging. We performed a blind and targeted search for emission lines in objects within the full field of view (FoV) of the GLASS prime pointings, including all the previously known multiple arc images. We report over 50 high quality spectroscopic redshifts, 4 of which are for the arc images. We also present an extensive analysis based on the HFF photometry, measuring the colors and photometric redshifts of all objects within the FoV, and comparing the spectroscopic and photometric results of the same ensemble of sources. In order to improve the lens model of Abell 2744, we develop a rigorous alogorithm to screen arc images, based on their colors and morphology, and selecting the most reliable ones to use. As a result, 21 systems (corresponding to 59 images) pass the screening process and are used to reconstruct the gravitational potential of the cluster pixellated on an adaptive mesh. The resulting total mass distribution is compared with a stellar mass map obtained from the deep Spitzer Frontier Fields data in a fashion very similar to the reduction of the Spitzer UltRa Faint SUrvey Program (SURFS UP) clusters, in order to study the relative distribution of stars and dark matter in the cluster. The maps of convergence, shear, and magnification are made publicly available in the standard HFF format.

Suzaku observations of low surface brightness cluster Abell 1631

NASA Astrophysics Data System (ADS)

Babazaki, Yasunori; Mitsuishi, Ikuyuki; Ota, Naomi; Sasaki, Shin; Böhringer, Hans; Chon, Gayoung; Pratt, Gabriel W.; Matsumoto, Hironori

2018-04-01

We present analysis results for a nearby galaxy cluster Abell 1631 at z = 0.046 using the X-ray observatory Suzaku. This cluster is categorized as a low X-ray surface brightness cluster. To study the dynamical state of the cluster, we conduct four-pointed Suzaku observations and investigate physical properties of the Mpc-scale hot gas associated with the A 1631 cluster for the first time. Unlike relaxed clusters, the X-ray image shows no strong peak at the center and an irregular morphology. We perform spectral analysis and investigate the radial profiles of the gas temperature, density, and entropy out to approximately 1.5 Mpc in the east, north, west, and south directions by combining with the XMM-Newton data archive. The measured gas density in the central region is relatively low (a few ×10-4 cm-3) at the given temperature (˜2.9 keV) compared with X-ray-selected clusters. The entropy profile and value within the central region (r < 0.1 r200) are found to be flatter and higher (≳400 keV cm2). The observed bolometric luminosity is approximately three times lower than that expected from the luminosity-temperature relation in previous studies of relaxed clusters. These features are also observed in another low surface brightness cluster, Abell 76. The spatial distributions of galaxies and the hot gas appear to be different. The X-ray luminosity is relatively lower than that expected from the velocity dispersion. A post-merger scenario may explain the observed results.

The Frontier Fields: Survey Design and Initial Results

NASA Astrophysics Data System (ADS)

Lotz, J. M.; Koekemoer, A.; Coe, D.; Grogin, N.; Capak, P.; Mack, J.; Anderson, J.; Avila, R.; Barker, E. A.; Borncamp, D.; Brammer, G.; Durbin, M.; Gunning, H.; Hilbert, B.; Jenkner, H.; Khandrika, H.; Levay, Z.; Lucas, R. A.; MacKenty, J.; Ogaz, S.; Porterfield, B.; Reid, N.; Robberto, M.; Royle, P.; Smith, L. J.; Storrie-Lombardi, L. J.; Sunnquist, B.; Surace, J.; Taylor, D. C.; Williams, R.; Bullock, J.; Dickinson, M.; Finkelstein, S.; Natarajan, P.; Richard, J.; Robertson, B.; Tumlinson, J.; Zitrin, A.; Flanagan, K.; Sembach, K.; Soifer, B. T.; Mountain, M.

2017-03-01

What are the faintest distant galaxies we can see with the Hubble Space Telescope (HST) now, before the launch of the James Webb Space Telescope? This is the challenge taken up by the Frontier Fields, a Director’s discretionary time campaign with HST and the Spitzer Space Telescope to see deeper into the universe than ever before. The Frontier Fields combines the power of HST and Spitzer with the natural gravitational telescopes of massive high-magnification clusters of galaxies to produce the deepest observations of clusters and their lensed galaxies ever obtained. Six clusters—Abell 2744, MACSJ0416.1-2403, MACSJ0717.5+3745, MACSJ1149.5+2223, Abell S1063, and Abell 370—have been targeted by the HST ACS/WFC and WFC3/IR cameras with coordinated parallel fields for over 840 HST orbits. The parallel fields are the second-deepest observations thus far by HST with 5σ point-source depths of ˜29th ABmag. Galaxies behind the clusters experience typical magnification factors of a few, with small regions magnified by factors of 10-100. Therefore, the Frontier Field cluster HST images achieve intrinsic depths of ˜30-33 mag over very small volumes. Spitzer has obtained over 1000 hr of Director’s discretionary imaging of the Frontier Field cluster and parallels in IRAC 3.6 and 4.5 μm bands to 5σ point-source depths of ˜26.5, 26.0 ABmag. We demonstrate the exceptional sensitivity of the HST Frontier Field images to faint high-redshift galaxies, and review the initial results related to the primary science goals.

Lens models under the microscope: comparison of Hubble Frontier Field cluster magnification maps

NASA Astrophysics Data System (ADS)

Priewe, Jett; Williams, Liliya L. R.; Liesenborgs, Jori; Coe, Dan; Rodney, Steven A.

2017-02-01

Using the power of gravitational lensing magnification by massive galaxy clusters, the Hubble Frontier Fields provide deep views of six patches of the high-redshift Universe. The combination of deep Hubble imaging and exceptional lensing strength has revealed the greatest numbers of multiply-imaged galaxies available to constrain models of cluster mass distributions. However, even with O(100) images per cluster, the uncertainties associated with the reconstructions are not negligible. The goal of this paper is to show the diversity of model magnification predictions. We examine seven and nine mass models of Abell 2744 and MACS J0416, respectively, submitted to the Mikulski Archive for Space Telescopes for public distribution in 2015 September. The dispersion between model predictions increases from 30 per cent at common low magnifications (μ ˜ 2) to 70 per cent at rare high magnifications (μ ˜ 40). MACS J0416 exhibits smaller dispersions than Abell 2744 for 2 < μ < 10. We show that magnification maps based on different lens inversion techniques typically differ from each other by more than their quoted statistical errors. This suggests that some models underestimate the true uncertainties, which are primarily due to various lensing degeneracies. Though the exact mass sheet degeneracy is broken, its generalized counterpart is not broken at least in Abell 2744. Other local degeneracies are also present in both clusters. Our comparison of models is complementary to the comparison of reconstructions of known synthetic mass distributions. By focusing on observed clusters, we can identify those that are best constrained, and therefore provide the clearest view of the distant Universe.

Collision-Induced Infrared Absorption by Collisional Complexes in Dense Hydrogen-Helium Gas Mixtures at Thousands of Kelvin

NASA Astrophysics Data System (ADS)

Abel, Martin; Frommhold, Lothar; Li, Xiaoping; Hunt, Katharine L. C.

2011-06-01

The interaction-induced absorption by collisional pairs of H{_2} molecules is an important opacity source in the atmospheres of the outer planets and cool stars. The emission spectra of cool white dwarf stars differ significantly in the infrared from the expected blackbody spectra of their cores, which is largely due to absorption by collisional H{_2}-H{_2}, H{_2}-He, and H{_2}-H complexes in the stellar atmospheres. Using quantum-chemical methods we compute the atmospheric absorption from hundreds to thousands of kelvin. Laboratory measurements of interaction-induced absorption spectra by H{_2} pairs exist only at room temperature and below. We show that our results reproduce these measurements closely, so that our computational data permit reliable modeling of stellar atmosphere opacities even for the higher temperatures. L. Frommhold, Collision-Induced Absorption in Gases, Cambridge University Press, Cambridge, New York, 1993 and 2006 Xiaoping Li, Katharine L. C. Hunt, Fei Wang, Martin Abel, and Lothar Frommhold, "Collision-Induced Infrared Absorption by Molecular Hydrogen Pairs at Thousands of Kelvin", International Journal of Spectroscopy, vol. 2010, Article ID 371201, 11 pages, 2010. doi: 10.1155/2010/371201 M. Abel, L. Frommhold, X. Li, and K. L. C. Hunt, "Collision-induced absorption by H{_2} pairs: From hundreds to thousands of Kelvin," J. Phys. Chem. A, published online, DOI: 10.1021/jp109441f L. Frommhold, M. Abel, F. Wang, M. Gustafsson, X. Li, and K. L. C. Hunt, "Infrared atmospheric emission and absorption by simple molecular complexes, from first principles", Mol. Phys. 108, 2265, 2010

Suzaku observations of low surface brightness cluster Abell 1631

NASA Astrophysics Data System (ADS)

Babazaki, Yasunori; Mitsuishi, Ikuyuki; Ota, Naomi; Sasaki, Shin; Böhringer, Hans; Chon, Gayoung; Pratt, Gabriel W.; Matsumoto, Hironori

2018-06-01

We present analysis results for a nearby galaxy cluster Abell 1631 at z = 0.046 using the X-ray observatory Suzaku. This cluster is categorized as a low X-ray surface brightness cluster. To study the dynamical state of the cluster, we conduct four-pointed Suzaku observations and investigate physical properties of the Mpc-scale hot gas associated with the A 1631 cluster for the first time. Unlike relaxed clusters, the X-ray image shows no strong peak at the center and an irregular morphology. We perform spectral analysis and investigate the radial profiles of the gas temperature, density, and entropy out to approximately 1.5 Mpc in the east, north, west, and south directions by combining with the XMM-Newton data archive. The measured gas density in the central region is relatively low (a few ×10-4 cm-3) at the given temperature (˜2.9 keV) compared with X-ray-selected clusters. The entropy profile and value within the central region (r < 0.1 r200) are found to be flatter and higher (≳400 keV cm2). The observed bolometric luminosity is approximately three times lower than that expected from the luminosity-temperature relation in previous studies of relaxed clusters. These features are also observed in another low surface brightness cluster, Abell 76. The spatial distributions of galaxies and the hot gas appear to be different. The X-ray luminosity is relatively lower than that expected from the velocity dispersion. A post-merger scenario may explain the observed results.

A spectral boundary integral equation method for the 2-D Helmholtz equation

NASA Technical Reports Server (NTRS)

Hu, Fang Q.

1994-01-01

In this paper, we present a new numerical formulation of solving the boundary integral equations reformulated from the Helmholtz equation. The boundaries of the problems are assumed to be smooth closed contours. The solution on the boundary is treated as a periodic function, which is in turn approximated by a truncated Fourier series. A Fourier collocation method is followed in which the boundary integral equation is transformed into a system of algebraic equations. It is shown that in order to achieve spectral accuracy for the numerical formulation, the nonsmoothness of the integral kernels, associated with the Helmholtz equation, must be carefully removed. The emphasis of the paper is on investigating the essential elements of removing the nonsmoothness of the integral kernels in the spectral implementation. The present method is robust for a general boundary contour. Aspects of efficient implementation of the method using FFT are also discussed. A numerical example of wave scattering is given in which the exponential accuracy of the present numerical method is demonstrated.

On one solution of Volterra integral equations of second kind

NASA Astrophysics Data System (ADS)

Myrhorod, V.; Hvozdeva, I.

2016-10-01

A solution of Volterra integral equations of the second kind with separable and difference kernels based on solutions of corresponding equations linking the kernel and resolvent is suggested. On the basis of a discrete functions class, the equations linking the kernel and resolvent are obtained and the methods of their analytical solutions are proposed. A mathematical model of the gas-turbine engine state modification processes in the form of Volterra integral equation of the second kind with separable kernel is offered.

A parameter study of the two-fluid solar wind

NASA Technical Reports Server (NTRS)

Sandbaek, Ornulf; Leer, Egil; Holzer, Thomas E.

1992-01-01

A two-fluid model of the solar wind was introduced by Sturrock and Hartle (1966) and Hartle and Sturrock (1968). In these studies the proton energy equation was integrated neglecting the heat conductive term. Later several authors solved the equations for the two-fluid solar wind model keeping the proton heat conductive term. Methods where the equations are integrated simultaneously outward and inward from the critical point were used. The equations were also integrated inward from a large heliocentric distance. These methods have been applied to cases with low coronal base electron densities and high base temperatures. In this paper we present a method of integrating the two-fluid solar wind equations using an iteration procedure where the equations are integrated separately and the proton flux is kept constant during the integrations. The technique is applicable for a wide range of coronal base densities and temperatures. The method is used to carry out a parameter study of the two-fluid solar wind.

GSFC_20170803_2017-13427_004

NASA Image and Video Library

2017-08-03

2017 interns participated in a summer poster session at Goddard on August 3,2017. Awards were given to top posters in categories of: computer science/IT, engineering, GSFC functional services and science. Colleen Hartman, Nancy Abell and Juan Ramon presented awards.

GSFC_20170803_2017-13427_013

NASA Image and Video Library

2017-08-03

2017 interns participated in a summer poster session at Goddard on August 3, 2017. Awards were given to top posters in categories of: computer science/IT, engineering, GSFC functional services, and science. Colleen Hartman, Nancy Abell and Juan Ramon presented awards.

Coma cluster of galaxies

NASA Image and Video Library

1999-12-02

Atlas Image mosaic, covering 34 x 34 on the sky, of the Coma cluster, aka Abell 1656. This is a particularly rich cluster of individual galaxies over 1000 members, most prominently the two giant ellipticals, NGC 4874 right and NGC 4889 left.

Reconstruction of the two-dimensional gravitational potential of galaxy clusters from X-ray and Sunyaev-Zel'dovich measurements

NASA Astrophysics Data System (ADS)

Tchernin, C.; Bartelmann, M.; Huber, K.; Dekel, A.; Hurier, G.; Majer, C. L.; Meyer, S.; Zinger, E.; Eckert, D.; Meneghetti, M.; Merten, J.

2018-06-01

Context. The mass of galaxy clusters is not a direct observable, nonetheless it is commonly used to probe cosmological models. Based on the combination of all main cluster observables, that is, the X-ray emission, the thermal Sunyaev-Zel'dovich (SZ) signal, the velocity dispersion of the cluster galaxies, and gravitational lensing, the gravitational potential of galaxy clusters can be jointly reconstructed. Aims: We derive the two main ingredients required for this joint reconstruction: the potentials individually reconstructed from the observables and their covariance matrices, which act as a weight in the joint reconstruction. We show here the method to derive these quantities. The result of the joint reconstruction applied to a real cluster will be discussed in a forthcoming paper. Methods: We apply the Richardson-Lucy deprojection algorithm to data on a two-dimensional (2D) grid. We first test the 2D deprojection algorithm on a β-profile. Assuming hydrostatic equilibrium, we further reconstruct the gravitational potential of a simulated galaxy cluster based on synthetic SZ and X-ray data. We then reconstruct the projected gravitational potential of the massive and dynamically active cluster Abell 2142, based on the X-ray observations collected with XMM-Newton and the SZ observations from the Planck satellite. Finally, we compute the covariance matrix of the projected reconstructed potential of the cluster Abell 2142 based on the X-ray measurements collected with XMM-Newton. Results: The gravitational potentials of the simulated cluster recovered from synthetic X-ray and SZ data are consistent, even though the potential reconstructed from X-rays shows larger deviations from the true potential. Regarding Abell 2142, the projected gravitational cluster potentials recovered from SZ and X-ray data reproduce well the projected potential inferred from gravitational-lensing observations. We also observe that the covariance matrix of the potential for Abell 2142 reconstructed from XMM-Newton data sensitively depends on the resolution of the deprojected grid and on the smoothing scale used in the deprojection. Conclusions: We show that the Richardson-Lucy deprojection method can be effectively applied on a grid and that the projected potential is well recovered from real and simulated data based on X-ray and SZ signal. The comparison between the reconstructed potentials from the different observables provides additional information on the validity of the assumptions as function of the projected radius.

The staircase method: integrals for periodic reductions of integrable lattice equations

NASA Astrophysics Data System (ADS)

van der Kamp, Peter H.; Quispel, G. R. W.

2010-11-01

We show, in full generality, that the staircase method (Papageorgiou et al 1990 Phys. Lett. A 147 106-14, Quispel et al 1991 Physica A 173 243-66) provides integrals for mappings, and correspondences, obtained as traveling wave reductions of (systems of) integrable partial difference equations. We apply the staircase method to a variety of equations, including the Korteweg-De Vries equation, the five-point Bruschi-Calogero-Droghei equation, the quotient-difference (QD)-algorithm and the Boussinesq system. We show that, in all these cases, if the staircase method provides r integrals for an n-dimensional mapping, with 2r, then one can introduce q <= 2r variables, which reduce the dimension of the mapping from n to q. These dimension-reducing variables are obtained as joint invariants of k-symmetries of the mappings. Our results support the idea that often the staircase method provides sufficiently many integrals for the periodic reductions of integrable lattice equations to be completely integrable. We also study reductions on other quad-graphs than the regular {\\ Z}^2 lattice, and we prove linear growth of the multi-valuedness of iterates of high-dimensional correspondences obtained as reductions of the QD-algorithm.

An integrable semi-discrete Degasperis-Procesi equation

NASA Astrophysics Data System (ADS)

Feng, Bao-Feng; Maruno, Ken-ichi; Ohta, Yasuhiro

2017-06-01

Based on our previous work on the Degasperis-Procesi equation (Feng et al J. Phys. A: Math. Theor. 46 045205) and the integrable semi-discrete analogue of its short wave limit (Feng et al J. Phys. A: Math. Theor. 48 135203), we derive an integrable semi-discrete Degasperis-Procesi equation by Hirota’s bilinear method. Furthermore, N-soliton solution to the semi-discrete Degasperis-Procesi equation is constructed. It is shown that both the proposed semi-discrete Degasperis-Procesi equation, and its N-soliton solution converge to ones of the original Degasperis-Procesi equation in the continuum limit.

The Kadomtsev{endash}Petviashvili equation as a source of integrable model equations

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

Maccari, A.

1996-12-01

A new integrable and nonlinear partial differential equation (PDE) in 2+1 dimensions is obtained, by an asymptotically exact reduction method based on Fourier expansion and spatiotemporal rescaling, from the Kadomtsev{endash}Petviashvili equation. The integrability property is explicitly demonstrated, by exhibiting the corresponding Lax pair, that is obtained by applying the reduction technique to the Lax pair of the Kadomtsev{endash}Petviashvili equation. This model equation is likely to be of applicative relevance, because it may be considered a consistent approximation of a large class of nonlinear evolution PDEs. {copyright} {ital 1996 American Institute of Physics.}

Simplifying Differential Equations for Multiscale Feynman Integrals beyond Multiple Polylogarithms.

PubMed

Adams, Luise; Chaubey, Ekta; Weinzierl, Stefan

2017-04-07

In this Letter we exploit factorization properties of Picard-Fuchs operators to decouple differential equations for multiscale Feynman integrals. The algorithm reduces the differential equations to blocks of the size of the order of the irreducible factors of the Picard-Fuchs operator. As a side product, our method can be used to easily convert the differential equations for Feynman integrals which evaluate to multiple polylogarithms to an ϵ form.

Solution of the nonlinear mixed Volterra-Fredholm integral equations by hybrid of block-pulse functions and Bernoulli polynomials.

PubMed

Mashayekhi, S; Razzaghi, M; Tripak, O

2014-01-01

A new numerical method for solving the nonlinear mixed Volterra-Fredholm integral equations is presented. This method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The operational matrices of integration and product are given. These matrices are then utilized to reduce the nonlinear mixed Volterra-Fredholm integral equations to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

Solution of the Nonlinear Mixed Volterra-Fredholm Integral Equations by Hybrid of Block-Pulse Functions and Bernoulli Polynomials

PubMed Central

Mashayekhi, S.; Razzaghi, M.; Tripak, O.

2014-01-01

A new numerical method for solving the nonlinear mixed Volterra-Fredholm integral equations is presented. This method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The operational matrices of integration and product are given. These matrices are then utilized to reduce the nonlinear mixed Volterra-Fredholm integral equations to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique. PMID:24523638

Two volume integral equations for the inhomogeneous and anisotropic forward problem in electroencephalography

NASA Astrophysics Data System (ADS)

Rahmouni, Lyes; Mitharwal, Rajendra; Andriulli, Francesco P.

2017-11-01

This work presents two new volume integral equations for the Electroencephalography (EEG) forward problem which, differently from the standard integral approaches in the domain, can handle heterogeneities and anisotropies of the head/brain conductivity profiles. The new formulations translate to the quasi-static regime some volume integral equation strategies that have been successfully applied to high frequency electromagnetic scattering problems. This has been obtained by extending, to the volume case, the two classical surface integral formulations used in EEG imaging and by introducing an extra surface equation, in addition to the volume ones, to properly handle boundary conditions. Numerical results corroborate theoretical treatments, showing the competitiveness of our new schemes over existing techniques and qualifying them as a valid alternative to differential equation based methods.

Algebraic Construction of Exact Difference Equations from Symmetry of Equations

NASA Astrophysics Data System (ADS)

Itoh, Toshiaki

2009-09-01

Difference equations or exact numerical integrations, which have general solutions, are treated algebraically. Eliminating the symmetries of the equation, we can construct difference equations (DCE) or numerical integrations equivalent to some ODEs or PDEs that means both have the same solution functions. When arbitrary functions are given, whether we can construct numerical integrations that have solution functions equal to given function or not are treated in this work. Nowadays, Lie's symmetries solver for ODE and PDE has been implemented in many symbolic software. Using this solver we can construct algebraic DCEs or numerical integrations which are correspond to some ODEs or PDEs. In this work, we treated exact correspondence between ODE or PDE and DCE or numerical integration with Gröbner base and Janet base from the view of Lie's symmetries.

Integral Equations in Computational Electromagnetics: Formulations, Properties and Isogeometric Analysis

NASA Astrophysics Data System (ADS)

Lovell, Amy Elizabeth

Computational electromagnetics (CEM) provides numerical methods to simulate electromagnetic waves interacting with its environment. Boundary integral equation (BIE) based methods, that solve the Maxwell's equations in the homogeneous or piecewise homogeneous medium, are both efficient and accurate, especially for scattering and radiation problems. Development and analysis electromagnetic BIEs has been a very active topic in CEM research. Indeed, there are still many open problems that need to be addressed or further studied. A short and important list includes (1) closed-form or quasi-analytical solutions to time-domain integral equations, (2) catastrophic cancellations at low frequencies, (3) ill-conditioning due to high mesh density, multi-scale discretization, and growing electrical size, and (4) lack of flexibility due to re-meshing when increasing number of forward numerical simulations are involved in the electromagnetic design process. This dissertation will address those several aspects of boundary integral equations in computational electromagnetics. The first contribution of the dissertation is to construct quasi-analytical solutions to time-dependent boundary integral equations using a direct approach. Direct inverse Fourier transform of the time-harmonic solutions is not stable due to the non-existence of the inverse Fourier transform of spherical Hankel functions. Using new addition theorems for the time-domain Green's function and dyadic Green's functions, time-domain integral equations governing transient scattering problems of spherical objects are solved directly and stably for the first time. Additional, the direct time-dependent solutions, together with the newly proposed time-domain dyadic Green's functions, can enrich the time-domain spherical multipole theory. The second contribution is to create a novel method of moments (MoM) framework to solve electromagnetic boundary integral equation on subdivision surfaces. The aim is to avoid the meshing and re-meshing stages to accelerate the design process when the geometry needs to be updated. Two schemes to construct basis functions on the subdivision surface have been explored. One is to use the div-conforming basis function, and the other one is to create a rigorous iso-geometric approach based on the subdivision basis function with better smoothness properties. This new framework provides us better accuracy, more stability and high flexibility. The third contribution is a new stable integral equation formulation to avoid catastrophic cancellations due to low-frequency breakdown or dense-mesh breakdown. Many of the conventional integral equations and their associated post-processing operations suffer from numerical catastrophic cancellations, which can lead to ill-conditioning of the linear systems or serious accuracy problems. Examples includes low-frequency breakdown and dense mesh breakdown. Another instability may come from nontrivial null spaces of involving integral operators that might be related with spurious resonance or topology breakdown. This dissertation presents several sets of new boundary integral equations and studies their analytical properties. The first proposed formulation leads to the scalar boundary integral equations where only scalar unknowns are involved. Besides the requirements of gaining more stability and better conditioning in the resulting linear systems, multi-physics simulation is another driving force for new formulations. Scalar and vector potentials (rather than electromagnetic field) based formulation have been studied for this purpose. Those new contributions focus on different stages of boundary integral equations in an almost independent manner, e.g. isogeometric analysis framework can be used to solve different boundary integral equations, and the time-dependent solutions to integral equations from different formulations can be achieved through the same methodology proposed.

Liouvillian propagators, Riccati equation and differential Galois theory

NASA Astrophysics Data System (ADS)

Acosta-Humánez, Primitivo; Suazo, Erwin

2013-11-01

In this paper a Galoisian approach to building propagators through Riccati equations is presented. The main result corresponds to the relationship between the Galois integrability of the linear Schrödinger equation and the virtual solvability of the differential Galois group of its associated characteristic equation. As the main application of this approach we solve Ince’s differential equation through the Hamiltonian algebrization procedure and the Kovacic algorithm to find the propagator for a generalized harmonic oscillator. This propagator has applications which describe the process of degenerate parametric amplification in quantum optics and light propagation in a nonlinear anisotropic waveguide. Toy models of propagators inspired by integrable Riccati equations and integrable characteristic equations are also presented.

Master equations and the theory of stochastic path integrals

NASA Astrophysics Data System (ADS)

Weber, Markus F.; Frey, Erwin

2017-04-01

This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. Since the 1930s, master equations have served as a fundamental tool to understand the role of fluctuations in complex biological, chemical, and physical systems. Despite their simple appearance, analyses of master equations most often rely on low-noise approximations such as the Kramers-Moyal or the system size expansion, or require ad-hoc closure schemes for the derivation of low-order moment equations. We focus on numerical and analytical methods going beyond the low-noise limit and provide a unified framework for the study of master equations. After deriving the forward and backward master equations from the Chapman-Kolmogorov equation, we show how the two master equations can be cast into either of four linear partial differential equations (PDEs). Three of these PDEs are discussed in detail. The first PDE governs the time evolution of a generalized probability generating function whose basis depends on the stochastic process under consideration. Spectral methods, WKB approximations, and a variational approach have been proposed for the analysis of the PDE. The second PDE is novel and is obeyed by a distribution that is marginalized over an initial state. It proves useful for the computation of mean extinction times. The third PDE describes the time evolution of a ‘generating functional’, which generalizes the so-called Poisson representation. Subsequently, the solutions of the PDEs are expressed in terms of two path integrals: a ‘forward’ and a ‘backward’ path integral. Combined with inverse transformations, one obtains two distinct path integral representations of the conditional probability distribution solving the master equations. We exemplify both path integrals in analysing elementary chemical reactions. Moreover, we show how a well-known path integral representation of averaged observables can be recovered from them. Upon expanding the forward and the backward path integrals around stationary paths, we then discuss and extend a recent method for the computation of rare event probabilities. Besides, we also derive path integral representations for processes with continuous state spaces whose forward and backward master equations admit Kramers-Moyal expansions. A truncation of the backward expansion at the level of a diffusion approximation recovers a classic path integral representation of the (backward) Fokker-Planck equation. One can rewrite this path integral in terms of an Onsager-Machlup function and, for purely diffusive Brownian motion, it simplifies to the path integral of Wiener. To make this review accessible to a broad community, we have used the language of probability theory rather than quantum (field) theory and do not assume any knowledge of the latter. The probabilistic structures underpinning various technical concepts, such as coherent states, the Doi-shift, and normal-ordered observables, are thereby made explicit.

Master equations and the theory of stochastic path integrals.

PubMed

Weber, Markus F; Frey, Erwin

2017-04-01

This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. Since the 1930s, master equations have served as a fundamental tool to understand the role of fluctuations in complex biological, chemical, and physical systems. Despite their simple appearance, analyses of master equations most often rely on low-noise approximations such as the Kramers-Moyal or the system size expansion, or require ad-hoc closure schemes for the derivation of low-order moment equations. We focus on numerical and analytical methods going beyond the low-noise limit and provide a unified framework for the study of master equations. After deriving the forward and backward master equations from the Chapman-Kolmogorov equation, we show how the two master equations can be cast into either of four linear partial differential equations (PDEs). Three of these PDEs are discussed in detail. The first PDE governs the time evolution of a generalized probability generating function whose basis depends on the stochastic process under consideration. Spectral methods, WKB approximations, and a variational approach have been proposed for the analysis of the PDE. The second PDE is novel and is obeyed by a distribution that is marginalized over an initial state. It proves useful for the computation of mean extinction times. The third PDE describes the time evolution of a 'generating functional', which generalizes the so-called Poisson representation. Subsequently, the solutions of the PDEs are expressed in terms of two path integrals: a 'forward' and a 'backward' path integral. Combined with inverse transformations, one obtains two distinct path integral representations of the conditional probability distribution solving the master equations. We exemplify both path integrals in analysing elementary chemical reactions. Moreover, we show how a well-known path integral representation of averaged observables can be recovered from them. Upon expanding the forward and the backward path integrals around stationary paths, we then discuss and extend a recent method for the computation of rare event probabilities. Besides, we also derive path integral representations for processes with continuous state spaces whose forward and backward master equations admit Kramers-Moyal expansions. A truncation of the backward expansion at the level of a diffusion approximation recovers a classic path integral representation of the (backward) Fokker-Planck equation. One can rewrite this path integral in terms of an Onsager-Machlup function and, for purely diffusive Brownian motion, it simplifies to the path integral of Wiener. To make this review accessible to a broad community, we have used the language of probability theory rather than quantum (field) theory and do not assume any knowledge of the latter. The probabilistic structures underpinning various technical concepts, such as coherent states, the Doi-shift, and normal-ordered observables, are thereby made explicit.

Evaluating four-loop conformal Feynman integrals by D-dimensional differential equations

NASA Astrophysics Data System (ADS)

Eden, Burkhard; Smirnov, Vladimir A.

2016-10-01

We evaluate a four-loop conformal integral, i.e. an integral over four four-dimensional coordinates, by turning to its dimensionally regularized version and applying differential equations for the set of the corresponding 213 master integrals. To solve these linear differential equations we follow the strategy suggested by Henn and switch to a uniformly transcendental basis of master integrals. We find a solution to these equations up to weight eight in terms of multiple polylogarithms. Further, we present an analytical result for the given four-loop conformal integral considered in four-dimensional space-time in terms of single-valued harmonic polylogarithms. As a by-product, we obtain analytical results for all the other 212 master integrals within dimensional regularization, i.e. considered in D dimensions.

Application of the Sumudu Transform to Discrete Dynamic Systems

ERIC Educational Resources Information Center

Asiru, Muniru Aderemi

2003-01-01

The Sumudu transform is an integral transform introduced to solve differential equations and control engineering problems. The transform possesses many interesting properties that make visualization easier and application has been demonstrated in the solution of partial differential equations, integral equations, integro-differential equations and…

Computational Algorithms or Identification of Distributed Parameter Systems

DTIC Science & Technology

1993-04-24

delay-differential equations, Volterra integral equations, and partial differential equations with memory terms . In particular we investigated a...tested for estimating parameters in a Volterra integral equation arising from a viscoelastic model of a flexible structure with Boltzmann damping. In...particular, one of the parameters identified was the order of the derivative in Volterra integro-differential equations containing fractional

Application of integral equation theory to analyze stability of electric field in multimode microwave heating cavity

NASA Astrophysics Data System (ADS)

Tang, Zhengming; Hong, Tao; Chen, Fangyuan; Zhu, Huacheng; Huang, Kama

2017-10-01

Microwave heating uniformity is mainly dependent on and affected by electric field. However, little study has paid attention to its stability characteristics in multimode cavity. In this paper, this problem is studied by the theory of Freedholm integral equation. Firstly, Helmholtz equation and the electric dyadic Green's function are used to derive the electric field integral equation. Then, the stability of electric field is demonstrated as the characteristics of solutions to Freedholm integral equation. Finally, the stability characteristics are obtained and verified by finite element calculation. This study not only can provide a comprehensive interpretation of electric field in multimode cavity but also help us make better use of microwave energy.

A semi-discrete Kadomtsev-Petviashvili equation and its coupled integrable system

NASA Astrophysics Data System (ADS)

Li, Chun-Xia; Lafortune, Stéphane; Shen, Shou-Feng

2016-05-01

We establish connections between two cascades of integrable systems generated from the continuum limits of the Hirota-Miwa equation and its remarkable nonlinear counterpart under the Miwa transformation, respectively. Among these equations, we are mainly concerned with the semi-discrete bilinear Kadomtsev-Petviashvili (KP) equation which is seldomly studied in literature. We present both of its Casorati and Grammian determinant solutions. Through the Pfaffianization procedure proposed by Hirota and Ohta, we are able to derive the coupled integrable system for the semi-discrete KP equation.

Whitham modulation theory for (2  +  1)-dimensional equations of Kadomtsev–Petviashvili type

NASA Astrophysics Data System (ADS)

Ablowitz, Mark J.; Biondini, Gino; Rumanov, Igor

2018-05-01

Whitham modulation theory for certain two-dimensional evolution equations of Kadomtsev–Petviashvili (KP) type is presented. Three specific examples are considered in detail: the KP equation, the two-dimensional Benjamin–Ono (2DBO) equation and a modified KP (m2KP) equation. A unified derivation is also provided. In the case of the m2KP equation, the corresponding Whitham modulation system exhibits features different from the other two. The approach presented here does not require integrability of the original evolution equation. Indeed, while the KP equation is known to be a completely integrable equation, the 2DBO equation and the m2KP equation are not known to be integrable. In each of the cases considered, the Whitham modulation system obtained consists of five first-order quasilinear partial differential equations. The Riemann problem (i.e. the analogue of the Gurevich–Pitaevskii problem) for the one-dimensional reduction of the m2KP equation is studied. For the m2KP equation, the system of modulation equations is used to analyze the linear stability of traveling wave solutions.

Applied Mathematical Methods in Theoretical Physics

NASA Astrophysics Data System (ADS)

Masujima, Michio

2005-04-01

All there is to know about functional analysis, integral equations and calculus of variations in a single volume. This advanced textbook is divided into two parts: The first on integral equations and the second on the calculus of variations. It begins with a short introduction to functional analysis, including a short review of complex analysis, before continuing a systematic discussion of different types of equations, such as Volterra integral equations, singular integral equations of Cauchy type, integral equations of the Fredholm type, with a special emphasis on Wiener-Hopf integral equations and Wiener-Hopf sum equations. After a few remarks on the historical development, the second part starts with an introduction to the calculus of variations and the relationship between integral equations and applications of the calculus of variations. It further covers applications of the calculus of variations developed in the second half of the 20th century in the fields of quantum mechanics, quantum statistical mechanics and quantum field theory. Throughout the book, the author presents over 150 problems and exercises -- many from such branches of physics as quantum mechanics, quantum statistical mechanics, and quantum field theory -- together with outlines of the solutions in each case. Detailed solutions are given, supplementing the materials discussed in the main text, allowing problems to be solved making direct use of the method illustrated. The original references are given for difficult problems. The result is complete coverage of the mathematical tools and techniques used by physicists and applied mathematicians Intended for senior undergraduates and first-year graduates in science and engineering, this is equally useful as a reference and self-study guide.

Green's function solution to heat transfer of a transparent gas through a tube

NASA Technical Reports Server (NTRS)

Frankel, J. I.

1989-01-01

A heat transfer analysis of a transparent gas flowing through a circular tube of finite thickness is presented. This study includes the effects of wall conduction, internal radiative exchange, and convective heat transfer. The natural mathematical formulation produces a nonlinear, integrodifferential equation governing the wall temperature and an ordinary differential equation describing the gas temperature. This investigation proposes to convert the original system of equations into an equivalent system of integral equations. The Green's function method permits the conversion of an integrodifferential equation into a pure integral equation. The proposed integral formulation and subsequent computational procedure are shown to be stable and accurate.

First integrals of the axisymmetric shape equation of lipid membranes

NASA Astrophysics Data System (ADS)

Zhang, Yi-Heng; McDargh, Zachary; Tu, Zhan-Chun

2018-03-01

The shape equation of lipid membranes is a fourth-order partial differential equation. Under the axisymmetric condition, this equation was transformed into a second-order ordinary differential equation (ODE) by Zheng and Liu (Phys. Rev. E 48 2856 (1993)). Here we try to further reduce this second-order ODE to a first-order ODE. First, we invert the usual process of variational calculus, that is, we construct a Lagrangian for which the ODE is the corresponding Euler–Lagrange equation. Then, we seek symmetries of this Lagrangian according to the Noether theorem. Under a certain restriction on Lie groups of the shape equation, we find that the first integral only exists when the shape equation is identical to the Willmore equation, in which case the symmetry leading to the first integral is scale invariance. We also obtain the mechanical interpretation of the first integral by using the membrane stress tensor. Project supported by the National Natural Science Foundation of China (Grant No. 11274046) and the National Science Foundation of the United States (Grant No. 1515007).

Derivation of the Schrodinger Equation from the Hamilton-Jacobi Equation in Feynman's Path Integral Formulation of Quantum Mechanics

ERIC Educational Resources Information Center

Field, J. H.

2011-01-01

It is shown how the time-dependent Schrodinger equation may be simply derived from the dynamical postulate of Feynman's path integral formulation of quantum mechanics and the Hamilton-Jacobi equation of classical mechanics. Schrodinger's own published derivations of quantum wave equations, the first of which was also based on the Hamilton-Jacobi…

Multiple scattering and the density distribution of a Cs MOT.

PubMed

Overstreet, K; Zabawa, P; Tallant, J; Schwettmann, A; Shaffer, J

2005-11-28

Multiple scattering is studied in a Cs magneto-optical trap (MOT). We use two Abel inversion algorithms to recover density distributions of the MOT from fluorescence images. Deviations of the density distribution from a Gaussian are attributed to multiple scattering.

L'astronomie dans le monde

NASA Astrophysics Data System (ADS)

Manfroid, J.

2017-05-01

matière sombre – Abell 2744 vu par ALMA – Bousculade dans Orion – Rotation stellaire – Tsunamis martiens – Planète X ou 9 – Formation d’étoiles dans les jets de trous noirs – Éjection d’un trou noir

Science Teacher Education: An International Perspective.

ERIC Educational Resources Information Center

Abell, Sandra K., Ed.

This book presents reform efforts in science teacher education from an international perspective. Chapters include: (1) "International Perspectives on Science Teacher Education: An Introduction" (Sandra K. Abell); (2) "The Development of Preservice Elementary Science Teacher Education in Australia" (Ken Appleton, Ian S. Ginns,…

Exponential Methods for the Time Integration of Schroedinger Equation

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

Cano, B.; Gonzalez-Pachon, A.

2010-09-30

We consider exponential methods of second order in time in order to integrate the cubic nonlinear Schroedinger equation. We are interested in taking profit of the special structure of this equation. Therefore, we look at symmetry, symplecticity and approximation of invariants of the proposed methods. That will allow to integrate till long times with reasonable accuracy. Computational efficiency is also our aim. Therefore, we make numerical computations in order to compare the methods considered and so as to conclude that explicit Lawson schemes projected on the norm of the solution are an efficient tool to integrate this equation.

LOFAR discovery of an ultra-steep radio halo and giant head-tail radio galaxy in Abell 1132

NASA Astrophysics Data System (ADS)

Wilber, A.; Brüggen, M.; Bonafede, A.; Savini, F.; Shimwell, T.; van Weeren, R. J.; Rafferty, D.; Mechev, A. P.; Intema, H.; Andrade-Santos, F.; Clarke, A. O.; Mahony, E. K.; Morganti, R.; Prandoni, I.; Brunetti, G.; Röttgering, H.; Mandal, S.; de Gasperin, F.; Hoeft, M.

2018-01-01

Low-Frequency Array (LOFAR) observations at 144 MHz have revealed large-scale radio sources in the unrelaxed galaxy cluster Abell 1132. The cluster hosts diffuse radio emission on scales of ∼650 kpc near the cluster centre and a head-tail (HT) radio galaxy, extending up to 1 Mpc, south of the cluster centre. The central diffuse radio emission is not seen in NRAO VLA FIRST Survey, Westerbork Northern Sky Survey, nor in C & D array VLA observations at 1.4 GHz, but is detected in our follow-up Giant Meterwave Radio Telescope (GMRT) observations at 325 MHz. Using LOFAR and GMRT data, we determine the spectral index of the central diffuse emission to be α = -1.75 ± 0.19 (S ∝ να). We classify this emission as an ultra-steep spectrum radio halo and discuss the possible implications for the physical origin of radio haloes. The HT radio galaxy shows narrow, collimated emission extending up to 1 Mpc and another 300 kpc of more diffuse, disturbed emission, giving a full projected linear size of 1.3 Mpc - classifying it as a giant radio galaxy (GRG) and making it the longest HT found to date. The head of the GRG coincides with an elliptical galaxy (SDSS J105851.01+564308.5) belonging to Abell 1132. In our LOFAR image, there appears to be a connection between the radio halo and the GRG. The turbulence that may have produced the halo may have also affected the tail of the GRG. In turn, the GRG may have provided seed electrons for the radio halo.

The first high resolution image of coronal gas in a starbursting cool core cluster

NASA Astrophysics Data System (ADS)

Johnson, Sean

2017-08-01

Galaxy clusters represent a unique laboratory for directly observing gas cooling and feedback due to their high masses and correspondingly high gas densities and temperatures. Cooling of X-ray gas observed in 1/3 of clusters, known as cool-core clusters, should fuel star formation at prodigious rates, but such high levels of star formation are rarely observed. Feedback from active galactic nuclei (AGN) is a leading explanation for the lack of star formation in most cool clusters, and AGN power is sufficient to offset gas cooling on average. Nevertheless, some cool core clusters exhibit massive starbursts indicating that our understanding of cooling and feedback is incomplete. Observations of 10^5 K coronal gas in cool core clusters through OVI emission offers a sensitive means of testing our understanding of cooling and feedback because OVI emission is a dominant coolant and sensitive tracer of shocked gas. Recently, Hayes et al. 2016 demonstrated that synthetic narrow-band imaging of OVI emission is possible through subtraction of long-pass filters with the ACS+SBC for targets at z=0.23-0.29. Here, we propose to use this exciting new technique to directly image coronal OVI emitting gas at high resolution in Abell 1835, a prototypical starbursting cool-core cluster at z=0.252. Abell 1835 hosts a strong cooling core, massive starburst, radio AGN, and at z=0.252, it offers a unique opportunity to directly image OVI at hi-res in the UV with ACS+SBC. With just 15 orbits of ACS+SBC imaging, the proposed observations will complete the existing rich multi-wavelength dataset available for Abell 1835 to provide new insights into cooling and feedback in clusters.

Discrete integration of continuous Kalman filtering equations for time invariant second-order structural systems

NASA Technical Reports Server (NTRS)

Park, K. C.; Belvin, W. Keith

1990-01-01

A general form for the first-order representation of the continuous second-order linear structural-dynamics equations is introduced to derive a corresponding form of first-order continuous Kalman filtering equations. Time integration of the resulting equations is carried out via a set of linear multistep integration formulas. It is shown that a judicious combined selection of computational paths and the undetermined matrices introduced in the general form of the first-order linear structural systems leads to a class of second-order discrete Kalman filtering equations involving only symmetric sparse N x N solution matrices.

Integrability and structural stability of solutions to the Ginzburg-Landau equation

NASA Technical Reports Server (NTRS)

Keefe, Laurence R.

1986-01-01

The integrability of the Ginzburg-Landau equation is studied to investigate if the existence of chaotic solutions found numerically could have been predicted a priori. The equation is shown not to possess the Painleveproperty, except for a special case of the coefficients that corresponds to the integrable, nonlinear Schroedinger (NLS) equation. Regarding the Ginzburg-Landau equation as a dissipative perturbation of the NLS, numerical experiments show all but one of a family of two-tori solutions, possessed by the NLS under particular conditions, to disappear under real perturbations to the NLS coefficients of O(10 to the -6th).

Symbolic computation of recurrence equations for the Chebyshev series solution of linear ODE's. [ordinary differential equations

NASA Technical Reports Server (NTRS)

Geddes, K. O.

1977-01-01

If a linear ordinary differential equation with polynomial coefficients is converted into integrated form then the formal substitution of a Chebyshev series leads to recurrence equations defining the Chebyshev coefficients of the solution function. An explicit formula is presented for the polynomial coefficients of the integrated form in terms of the polynomial coefficients of the differential form. The symmetries arising from multiplication and integration of Chebyshev polynomials are exploited in deriving a general recurrence equation from which can be derived all of the linear equations defining the Chebyshev coefficients. Procedures for deriving the general recurrence equation are specified in a precise algorithmic notation suitable for translation into any of the languages for symbolic computation. The method is algebraic and it can therefore be applied to differential equations containing indeterminates.

Effective quadrature formula in solving linear integro-differential equations of order two

NASA Astrophysics Data System (ADS)

Eshkuvatov, Z. K.; Kammuji, M.; Long, N. M. A. Nik; Yunus, Arif A. M.

2017-08-01

In this note, we solve general form of Fredholm-Volterra integro-differential equations (IDEs) of order 2 with boundary condition approximately and show that proposed method is effective and reliable. Initially, IDEs is reduced into integral equation of the third kind by using standard integration techniques and identity between multiple and single integrals then truncated Legendre series are used to estimate the unknown function. For the kernel integrals, we have applied Gauss-Legendre quadrature formula and collocation points are chosen as the roots of the Legendre polynomials. Finally, reduce the integral equations of the third kind into the system of algebraic equations and Gaussian elimination method is applied to get approximate solutions. Numerical examples and comparisons with other methods reveal that the proposed method is very effective and dominated others in many cases. General theory of existence of the solution is also discussed.

An integrable family of Monge-Ampère equations and their multi-Hamiltonian structure

NASA Astrophysics Data System (ADS)

Nutku, Y.; Sarioǧlu, Ö.

1993-02-01

We have identified a completely integrable family of Monge-Ampère equations through an examination of their Hamiltonian structure. Starting with a variational formulation of the Monge-Ampère equations we have constructed the first Hamiltonian operator through an application of Dirac's theory of constraints. The completely integrable class of Monge-Ampère equations are then obtained by solving the Jacobi identities for a sufficiently general form of the second Hamiltonian operator that is compatible with the first.

Extremely Fast Numerical Integration of Ocean Surface Wave Dynamics

DTIC Science & Technology

2007-09-30

sub-processor must be added as shown in the blue box of Fig. 1. We first consider the Kadomtsev - Petviashvili (KP) equation ηt + coηx +αηηx + βη ...analytic integration of the so-called “soliton equations ,” I have discovered how the GFT can be used to solved higher order equations for which study...analytical study and extremely fast numerical integration of the extended nonlinear Schroedinger equation for fully three dimensional wave motion

Alternate Solution to Generalized Bernoulli Equations via an Integrating Factor: An Exact Differential Equation Approach

ERIC Educational Resources Information Center

Tisdell, C. C.

2017-01-01

Solution methods to exact differential equations via integrating factors have a rich history dating back to Euler (1740) and the ideas enjoy applications to thermodynamics and electromagnetism. Recently, Azevedo and Valentino presented an analysis of the generalized Bernoulli equation, constructing a general solution by linearizing the problem…

Continuous properties of the data-to-solution map for a generalized μ-Camassa-Holm integrable equation

NASA Astrophysics Data System (ADS)

Yu, Shengqi

2018-05-01

This work studies a generalized μ-type integrable equation with both quadratic and cubic nonlinearities; the μ-Camassa-Holm and modified μ-Camassa-Holm equations are members of this family of equations. It has been shown that the Cauchy problem for this generalized μ-Camassa-Holm integrable equation is locally well-posed for initial data u0 ∈ Hs, s > 5/2. In this work, we further investigate the continuity properties to this equation. It is proved in this work that the data-to-solution map of the proposed equation is not uniformly continuous. It is also found that the solution map is Hölder continuous in the Hr-topology when 0 ≤ r < s with Hölder exponent α depending on both s and r.

Watching conformational- and photo-dynamics of single fluorescent proteins in solution.

PubMed

Goldsmith, Randall H; Moerner, W E

2010-03-01

Observing the dynamics of single biomolecules over prolonged time periods is difficult to achieve without significantly altering the molecule through immobilization. It can, however, be accomplished using the Anti-Brownian ELectrokinetic (ABEL) Trap, which allows extended investigation of solution-phase biomolecules - without immobilization -through real-time electrokinetic feedback. Here we apply the ABEL trap to study an important photosynthetic antenna protein, Allophycocyanin (APC). The technique allows the observation of single molecules of solution-phase APC for more than one second. We observe a complex relationship between fluorescence intensity and lifetime that cannot be explained by simple static kinetic models. Light-induced conformational changes are shown to occur and evidence is obtained for fluctuations in the spontaneous emission lifetime, which is typically assumed to be constant. Our methods provide a new window into the dynamics of fluorescent proteins and the observations are relevant for the interpretation of in vivo single-molecule imaging experiments, bacterial photosynthetic regulation, and biomaterials for solar energy harvesting.

Diffuse X-ray emission from Abell clusters 401 and 399 - A gravitationally bound system

NASA Technical Reports Server (NTRS)

Ulmer, M. P.; Kinzer, R.; Cruddace, R. G.; Wood, K.; Evans, W.; Byram, E. T.; Chubb, T. A.; Friedman, H.

1979-01-01

The X-ray emission from the Abell 401-399 region has been studied using data obtained by the A-1 proportional counter aboard HEAO 1 in two different ways. The first involved routine scanning of the region during the all-sky survey, and the second was an observation in which the instrument was pointed at A401 during a lunar occultation. The emission is shown to be unusually extended and to be centered on a point lying between A401 and A399. The best fit of a uniform disk model to the data yielded a radius of 25.5 + or -4.4 arcmin for the lunar occultation and 42 + or - 17 arcmin for the scans. A possible explanation of the results is that A401 and A399 are both diffuse cluster X-ray sources. Alternatively, the emission may come from a large gas cloud of at least 10 to the 15th solar masses enveloping both clusters.

Spatially-resolved velocities of thermally-produced spray droplets using a velocity-divided Abel inversion of photographed streaks

NASA Astrophysics Data System (ADS)

Kawaguchi, Y.; Kobayashi, N.; Yamagata, Y.; Miyazaki, F.; Yamasaki, M.; Muraoka, K.

2017-10-01

Droplet velocities of thermal spray are known to have profound effects on important coating qualities, such as adhesive strength, porosity, and hardness, for various applications. For obtaining the droplet velocities, therefore, the TOF (time-of-flight) technique has been widely used, which relies on observations of emitted radiation from the droplets, where all droplets along the line-of-sight contribute to signals. Because droplets at and near the flow axis mostly contribute coating layers, it has been hoped to get spatially resolved velocities. For this purpose, a velocity-divided Abel inversion was devised from CMOS photographic data. From this result, it has turned out that the central velocity is about 25% higher than that obtained from the TOF technique for the case studied (at the position 150 mm downstream of the plasma spray gun, where substrates for spray coatings are usually placed). Further implications of the obtained results are discussed.

Watching conformational- and photo-dynamics of single fluorescent proteins in solution

PubMed Central

Goldsmith, Randall H.

2010-01-01

Observing the dynamics of single biomolecules over prolonged time periods is difficult to achieve without significantly altering the molecule through immobilization. It can, however, be accomplished using the Anti-Brownian ELectrokinetic (ABEL) Trap, which allows extended investigation of solution-phase biomolecules - without immobilization -through real-time electrokinetic feedback. Here we apply the ABEL trap to study an important photosynthetic antenna protein, Allophycocyanin (APC). The technique allows the observation of single molecules of solution-phase APC for more than one second. We observe a complex relationship between fluorescence intensity and lifetime that cannot be explained by simple static kinetic models. Light-induced conformational changes are shown to occur and evidence is obtained for fluctuations in the spontaneous emission lifetime, which is typically assumed to be constant. Our methods provide a new window into the dynamics of fluorescent proteins and the observations are relevant for the interpretation of in vivo single-molecule imaging experiments, bacterial photosynthetic regulation, and biomaterials for solar energy harvesting. PMID:20625479

Abell 1142 and the Missing Central Galaxy – A Cluster in Transition?

NASA Astrophysics Data System (ADS)

Jones, Alexander; Su, Yuanyuan; Buote, David; Forman, William; van Weeren, Reinout; Jones, Christine; Gastaldello, Fabio; Kraft, Ralph; Randall, Scott

2018-01-01

Two types of galaxy clusters exist: cool core (CC) clusters which exhibit centrally-peaked metallicity and X-ray emission and non-cool core (NCC) clusters, possessing comparably homogeneous metallicity and X-ray emission distributions. However, the origin of this dichotomy is still unknown. The current prevailing theories state that either there is a primordial entropy limit, above which a CC is unable to form, or that clusters can change type through major mergers and radiative cooling. Abell 1142 is a galaxy cluster that can provide a unique probe of the root of this cluster-type division. It is formed of two merging sub-clusters, each with its own brightest cluster galaxies (BCG). Its enriched X-ray centroid (possible CC remnant) lies between these two BCGs. We present the thermal and chemical distributions of this system using deep (180ks) XMM-Newton observations to shed light on the role of mergers in the evolution of galaxy clusters.

A series of shocks and edges in Abell 2219

DOE PAGES

Canning, R. E. A.; Allen, S. W.; Applegate, D. E.; ...

2016-09-22

Here, we present deep, 170 ks, Chandra X-ray observations of Abell 2219 (z = 0.23), one of the hottest and most X-ray luminous clusters known, and which is experiencing a major merger event. We discover a ‘horseshoe’ of high-temperature gas surrounding the ram-pressure-stripped, bright, hot, X-ray cores. We confirm an X-ray shock front located north-west of the X-ray centroid and along the projected merger axis. We also find a second shock front to the south-east of the X-ray centroid making this only the second cluster where both the shock and reverse shock are confirmed with X-ray temperature measurements. We alsomore » present evidence for a possible sloshing cold front in the ‘remnant tail’ of one of the sub-cluster cores. The cold front and north-west shock front geometrically bound the radio halo and appear to be directly influencing the radio properties of the cluster.« less

X-Ray Spectroscopy of the Cluster of Galaxies Abell 1795 with XMM-Newton

NASA Technical Reports Server (NTRS)

Tamura, T.; Kaastra, J. S.; Peterson, J. R.; Paerels, F.; Mittaz, J. P. D.; Trudolyubov, S. P.; Stewart, G.; Fabian, A. C.; Mushotzky, R. F.; Lumb, D. H.

2000-01-01

The initial results from XMM-Newton observations of the rich cluster of galaxies Abell 1795 are presented. The spatially-resolved X-ray spectra taken by the European Photon Imaging Cameras (EPIC) show a temperature drop at a radius of - 200 kpc from the cluster center, indicating that the ICM is cooling. Both the EPIC and the Reflection Grating Spectrometers (RGS) spectra extracted from the cluster center can be described by an isothermal model with a temperature of approx. 4 keV. The volume emission measure of any cool component (less than 1 keV) is less than a few % of the hot component at the cluster center. A strong O VIII Lyman alpha line was detected with the RGS from the cluster core. The O abundance of the ICM is 0.2-0.5 times the solar value. The O to Fe ratio at the cluster center is 0.5 - 1.5 times the solar ratio.

Swimming in Sculptor

NASA Image and Video Library

2016-03-07

Peering deep into the early Universe, this picturesque parallel field observation from the NASA/ESA Hubble Space Telescope reveals thousands of colourful galaxies swimming in the inky blackness of space. A few foreground stars from our own galaxy, the Milky Way, are also visible. In October 2013 Hubble’s Wide Field Camera 3 (WFC3) and Advanced Camera for Surveys (ACS) began observing this portion of sky as part of the Frontier Fields programme. This spectacular skyscape was captured during the study of the giant galaxy cluster Abell 2744, otherwise known as Pandora’s Box. While one of Hubble’s cameras concentrated on Abell 2744, the other camera viewed this adjacent patch of sky near to the cluster. Containing countless galaxies of various ages, shapes and sizes, this parallel field observation is nearly as deep as the Hubble Ultra-Deep Field. In addition to showcasing the stunning beauty of the deep Universe in incredible detail, this parallel field — when compared to other deep fields — will help astronomers understand how similar the Universe looks in different directions

MT Ser, a binary blue subdwarf

NASA Astrophysics Data System (ADS)

Shimanskii, V. V.; Borisov, N. V.; Sakhibullin, N. A.; Sheveleva, D. V.

2008-06-01

We have classified and determined the parameters of the evolved close binary MT Ser. Our moderate-resolution spectra covering various phases of the orbital period were taken with the 6-m telescope of the Special Astrophysical Observatory. The spectra of MT Ser freed from the contribution of the surrounding nebula Abell 41 contained no emission lines due to the reflection effect. The radial velocities measured from lines of different elements showed them to be constant on a time scale corresponding to the orbital period. At the same time, we find effects of broadening for the HeII absorption lines, due to the orbital motion of two hot stars of similar types. As a result, we classify MT Ser as a system with two blue subdwarfs after the common-envelope stage. We estimate the component masses and the distance to the object from the Doppler broadening of the HeII lines. We demonstrate that the age of the ambient nebula, Abell 41, is about 35 000 years.

The Sunyaev-Zeldovich Effect in Abell 370

NASA Technical Reports Server (NTRS)

Grego, Laura; Carlstrom, John E.; Joy, Marshall K.; Reese, Erik D.; Holder, Gilbert P.; Patel, Sandeep; Cooray, Asantha R.; Holzappel, William L.

2000-01-01

We present interferometric measurements of the Sunyaev-Zeldovich (SZ) effect toward the galaxy cluster Abell 370. These measurements, which directly probe the pressure of the cluster's gas, show the gas distribution to be strongly aspherical, as do the X-ray and gravitational lensing observations. We calculate the cluster's gas mass fraction in two ways. We first compare the gas mass derived from the SZ measurements to the lensing-derived gravitational mass near the critical lensing radius. We also calculate the gas mass fraction from the SZ data by deprojecting the three-dimensional gas density distribution and deriving the total mass under the assumption that the gas is in hydrostatic equilibrium (HSE). We test the assumptions in the HSE method by comparing the total cluster mass implied by the two methods and find that they agree within the errors of the measurement. We discuss the possible system- atic errors in the gas mass fraction measurement and the constraints it places on the matter density parameter, Omega(sub M).

A family of wave equations with some remarkable properties.

PubMed

da Silva, Priscila Leal; Freire, Igor Leite; Sampaio, Júlio Cesar Santos

2018-02-01

We consider a family of homogeneous nonlinear dispersive equations with two arbitrary parameters. Conservation laws are established from the point symmetries and imply that the whole family admits square integrable solutions. Recursion operators are found for two members of the family investigated. For one of them, a Lax pair is also obtained, proving its complete integrability. From the Lax pair, we construct a Miura-type transformation relating the original equation to the Korteweg-de Vries (KdV) equation. This transformation, on the other hand, enables us to obtain solutions of the equation from the kernel of a Schrödinger operator with potential parametrized by the solutions of the KdV equation. In particular, this allows us to exhibit a kink solution to the completely integrable equation from the 1-soliton solution of the KdV equation. Finally, peakon-type solutions are also found for a certain choice of the parameters, although for this particular case the equation is reduced to a homogeneous second-order nonlinear evolution equation.

A New Formulation of Time Domain Boundary Integral Equation for Acoustic Wave Scattering in the Presence of a Uniform Mean Flow

NASA Technical Reports Server (NTRS)

Hu, Fang; Pizzo, Michelle E.; Nark, Douglas M.

2017-01-01

It has been well-known that under the assumption of a constant uniform mean flow, the acoustic wave propagation equation can be formulated as a boundary integral equation, in both the time domain and the frequency domain. Compared with solving partial differential equations, numerical methods based on the boundary integral equation have the advantage of a reduced spatial dimension and, hence, requiring only a surface mesh. However, the constant uniform mean flow assumption, while convenient for formulating the integral equation, does not satisfy the solid wall boundary condition wherever the body surface is not aligned with the uniform mean flow. In this paper, we argue that the proper boundary condition for the acoustic wave should not have its normal velocity be zero everywhere on the solid surfaces, as has been applied in the literature. A careful study of the acoustic energy conservation equation is presented that shows such a boundary condition in fact leads to erroneous source or sink points on solid surfaces not aligned with the mean flow. A new solid wall boundary condition is proposed that conserves the acoustic energy and a new time domain boundary integral equation is derived. In addition to conserving the acoustic energy, another significant advantage of the new equation is that it is considerably simpler than previous formulations. In particular, tangential derivatives of the solution on the solid surfaces are no longer needed in the new formulation, which greatly simplifies numerical implementation. Furthermore, stabilization of the new integral equation by Burton-Miller type reformulation is presented. The stability of the new formulation is studied theoretically as well as numerically by an eigenvalue analysis. Numerical solutions are also presented that demonstrate the stability of the new formulation.

On a new semi-discrete integrable combination of Burgers and Sharma-Tasso-Olver equation

NASA Astrophysics Data System (ADS)

Zhao, Hai-qiong

2017-02-01

In this paper, a new semi-discrete integrable combination of Burgers and Sharma-Tasso-Olver equation is investigated. The underlying integrable structures like the Lax pair, the infinite number of conservation laws, the Darboux-Bäcklund transformation, and the solutions are presented in the explicit form. The theory of the semi-discrete equation including integrable properties yields the corresponding theory of the continuous counterpart in the continuous limit. Finally, numerical experiments are provided to demonstrate the effectiveness of the developed integrable semi-discretization algorithms.

Calculation of Moment Matrix Elements for Bilinear Quadrilaterals and Higher-Order Basis Functions

DTIC Science & Technology

2016-01-06

methods are known as boundary integral equation (BIE) methods and the present study falls into this category. The numerical solution of the BIE is...iterated integrals. The inner integral involves the product of the free-space Green’s function for the Helmholtz equation multiplied by an appropriate...Website: http://www.wipl-d.com/ 5. Y. Zhang and T. K. Sarkar, Parallel Solution of Integral Equation -Based EM Problems in the Frequency Domain. New

A numerical solution for two-dimensional Fredholm integral equations of the second kind with kernels of the logarithmic potential form

NASA Technical Reports Server (NTRS)

Gabrielsen, R. E.; Uenal, A.

1981-01-01

Two dimensional Fredholm integral equations with logarithmic potential kernels are numerically solved. The explicit consequence of these solutions to their true solutions is demonstrated. The results are based on a previous work in which numerical solutions were obtained for Fredholm integral equations of the second kind with continuous kernels.

Properties of the two-dimensional heterogeneous Lennard-Jones dimers: An integral equation study

PubMed Central

Urbic, Tomaz

2016-01-01

Structural and thermodynamic properties of a planar heterogeneous soft dumbbell fluid are examined using Monte Carlo simulations and integral equation theory. Lennard-Jones particles of different sizes are the building blocks of the dimers. The site-site integral equation theory in two dimensions is used to calculate the site-site radial distribution functions and the thermodynamic properties. Obtained results are compared to Monte Carlo simulation data. The critical parameters for selected types of dimers were also estimated and the influence of the Lennard-Jones parameters was studied. We have also tested the correctness of the site-site integral equation theory using different closures. PMID:27875894

Radial density distribution of a warm dense plasma formed by underwater electrical explosion of a copper wire

NASA Astrophysics Data System (ADS)

Nitishinskiy, M.; Yanuka, D.; Virozub, A.; Krasik, Ya. E.

2017-12-01

Time- and space-resolved evolution of the density (down to 0.07 of solid state density) of a copper wire during its microsecond timescale electrical explosion in water was obtained by X-ray backlighting. In the present research, a flash X-ray source of 20 ns pulse-width and >60 keV photon energy was used. The conductivity of copper was evaluated for a temperature of 10 kK and found to be in good agreement with the data obtained in earlier experiments [DeSilva and Katsouros, Phys. Rev. E 57, 5945 (1998) and Sheftman and Krasik, Phys. Plasmas 18, 092704 (2011)] where only electrical and optical diagnostics were applied. Magneto-hydrodynamic simulation shows a good agreement between the simulated and experimental waveforms of the current and voltage and measured the radial expansion of the exploding wire. Also, the radial density distribution obtained by an inverse Abel transform analysis agrees with the results of these simulations. Thus, the validity of the equations of state for copper and the conductivity model used in the simulations was confirmed for the parameters of the exploding wire realized in the present research.

Universal and integrable nonlinear evolution systems of equations in 2+1 dimensions

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

Maccari, A.

1997-08-01

Integrable systems of nonlinear partial differential equations (PDEs) are obtained from integrable equations in 2+1 dimensions, by means of a reduction method of broad applicability based on Fourier expansion and spatio{endash}temporal rescalings, which is asymptotically exact in the limit of weak nonlinearity. The integrability by the spectral transform is explicitly demonstrated, because the corresponding Lax pairs have been derived, applying the same reduction method to the Lax pair of the initial equation. These systems of nonlinear PDEs are likely to be of applicative relevance and have a {open_quotes}universal{close_quotes} character, inasmuch as they may be derived from a very large classmore » of nonlinear evolution equations with a linear dispersive part. {copyright} {ital 1997 American Institute of Physics.}« less

Comparison of various methods for mathematical analysis of the Foucault knife edge test pattern to determine optical imperfections

NASA Technical Reports Server (NTRS)

Gatewood, B. E.

1971-01-01

The linearized integral equation for the Foucault test of a solid mirror was solved by various methods: power series, Fourier series, collocation, iteration, and inversion integral. The case of the Cassegrain mirror was solved by a particular power series method, collocation, and inversion integral. The inversion integral method appears to be the best overall method for both the solid and Cassegrain mirrors. Certain particular types of power series and Fourier series are satisfactory for the Cassegrain mirror. Numerical integration of the nonlinear equation for selected surface imperfections showed that results start to deviate from those given by the linearized equation at a surface deviation of about 3 percent of the wavelength of light. Several possible procedures for calibrating and scaling the input data for the integral equation are described.

Green function of the double-fractional Fokker-Planck equation: path integral and stochastic differential equations.

PubMed

Kleinert, H; Zatloukal, V

2013-11-01

The statistics of rare events, the so-called black-swan events, is governed by non-Gaussian distributions with heavy power-like tails. We calculate the Green functions of the associated Fokker-Planck equations and solve the related stochastic differential equations. We also discuss the subject in the framework of path integration.

Localization of the eigenvalues of linear integral equations with applications to linear ordinary differential equations.

NASA Technical Reports Server (NTRS)

Sloss, J. M.; Kranzler, S. K.

1972-01-01

The equivalence of a considered integral equation form with an infinite system of linear equations is proved, and the localization of the eigenvalues of the infinite system is expressed. Error estimates are derived, and the problems of finding upper bounds and lower bounds for the eigenvalues are solved simultaneously.

Finite-volume spectra of the Lee-Yang model

NASA Astrophysics Data System (ADS)

Bajnok, Zoltan; el Deeb, Omar; Pearce, Paul A.

2015-04-01

We consider the non-unitary Lee-Yang minimal model in three different finite geometries: (i) on the interval with integrable boundary conditions labelled by the Kac labels ( r, s) = (1 , 1) , (1 , 2), (ii) on the circle with periodic boundary conditions and (iii) on the periodic circle including an integrable purely transmitting defect. We apply φ 1,3 integrable perturbations on the boundary and on the defect and describe the flow of the spectrum. Adding a Φ1,3 integrable perturbation to move off-criticality in the bulk, we determine the finite size spectrum of the massive scattering theory in the three geometries via Thermodynamic Bethe Ansatz (TBA) equations. We derive these integral equations for all excitations by solving, in the continuum scaling limit, the TBA functional equations satisfied by the transfer matrices of the associated A 4 RSOS lattice model of Forrester and Baxter in Regime III. The excitations are classified in terms of ( m, n) systems. The excited state TBA equations agree with the previously conjectured equations in the boundary and periodic cases. In the defect case, new TBA equations confirm previously conjectured transmission factors.

The Green's matrix and the boundary integral equations for analysis of time-harmonic dynamics of elastic helical springs.

PubMed

Sorokin, Sergey V

2011-03-01

Helical springs serve as vibration isolators in virtually any suspension system. Various exact and approximate methods may be employed to determine the eigenfrequencies of vibrations of these structural elements and their dynamic transfer functions. The method of boundary integral equations is a meaningful alternative to obtain exact solutions of problems of the time-harmonic dynamics of elastic springs in the framework of Bernoulli-Euler beam theory. In this paper, the derivations of the Green's matrix, of the Somigliana's identities, and of the boundary integral equations are presented. The vibrational power transmission in an infinitely long spring is analyzed by means of the Green's matrix. The eigenfrequencies and the dynamic transfer functions are found by solving the boundary integral equations. In the course of analysis, the essential features and advantages of the method of boundary integral equations are highlighted. The reported analytical results may be used to study the time-harmonic motion in any wave guide governed by a system of linear differential equations in a single spatial coordinate along its axis. © 2011 Acoustical Society of America

Nonzero solutions of nonlinear integral equations modeling infectious disease

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

Williams, L.R.; Leggett, R.W.

1982-01-01

Sufficient conditions to insure the existence of periodic solutions to the nonlinear integral equation, x(t) = ..integral../sup t//sub t-tau/f(s,x(s))ds, are given in terms of simple product and product integral inequalities. The equation can be interpreted as a model for the spread of infectious diseases (e.g., gonorrhea or any of the rhinovirus viruses) if x(t) is the proportion of infectives at time t and f(t,x(t)) is the proportion of new infectives per unit time.

Numerical integration of asymptotic solutions of ordinary differential equations

NASA Technical Reports Server (NTRS)

Thurston, Gaylen A.

1989-01-01

Classical asymptotic analysis of ordinary differential equations derives approximate solutions that are numerically stable. However, the analysis also leads to tedious expansions in powers of the relevant parameter for a particular problem. The expansions are replaced with integrals that can be evaluated by numerical integration. The resulting numerical solutions retain the linear independence that is the main advantage of asymptotic solutions. Examples, including the Falkner-Skan equation from laminar boundary layer theory, illustrate the method of asymptotic analysis with numerical integration.

Multistep integration formulas for the numerical integration of the satellite problem

NASA Technical Reports Server (NTRS)

Lundberg, J. B.; Tapley, B. D.

1981-01-01

The use of two Class 2/fixed mesh/fixed order/multistep integration packages of the PECE type for the numerical integration of the second order, nonlinear, ordinary differential equation of the satellite orbit problem. These two methods are referred to as the general and the second sum formulations. The derivation of the basic equations which characterize each formulation and the role of the basic equations in the PECE algorithm are discussed. Possible starting procedures are examined which may be used to supply the initial set of values required by the fixed mesh/multistep integrators. The results of the general and second sum integrators are compared to the results of various fixed step and variable step integrators.

Direct linearizing transform for three-dimensional discrete integrable systems: the lattice AKP, BKP and CKP equations.

PubMed

Fu, Wei; Nijhoff, Frank W

2017-07-01

A unified framework is presented for the solution structure of three-dimensional discrete integrable systems, including the lattice AKP, BKP and CKP equations. This is done through the so-called direct linearizing transform, which establishes a general class of integral transforms between solutions. As a particular application, novel soliton-type solutions for the lattice CKP equation are obtained.

Integrability of the Kruskal--Zabusky Discrete Equation by Multiscale Expansion

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

Levi, Decio; Scimiterna, Christian

2010-03-08

In 1965 Kruskal and Zabusky in a very famous article in Physical Review Letters introduced the notion of 'soliton' to describe the interaction of solitary waves solutions of the Korteweg de Vries equation (KdV). To do so they introduced a discrete approximation to the KdV, the Kruskal-Zabusky equation (KZ). Here we analyze the KZ equation using the multiscale expansion and show that the equation is only A{sub 2} integrable.

Integrability and Poisson Structures of Three Dimensional Dynamical Systems and Equations of Hydrodynamic Type

NASA Astrophysics Data System (ADS)

Gumral, Hasan

Poisson structure of completely integrable 3 dimensional dynamical systems can be defined in terms of an integrable 1-form. We take advantage of this fact and use the theory of foliations in discussing the geometrical structure underlying complete and partial integrability. We show that the Halphen system can be formulated in terms of a flat SL(2,R)-valued connection and belongs to a non-trivial Godbillon-Vey class. On the other hand, for the Euler top and a special case of 3-species Lotka-Volterra equations which are contained in the Halphen system as limiting cases, this structure degenerates into the form of globally integrable bi-Hamiltonian structures. The globally integrable bi-Hamiltonian case is a linear and the sl_2 structure is a quadratic unfolding of an integrable 1-form in 3 + 1 dimensions. We complete the discussion of the Hamiltonian structure of 2-component equations of hydrodynamic type by presenting the Hamiltonian operators for Euler's equation and a continuum limit of Toda lattice. We present further infinite sequences of conserved quantities for shallow water equations and show that their generalizations by Kodama admit bi-Hamiltonian structure. We present a simple way of constructing the second Hamiltonian operators for N-component equations admitting some scaling properties. The Kodama reduction of the dispersionless-Boussinesq equations and the Lax reduction of the Benney moment equations are shown to be equivalent by a symmetry transformation. They can be cast into the form of a triplet of conservation laws which enable us to recognize a non-trivial scaling symmetry. The resulting bi-Hamiltonian structure generates three infinite sequences of conserved densities.

Time-dependent integral equations of neutron transport for calculating the kinetics of nuclear reactors by the Monte Carlo method

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

Davidenko, V. D., E-mail: Davidenko-VD@nrcki.ru; Zinchenko, A. S., E-mail: zin-sn@mail.ru; Harchenko, I. K.

2016-12-15

Integral equations for the shape functions in the adiabatic, quasi-static, and improved quasi-static approximations are presented. The approach to solving these equations by the Monte Carlo method is described.

On the solution of integral equations with a generalized cauchy kernal

NASA Technical Reports Server (NTRS)

Kaya, A. C.; Erdogan, F.

1986-01-01

A certain class of singular integral equations that may arise from the mixed boundary value problems in nonhonogeneous materials is considered. The distinguishing feature of these equations is that in addition to the Cauchy singularity, the kernels contain terms that are singular only at the end points. In the form of the singular integral equations adopted, the density function is a potential or a displacement and consequently the kernal has strong singularities of the form (t-x)(-2), x(n-2) (t+x)(n), (n is = or 2, 0 x, t b). The complex function theory is used to determine the fundamental function of the problem for the general case and a simple numerical technique is described to solve the integral equation. Two examples from the theory of elasticity are then considered to show the application of the technique.

On the solution of integral equations with strongly singular kernels

NASA Technical Reports Server (NTRS)

Kaya, A. C.; Erdogan, F.

1986-01-01

Some useful formulas are developed to evaluate integrals having a singularity of the form (t-x) sup-m ,m greater than or equal 1. Interpreting the integrals with strong singularities in Hadamard sense, the results are used to obtain approximate solutions of singular integral equations. A mixed boundary value problem from the theory of elasticity is considered as an example. Particularly for integral equations where the kernel contains, in addition to the dominant term (t-x) sup -m , terms which become unbounded at the end points, the present technique appears to be extremely effective to obtain rapidly converging numerical results.

On the solution of integral equations with strong ly singular kernels

NASA Technical Reports Server (NTRS)

Kaya, A. C.; Erdogan, F.

1985-01-01

In this paper some useful formulas are developed to evaluate integrals having a singularity of the form (t-x) sup-m, m or = 1. Interpreting the integrals with strong singularities in Hadamard sense, the results are used to obtain approximate solutions of singular integral equations. A mixed boundary value problem from the theory of elasticity is considered as an example. Particularly for integral equations where the kernel contains, in addition to the dominant term (t,x) sup-m, terms which become unbounded at the end points, the present technique appears to be extremely effective to obtain rapidly converging numerical results.

On the solution of integral equations with strongly singular kernels

NASA Technical Reports Server (NTRS)

Kaya, A. C.; Erdogan, F.

1987-01-01

Some useful formulas are developed to evaluate integrals having a singularity of the form (t-x) sup-m, m greater than or equal 1. Interpreting the integrals with strong singularities in Hadamard sense, the results are used to obtain approximate solutions of singular integral equations. A mixed boundary value problem from the theory of elasticity is considered as an example. Particularly for integral equations where the kernel contains, in addition to the dominant term (t-x) sup-m, terms which become unbounded at the end points, the present technique appears to be extremely effective to obtain rapidly converging numerical results.

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

Urbic, Tomaz, E-mail: tomaz.urbic@fkkt.uni-lj.si; Dias, Cristiano L.

The thermodynamic and structural properties of the planar soft-sites dumbbell fluid are examined by Monte Carlo simulations and integral equation theory. The dimers are built of two Lennard-Jones segments. Site-site integral equation theory in two dimensions is used to calculate the site-site radial distribution functions for a range of elongations and densities and the results are compared with Monte Carlo simulations. The critical parameters for selected types of dimers were also estimated. We analyze the influence of the bond length on critical point as well as tested correctness of site-site integral equation theory with different closures. The integral equations canmore » be used to predict the phase diagram of dimers whose molecular parameters are known.« less

Numerical techniques in radiative heat transfer for general, scattering, plane-parallel media

NASA Technical Reports Server (NTRS)

Sharma, A.; Cogley, A. C.

1982-01-01

The study of radiative heat transfer with scattering usually leads to the solution of singular Fredholm integral equations. The present paper presents an accurate and efficient numerical method to solve certain integral equations that govern radiative equilibrium problems in plane-parallel geometry for both grey and nongrey, anisotropically scattering media. In particular, the nongrey problem is represented by a spectral integral of a system of nonlinear integral equations in space, which has not been solved previously. The numerical technique is constructed to handle this unique nongrey governing equation as well as the difficulties caused by singular kernels. Example problems are solved and the method's accuracy and computational speed are analyzed.

Generalization of Boundary-Layer Momentum-Integral Equations to Three-Dimensional Flows Including Those of Rotating System

NASA Technical Reports Server (NTRS)

Mager, Arthur

1952-01-01

The Navier-Stokes equations of motion and the equation of continuity are transformed so as to apply to an orthogonal curvilinear coordinate system rotating with a uniform angular velocity about an arbitrary axis in space. A usual simplification of these equations as consistent with the accepted boundary-layer theory and an integration of these equations through the boundary layer result in boundary-layer momentum-integral equations for three-dimensional flows that are applicable to either rotating or nonrotating fluid boundaries. These equations are simplified and an approximate solution in closed integral form is obtained for a generalized boundary-layer momentum-loss thickness and flow deflection at the wall in the turbulent case. A numerical evaluation of this solution carried out for data obtained in a curving nonrotating duct shows a fair quantitative agreement with the measures values. The form in which the equations are presented is readily adaptable to cases of steady, three-dimensional, incompressible boundary-layer flow like that over curved ducts or yawed wings; and it also may be used to describe the boundary-layer flow over various rotating surfaces, thus applying to turbomachinery, propellers, and helicopter blades.

Evaluation of atomic pressure in the multiple time-step integration algorithm.

PubMed

Andoh, Yoshimichi; Yoshii, Noriyuki; Yamada, Atsushi; Okazaki, Susumu

2017-04-15

In molecular dynamics (MD) calculations, reduction in calculation time per MD loop is essential. A multiple time-step (MTS) integration algorithm, the RESPA (Tuckerman and Berne, J. Chem. Phys. 1992, 97, 1990-2001), enables reductions in calculation time by decreasing the frequency of time-consuming long-range interaction calculations. However, the RESPA MTS algorithm involves uncertainties in evaluating the atomic interaction-based pressure (i.e., atomic pressure) of systems with and without holonomic constraints. It is not clear which intermediate forces and constraint forces in the MTS integration procedure should be used to calculate the atomic pressure. In this article, we propose a series of equations to evaluate the atomic pressure in the RESPA MTS integration procedure on the basis of its equivalence to the Velocity-Verlet integration procedure with a single time step (STS). The equations guarantee time-reversibility even for the system with holonomic constrants. Furthermore, we generalize the equations to both (i) arbitrary number of inner time steps and (ii) arbitrary number of force components (RESPA levels). The atomic pressure calculated by our equations with the MTS integration shows excellent agreement with the reference value with the STS, whereas pressures calculated using the conventional ad hoc equations deviated from it. Our equations can be extended straightforwardly to the MTS integration algorithm for the isothermal NVT and isothermal-isobaric NPT ensembles. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

Some Exact Solutions of a Nonintegrable Toda-type Equation

NASA Astrophysics Data System (ADS)

Kim, Chanju

2018-05-01

We study a Toda-type equation with two scalar fields which is not integrable and construct two families of exact solutions which are expressed in terms of rational functions. The equation appears in U(1) Chern-Simons theories coupled to two nonrelativistic matter fields with opposite charges. One family of solutions is a trivial embedding of Liouville-type solutions. The other family is obtained by transforming the equation into the Taubes vortex equation on the hyperbolic space. Though the Taubes equation is not integrable, a trivial vacuum solution provides nontrivial solutions to the original Toda-type equation.

Painlevé equations, elliptic integrals and elementary functions

NASA Astrophysics Data System (ADS)

Żołądek, Henryk; Filipuk, Galina

2015-02-01

The six Painlevé equations can be written in the Hamiltonian form, with time dependent Hamilton functions. We present a rather new approach to this result, leading to rational Hamilton functions. By a natural extension of the phase space one gets corresponding autonomous Hamiltonian systems with two degrees of freedom. We realize the Bäcklund transformations of the Painlevé equations as symplectic birational transformations in C4 and we interpret the cases with classical solutions as the cases of partial integrability of the extended Hamiltonian systems. We prove that the extended Hamiltonian systems do not have any additional algebraic first integral besides the known special cases of the third and fifth Painlevé equations. We also show that the original Painlevé equations admit the first integrals expressed in terms of the elementary functions only in the special cases mentioned above. In the proofs we use equations in variations with respect to a parameter and Liouville's theory of elementary functions.

National Centers for Environmental Prediction

Science.gov Websites

Modeling Mesoscale Modeling Marine Modeling and Analysis Teams Climate Data Assimilation Ensembles and Post Documentation, experiments, web content Nicole McKee Makefiles, scripts, launcher Edward Colon NEMSIO, post Yang GFS post Hui-ya Chuang NAM development Tom Black Dusan Jovic Jim Abeles GFS development S Moorthi

The Crucial Role of the Teacher

ERIC Educational Resources Information Center

Olson, Joanne K.

2008-01-01

In the Perspectives column of this issue, Meredith Park Rogers and Sandra Abel address the importance of teacher questions on student thinking. With school improvement efforts often focused on the curriculum, standards, outcomes, and student work, it becomes easy to overlook the fact that the teacher is the single most important school-based…

Examining EXPRESS with Simulation

DTIC Science & Technology

2012-03-01

warfighter communities. iv AFIT-OR-MS-ENS-12-27 The God of the universe presents marvelous fingerprints of his glory throughout creation ( Isaiah 6:3...Redistribution Decision Support”, Air Force Journal of Logistics, 21(3):14–20, 25, 1997. [23] Cohen, Irv K., J. Abell, and Thomas F. Lippiatt. Coupling Logistics

Numerical solution of boundary-integral equations for molecular electrostatics.

PubMed

Bardhan, Jaydeep P

2009-03-07

Numerous molecular processes, such as ion permeation through channel proteins, are governed by relatively small changes in energetics. As a result, theoretical investigations of these processes require accurate numerical methods. In the present paper, we evaluate the accuracy of two approaches to simulating boundary-integral equations for continuum models of the electrostatics of solvation. The analysis emphasizes boundary-element method simulations of the integral-equation formulation known as the apparent-surface-charge (ASC) method or polarizable-continuum model (PCM). In many numerical implementations of the ASC/PCM model, one forces the integral equation to be satisfied exactly at a set of discrete points on the boundary. We demonstrate in this paper that this approach to discretization, known as point collocation, is significantly less accurate than an alternative approach known as qualocation. Furthermore, the qualocation method offers this improvement in accuracy without increasing simulation time. Numerical examples demonstrate that electrostatic part of the solvation free energy, when calculated using the collocation and qualocation methods, can differ significantly; for a polypeptide, the answers can differ by as much as 10 kcal/mol (approximately 4% of the total electrostatic contribution to solvation). The applicability of the qualocation discretization to other integral-equation formulations is also discussed, and two equivalences between integral-equation methods are derived.

A nodal domain theorem for integrable billiards in two dimensions

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

Samajdar, Rhine; Jain, Sudhir R., E-mail: srjain@barc.gov.in

Eigenfunctions of integrable planar billiards are studied — in particular, the number of nodal domains, ν of the eigenfunctions with Dirichlet boundary conditions are considered. The billiards for which the time-independent Schrödinger equation (Helmholtz equation) is separable admit trivial expressions for the number of domains. Here, we discover that for all separable and non-separable integrable billiards, ν satisfies certain difference equations. This has been possible because the eigenfunctions can be classified in families labelled by the same value of mmodkn, given a particular k, for a set of quantum numbers, m,n. Further, we observe that the patterns in a familymore » are similar and the algebraic representation of the geometrical nodal patterns is found. Instances of this representation are explained in detail to understand the beauty of the patterns. This paper therefore presents a mathematical connection between integrable systems and difference equations. - Highlights: • We find that the number of nodal domains of eigenfunctions of integrable, planar billiards satisfy a class of difference equations. • The eigenfunctions labelled by quantum numbers (m,n) can be classified in terms of mmodkn. • A theorem is presented, realising algebraic representations of geometrical patterns exhibited by the domains. • This work presents a connection between integrable systems and difference equations.« less

Oblique scattering from radially inhomogeneous dielectric cylinders: An exact Volterra integral equation formulation

NASA Astrophysics Data System (ADS)

Tsalamengas, John L.

2018-07-01

We study plane-wave electromagnetic scattering by radially and strongly inhomogeneous dielectric cylinders at oblique incidence. The method of analysis relies on an exact reformulation of the underlying field equations as a first-order 4 × 4 system of differential equations and on the ability to restate the associated initial-value problem in the form of a system of coupled linear Volterra integral equations of the second kind. The integral equations so derived are discretized via a sophisticated variant of the Nyström method. The proposed method yields results accurate up to machine precision without relying on approximations. Numerical results and case studies ably demonstrate the efficiency and high accuracy of the algorithms.

The Case of Abel: Religion as Boon and Bane for a Catholic Gay Man.

PubMed

Cerbone, Armand R; Danzer, Graham

2017-08-01

Conservative religions that condemn homosexual sexual orientation and acts as unnatural and sinful pose significant challenges for gay persons whose faith is a core part of their identity. The condemnation presents a serious barrier to the acceptance and integration of their sexuality, a primary task of psychosexual development. As a result, they can manifest depression, anxiety, suicidal ideation, and even suicide attempts. The ecclesiastical censure also imposes an untenable dilemma for homosexuals in that they feel pressed to reject their sexual identity or renounce their spiritual identity and heritage. Psychotherapists who treat gay persons caught in this quandary can find themselves facing a similar problem: how to help their homosexual client reconcile their proscribed sexuality with their spiritual commitments. The case presented here recounts the treatment over many years of a gay man suffering from such a conflict and his eventual accommodation of both his homosexuality and his faith. Recommendations are offered for constructive treatment with those torn between two conflicting core identities. © 2017 Wiley Periodicals, Inc.

Solving Ordinary Differential Equations

NASA Technical Reports Server (NTRS)

Krogh, F. T.

1987-01-01

Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

FAST TRACK COMMUNICATION: On the Liouvillian solution of second-order linear differential equations and algebraic invariant curves

NASA Astrophysics Data System (ADS)

Man, Yiu-Kwong

2010-10-01

In this communication, we present a method for computing the Liouvillian solution of second-order linear differential equations via algebraic invariant curves. The main idea is to integrate Kovacic's results on second-order linear differential equations with the Prelle-Singer method for computing first integrals of differential equations. Some examples on using this approach are provided.

On randomized algorithms for numerical solution of applied Fredholm integral equations of the second kind

NASA Astrophysics Data System (ADS)

Voytishek, Anton V.; Shipilov, Nikolay M.

2017-11-01

In this paper, the systematization of numerical (implemented on a computer) randomized functional algorithms for approximation of a solution of Fredholm integral equation of the second kind is carried out. Wherein, three types of such algorithms are distinguished: the projection, the mesh and the projection-mesh methods. The possibilities for usage of these algorithms for solution of practically important problems is investigated in detail. The disadvantages of the mesh algorithms, related to the necessity of calculation values of the kernels of integral equations in fixed points, are identified. On practice, these kernels have integrated singularities, and calculation of their values is impossible. Thus, for applied problems, related to solving Fredholm integral equation of the second kind, it is expedient to use not mesh, but the projection and the projection-mesh randomized algorithms.

Initial-boundary value problems associated with the Ablowitz-Ladik system

NASA Astrophysics Data System (ADS)

Xia, Baoqiang; Fokas, A. S.

2018-02-01

We employ the Ablowitz-Ladik system as an illustrative example in order to demonstrate how to analyze initial-boundary value problems for integrable nonlinear differential-difference equations via the unified transform (Fokas method). In particular, we express the solutions of the integrable discrete nonlinear Schrödinger and integrable discrete modified Korteweg-de Vries equations in terms of the solutions of appropriate matrix Riemann-Hilbert problems. We also discuss in detail, for both the above discrete integrable equations, the associated global relations and the process of eliminating of the unknown boundary values.

Simulation electromagnetic scattering on bodies through integral equation and neural networks methods

NASA Astrophysics Data System (ADS)

Lvovich, I. Ya; Preobrazhenskiy, A. P.; Choporov, O. N.

2018-05-01

The paper deals with the issue of electromagnetic scattering on a perfectly conducting diffractive body of a complex shape. Performance calculation of the body scattering is carried out through the integral equation method. Fredholm equation of the second time was used for calculating electric current density. While solving the integral equation through the moments method, the authors have properly described the core singularity. The authors determined piecewise constant functions as basic functions. The chosen equation was solved through the moments method. Within the Kirchhoff integral approach it is possible to define the scattered electromagnetic field, in some way related to obtained electrical currents. The observation angles sector belongs to the area of the front hemisphere of the diffractive body. To improve characteristics of the diffractive body, the authors used a neural network. All the neurons contained a logsigmoid activation function and weighted sums as discriminant functions. The paper presents the matrix of weighting factors of the connectionist model, as well as the results of the optimized dimensions of the diffractive body. The paper also presents some basic steps in calculation technique of the diffractive bodies, based on the combination of integral equation and neural networks methods.

On the solution of integral equations with a generalized cauchy kernel

NASA Technical Reports Server (NTRS)

Kaya, A. C.; Erdogan, F.

1986-01-01

In this paper a certain class of singular integral equations that may arise from the mixed boundary value problems in nonhomogeneous materials is considered. The distinguishing feature of these equations is that in addition to the Cauchy singularity, the kernels contain terms that are singular only at the end points. In the form of the singular integral equations adopted, the density function is a potential or a displacement and consequently the kernel has strong singularities of the form (t-x) sup-2, x sup n-2 (t+x) sup n, (n or = 2, 0x,tb). The complex function theory is used to determine the fundamental function of the problem for the general case and a simple numerical technique is described to solve the integral equation. Two examples from the theory of elasticity are then considered to show the application of the technique.

An exterior Poisson solver using fast direct methods and boundary integral equations with applications to nonlinear potential flow

NASA Technical Reports Server (NTRS)

Young, D. P.; Woo, A. C.; Bussoletti, J. E.; Johnson, F. T.

1986-01-01

A general method is developed combining fast direct methods and boundary integral equation methods to solve Poisson's equation on irregular exterior regions. The method requires O(N log N) operations where N is the number of grid points. Error estimates are given that hold for regions with corners and other boundary irregularities. Computational results are given in the context of computational aerodynamics for a two-dimensional lifting airfoil. Solutions of boundary integral equations for lifting and nonlifting aerodynamic configurations using preconditioned conjugate gradient are examined for varying degrees of thinness.

Davidenko’s Method for the Solution of Nonlinear Operator Equations.

DTIC Science & Technology

NONLINEAR DIFFERENTIAL EQUATIONS, NUMERICAL INTEGRATION), OPERATORS(MATHEMATICS), BANACH SPACE , MAPPING (TRANSFORMATIONS), NUMERICAL METHODS AND PROCEDURES, INTEGRALS, SET THEORY, CONVERGENCE, MATRICES(MATHEMATICS)

Integrable Equations in Multi-Dimensions (2+1) are Bi-Hamiltonian Systems,

DTIC Science & Technology

1987-02-01

equation [18]. It should be noted that the 80 equation has more similarities [19] with the Kadomtsev - Petviashvili (KP...Cimento, 39B, 1 (1977). [31] P. Caudrey, Discrete and Periodic Spectral Transforms Related to the Kadomtsev - Petviashvili Equation , preprint U.M.I.S.T. (1985). II ’AI D p-I 4, - -- - -- - - -w 4 ...TOM NONLINEAR STUDIES IDTIC I IELEC )// MAR 2 51988 I / \\ / Integrable Equations in Multi- dimensions (2+1) are Bi-Hamiltonian Systems by A.S.

The non-autonomous YdKN equation and generalized symmetries of Boll equations

NASA Astrophysics Data System (ADS)

Gubbiotti, G.; Scimiterna, C.; Levi, D.

2017-05-01

In this paper, we study the integrability of a class of nonlinear non-autonomous quad graph equations compatible around the cube introduced by Boll in the framework of the generalized Adler, Bobenko, and Suris (ABS) classification. We show that all these equations possess three-point generalized symmetries which are subcases of either the Yamilov discretization of the Krichever-Novikov equation or of its non-autonomous extension. We also prove that all those symmetries are integrable as they pass the algebraic entropy test.

Development and application of a local linearization algorithm for the integration of quaternion rate equations in real-time flight simulation problems

NASA Technical Reports Server (NTRS)

Barker, L. E., Jr.; Bowles, R. L.; Williams, L. H.

1973-01-01

High angular rates encountered in real-time flight simulation problems may require a more stable and accurate integration method than the classical methods normally used. A study was made to develop a general local linearization procedure of integrating dynamic system equations when using a digital computer in real-time. The procedure is specifically applied to the integration of the quaternion rate equations. For this application, results are compared to a classical second-order method. The local linearization approach is shown to have desirable stability characteristics and gives significant improvement in accuracy over the classical second-order integration methods.

Solving Simple Kinetics without Integrals

ERIC Educational Resources Information Center

de la Pen~a, Lisandro Herna´ndez

2016-01-01

The solution of simple kinetic equations is analyzed without referencing any topic from differential equations or integral calculus. Guided by the physical meaning of the rate equation, a systematic procedure is used to generate an approximate solution that converges uniformly to the exact solution in the case of zero, first, and second order…

Extended nonlinear Schrödinger equation with higher-order odd and even terms and its rogue wave solutions.

PubMed

Ankiewicz, Adrian; Wang, Yan; Wabnitz, Stefan; Akhmediev, Nail

2014-01-01

We consider an extended nonlinear Schrödinger equation with higher-order odd (third order) and even (fourth order) terms with variable coefficients. The resulting equation has soliton solutions and approximate rogue wave solutions. We present these solutions up to second order. Moreover, specific constraints on the parameters of higher-order terms provide integrability of the resulting equation, providing a corresponding Lax pair. Particular cases of this equation are the Hirota and the Lakshmanan-Porsezian-Daniel equations. The resulting integrable equation admits exact rogue wave solutions. In particular cases, mentioned above, these solutions are reduced to the rogue wave solutions of the corresponding equations.

Compacton solutions in a class of generalized fifth-order Korteweg-de Vries equations.

PubMed

Cooper, F; Hyman, J M; Khare, A

2001-08-01

Solitons play a fundamental role in the evolution of general initial data for quasilinear dispersive partial differential equations, such as the Korteweg-de Vries (KdV), nonlinear Schrödinger, and the Kadomtsev-Petviashvili equations. These integrable equations have linear dispersion and the solitons have infinite support. We have derived and investigate a new KdV-like Hamiltonian partial differential equation from a four-parameter Lagrangian where the nonlinear dispersion gives rise to solitons with compact support (compactons). The new equation does not seem to be integrable and only mass, momentum, and energy seem to be conserved; yet, the solitons display almost the same modal decompositions and structural stability observed in integrable partial differential equations. The compactons formed from arbitrary initial data, are nonlinearly self-stabilizing, and maintain their coherence after multiple collisions. The robustness of these compactons and the inapplicability of the inverse scattering tools, that worked so well for the KdV equation, make it clear that there is a fundamental mechanism underlying the processes beyond integrability. We have found explicit formulas for multiple classes of compact traveling wave solutions. When there are more than one compacton solution for a particular set of parameters, the wider compacton is the minimum of a reduced Hamiltonian and is the only one that is stable.

Integral equation approach to time-dependent kinematic dynamos in finite domains

NASA Astrophysics Data System (ADS)

Xu, Mingtian; Stefani, Frank; Gerbeth, Gunter

2004-11-01

The homogeneous dynamo effect is at the root of cosmic magnetic field generation. With only a very few exceptions, the numerical treatment of homogeneous dynamos is carried out in the framework of the differential equation approach. The present paper tries to facilitate the use of integral equations in dynamo research. Apart from the pedagogical value to illustrate dynamo action within the well-known picture of the Biot-Savart law, the integral equation approach has a number of practical advantages. The first advantage is its proven numerical robustness and stability. The second and perhaps most important advantage is its applicability to dynamos in arbitrary geometries. The third advantage is its intimate connection to inverse problems relevant not only for dynamos but also for technical applications of magnetohydrodynamics. The paper provides the first general formulation and application of the integral equation approach to time-dependent kinematic dynamos, with stationary dynamo sources, in finite domains. The time dependence is restricted to the magnetic field, whereas the velocity or corresponding mean-field sources of dynamo action are supposed to be stationary. For the spherically symmetric α2 dynamo model it is shown how the general formulation is reduced to a coupled system of two radial integral equations for the defining scalars of the poloidal and toroidal field components. The integral equation formulation for spherical dynamos with general stationary velocity fields is also derived. Two numerical examples—the α2 dynamo model with radially varying α and the Bullard-Gellman model—illustrate the equivalence of the approach with the usual differential equation method. The main advantage of the method is exemplified by the treatment of an α2 dynamo in rectangular domains.

A boundary integral approach to the scattering of nonplanar acoustic waves by rigid bodies

NASA Technical Reports Server (NTRS)

Gallman, Judith M.; Myers, M. K.; Farassat, F.

1990-01-01

The acoustic scattering of an incident wave by a rigid body can be described by a singular Fredholm integral equation of the second kind. This equation is derived by solving the wave equation using generalized function theory, Green's function for the wave equation in unbounded space, and the acoustic boundary condition for a perfectly rigid body. This paper will discuss the derivation of the wave equation, its reformulation as a boundary integral equation, and the solution of the integral equation by the Galerkin method. The accuracy of the Galerkin method can be assessed by applying the technique outlined in the paper to reproduce the known pressure fields that are due to various point sources. From the analysis of these simpler cases, the accuracy of the Galerkin solution can be inferred for the scattered pressure field caused by the incidence of a dipole field on a rigid sphere. The solution by the Galerkin technique can then be applied to such problems as a dipole model of a propeller whose pressure field is incident on a rigid cylinder. This is the groundwork for modeling the scattering of rotating blade noise by airplane fuselages.

Almost analytical Karhunen-Loeve representation of irregular waves based on the prolate spheroidal wave functions

NASA Astrophysics Data System (ADS)

Lee, Gibbeum; Cho, Yeunwoo

2017-11-01

We present an almost analytical new approach to solving the matrix eigenvalue problem or the integral equation in Karhunen-Loeve (K-L) representation of random data such as irregular ocean waves. Instead of solving this matrix eigenvalue problem purely numerically, which may suffer from the computational inaccuracy for big data, first, we consider a pair of integral and differential equations, which are related to the so-called prolate spheroidal wave functions (PSWF). For the PSWF differential equation, the pair of the eigenvectors (PSWF) and eigenvalues can be obtained from a relatively small number of analytical Legendre functions. Then, the eigenvalues in the PSWF integral equation are expressed in terms of functional values of the PSWF and the eigenvalues of the PSWF differential equation. Finally, the analytically expressed PSWFs and the eigenvalues in the PWSF integral equation are used to form the kernel matrix in the K-L integral equation for the representation of exemplary wave data; ordinary irregular waves and rogue waves. We found that the present almost analytical method is better than the conventional data-independent Fourier representation and, also, the conventional direct numerical K-L representation in terms of both accuracy and computational cost. This work was supported by the National Research Foundation of Korea (NRF). (NRF-2017R1D1A1B03028299).

On an example of a system of differential equations that are integrated in Abelian functions

NASA Astrophysics Data System (ADS)

Malykh, M. D.; Sevastianov, L. A.

2017-12-01

The short review of the theory of Abelian functions and its applications in mechanics and analytical theory of differential equations is given. We think that Abelian functions are the natural generalization of commonly used functions because if the general solution of the 2nd order differential equation depends algebraically on the constants of integration, then integrating this equation does not lead out of the realm of commonly used functions complemented by the Abelian functions (Painlevé theorem). We present a relatively simple example of a dynamical system that is integrated in Abelian integrals by “pairing” two copies of a hyperelliptic curve. Unfortunately, initially simple formulas unfold into very long ones. Apparently the theory of Abelian functions hasn’t been finished in the last century because without computer algebra systems it was impossible to complete the calculations to the end. All calculations presented in our report are performed in Sage.

GENERIC Integrators: Structure Preserving Time Integration for Thermodynamic Systems

NASA Astrophysics Data System (ADS)

Öttinger, Hans Christian

2018-04-01

Thermodynamically admissible evolution equations for non-equilibrium systems are known to possess a distinct mathematical structure. Within the GENERIC (general equation for the non-equilibrium reversible-irreversible coupling) framework of non-equilibrium thermodynamics, which is based on continuous time evolution, we investigate the possibility of preserving all the structural elements in time-discretized equations. Our approach, which follows Moser's [1] construction of symplectic integrators for Hamiltonian systems, is illustrated for the damped harmonic oscillator. Alternative approaches are sketched.

The application of the integral equation theory to study the hydrophobic interaction

PubMed Central

Mohorič, Tomaž; Urbic, Tomaz; Hribar-Lee, Barbara

2014-01-01

The Wertheim's integral equation theory was tested against newly obtained Monte Carlo computer simulations to describe the potential of mean force between two hydrophobic particles. An excellent agreement was obtained between the theoretical and simulation results. Further, the Wertheim's integral equation theory with polymer Percus-Yevick closure qualitatively correctly (with respect to the experimental data) describes the solvation structure under conditions where the simulation results are difficult to obtain with good enough accuracy. PMID:24437891

Algorithms For Integrating Nonlinear Differential Equations

NASA Technical Reports Server (NTRS)

Freed, A. D.; Walker, K. P.

1994-01-01

Improved algorithms developed for use in numerical integration of systems of nonhomogenous, nonlinear, first-order, ordinary differential equations. In comparison with integration algorithms, these algorithms offer greater stability and accuracy. Several asymptotically correct, thereby enabling retention of stability and accuracy when large increments of independent variable used. Accuracies attainable demonstrated by applying them to systems of nonlinear, first-order, differential equations that arise in study of viscoplastic behavior, spread of acquired immune-deficiency syndrome (AIDS) virus and predator/prey populations.

Solving differential equations for Feynman integrals by expansions near singular points

NASA Astrophysics Data System (ADS)

Lee, Roman N.; Smirnov, Alexander V.; Smirnov, Vladimir A.

2018-03-01

We describe a strategy to solve differential equations for Feynman integrals by powers series expansions near singular points and to obtain high precision results for the corresponding master integrals. We consider Feynman integrals with two scales, i.e. non-trivially depending on one variable. The corresponding algorithm is oriented at situations where canonical form of the differential equations is impossible. We provide a computer code constructed with the help of our algorithm for a simple example of four-loop generalized sunset integrals with three equal non-zero masses and two zero masses. Our code gives values of the master integrals at any given point on the real axis with a required accuracy and a given order of expansion in the regularization parameter ɛ.

Contact interaction of thin-walled elements with an elastic layer and an infinite circular cylinder under torsion

NASA Astrophysics Data System (ADS)

Kanetsyan, E. G.; Mkrtchyan, M. S.; Mkhitaryan, S. M.

2018-04-01

We consider a class of contact torsion problems on interaction of thin-walled elements shaped as an elastic thin washer – a flat circular plate of small height – with an elastic layer, in particular, with a half-space, and on interaction of thin cylindrical shells with a solid elastic cylinder, infinite in both directions. The governing equations of the physical models of elastic thin washers and thin circular cylindrical shells under torsion are derived from the exact equations of mathematical theory of elasticity using the Hankel and Fourier transforms. Within the framework of the accepted physical models, the solution of the contact problem between an elastic washer and an elastic layer is reduced to solving the Fredholm integral equation of the first kind with a kernel representable as a sum of the Weber–Sonin integral and some integral regular kernel, while solving the contact problem between a cylindrical shell and solid cylinder is reduced to a singular integral equation (SIE). An effective method for solving the governing integral equations of these problems are specified.

Comparison of numerical techniques for integration of stiff ordinary differential equations arising in combustion chemistry

NASA Technical Reports Server (NTRS)

Radhakrishnan, K.

1984-01-01

The efficiency and accuracy of several algorithms recently developed for the efficient numerical integration of stiff ordinary differential equations are compared. The methods examined include two general-purpose codes, EPISODE and LSODE, and three codes (CHEMEQ, CREK1D, and GCKP84) developed specifically to integrate chemical kinetic rate equations. The codes are applied to two test problems drawn from combustion kinetics. The comparisons show that LSODE is the fastest code currently available for the integration of combustion kinetic rate equations. An important finding is that an interactive solution of the algebraic energy conservation equation to compute the temperature does not result in significant errors. In addition, this method is more efficient than evaluating the temperature by integrating its time derivative. Significant reductions in computational work are realized by updating the rate constants (k = at(supra N) N exp(-E/RT) only when the temperature change exceeds an amount delta T that is problem dependent. An approximate expression for the automatic evaluation of delta T is derived and is shown to result in increased efficiency.

Differential equations for loop integrals in Baikov representation

NASA Astrophysics Data System (ADS)

Bosma, Jorrit; Larsen, Kasper J.; Zhang, Yang

2018-05-01

We present a proof that differential equations for Feynman loop integrals can always be derived in Baikov representation without involving dimension-shift identities. We moreover show that in a large class of two- and three-loop diagrams it is possible to avoid squared propagators in the intermediate steps of setting up the differential equations.

Monograph - The Numerical Integration of Ordinary Differential Equations.

ERIC Educational Resources Information Center

Hull, T. E.

The materials presented in this monograph are intended to be included in a course on ordinary differential equations at the upper division level in a college mathematics program. These materials provide an introduction to the numerical integration of ordinary differential equations, and they can be used to supplement a regular text on this…

An Analytical Comparison of the Acoustic Analogy and Kirchhoff Formulation for Moving Surfaces

NASA Technical Reports Server (NTRS)

Brentner, Kenneth S.; Farassat, F.

1997-01-01

The Lighthill acoustic analogy, as embodied in the Ffowcs Williams-Hawkings (FW-H) equation, is compared with the Kirchhoff formulation for moving surfaces. A comparison of the two governing equations reveals that the main Kirchhoff advantage (namely nonlinear flow effects are included in the surface integration) is also available to the FW-H method if the integration surface used in the FW-H equation is not assumed impenetrable. The FW-H equation is analytically superior for aeroacoustics because it is based upon the conservation laws of fluid mechanics rather than the wave equation. This means that the FW-H equation is valid even if the integration surface is in the nonlinear region. This is demonstrated numerically in the paper. The Kirchhoff approach can lead to substantial errors if the integration surface is not positioned in the linear region. These errors may be hard to identify. Finally, new metrics based on the Sobolev norm are introduced which may be used to compare input data for both quadrupole noise calculations and Kirchhoff noise predictions.

Why Can't Johnny Read? The Abell Report. Volume 23, No.7

ERIC Educational Resources Information Center

Jacobson, Joan

2010-01-01

Baltimore's school-based vision-screening program may be leaving thousands of children with uncorrected eyesight problems. Vision screening in public schools is essential for students to learn, especially when low-income children face a high rate of eyesight problems and have poor access to health care. Left undetected and uncorrected, vision…

Diagnostic Opportunities Using Rasch Measurement in the Context of a Misconceptions-Based Physical Science Assessment

ERIC Educational Resources Information Center

Wind, Stefanie A.; Gale, Jessica D.

2015-01-01

Multiple-choice (MC) items that are constructed such that distractors target known misconceptions for a particular domain provide useful diagnostic information about student misconceptions (Herrmann-Abell & DeBoer, 2011, 2014; Sadler, 1998). Item response theory models can be used to examine misconceptions distractor-driven multiple-choice…

Numerical quadrature methods for integrals of singular periodic functions and their application to singular and weakly singular integral equations

NASA Technical Reports Server (NTRS)

Sidi, A.; Israeli, M.

1986-01-01

High accuracy numerical quadrature methods for integrals of singular periodic functions are proposed. These methods are based on the appropriate Euler-Maclaurin expansions of trapezoidal rule approximations and their extrapolations. They are used to obtain accurate quadrature methods for the solution of singular and weakly singular Fredholm integral equations. Such periodic equations are used in the solution of planar elliptic boundary value problems, elasticity, potential theory, conformal mapping, boundary element methods, free surface flows, etc. The use of the quadrature methods is demonstrated with numerical examples.

The Sunyaev-Zel'dovich Effect Spectrum of Abell 2163

NASA Technical Reports Server (NTRS)

LaRoque, S. J.; Carlstrom, J. E.; Reese, E. D.; Holder, G. P.; Holzapfel, W. L.; Joy, M.; Grego, L.; Six, N. Frank (Technical Monitor)

2002-01-01

We present an interferometric measurement of the Sunyaev-Zel'dovich effect (SZE) at 1 cm for the galaxy cluster Abell 2163. We combine this data point with previous measurements at 1.1, 1.4, and 2.1 mm from the SuZIE experiment to construct the most complete SZE spectrum to date. The intensity in four wavelength bands is fit to determine the Compton y-parameter (y(sub 0)) and the peculiar velocity (v(sub p)) for this cluster. Our results are y(sub 0) = 3.56((sup +0.41+0.27)(sub -0.41-0.19)) X 10(exp -4) and v(sub p) = 410((sup +1030+460) (sub -850-440)) km s(exp -1) where we list statistical and systematic uncertainties, respectively, at 68% confidence. These results include corrections for contamination by Galactic dust emission. We find less contamination by dust emission than previously reported. The dust emission is distributed over much larger angular scales than the cluster signal and contributes little to the measured signal when the details of the SZE observing strategy are taken into account.

STRONG GRAVITATIONAL LENSING BY THE SUPER-MASSIVE cD GALAXY IN ABELL 3827

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

Carrasco, E. R.; Gomez, P. L.; Lee, H.

2010-06-01

We have discovered strong gravitational lensing features in the core of the nearby cluster Abell 3827 by analyzing Gemini South GMOS images. The most prominent strong lensing feature is a highly magnified, ring-shaped configuration of four images around the central cD galaxy. GMOS spectroscopic analysis puts this source at z {approx} 0.2. Located {approx}20'' away from the central galaxy is a secondary tangential arc feature which has been identified as a background galaxy with z {approx} 0.4. We have modeled the gravitational potential of the cluster core, taking into account the mass from the cluster, the brightest cluster galaxy (BCG),more » and other galaxies. We derive a total mass of (2.7 {+-} 0.4) x 10{sup 13} M {sub sun} within 37 h {sup -1} kpc. This mass is an order of magnitude larger than that derived from X-ray observations. The total mass derived from lensing data suggests that the BCG in this cluster is perhaps the most massive galaxy in the nearby universe.« less

Canibalismo Extremo y Lente Gravitacional Intensa en el Cúmulo de Galaxias Abell 3827

NASA Astrophysics Data System (ADS)

Díaz, R. J.; West, M.; Bergmann, M.; Carrasco, E. R.; Gomez, P.; Lee, H.; Miller, B.; Turner, J.

Abell 3827 is one of the most massive known clusters and at its center we observe an extreme example of galactic canibalism: a super giant elliptical galaxy in its formation process, devoring five massive galaxies at the same time. Using high spatial resolution Gemini+GMOS imagery and multi-object spectroscopy, we derived the redshift (z=0.099) and the radial velocity dispersion of the 55 brightest galaxies in the cluster central region (1134 +- 125 km/s). The estimated virial mass is ~ 1E14 M(sun) inside a radius of 300 kpc of the cluster center. We have also found features corresponding to a strong gravitational lense, four anular features arranged in an Einstein Ring from a galaxy (z=0.2) at double redshift than the cluster, and a fifth arclet feature corresponding to the lensed light of a farther galaxy (z=0.4). The possible Einstein Ring is of small angular size and the gravitational lense morphology would confirm that the cluster is indeed very massive and dense. FULL TEXT IN SPANISH.

VizieR Online Data Catalog: LaCoSSPAr in the Southern Galactic Cap. I. (Yang+, 2018)

NASA Astrophysics Data System (ADS)

Yang, M.; Wu, H.; Yang, F.; Lam, M. I.; Cao, T.-W.; Wu, C.-J.; Zhao, P.-S.; Zhang, T.-M.; Zhou, Z.-M.; Wu, X.-B.; Zhang, Y.-X.; Shao, Z.-Y.; Jing, Y.-P.; Shen, S.-Y.; Zhu, Y.-N.; Du, W.; Lei, F.-J.; He, M.; Jin, J.-J.; Shi, J.-R.; Zhang, W.; Wang, J.-L.; Wu, Y.-Z.; Zhang, H.-T.; Luo, A.-L.; Yuan, H.-L.; Bai, Z.-R.; Kong, X.; Gu, Q.-S.; Zhou, X.; Ma, J.; Hu, Z.; Nie, J.-D.; Wang, J.-L.; Zhang, Y.; Hou, Y.-H.; Zhao, Y.-H.

2018-03-01

We have selected two FOVs according to the distribution of galaxy clusters from the Abell rich galaxy clusters catalog (Abell+ 1989, VII/110) in the region of the South Galactic Cap u-band Sky Survey (SCUSS, Zhou+ 2016RAA....16....7Z). The central coordinates of the two FOVs we selected are RA=37.88°,DE=3.44° (Field A) and RA=21.53,DE=-2.20° (Field B) as shown in Figure 1. The observation of LAMOST is automatically managed by the Survey Strategy System (SSS). We conduct the observation from 2012 September to 2014 January (except July through August, which is the maintain period of the telescope). Field A contains 2519 galaxies and 13930 stars in which 2447 (~97%) and 13278 (~95%) of them have been observed with 5 B and 12 F plates (redundant F plates are caused by a technical issue), respectively. Field B contains 3104 galaxies and 11381 stars in which 2995 (~97%) and 10224 (~90%) of them have been observed with six B and five F plates, respectively. (2 data files).

Cool Core Disruption in Abell 1763

NASA Astrophysics Data System (ADS)

Douglass, Edmund; Blanton, Elizabeth L.; Clarke, Tracy E.; Randall, Scott W.; Edwards, Louise O. V.; Sabry, Ziad

2017-01-01

We present the analysis of a 20 ksec Chandra archival observation of the massive galaxy cluster Abell 1763. A model-subtracted image highlighting excess cluster emission reveals a large spiral structure winding outward from the core to a radius of ~950 kpc. We measure the gas of the inner spiral to have significantly lower entropy than non-spiral regions at the same radius. This is consistent with the structure resulting from merger-induced motion of the cluster’s cool core, a phenomenon seen in many systems. Atypical of spiral-hosting clusters, an intact cool core is not detected. Its absence suggests the system has experienced significant disruption since the initial dynamical encounter that set the sloshing core in motion. Along the major axis of the elongated ICM distribution we detect thermal features consistent with the merger event most likely responsible for cool core disruption. The merger-induced transition towards non-cool core status will be discussed. The interaction between the powerful (P1.4 ~ 1026 W Hz-1) cluster-center WAT radio source and its ICM environment will also be discussed.

A Corresponding Lie Algebra of a Reductive homogeneous Group and Its Applications

NASA Astrophysics Data System (ADS)

Zhang, Yu-Feng; Wu, Li-Xin; Rui, Wen-Juan

2015-05-01

With the help of a Lie algebra of a reductive homogeneous space G/K, where G is a Lie group and K is a resulting isotropy group, we introduce a Lax pair for which an expanding (2+1)-dimensional integrable hierarchy is obtained by applying the binormial-residue representation (BRR) method, whose Hamiltonian structure is derived from the trace identity for deducing (2+1)-dimensional integrable hierarchies, which was proposed by Tu, et al. We further consider some reductions of the expanding integrable hierarchy obtained in the paper. The first reduction is just right the (2+1)-dimensional AKNS hierarchy, the second-type reduction reveals an integrable coupling of the (2+1)-dimensional AKNS equation (also called the Davey-Stewartson hierarchy), a kind of (2+1)-dimensional Schrödinger equation, which was once reobtained by Tu, Feng and Zhang. It is interesting that a new (2+1)-dimensional integrable nonlinear coupled equation is generated from the reduction of the part of the (2+1)-dimensional integrable coupling, which is further reduced to the standard (2+1)-dimensional diffusion equation along with a parameter. In addition, the well-known (1+1)-dimensional AKNS hierarchy, the (1+1)-dimensional nonlinear Schrödinger equation are all special cases of the (2+1)-dimensional expanding integrable hierarchy. Finally, we discuss a few discrete difference equations of the diffusion equation whose stabilities are analyzed by making use of the von Neumann condition and the Fourier method. Some numerical solutions of a special stationary initial value problem of the (2+1)-dimensional diffusion equation are obtained and the resulting convergence and estimation formula are investigated. Supported by the Innovation Team of Jiangsu Province hosted by China University of Mining and Technology (2014), the National Natural Science Foundation of China under Grant No. 11371361, the Fundamental Research Funds for the Central Universities (2013XK03), and the Natural Science Foundation of Shandong Province under Grant No. ZR2013AL016

Solving the hypersingular boundary integral equation in three-dimensional acoustics using a regularization relationship.

PubMed

Yan, Zai You; Hung, Kin Chew; Zheng, Hui

2003-05-01

Regularization of the hypersingular integral in the normal derivative of the conventional Helmholtz integral equation through a double surface integral method or regularization relationship has been studied. By introducing the new concept of discretized operator matrix, evaluation of the double surface integrals is reduced to calculate the product of two discretized operator matrices. Such a treatment greatly improves the computational efficiency. As the number of frequencies to be computed increases, the computational cost of solving the composite Helmholtz integral equation is comparable to that of solving the conventional Helmholtz integral equation. In this paper, the detailed formulation of the proposed regularization method is presented. The computational efficiency and accuracy of the regularization method are demonstrated for a general class of acoustic radiation and scattering problems. The radiation of a pulsating sphere, an oscillating sphere, and a rigid sphere insonified by a plane acoustic wave are solved using the new method with curvilinear quadrilateral isoparametric elements. It is found that the numerical results rapidly converge to the corresponding analytical solutions as finer meshes are applied.

On solvability of boundary value problems for hyperbolic fourth-order equations with nonlocal boundary conditions of integral type

NASA Astrophysics Data System (ADS)

Popov, Nikolay S.

2017-11-01

Solvability of some initial-boundary value problems for linear hyperbolic equations of the fourth order is studied. A condition on the lateral boundary in these problems relates the values of a solution or the conormal derivative of a solution to the values of some integral operator applied to a solution. Nonlocal boundary-value problems for one-dimensional hyperbolic second-order equations with integral conditions on the lateral boundary were considered in the articles by A.I. Kozhanov. Higher-dimensional hyperbolic equations of higher order with integral conditions on the lateral boundary were not studied earlier. The existence and uniqueness theorems of regular solutions are proven. The method of regularization and the method of continuation in a parameter are employed to establish solvability.

Reply to "Comment on 'Defocusing complex short-pulse equation and its multi-dark-soliton solution' ".

PubMed

Feng, Bao-Feng; Ling, Liming; Zhu, Zuonong

2017-08-01

Our paper [Phys. Rev. E 93, 052227 (2016)PREHBM2470-004510.1103/PhysRevE.93.052227], proposing an integrable model for the propagation of ultrashort pulses, has recently received a Comment by Youssoufa et al. [Phys. Rev. E 96, 026201 (2017)10.1103/PhysRevE.96.026201] about a possible flaw in its derivation. We point out that their claim is incorrect since we have stated explicitly that a term is neglected to derive our model equation in our paper. Furthermore, the integrable model is validated by comparing with the normalized Maxwell equation and other known integrable models. Moreover, we show that a similar approximation has to be performed in deriving the same integrable equation as explained in the Comment.

A new aerodynamic integral equation based on an acoustic formula in the time domain

NASA Technical Reports Server (NTRS)

Farassat, F.

1984-01-01

An aerodynamic integral equation for bodies moving at transonic and supersonic speeds is presented. Based on a time-dependent acoustic formula for calculating the noise emanating from the outer portion of a propeller blade travelling at high speed (the Ffowcs Williams-Hawking formulation), the loading terms and a conventional thickness source terms are retained. Two surface and three line integrals are employed to solve an equation for the loading noise. The near-field term is regularized using the collapsing sphere approach to obtain semiconvergence on the blade surface. A singular integral equation is thereby derived for the unknown surface pressure, and is amenable to numerical solutions using Galerkin or collocation methods. The technique is useful for studying the nonuniform inflow to the propeller.

Integrable equations of the infinite nonlinear Schrödinger equation hierarchy with time variable coefficients.

PubMed

Kedziora, D J; Ankiewicz, A; Chowdury, A; Akhmediev, N

2015-10-01

We present an infinite nonlinear Schrödinger equation hierarchy of integrable equations, together with the recurrence relations defining it. To demonstrate integrability, we present the Lax pairs for the whole hierarchy, specify its Darboux transformations and provide several examples of solutions. These resulting wavefunctions are given in exact analytical form. We then show that the Lax pair and Darboux transformation formalisms still apply in this scheme when the coefficients in the hierarchy depend on the propagation variable (e.g., time). This extension thus allows for the construction of complicated solutions within a greatly diversified domain of generalised nonlinear systems.

Classical integrable defects as quasi Bäcklund transformations

NASA Astrophysics Data System (ADS)

Doikou, Anastasia

2016-10-01

We consider the algebraic setting of classical defects in discrete and continuous integrable theories. We derive the ;equations of motion; on the defect point via the space-like and time-like description. We then exploit the structural similarity of these equations with the discrete and continuous Bäcklund transformations. And although these equations are similar they are not exactly the same to the Bäcklund transformations. We also consider specific examples of integrable models to demonstrate our construction, i.e. the Toda chain and the sine-Gordon model. The equations of the time (space) evolution of the defect (discontinuity) degrees of freedom for these models are explicitly derived.

Analytical expressions for the correlation function of a hard sphere dimer fluid

NASA Astrophysics Data System (ADS)

Kim, Soonho; Chang, Jaeeon; Kim, Hwayong

A closed form expression is given for the correlation function of a hard sphere dimer fluid. A set of integral equations is obtained from Wertheim's multidensity Ornstein-Zernike integral equation theory with Percus-Yevick approximation. Applying the Laplace transformation method to the integral equations and then solving the resulting equations algebraically, the Laplace transforms of the individual correlation functions are obtained. By the inverse Laplace transformation, the radial distribution function (RDF) is obtained in closed form out to 3D (D is the segment diameter). The analytical expression for the RDF of the hard dimer should be useful in developing the perturbation theory of dimer fluids.

Analytical expression for the correlation function of a hard sphere chain fluid

NASA Astrophysics Data System (ADS)

Chang, Jaeeon; Kim, Hwayong

A closed form expression is given for the correlation function of flexible hard sphere chain fluid. A set of integral equations obtained from Wertheim's multidensity Ornstein-Zernike integral equation theory with the polymer Percus-Yevick ideal chain approximation is considered. Applying the Laplace transformation method to the integral equations and then solving the resulting equations algebraically, the Laplace transforms of individual correlation functions are obtained. By inverse Laplace transformation the inter- and intramolecular radial distribution functions (RDFs) are obtained in closed forms up to 3D(D is segment diameter). These analytical expressions for the RDFs would be useful in developing the perturbation theory of chain fluids.

Simulation of RF-fields in a fusion device

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

De Witte, Dieter; Bogaert, Ignace; De Zutter, Daniel

2009-11-26

In this paper the problem of scattering off a fusion plasma is approached from the point of view of integral equations. Using the volume equivalence principle an integral equation is derived which describes the electromagnetic fields in a plasma. The equation is discretized with MoM using conforming basis functions. This reduces the problem to solving a dense matrix equation. This can be done iteratively. Each iteration can be sped up using FFTs.

On the conservation laws and solutions of a (2+1) dimensional KdV-mKdV equation of mathematical physics

NASA Astrophysics Data System (ADS)

Motsepa, Tanki; Masood Khalique, Chaudry

2018-05-01

In this paper, we study a (2+1) dimensional KdV-mKdV equation, which models many physical phenomena of mathematical physics. This equation has two integral terms in it. By an appropriate substitution, we convert this equation into two partial differential equations, which do not have integral terms and are equivalent to the original equation. We then work with the system of two equations and obtain its exact travelling wave solutions in form of Jacobi elliptic functions. Furthermore, we employ the multiplier method to construct conservation laws for the system. Finally, we revert the results obtained into the original variables of the (2+1) dimensional KdV-mKdV equation.

New integrable model of propagation of the few-cycle pulses in an anisotropic microdispersed medium

NASA Astrophysics Data System (ADS)

Sazonov, S. V.; Ustinov, N. V.

2018-03-01

We investigate the propagation of the few-cycle electromagnetic pulses in the anisotropic microdispersed medium. The effects of the anisotropy and spatial dispersion of the medium are created by the two sorts of the two-level atoms. The system of the material equations describing an evolution of the states of the atoms and the wave equations for the ordinary and extraordinary components of the pulses is derived. By applying the approximation of the sudden excitation to exclude the material variables, we reduce this system to the single nonlinear wave equation that generalizes the modified sine-Gordon equation and the Rabelo-Fokas equation. It is shown that this equation is integrable by means of the inverse scattering transformation method if an additional restriction on the parameters is imposed. The multisoliton solutions of this integrable generalization are constructed and investigated.

First integrals and parametric solutions of third-order ODEs admitting {\\mathfrak{sl}(2, {R})}

NASA Astrophysics Data System (ADS)

Ruiz, A.; Muriel, C.

2017-05-01

A complete set of first integrals for any third-order ordinary differential equation admitting a Lie symmetry algebra isomorphic to sl(2, {R}) is explicitly computed. These first integrals are derived from two linearly independent solutions of a linear second-order ODE, without additional integration. The general solution in parametric form can be obtained by using the computed first integrals. The study includes a parallel analysis of the four inequivalent realizations of sl(2, {R}) , and it is applied to several particular examples. These include the generalized Chazy equation, as well as an example of an equation which admits the most complicated of the four inequivalent realizations.

PREFACE: Symmetries and Integrability of Difference Equations

NASA Astrophysics Data System (ADS)

Doliwa, Adam; Korhonen, Risto; Lafortune, Stéphane

2007-10-01

The notion of integrability was first introduced in the 19th century in the context of classical mechanics with the definition of Liouville integrability for Hamiltonian flows. Since then, several notions of integrability have been introduced for partial and ordinary differential equations. Closely related to integrability theory is the symmetry analysis of nonlinear evolution equations. Symmetry analysis takes advantage of the Lie group structure of a given equation to study its properties. Together, integrability theory and symmetry analysis provide the main method by which nonlinear evolution equations can be solved explicitly. Difference equations (DE), like differential equations, are important in numerous fields of science and have a wide variety of applications in such areas as mathematical physics, computer visualization, numerical analysis, mathematical biology, economics, combinatorics, and quantum field theory. It is thus crucial to develop tools to study and solve DEs. While the theory of symmetry and integrability for differential equations is now largely well-established, this is not yet the case for discrete equations. Although over recent years there has been significant progress in the development of a complete analytic theory of difference equations, further tools are still needed to fully understand, for instance, the symmetries, asymptotics and the singularity structure of difference equations. The series of SIDE meetings on Symmetries and Integrability of Difference Equations started in 1994. Its goal is to provide a platform for an international and interdisciplinary communication for researchers working in areas associated with integrable discrete systems, such as classical and quantum physics, computer science and numerical analysis, mathematical biology and economics, discrete geometry and combinatorics, theory of special functions, etc. The previous SIDE meetings took place in Estérel near Montréal, Canada (1994), at the University of Kent in Canterbury, UK (1996), in Sabaudia near Rome, Italy (1998), at the University of Tokyo, Japan (2000), in Giens, France (2002), and in Helsinki, Finland (2004). The SIDE VII meeting was held at the University of Melbourne from 10-14 July 2006. The scientific committee consisted of Nalini Joshi (The University of Sydney), Frank W Nijhoff (University of Leeds), Reinout Quispel (La Trobe University) and Colin Rogers (University of New South Wales). The local organization was in the hands of John A G Roberts and Wolfgang K Schief. Proceedings of all the previous SIDE meetings have been published; the 1994 and 1988 meetings (edited respectively by D Levi, L Vinet and P Winternitz, and by D Levi and O Ragnisco) as volumes of the CRM Proceedings and Lecture Notes (AMS Publications), the 1996 meeting (edited by P Clarkson and F W Nijhoff) as Volume 255 in the LMS Lecture Note Series. Starting from the 1996 meeting the formula of publication has been changed to include rather selected refereed contributions submitted in response to a call for papers issued after the meetings and not restricted to their participants. Thus publications reflecting the scope of the 1996 meeting (edited by J Hietarinta, F W Nijhoff and J Satsuma) appeared in Journal of Physics A: Mathematical and General 34 48 (special issue), and of the 1998 and 2000 meetings (edited respectively by F W Nijhoff, Yu B Suris and C-M Viallet, and by J F van Diejen and R Halburd) in Journal of Nonlinear Mathematical Physics 10 (Suppl. 2) and 12 (Suppl. 2). The aim of this special issue is to benefit from the occasion offered by the SIDE VII meeting, producing an issue containing papers which represent the state-of-the-art knowledge for studying integrability and symmetry properties of difference equations. This special issue features high quality research papers and invited reviews which deal with themes that were covered by the SIDE VII conference. These are in alphabetical order: Algebraic-geometric approaches to integrability. The first section contains a paper by T Hamamoto and K Kajiwara on hypergeometric solutions to the q-Painlevé equation of type A4(1). Discrete geometry. In this category there are three papers. J Cielinski offers a geometric definition and a spectral approach on pseudospherical surfaces on time scales, while A Doliwa considers generalized isothermic lattices. The paper by U Pinkall, B Springborn and S Weiss mann is concerned with a new doubly discrete analogue of smoke ring flow and the real time simulation of fluid flow. Integrable systems in statistical physics. Under this heading there is a paper by R J Baxter on corner transfer matrices in statistical mechanics, and a paper by S Boukraa, S Hassani, J-M Maillard, B M McCoy, J-A Weil and N Zenine where the authors consider Fuchs-Painlevé elliptic representation of the Painlevé VI equation. KP lattices and differential-difference hierarchies. In this section we have seven articles. C R Gilson, J J C Nimmo and Y Ohta consider quasideterminant solutions of a non-Abelian Hirota-Miwa equation, while B Grammaticos, A Ramani, V Papageorgiou, J Satsuma and R Willox discuss the construction of lump-like solutions of the Hirota-Miwa equation. J Hietarinta and C Viallet analyze the factorization process for lattice maps searching for integrable cases, the paper by X-B Hu and G-F Yu is concerned with integrable discretizations of the (2+1)-dimensional sinh-Gordon equation, and K Kajiwara, M Mazzocco and Y Ohta consider the Hankel determinant formula of the tau-functions of the Toda equation. Finally, V G Papageorgiou and A G Tongas study Yang-Baxter maps and multi-field integrable lattice equations, and H-Y Wang, X-B Hu and H-W Tam consider the two-dimensional Leznov lattice equation with self-consistent sources. Quantum integrable systems. This category contains a paper on q-extended eigenvectors of the integral and finite Fourier transforms by N M Atakishiyev, J P Rueda and K B Wolf, and an article by S M Sergeev on quantization of three-wave equations. Random matrix theory. This section contains a paper by A V Kitaev on the boundary conditions for scaled random matrix ensembles in the bulk of the spectrum. Symmetries and conservation laws. In this section we have five articles. H Gegen, X-B Hu, D Levi and S Tsujimoto consider a difference-analogue of Davey-Stewartson system giving its discrete Gram-type determinant solution and Lax pair. The paper by D Levi, M Petrera, and C Scimiterna is about the lattice Schwarzian KDV equation and its symmetries, while O G Rasin and P E Hydon study the conservation laws for integrable difference equations. S Saito and N Saitoh discuss recurrence equations associated with invariant varieties of periodic points, and P H van der Kamp presents closed-form expressions for integrals of MKDV and sine-Gordon maps. Ultra-discrete systems. This final category contains an article by C Ormerod on connection matrices for ultradiscrete linear problems. We would like to express our sincerest thanks to all contributors, and to everyone involved in compiling this special issue.

The ε-form of the differential equations for Feynman integrals in the elliptic case

NASA Astrophysics Data System (ADS)

Adams, Luise; Weinzierl, Stefan

2018-06-01

Feynman integrals are easily solved if their system of differential equations is in ε-form. In this letter we show by the explicit example of the kite integral family that an ε-form can even be achieved, if the Feynman integrals do not evaluate to multiple polylogarithms. The ε-form is obtained by a (non-algebraic) change of basis for the master integrals.

Distribution theory for Schrödinger’s integral equation

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

Lange, Rutger-Jan, E-mail: rutger-jan.lange@cantab.net

2015-12-15

Much of the literature on point interactions in quantum mechanics has focused on the differential form of Schrödinger’s equation. This paper, in contrast, investigates the integral form of Schrödinger’s equation. While both forms are known to be equivalent for smooth potentials, this is not true for distributional potentials. Here, we assume that the potential is given by a distribution defined on the space of discontinuous test functions. First, by using Schrödinger’s integral equation, we confirm a seminal result by Kurasov, which was originally obtained in the context of Schrödinger’s differential equation. This hints at a possible deeper connection between bothmore » forms of the equation. We also sketch a generalisation of Kurasov’s [J. Math. Anal. Appl. 201(1), 297–323 (1996)] result to hypersurfaces. Second, we derive a new closed-form solution to Schrödinger’s integral equation with a delta prime potential. This potential has attracted considerable attention, including some controversy. Interestingly, the derived propagator satisfies boundary conditions that were previously derived using Schrödinger’s differential equation. Third, we derive boundary conditions for “super-singular” potentials given by higher-order derivatives of the delta potential. These boundary conditions cannot be incorporated into the normal framework of self-adjoint extensions. We show that the boundary conditions depend on the energy of the solution and that probability is conserved. This paper thereby confirms several seminal results and derives some new ones. In sum, it shows that Schrödinger’s integral equation is a viable tool for studying singular interactions in quantum mechanics.« less

A boundary integral approach in primitive variables for free surface flows

NASA Astrophysics Data System (ADS)

Casciola, C.; Piva, R.

The boundary integral formulation, very efficient for free surface potential flows, was considered for its possible extension to rotational flows either inviscid or viscous. We first analyze a general formulation for unsteady Navier-Stokes equations in primitive variables, which reduces to a representation for the Euler equations in the limiting case of Reynolds infinity. A first simplified model for rotational flows, obtained by decoupling kinematics and dynamics, reduces the integral equations to a known kinematical form whose mathematical and numerical properties have been studied. The dynamics equations to complete the model are obtained for the free surface and the wake. A simple and efficient scheme for the study of the non linear evolution of the wave system and its interaction with the body wake is presented. A steady state version for the calculation of the wave resistance is also reported. A second model was proposed for the simulation of rotational separated regions, by coupling the integral equations in velocity with an integral equation for the vorticity at the body boundary. The same procedure may be extended to include the diffusion of the vorticity in the flowfield. The vortex shedding from a cylindrical body in unsteady motion is discussed, as a first application of the model.

Chordwise and compressibility corrections to slender-wing theory

NASA Technical Reports Server (NTRS)

Lomax, Harvard; Sluder, Loma

1952-01-01

Corrections to slender-wing theory are obtained by assuming a spanwise distribution of loading and determining the chordwise variation which satisfies the appropriate integral equation. Such integral equations are set up in terms of the given vertical induced velocity on the center line or, depending on the type of wing plan form, its average value across the span at a given chord station. The chordwise distribution is then obtained by solving these integral equations. Results are shown for flat-plate rectangular, and triangular wings.

The ATOMFT integrator - Using Taylor series to solve ordinary differential equations

NASA Technical Reports Server (NTRS)

Berryman, Kenneth W.; Stanford, Richard H.; Breckheimer, Peter J.

1988-01-01

This paper discusses the application of ATOMFT, an integration package based on Taylor series solution with a sophisticated user interface. ATOMFT has the capabilities to allow the implementation of user defined functions and the solution of stiff and algebraic equations. Detailed examples, including the solutions to several astrodynamics problems, are presented. Comparisons with its predecessor ATOMCC and other modern integrators indicate that ATOMFT is a fast, accurate, and easy method to use to solve many differential equation problems.

Matrix algorithms for solving (in)homogeneous bound state equations

PubMed Central

Blank, M.; Krassnigg, A.

2011-01-01

In the functional approach to quantum chromodynamics, the properties of hadronic bound states are accessible via covariant integral equations, e.g. the Bethe–Salpeter equation for mesons. In particular, one has to deal with linear, homogeneous integral equations which, in sophisticated model setups, use numerical representations of the solutions of other integral equations as part of their input. Analogously, inhomogeneous equations can be constructed to obtain off-shell information in addition to bound-state masses and other properties obtained from the covariant analogue to a wave function of the bound state. These can be solved very efficiently using well-known matrix algorithms for eigenvalues (in the homogeneous case) and the solution of linear systems (in the inhomogeneous case). We demonstrate this by solving the homogeneous and inhomogeneous Bethe–Salpeter equations and find, e.g. that for the calculation of the mass spectrum it is as efficient or even advantageous to use the inhomogeneous equation as compared to the homogeneous. This is valuable insight, in particular for the study of baryons in a three-quark setup and more involved systems. PMID:21760640

Analytical Theory of the Destruction Terms in Dissipation Rate Transport Equations

NASA Technical Reports Server (NTRS)

Rubinstein, Robert; Zhou, Ye

1996-01-01

Modeled dissipation rate transport equations are often derived by invoking various hypotheses to close correlations in the corresponding exact equations. D. C. Leslie suggested that these models might be derived instead from Kraichnan's wavenumber space integrals for inertial range transport power. This suggestion is applied to the destruction terms in the dissipation rate equations for incompressible turbulence, buoyant turbulence, rotating incompressible turbulence, and rotating buoyant turbulence. Model constants like C(epsilon 2) are expressed as integrals; convergence of these integrals implies the absence of Reynolds number dependence in the corresponding destruction term. The dependence of C(epsilon 2) on rotation rate emerges naturally; sensitization of the modeled dissipation rate equation to rotation is not required. A buoyancy related effect which is absent in the exact transport equation for temperature variance dissipation, but which sometimes improves computational predictions, also arises naturally. Both the presence of this effect and the appropriate time scale in the modeled transport equation depend on whether Bolgiano or Kolmogorov inertial range scaling applies. A simple application of these methods leads to a preliminary, dissipation rate equation for rotating buoyant turbulence.

Efficiently and easily integrating differential equations with JiTCODE, JiTCDDE, and JiTCSDE

NASA Astrophysics Data System (ADS)

Ansmann, Gerrit

2018-04-01

We present a family of Python modules for the numerical integration of ordinary, delay, or stochastic differential equations. The key features are that the user enters the derivative symbolically and it is just-in-time-compiled, allowing the user to efficiently integrate differential equations from a higher-level interpreted language. The presented modules are particularly suited for large systems of differential equations such as those used to describe dynamics on complex networks. Through the selected method of input, the presented modules also allow almost complete automatization of the process of estimating regular as well as transversal Lyapunov exponents for ordinary and delay differential equations. We conceptually discuss the modules' design, analyze their performance, and demonstrate their capabilities by application to timely problems.

Asymptotic integration algorithms for first-order ODEs with application to viscoplasticity

NASA Technical Reports Server (NTRS)

Freed, Alan D.; Yao, Minwu; Walker, Kevin P.

1992-01-01

When constructing an algorithm for the numerical integration of a differential equation, one must first convert the known ordinary differential equation (ODE), which is defined at a point, into an ordinary difference equation (O(delta)E), which is defined over an interval. Asymptotic, generalized, midpoint, and trapezoidal, O(delta)E algorithms are derived for a nonlinear first order ODE written in the form of a linear ODE. The asymptotic forward (typically underdamped) and backward (typically overdamped) integrators bound these midpoint and trapezoidal integrators, which tend to cancel out unwanted numerical damping by averaging, in some sense, the forward and backward integrations. Viscoplasticity presents itself as a system of nonlinear, coupled first-ordered ODE's that are mathematically stiff, and therefore, difficult to numerically integrate. They are an excellent application for the asymptotic integrators. Considering a general viscoplastic structure, it is demonstrated that one can either integrate the viscoplastic stresses or their associated eigenstrains.

An off-axis galaxy cluster merger: Abell 0141

NASA Astrophysics Data System (ADS)

Caglar, Turgay

2018-04-01

We present structural analysis results of Abell 0141 (z = 0.23) based on X-ray data. The X-ray luminosity map demonstrates that Abell 0141 (A0141) is a bimodal galaxy cluster, which is separated on the sky by ˜0.65 Mpc with an elongation along the north-south direction. The optical galaxy density map also demonstrates this bimodality. We estimate sub-cluster ICM temperatures of 5.17^{+0.20}_{-0.19} keV for A0141N and 5.23^{+0.24}_{-0.23} keV for A0141S. We obtain X-ray morphological parameters w = 0.034 ± 0.004, c = 0.113 ± 0.004, and w = 0.039 ± 0.004, c = 0.104 ± 0.005 for A0141N and A0141S, respectively. The resulting X-ray morphological parameters indicate that both sub-clusters are moderately disturbed non-cool core structures. We find a slight brightness jump in the bridge region, and yet, there is still an absence of strong X-ray emitting gas between sub-clusters. We discover a significantly hotspot (˜10 keV) between sub-clusters, and a Mach number M = 1.69^{+0.40}_{-0.37} is obtained by using the temperature jump condition. However, we did not find direct evidence for shock-heating between sub-clusters. We estimate the sub-clusters' central entropies as K0 > 100 keV cm2, which indicates that the sub-clusters are not cool cores. We find some evidence that the system undergoes an off-axis collision; however, the cores of each sub-clusters have not yet been destroyed. Due to the orientation of X-ray tails of sub-clusters, we suggest that the northern sub-cluster moves through the south-west direction, and the southern cluster moves through the north-east direction. In conclusion, we are witnessing an earlier phase of close core passage between sub-clusters.

A Census of Star Formation and Active Galactic Nuclei Populations in Abell 1689

NASA Astrophysics Data System (ADS)

Jones, Logan H.; Atlee, David Wesley

2016-01-01

A recent survey of low-z galaxy clusters observed a disjunction between X-ray and mid-infrared selected populations of active galactic nuclei (X-ray and IR AGNs) (Atlee+ 2011, ApJ 729, 22.). Here we present an analysis of near-infrared spectroscopic data of star-forming galaxies in cluster Abell 1689 in order to confirm the identity of some of their IR AGN and to provide a check on their reported star formation rates. Our sample consists of 24 objects in Abell 1689. H and K band spectroscopic observations of target objects and standard stars were obtained by David Atlee between 2010 May 17 and 2011 June 6 using the Large Binocular Telescope's LUCI instrument. After undergoing initial reductions, standard stars were corrected for telluric absorption using TelFit (Gullikson+ 2014, AJ, 158, 53). Raw detector counts were converted to physical units using the wavelength-dependent response of the grating and the star's reported H and K band magnitudes to produce conversion factors that fully correct for instrumental effects. Target spectra were flux-calibrated using the airmass-corrected transmission profiles produced by TelFit and the associated H band conversion factor (or the average of the two factors, for nights with two standard stars). Star formation rates were calculated using the SFR-L(Ha) relation reported in Kennicutt (1998), with the measured luminosity of the Pa-a emission line at the luminosity distance of the cluster used as a proxy for L(Ha) (Kennicutt 1998, ARA&A 36, 189; Hummer & Stoney 1987, MNRAS 346, 1055). The line ratios H2 2.121 mm/Brg and [FeII]/Pab were used to classify targets as starburst galaxies, AGNs, or LINERs (Rodriguez-Ardila+ 2005, MNRAS, 364, 1041). Jones was supported by the NOAO/KPNO Research Experience for Undergraduates (REU) Program, which is funded by the National Science Foundation Research Experiences for Undergraduates Program (AST-1262829).

On the merging cluster Abell 578 and its central radio galaxy 4C+67.13

DOE PAGES

Hagino, K.; Stawarz, Ł.; Siemiginowska, A.; ...

2015-05-26

Here we analyze radio, optical, and X-ray data for the peculiar cluster Abell 578. This cluster is not fully relaxed and consists of two merging sub-systems. The brightest cluster galaxy (BCG), CGPG 0719.8+6704, is a pair of interacting ellipticals with projected separation ~10 kpc, the brighter of which hosts the radio source 4C+67.13. The Fanaroff–Riley type-II radio morphology of 4C+67.13 is unusual for central radio galaxies in local Abell clusters. Our new optical spectroscopy revealed that both nuclei of the CGPG 0719.8+6704 pair are active, albeit at low accretion rates corresponding to the Eddington ratiomore » $$\\sim {{10}^{-4}}$$ (for the estimated black hole masses of $$\\sim 3\\times {{10}^{8}}\\;{{M}_{\\odot }}$$ and $$\\sim {{10}^{9}}\\;{{M}_{\\odot }}$$). The gathered X-ray (Chandra) data allowed us to confirm and to quantify robustly the previously noted elongation of the gaseous atmosphere in the dominant sub-cluster, as well as a large spatial offset (~60 kpc projected) between the position of the BCG and the cluster center inferred from the modeling of the X-ray surface brightness distribution. Detailed analysis of the brightness profiles and temperature revealed also that the cluster gas in the vicinity of 4C+67.13 is compressed (by a factor of about ~1.4) and heated (from $$\\simeq 2.0$$ keV up to 2.7 keV), consistent with the presence of a weak shock (Mach number ~1.3) driven by the expanding jet cocoon. As a result, this would then require the jet kinetic power of the order of $$\\sim {{10}^{45}}$$ erg s –1, implying either a very high efficiency of the jet production for the current accretion rate, or a highly modulated jet/accretion activity in the system.« less

Size–Luminosity Relations and UV Luminosity Functions at z = 6–9 Simultaneously Derived from the Complete Hubble Frontier Fields Data

NASA Astrophysics Data System (ADS)

Kawamata, Ryota; Ishigaki, Masafumi; Shimasaku, Kazuhiro; Oguri, Masamune; Ouchi, Masami; Tanigawa, Shingo

2018-03-01

We construct z ∼ 6–7, 8, and 9 faint Lyman break galaxy samples (334, 61, and 37 galaxies, respectively) with accurate size measurements with the software glafic from the complete Hubble Frontier Fields (HFF) cluster and parallel fields data. These are the largest samples hitherto and reach down to the faint ends of recently obtained deep luminosity functions. At faint magnitudes, however, these samples are highly incomplete for galaxies with large sizes, implying that derivation of the luminosity function sensitively depends on the intrinsic size–luminosity relation. We thus conduct simultaneous maximum-likelihood estimation of luminosity function and size–luminosity relation parameters from the observed distribution of galaxies on the size–luminosity plane with the help of a completeness map as a function of size and luminosity. At z ∼ 6–7, we find that the intrinsic size–luminosity relation expressed as r e ∝ L β has a notably steeper slope of β ={0.46}-0.09+0.08 than those at lower redshifts, which in turn implies that the luminosity function has a relatively shallow faint-end slope of α =-{1.86}-0.18+0.17. This steep β can be reproduced by a simple analytical model in which smaller galaxies have lower specific angular momenta. The β and α values for the z ∼ 8 and 9 samples are consistent with those for z ∼ 6–7 but with larger errors. For all three samples, there is a large, positive covariance between β and α, implying that the simultaneous determination of these two parameters is important. We also provide new strong lens mass models of Abell S1063 and Abell 370, as well as updated mass models of Abell 2744 and MACS J0416.1‑2403.

Validation of ionospheric electron density profiles inferred from GPS occultation observations of the GPS/MET experiment

NASA Astrophysics Data System (ADS)

Kawakami, Todd Mori

In April of 1995, the launch of the GPS Meteorology Experiment (GPS/MET) onboard the Orbview-1 satellite, formerly known as Microlab-1, provided the first technology demonstration of active limb sounding of the Earth's atmosphere with a low Earth orbiting spacecraft utilizing the signals transmitted by the satellites of the Global Positioning System (GPS). Though the experiment's primary mission was to probe the troposphere and stratosphere, GPS/MET was also capable of making radio occultation observations of the ionosphere. The application of the GPS occultation technique to the upper atmosphere created a unique opportunity to conduct ionospheric research with an unprecedented global distribution of observations. For operational support requirements, the Abel transform could be employed to invert the horizontal TEC profiles computed from the L1 and L2 phase measurements observed by GPS/MET into electron density profiles versus altitude in near real time. The usefulness of the method depends on how effectively the TEC limb profiles can be transformed into vertical electron density profiles. An assessment of GPS/MET's ability to determine electron density profiles needs to be examined to validate the significance of the GPS occultation method as a new and complementary ionospheric research tool to enhance the observational databases and improve space weather modeling and forecasting. To that end, simulations of the occultation observations and their inversions have been conducted to test the Abel transform algorithm and to provide qualitative information about the type and range of errors that might be experienced during the processing of real data. Comparisons of the electron density profiles inferred from real GPS/MET observations are then compared with coincident in situ measurements from the satellites of Defense Meteorological Satellite Program (DMSP) and ground-based remote sensing from digisonde and incoherent scatter radar facilities. The principal focus of this study is the validation of the electron density profiles inferred from GPS occultation observations using the Abel transform.

Gemini Frontier Fields: Wide-field Adaptive Optics Ks-band Imaging of the Galaxy Clusters MACS J0416.1-2403 and Abell 2744

NASA Astrophysics Data System (ADS)

Schirmer, M.; Carrasco, E. R.; Pessev, P.; Garrel, V.; Winge, C.; Neichel, B.; Vidal, F.

2015-04-01

We have observed two of the six Frontier Fields galaxy clusters, MACS J0416.1-2403 and Abell 2744, using the Gemini Multi-Conjugate Adaptive Optics System (GeMS) and the Gemini South Adaptive Optics Imager (GSAOI). With 0.″ 08-0.″ 10 FWHM our data are nearly diffraction-limited over a 100\\prime\\prime × 100\\prime\\prime wide area. GeMS/GSAOI complements the Hubble Space Telescope (HST) redwards of 1.6 μm with twice the angular resolution. We reach a 5σ depth of {{K}s}˜ 25.6 mag (AB) for compact sources. In this paper, we describe the observations, data processing, and initial public data release. We provide fully calibrated, co-added images matching the native GSAOI pixel scale as well as the larger plate scales of the HST release, adding to the legacy value of the Frontier Fields. Our work demonstrates that even for fields at high galactic latitude where natural guide stars are rare, current multi-conjugated adaptive optics technology at 8 m telescopes has opened a new window on the distant universe. Observations of a third Frontier Field, Abell 370, are planned. Based on observations obtained at the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini partnership: the National Science Foundation (United States), the Science and Technology Facilities Council (United Kingdom), the National Research Council (Canada), CONICYT (Chile), the Australian Research Council (Australia), Ministério da Ciência, Tecnologia e Inovação (Brazil) and Ministerio de Ciencia, Tecnología e Innovación Productiva (Argentina). Based on observations made with ESO Telescopes at the La Silla and Paranal Observatories, Chile.

Semi-analytical Karhunen-Loeve representation of irregular waves based on the prolate spheroidal wave functions

NASA Astrophysics Data System (ADS)

Lee, Gibbeum; Cho, Yeunwoo

2018-01-01

A new semi-analytical approach is presented to solving the matrix eigenvalue problem or the integral equation in Karhunen-Loeve (K-L) representation of random data such as irregular ocean waves. Instead of direct numerical approach to this matrix eigenvalue problem, which may suffer from the computational inaccuracy for big data, a pair of integral and differential equations are considered, which are related to the so-called prolate spheroidal wave functions (PSWF). First, the PSWF is expressed as a summation of a small number of the analytical Legendre functions. After substituting them into the PSWF differential equation, a much smaller size matrix eigenvalue problem is obtained than the direct numerical K-L matrix eigenvalue problem. By solving this with a minimal numerical effort, the PSWF and the associated eigenvalue of the PSWF differential equation are obtained. Then, the eigenvalue of the PSWF integral equation is analytically expressed by the functional values of the PSWF and the eigenvalues obtained in the PSWF differential equation. Finally, the analytically expressed PSWFs and the eigenvalues in the PWSF integral equation are used to form the kernel matrix in the K-L integral equation for the representation of exemplary wave data such as ordinary irregular waves. It is found that, with the same accuracy, the required memory size of the present method is smaller than that of the direct numerical K-L representation and the computation time of the present method is shorter than that of the semi-analytical method based on the sinusoidal functions.

The integrated Michaelis-Menten rate equation: déjà vu or vu jàdé?

PubMed

Goličnik, Marko

2013-08-01

A recent article of Johnson and Goody (Biochemistry, 2011;50:8264-8269) described the almost-100-years-old paper of Michaelis and Menten. Johnson and Goody translated this classic article and presented the historical perspective to one of incipient enzyme-reaction data analysis, including a pioneering global fit of the integrated rate equation in its implicit form to the experimental time-course data. They reanalyzed these data, although only numerical techniques were used to solve the model equations. However, there is also the still little known algebraic rate-integration equation in a closed form that enables direct fitting of the data. Therefore, in this commentary, I briefly present the integral solution of the Michaelis-Menten rate equation, which has been largely overlooked for three decades. This solution is expressed in terms of the Lambert W function, and I demonstrate here its use for global nonlinear regression curve fitting, as carried out with the original time-course dataset of Michaelis and Menten.

The Boundary Integral Equation Method for Porous Media Flow

NASA Astrophysics Data System (ADS)

Anderson, Mary P.

Just as groundwater hydrologists are breathing sighs of relief after the exertions of learning the finite element method, a new technique has reared its nodes—the boundary integral equation method (BIEM) or the boundary equation method (BEM), as it is sometimes called. As Liggett and Liu put it in the preface to The Boundary Integral Equation Method for Porous Media Flow, “Lately, the Boundary Integral Equation Method (BIEM) has emerged as a contender in the computation Derby.” In fact, in July 1984, the 6th International Conference on Boundary Element Methods in Engineering will be held aboard the Queen Elizabeth II, en route from Southampton to New York. These conferences are sponsored by the Department of Civil Engineering at Southampton College (UK), whose members are proponents of BIEM. The conferences have featured papers on applications of BIEM to all aspects of engineering, including flow through porous media. Published proceedings are available, as are textbooks on application of BIEM to engineering problems. There is even a 10-minute film on the subject.

Mass dependent galaxy transformation mechanisms in the complex environment of SuperGroup Abell 1882

NASA Astrophysics Data System (ADS)

Sengupta, Aparajita

We present our data and results from panchromatic photometry and optical spectrometry of the nearest (extremely rich) filamentary large scale structure, SuperGroup Abell 1882. It is a precursor of a cluster and is an inevitable part of the narrative in the study of galaxy transformations. There has been strong empirical evidence over the past three decades that galaxy environment affects galaxy properties. Blue disky galaxies transform into red bulge-like galaxies as they traverse into the deeper recesses of a cluster. However, we have little insight into the story of galaxy evolution in the early stages of cluster formation. Besides, in relaxed clusters that have been studied extensively, several evolutionary mechanisms take effect on similar spatial and temporal scales, making it almost impossible to disentangle different local and global mechanisms. A SuperGroup on the other hand, has a shallower dark-matter potential. Here, the accreting galaxies are subjected to evolutionary mechanisms over larger time and spatial scales. This separates processes that are otherwise superimposed in rich cluster-filament interfaces. As has been found from cluster studies, galaxy color and morphology tie very strongly with local galaxy density even in a complex and nascent structure like Abell 1882. Our major results indicate that there is a strong dependence of galaxy transformations on the galaxy masses themselves. Mass- dependent evolutionary mechanisms affect galaxies at different spatial scales. The galaxy color also varies with radial projected distance from the assumed center of the structure for a constant local galaxy density, indicating the underlying large scale structure as a second order evolutionary driver. We have looked for clues to the types of mechanisms that might cause the transformations at various mass regimes. We have found the thoroughly quenched low mass galaxies confined to the groups, whereas there are evidences of intermediate-mass quenched galaxies even in the far outskirts. However, unlike what we observe in this system, ideally would we expect the dwarf galaxies with their shallow potentials to be more vulnerable than more massive galaxies, and hence be quenched earlier. We propose harassment and/or ram-pressure stripping as the mechanism that might lead to the quenched galaxies near or inside the high density, high velocity dispersion region in and near the groups; and mergers as the mechanism for the intermediate mass quenched galaxies at the low density, low velocity dispersion outskirts. We also identify a starburst population preferentially occurring within the filaments, at least a subset of which must be progenitors of the quenched galaxies at the core of Abell 1882. This also indicates a higher degree of preprocessing within the filaments as compared to that of the field.

Numerical integration of ordinary differential equations of various orders

NASA Technical Reports Server (NTRS)

Gear, C. W.

1969-01-01

Report describes techniques for the numerical integration of differential equations of various orders. Modified multistep predictor-corrector methods for general initial-value problems are discussed and new methods are introduced.

Neglected transport equations: extended Rankine-Hugoniot conditions and J -integrals for fracture

NASA Astrophysics Data System (ADS)

Davey, K.; Darvizeh, R.

2016-09-01

Transport equations in integral form are well established for analysis in continuum fluid dynamics but less so for solid mechanics. Four classical continuum mechanics transport equations exist, which describe the transport of mass, momentum, energy and entropy and thus describe the behaviour of density, velocity, temperature and disorder, respectively. However, one transport equation absent from the list is particularly pertinent to solid mechanics and that is a transport equation for movement, from which displacement is described. This paper introduces the fifth transport equation along with a transport equation for mechanical energy and explores some of the corollaries resulting from the existence of these equations. The general applicability of transport equations to discontinuous physics is discussed with particular focus on fracture mechanics. It is well established that bulk properties can be determined from transport equations by application of a control volume methodology. A control volume can be selected to be moving, stationary, mass tracking, part of, or enclosing the whole system domain. The flexibility of transport equations arises from their ability to tolerate discontinuities. It is insightful thus to explore the benefits derived from the displacement and mechanical energy transport equations, which are shown to be beneficial for capturing the physics of fracture arising from a displacement discontinuity. Extended forms of the Rankine-Hugoniot conditions for fracture are established along with extended forms of J -integrals.

A Tensor-Train accelerated solver for integral equations in complex geometries

NASA Astrophysics Data System (ADS)

Corona, Eduardo; Rahimian, Abtin; Zorin, Denis

2017-04-01

We present a framework using the Quantized Tensor Train (QTT) decomposition to accurately and efficiently solve volume and boundary integral equations in three dimensions. We describe how the QTT decomposition can be used as a hierarchical compression and inversion scheme for matrices arising from the discretization of integral equations. For a broad range of problems, computational and storage costs of the inversion scheme are extremely modest O (log ⁡ N) and once the inverse is computed, it can be applied in O (Nlog ⁡ N) . We analyze the QTT ranks for hierarchically low rank matrices and discuss its relationship to commonly used hierarchical compression techniques such as FMM and HSS. We prove that the QTT ranks are bounded for translation-invariant systems and argue that this behavior extends to non-translation invariant volume and boundary integrals. For volume integrals, the QTT decomposition provides an efficient direct solver requiring significantly less memory compared to other fast direct solvers. We present results demonstrating the remarkable performance of the QTT-based solver when applied to both translation and non-translation invariant volume integrals in 3D. For boundary integral equations, we demonstrate that using a QTT decomposition to construct preconditioners for a Krylov subspace method leads to an efficient and robust solver with a small memory footprint. We test the QTT preconditioners in the iterative solution of an exterior elliptic boundary value problem (Laplace) formulated as a boundary integral equation in complex, multiply connected geometries.

Feynman path integral application on deriving black-scholes diffusion equation for european option pricing

NASA Astrophysics Data System (ADS)

Utama, Briandhika; Purqon, Acep

2016-08-01

Path Integral is a method to transform a function from its initial condition to final condition through multiplying its initial condition with the transition probability function, known as propagator. At the early development, several studies focused to apply this method for solving problems only in Quantum Mechanics. Nevertheless, Path Integral could also apply to other subjects with some modifications in the propagator function. In this study, we investigate the application of Path Integral method in financial derivatives, stock options. Black-Scholes Model (Nobel 1997) was a beginning anchor in Option Pricing study. Though this model did not successfully predict option price perfectly, especially because its sensitivity for the major changing on market, Black-Scholes Model still is a legitimate equation in pricing an option. The derivation of Black-Scholes has a high difficulty level because it is a stochastic partial differential equation. Black-Scholes equation has a similar principle with Path Integral, where in Black-Scholes the share's initial price is transformed to its final price. The Black-Scholes propagator function then derived by introducing a modified Lagrange based on Black-Scholes equation. Furthermore, we study the correlation between path integral analytical solution and Monte-Carlo numeric solution to find the similarity between this two methods.

An integral equation-based numerical solver for Taylor states in toroidal geometries

NASA Astrophysics Data System (ADS)

O'Neil, Michael; Cerfon, Antoine J.

2018-04-01

We present an algorithm for the numerical calculation of Taylor states in toroidal and toroidal-shell geometries using an analytical framework developed for the solution to the time-harmonic Maxwell equations. Taylor states are a special case of what are known as Beltrami fields, or linear force-free fields. The scheme of this work relies on the generalized Debye source representation of Maxwell fields and an integral representation of Beltrami fields which immediately yields a well-conditioned second-kind integral equation. This integral equation has a unique solution whenever the Beltrami parameter λ is not a member of a discrete, countable set of resonances which physically correspond to spontaneous symmetry breaking. Several numerical examples relevant to magnetohydrodynamic equilibria calculations are provided. Lastly, our approach easily generalizes to arbitrary geometries, both bounded and unbounded, and of varying genus.

A Cluster and a Sea of Galaxies

NASA Astrophysics Data System (ADS)

2010-05-01

A new wide-field image released today by ESO displays many thousands of distant galaxies, and more particularly a large group belonging to the massive galaxy cluster known as Abell 315. As crowded as it may appear, this assembly of galaxies is only the proverbial "tip of the iceberg", as Abell 315 - like most galaxy clusters - is dominated by dark matter. The huge mass of this cluster deflects light from background galaxies, distorting their observed shapes slightly. When looking at the sky with the unaided eye, we mostly only see stars within our Milky Way galaxy and some of its closest neighbours. More distant galaxies are just too faint to be perceived by the human eye, but if we could see them, they would literally cover the sky. This new image released by ESO is both a wide-field and long-exposure one, and reveals thousands of galaxies crowding an area on the sky roughly as large as the full Moon. These galaxies span a vast range of distances from us. Some are relatively close, as it is possible to distinguish their spiral arms or elliptical halos, especially in the upper part of the image. The more distant appear just like the faintest of blobs - their light has travelled through the Universe for eight billion years or more before reaching Earth. Beginning in the centre of the image and extending below and to the left, a concentration of about a hundred yellowish galaxies identifies a massive galaxy cluster, designated with the number 315 in the catalogue compiled by the American astronomer George Abell in 1958 [1]. The cluster is located between the faint, red and blue galaxies and the Earth, about two billion light-years away from us. It lies in the constellation of Cetus (the Whale). Galaxy clusters are some of the largest structures in the Universe held together by gravity. But there is more in these structures than the many galaxies we can see. Galaxies in these giants contribute to only ten percent of the mass, with hot gas in between galaxies accounting for another ten percent [2]. The remaining 80 percent is made of an invisible and unknown ingredient called dark matter that lies in between the galaxies. The presence of dark matter is revealed through its gravitational effect: the enormous mass of a galaxy cluster acts on the light from galaxies behind the cluster like a cosmic magnifying glass, bending the trajectory of the light and thus making the galaxies appear slightly distorted [3]. By observing and analysing the twisted shapes of these background galaxies, astronomers can infer the total mass of the cluster responsible for the distortion, even when this mass is mostly invisible. However, this effect is usually tiny, and it is necessary to measure it over a huge number of galaxies to obtain significant results: in the case of Abell 315, the shapes of almost 10 000 faint galaxies in this image were studied in order to estimate the total mass of the cluster, which amounts to over a hundred thousand billion times the mass of our Sun [4]. To complement the enormous range of cosmic distances and sizes surveyed by this image, a handful of objects much smaller than galaxies and galaxy clusters and much closer to Earth are scattered throughout the field: besides several stars belonging to our galaxy, many asteroids are also visible as blue, green or red trails [5]. These objects belong to the main asteroid belt, located between the orbits of Mars and Jupiter, and their dimensions vary from some tens of kilometres, for the brightest ones, to just a few kilometres in the case of the faintest ones. This image has been taken with the Wide Field Imager on the MPG/ESO 2.2-metre telescope at ESO's La Silla Observatory in Chile. It is a composite of several exposures acquired using three different broadband filters, for a total of almost one hour in the B filter and about one and a half hours in the V and R filters. The field of view is 34 x 33 arcminutes. Notes [1] The Abell catalogue from 1958 comprised 2712 clusters of galaxies, and was integrated with an additional 1361 clusters in 1989. Abell put together this impressive collection by visual inspection of photographic plates of the sky, seeking those areas where more galaxies than average were found at approximately the same distance from us. [2] Ten percent of a galaxy cluster's mass consists of a very hot mixture of protons and electrons (a plasma), with temperatures as high as ten million degrees or more, which makes it visible to X-ray telescopes. [3] Astronomers refer to these slight distortions as weak gravitational lensing, as opposed to strong gravitational lensing, characterised by more spectacular phenomena such as giant arcs, rings and multiple images. [4] A weak lensing study of the galaxy cluster Abell 315 has been published in a paper that appeared in Astronomy & Astrophysics in 2009 ("Weak lensing observations of potentially X-ray underluminous galaxy clusters", by J. Dietrich et al.). [5] The blue, green or red tracks indicate that each asteroid has been detected through one of the three filters, respectively. Each track is composed of several, smaller sub-tracks, reflecting the sequence of several exposures performed in each of the filters; from the length of these sub-tracks, the distance to the asteroid can be calculated. More information ESO, the European Southern Observatory, is the foremost intergovernmental astronomy organisation in Europe and the world's most productive astronomical observatory. It is supported by 14 countries: Austria, Belgium, the Czech Republic, Denmark, France, Finland, Germany, Italy, the Netherlands, Portugal, Spain, Sweden, Switzerland and the United Kingdom. ESO carries out an ambitious programme focused on the design, construction and operation of powerful ground-based observing facilities enabling astronomers to make important scientific discoveries. ESO also plays a leading role in promoting and organising cooperation in astronomical research. ESO operates three unique world-class observing sites in Chile: La Silla, Paranal and Chajnantor. At Paranal, ESO operates the Very Large Telescope, the world's most advanced visible-light astronomical observatory and VISTA, the world's largest survey telescope. ESO is the European partner of a revolutionary astronomical telescope ALMA, the largest astronomical project in existence. ESO is currently planning a 42-metre European Extremely Large optical/near-infrared Telescope, the E-ELT, which will become "the world's biggest eye on the sky".

CALL FOR PAPERS: Special issue on Symmetries and Integrability of Difference Equations

NASA Astrophysics Data System (ADS)

Doliwa, Adam; Korhonen, Risto; Lafortune, Stephane

2006-10-01

This is a call for contributions to a special issue of Journal of Physics A: Mathematical and General entitled `Special issue on Symmetries and Integrability of Difference Equations' as featured at the SIDE VII meeting held during July 2006 in Melbourne (http://web.maths.unsw.edu.au/%7Eschief/side/side.html). Participants at that meeting, as well as other researchers working in the field of difference equations and discrete systems, are invited to submit a research paper to this issue. This meeting was the seventh of a series of biennial meetings devoted to the study of integrable difference equations and related topics. The notion of integrability was first introduced in the 19th century in the context of classical mechanics with the definition of Liouville integrability for Hamiltonian flows. Since then, several notions of integrability have been introduced for partial and ordinary differential equations. Closely related to integrability theory is the symmetry analysis of nonlinear evolution equations. Symmetry analysis takes advantage of the Lie group structure of a given equation to study its properties. Together, integrability theory and symmetry analysis provide the main method by which nonlinear evolution equations can be solved explicitly. Difference equations, just as differential equations, are important in numerous fields of science and have a wide variety of applications in such areas as: mathematical physics, computer visualization, numerical analysis, mathematical biology, economics, combinatorics, quantum field theory, etc. It is thus crucial to develop tools to study and solve difference equations. While the theory of symmetry and integrability for differential equations is now well-established, this is not yet the case for discrete equations. The situation has undergone impressive development in recent years and has affected a broad range of fields, including the theory of special functions, quantum integrable systems, numerical analysis, cellular automata, representations of quantum groups, symmetries of difference equations, discrete (difference) geometry, etc. Consequently, the aim of the special issue is to benefit from the occasion offered by the SIDE VII meeting to provide a collection of papers which represent the state-of-the-art knowledge for studying integrability and symmetry properties of difference equations. Scope of the special issue The special issue will feature papers which deal with themes that were covered by the SIDE VII Conference. These are •Integrability testing •Discrete geometry and visualization •Laurent phenomena and cluster algebras •Ultra-discrete systems •Random matrix theory •Algebraic-geometric approaches to integrability •Yang-Baxter equations •Quantum and classical integrable systems •Difference Galois theory Editorial policy •The subject of the paper should relate to the subject of the meeting. The Guest Editors will reserve the right to judge whether a contribution fits the scope of the topic of the special issue. •Contributions will be refereed and processed according to the usual procedure of the journal. •Conference papers may be based on already published work but should either •contain significant additional new results and/or insights or •give a survey of the present state of the art, a critical assessment of the present understanding of a topic, and a discussion of open problems. •Papers submitted by non-participants should be original and contain substantial new results. Guidelines for preparation of contributions • The deadline for contributed papers will be 15 January 2007. •There is a page limit of 16 printed pages (approximately 9600 words) per contribution. For submitted papers exceeding this length the Guest Editors reserve the right to request a reduction in length. Further advice on document preparation can be found at www.iop.org/Journals/jphysa •Contributions to the special issue should if possible be submitted electronically by web upload at www.iop.org/Journals/jphysa, or by email to jphysa@iop.org, quoting 'J. Phys. A Special Issue: SIDE VII'. Submissions should ideally be in standard LaTeX form; we are, however, able to accept most formats including Microsoft Word. Please see the website for further information on electronic submissions. •Authors unable to submit electronically may send hard-copy contributions to: Publishing Administrators, Journal of Physics A, Institute of Physics Publishing, Dirac House, Temple Back, Bristol BS1 6BE, UK, enclosing electronic code on floppy disk if available and quoting 'J. Phys. A Special Issue: SIDE VII'. • All contributions should be accompanied by a read-me file or covering letter giving the postal and email address for correspondence. The Publishing Office should be notified of any subsequent change of address. •The special issue will be published in the paper and online version of the journal. The corresponding author of each contribution will receive a complimentary copy of the issue.

On Reductions of the Hirota-Miwa Equation

NASA Astrophysics Data System (ADS)

Hone, Andrew N. W.; Kouloukas, Theodoros E.; Ward, Chloe

2017-07-01

The Hirota-Miwa equation (also known as the discrete KP equation, or the octahedron recurrence) is a bilinear partial difference equation in three independent variables. It is integrable in the sense that it arises as the compatibility condition of a linear system (Lax pair). The Hirota-Miwa equation has infinitely many reductions of plane wave type (including a quadratic exponential gauge transformation), defined by a triple of integers or half-integers, which produce bilinear ordinary difference equations of Somos/Gale-Robinson type. Here it is explained how to obtain Lax pairs and presymplectic structures for these reductions, in order to demonstrate Liouville integrability of some associated maps, certain of which are related to reductions of discrete Toda and discrete KdV equations.

Diffuse light and building history of the galaxy cluster Abell 2667

NASA Astrophysics Data System (ADS)

Covone, G.; Adami, C.; Durret, F.; Kneib, J.-P.; Lima Neto, G. B.; Slezak, E.

2006-12-01

Aims.We searched for diffuse intracluster light in the galaxy cluster Abell 2667 (z=0.233) from HST images in three broad band-filters. Methods: .We applied an iterative multi-scale wavelet analysis and reconstruction technique to these images, which allows to subtract stars and galaxies from the original images. Results: .We detect a zone of diffuse emission southwest of the cluster center (DS1) and a second faint object (ComDif) within DS1. Another diffuse source (DS2) may be detected at lower confidence level northeast of the center. These sources of diffuse light contribute to 10-15% of the total visible light in the cluster. Whether they are independent entities or part of the very elliptical external envelope of the central galaxy remains unclear. Deep VLT VIMOS integral field spectroscopy reveals a faint continuum at the positions of DS1 and ComDif but do not allow a redshift to be computed, so we conclude if these sources are part of the central galaxy or not. A hierarchical substructure detection method reveals the presence of several galaxy pairs and groups defining a similar direction to the one drawn by the DS1 - central galaxy - DS2 axis. The analysis of archive XMM-Newton and Chandra observations shows X-ray emission elongated in the same direction. The X-ray temperature map shows the presence of a cool core, a broad cool zone stretching from north to south, and hotter regions towards the northeast, southwest, and northwest. This might suggest shock fronts along these directions produced by infalling material, even if uncertainties remain quite large on the temperature determination far from the center. Conclusions: .These various data are consistent with a picture in which diffuse sources are concentrations of tidal debris and harassed matter expelled from infalling galaxies by tidal stripping and undergoing an accretion process onto the central cluster galaxy; as such, they are expected to be found along the main infall directions. Note, however, that the limited signal to noise of the various data and the apparent lack of large numbers of well-defined independent tidal tails, besides the one named ComDif, preclude definitive conclusions on this scenario.

The VLT/MUSE view of the central galaxy in Abell 2052. Ionized gas swept by the expanding radio source

NASA Astrophysics Data System (ADS)

Balmaverde, Barbara; Capetti, Alessandro; Marconi, Alessandro; Venturi, Giacomo

2018-04-01

We report observations of the radio galaxy 3C 317 (at z = 0.0345) located at the center of the Abell cluster A2052, obtained with the VLT/MUSE integral field spectrograph. The Chandra images of this cluster show cavities in the X-ray emitting gas, which were produced by the expansion of the radio lobes inflated by the active galactic nucleus (AGN). Our exquisite MUSE data show with unprecedented detail the complex network of line emitting filaments enshrouding the northern X-ray cavity. We do not detect any emission lines from the southern cavity, with a luminosity asymmetry between the two regions higher than 75. The emission lines produced by the warm phase of the interstellar medium (WIM) enable us to obtain unique information on the properties of the emitting gas. We find dense gas (up to 270 cm-3) that makes up part of a global quasi spherical outflow that is driven by the radio source, and obtain a direct estimate of the expansion velocity of the cavities (265 km s-1). The emission lines diagnostic rules out ionization from the AGN or from star-forming regions, suggesting instead ionization from slow shocks or from cosmic rays. The striking asymmetric line emission observed between the two cavities contrasts with the less pronounced differences between the north and south sides in the hot gas; this represents a significant new ingredient for our understanding of the process of the exchange of energy between the relativistic plasma and the external medium. We conclude that the expanding radio lobes displace the hot tenuous phase of the interstellar medium (ISM), but also impact the colder and denser ISM phases. These results show the effects of the AGN on its host and the importance of radio mode feedback. The reduced datacube is only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (http://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/612/A19

Symmetric and arbitrarily high-order Birkhoff-Hermite time integrators and their long-time behaviour for solving nonlinear Klein-Gordon equations

NASA Astrophysics Data System (ADS)

Liu, Changying; Iserles, Arieh; Wu, Xinyuan

2018-03-01

The Klein-Gordon equation with nonlinear potential occurs in a wide range of application areas in science and engineering. Its computation represents a major challenge. The main theme of this paper is the construction of symmetric and arbitrarily high-order time integrators for the nonlinear Klein-Gordon equation by integrating Birkhoff-Hermite interpolation polynomials. To this end, under the assumption of periodic boundary conditions, we begin with the formulation of the nonlinear Klein-Gordon equation as an abstract second-order ordinary differential equation (ODE) and its operator-variation-of-constants formula. We then derive a symmetric and arbitrarily high-order Birkhoff-Hermite time integration formula for the nonlinear abstract ODE. Accordingly, the stability, convergence and long-time behaviour are rigorously analysed once the spatial differential operator is approximated by an appropriate positive semi-definite matrix, subject to suitable temporal and spatial smoothness. A remarkable characteristic of this new approach is that the requirement of temporal smoothness is reduced compared with the traditional numerical methods for PDEs in the literature. Numerical results demonstrate the advantage and efficiency of our time integrators in comparison with the existing numerical approaches.

Soliton solution and gauge equivalence for an integrable nonlocal complex modified Korteweg-de Vries equation

NASA Astrophysics Data System (ADS)

Ma, Li-Yuan; Shen, Shou-Feng; Zhu, Zuo-Nong

2017-10-01

In this paper, we prove that an integrable nonlocal complex modified Korteweg-de Vries (mKdV) equation introduced by Ablowitz and Musslimani [Nonlinearity 29, 915-946 (2016)] is gauge equivalent to a spin-like model. From the gauge equivalence, one can see that there exists significant difference between the nonlocal complex mKdV equation and the classical complex mKdV equation. Through constructing the Darboux transformation for nonlocal complex mKdV equation, a variety of exact solutions including dark soliton, W-type soliton, M-type soliton, and periodic solutions are derived.

U.S. EPA, Pesticide Product Label, ATRA-5, 04/17/1990

EPA Pesticide Factsheets

2011-04-19

... '.. 1.1 I , i: i ":11 ' ~:, (f··.,~r! 11 c~l(n (>:"I.pi 1 I ~:\\rt·.·). yn·lI QlIJ ... For mi x inq instruc:tiorls ~ 5f.·~E:·~ th~~ "t'li xing Instruc.tinn::;" se(:ti(]n of tllis l.abel. ...

Perspectives on Early Childhood Education in Egypt and Kuwait.

ERIC Educational Resources Information Center

El-Beblawi, Viola F.

Early childhood education is rooted in the Arab culture. Of particular importance for the implementation of early childhood education is the academic psycho-educational movement in the Arab world (initiated by Tsmail El Kabani and Dr. Abel Aziz El Koussy), which began in the 1920s. This movement, combined with rapid social change (including the…

The Use of Lego Technologies in Elementary Teacher Preparation

ERIC Educational Resources Information Center

Hadjiachilleos, Stella; Avraamidou, Lucy; Papastavrou, Stavros

2013-01-01

The need to reform science teacher preparation programs has been pointed out in research (Bryan and Abell in "J Res Sci Teach" 36:121-140, 1999; Bryan and Atwater in "Sci Educ" 8(6):821-839, 2002; Harrington and Hathaway in "J Teach Educ" 46(4):275-284, 1995). Science teachers are charged with the responsibility of…

International Adventures: A Recreational Main Course with Some Learning on the Side

ERIC Educational Resources Information Center

Mertz, Tim

2008-01-01

This past Winter, Stout Adventures at the University of Wisconsin-Stout took off for its first International Trip. Nine students, two student trip leaders and the author traveled New Zealand's South Island for twenty-two days. Jumping out of planes, rafting rivers, leaping off bungy platforms, sea-kayaking both Milford Sound and Abel Tasman…

African American Men, Identity, and Participation in Adult Basic Education and Literacy Programs. Research Brief #6

ERIC Educational Resources Information Center

Drayton, Brendaly; Prins, Esther

2011-01-01

Although the national graduation rate for African American males is only 47% (Schott Foundation for Public Education, 2010), few studies have explored their experiences in adult basic and literacy education (ABEL) programs. This study draws on prior research to explore the relationship between literacy and identity and its potential for…

Low-Frequency VLA Observations of Abell 754: Evidence for a Cluster Radio Halo and Possible Radio Relics

DTIC Science & Technology

2001-10-01

core passage of the dark matter subcluster, was not violent enough to produce a shock wave in the dense main cluster core. The core was only...such as Chandra. At later merger stages, turbulent gas motion, which is stirred by violently relaxing dark matter cores, should have erased many of

Hard X-Ray Properties of the Merging Cluster Abell 3667 as Observed with Suzaku

DTIC Science & Technology

2008-08-01

3667 as Observed with Suzaku Kazuhiro NAKAZAWA Department of Physics, The University of Tokyo, 7-3-1 Hongo , Bunkyo-ku, Tokyo 113-0033 nakazawa...of Tokyo, 7-3-1 Hongo , Bunkyo-ku, Tokyo 113-0033 Kazuo MAKISHIMA Department of Physics, The University of Tokyo, 7-3-1 Hongo , Bunkyo-ku, Tokyo 113

Students with Disabilities Can Succeed! The Abell Report. Volume 26, No.7

ERIC Educational Resources Information Center

Hettleman, Kalman R.

2013-01-01

The One Year Plus policy of Baltimore City Public Schools described in this Newsletter has the potential to breathe new life into "special education" for students with disabilities. In recent decades, many waves of K-12 education reform--including the No Child Left Behind Act, charter schools, alternative teacher recruitment paths,…

City Connects: Redesigning Student Support for Academic Success. The Abell Report. Volume 29, No. 3

ERIC Educational Resources Information Center

Manekin, Sarah

2016-01-01

Public school systems employ a range of professionals to provide support to children and youth in schools. For students living in poverty and experiencing trauma, the work of these professionals is particularly necessary and urgent. Ranging from the treatment of acute mental health issues and accommodations for students with special needs, to…

Documentation for the machine-readable version of a table of Redshifts for Abell clusters (Sarazin, Rood and Struble 1982)

NASA Technical Reports Server (NTRS)

Warren, W. H., Jr.

1983-01-01

The machine readable catalog is described. The machine version contains the same data as the published table, which includes a second file with the notes. The computerized data files are prepared at the Astronomical Data Center. Detected discrepancies and cluster identifications based on photometric estimators are included.

Solvability of a Nonlinear Integral Equation in Dynamical String Theory

NASA Astrophysics Data System (ADS)

Khachatryan, A. Kh.; Khachatryan, Kh. A.

2018-04-01

We investigate an integral equation of the convolution type with a cubic nonlinearity on the entire real line. This equation has a direct application in open-string field theory and in p-adic string theory and describes nonlocal interactions. We prove that there exists a one-parameter family of bounded monotonic solutions and calculate the limits of solutions constructed at infinity.

Modelling gas dynamics in 1D ducts with abrupt area change

NASA Astrophysics Data System (ADS)

Menina, R.; Saurel, R.; Zereg, M.; Houas, L.

2011-09-01

Most gas dynamic computations in industrial ducts are done in one dimension with cross-section-averaged Euler equations. This poses a fundamental difficulty as soon as geometrical discontinuities are present. The momentum equation contains a non-conservative term involving a surface pressure integral, responsible for momentum loss. Definition of this integral is very difficult from a mathematical standpoint as the flow may contain other discontinuities (shocks, contact discontinuities). From a physical standpoint, geometrical discontinuities induce multidimensional vortices that modify the surface pressure integral. In the present paper, an improved 1D flow model is proposed. An extra energy (or entropy) equation is added to the Euler equations expressing the energy and turbulent pressure stored in the vortices generated by the abrupt area variation. The turbulent energy created by the flow-area change interaction is determined by a specific estimate of the surface pressure integral. Model's predictions are compared with 2D-averaged results from numerical solution of the Euler equations. Comparison with shock tube experiments is also presented. The new 1D-averaged model improves the conventional cross-section-averaged Euler equations and is able to reproduce the main flow features.

Some integrable maps and their Hirota bilinear forms

NASA Astrophysics Data System (ADS)

Hone, A. N. W.; Kouloukas, T. E.; Quispel, G. R. W.

2018-01-01

We introduce a two-parameter family of birational maps, which reduces to a family previously found by Demskoi, Tran, van der Kamp and Quispel (DTKQ) when one of the parameters is set to zero. The study of the singularity confinement pattern for these maps leads to the introduction of a tau function satisfying a homogeneous recurrence which has the Laurent property, and the tropical (or ultradiscrete) analogue of this homogeneous recurrence confirms the quadratic degree growth found empirically by Demskoi et al. We prove that the tau function also satisfies two different bilinear equations, each of which is a reduction of the Hirota-Miwa equation (also known as the discrete KP equation, or the octahedron recurrence). Furthermore, these bilinear equations are related to reductions of particular two-dimensional integrable lattice equations, of discrete KdV or discrete Toda type. These connections, as well as the cluster algebra structure of the bilinear equations, allow a direct construction of Poisson brackets, Lax pairs and first integrals for the birational maps. As a consequence of the latter results, we show how each member of the family can be lifted to a system that is integrable in the Liouville sense, clarifying observations made previously in the original DTKQ case.

Applying integrals of motion to the numerical solution of differential equations

NASA Technical Reports Server (NTRS)

Vezewski, D. J.

1980-01-01

A method is developed for using the integrals of systems of nonlinear, ordinary, differential equations in a numerical integration process to control the local errors in these integrals and reduce the global errors of the solution. The method is general and can be applied to either scalar or vector integrals. A number of example problems, with accompanying numerical results, are used to verify the analysis and support the conjecture of global error reduction.

Sixth-Order Lie Group Integrators

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

Forest, E.

1990-03-01

In this paper we present the coefficients of several 6th order symplectic integrator of the type developed by R. Ruth. To get these results we fully exploit the connection with Lie groups. This integrator, as well as all the explicit integrators of Ruth, may be used in any equation where some sort of Lie bracket is preserved. In fact, if the Lie operator governing the equation of motion is separable into two solvable parts, the Ruth integrators can be used.

Applying integrals of motion to the numerical solution of differential equations

NASA Technical Reports Server (NTRS)

Jezewski, D. J.

1979-01-01

A method is developed for using the integrals of systems of nonlinear, ordinary differential equations in a numerical integration process to control the local errors in these integrals and reduce the global errors of the solution. The method is general and can be applied to either scaler or vector integrals. A number of example problems, with accompanying numerical results, are used to verify the analysis and support the conjecture of global error reduction.

Extension of the KLI approximation toward the exact optimized effective potential.

PubMed

Iafrate, G J; Krieger, J B

2013-03-07

The integral equation for the optimized effective potential (OEP) is utilized in a compact form from which an accurate OEP solution for the spin-unrestricted exchange-correlation potential, Vxcσ, is obtained for any assumed orbital-dependent exchange-correlation energy functional. The method extends beyond the Krieger-Li-Iafrate (KLI) approximation toward the exact OEP result. The compact nature of the OEP equation arises by replacing the integrals involving the Green's function terms in the traditional OEP equation by an equivalent first-order perturbation theory wavefunction often referred to as the "orbital shift" function. Significant progress is then obtained by solving the equation for the first order perturbation theory wavefunction by use of Dalgarno functions which are determined from well known methods of partial differential equations. The use of Dalgarno functions circumvents the need to explicitly address the Green's functions and the associated problems with "sum over states" numerics; as well, the Dalgarno functions provide ease in dealing with inherent singularities arising from the origin and the zeros of the occupied orbital wavefunctions. The Dalgarno approach for finding a solution to the OEP equation is described herein, and a detailed illustrative example is presented for the special case of a spherically symmetric exchange-correlation potential. For the case of spherical symmetry, the relevant Dalgarno function is derived by direct integration of the appropriate radial equation while utilizing a user friendly method which explicitly treats the singular behavior at the origin and at the nodal singularities arising from the zeros of the occupied states. The derived Dalgarno function is shown to be an explicit integral functional of the exact OEP Vxcσ, thus allowing for the reduction of the OEP equation to a self-consistent integral equation for the exact exchange-correlation potential; the exact solution to this integral equation can be determined by iteration with the natural zeroth order correction given by the KLI exchange-correlation potential. Explicit analytic results are provided to illustrate the first order iterative correction beyond the KLI approximation. The derived correction term to the KLI potential explicitly involves spatially weighted products of occupied orbital densities in any assumed orbital-dependent exchange-correlation energy functional; as well, the correction term is obtained with no adjustable parameters. Moreover, if the equation for the exact optimized effective potential is further iterated, one can obtain the OEP as accurately as desired.

Extension of the KLI approximation toward the exact optimized effective potential

NASA Astrophysics Data System (ADS)

Iafrate, G. J.; Krieger, J. B.

2013-03-01

The integral equation for the optimized effective potential (OEP) is utilized in a compact form from which an accurate OEP solution for the spin-unrestricted exchange-correlation potential, Vxcσ, is obtained for any assumed orbital-dependent exchange-correlation energy functional. The method extends beyond the Krieger-Li-Iafrate (KLI) approximation toward the exact OEP result. The compact nature of the OEP equation arises by replacing the integrals involving the Green's function terms in the traditional OEP equation by an equivalent first-order perturbation theory wavefunction often referred to as the "orbital shift" function. Significant progress is then obtained by solving the equation for the first order perturbation theory wavefunction by use of Dalgarno functions which are determined from well known methods of partial differential equations. The use of Dalgarno functions circumvents the need to explicitly address the Green's functions and the associated problems with "sum over states" numerics; as well, the Dalgarno functions provide ease in dealing with inherent singularities arising from the origin and the zeros of the occupied orbital wavefunctions. The Dalgarno approach for finding a solution to the OEP equation is described herein, and a detailed illustrative example is presented for the special case of a spherically symmetric exchange-correlation potential. For the case of spherical symmetry, the relevant Dalgarno function is derived by direct integration of the appropriate radial equation while utilizing a user friendly method which explicitly treats the singular behavior at the origin and at the nodal singularities arising from the zeros of the occupied states. The derived Dalgarno function is shown to be an explicit integral functional of the exact OEP Vxcσ, thus allowing for the reduction of the OEP equation to a self-consistent integral equation for the exact exchange-correlation potential; the exact solution to this integral equation can be determined by iteration with the natural zeroth order correction given by the KLI exchange-correlation potential. Explicit analytic results are provided to illustrate the first order iterative correction beyond the KLI approximation. The derived correction term to the KLI potential explicitly involves spatially weighted products of occupied orbital densities in any assumed orbital-dependent exchange-correlation energy functional; as well, the correction term is obtained with no adjustable parameters. Moreover, if the equation for the exact optimized effective potential is further iterated, one can obtain the OEP as accurately as desired.

Efficient Solution of Three-Dimensional Problems of Acoustic and Electromagnetic Scattering by Open Surfaces

NASA Technical Reports Server (NTRS)

Turc, Catalin; Anand, Akash; Bruno, Oscar; Chaubell, Julian

2011-01-01

We present a computational methodology (a novel Nystrom approach based on use of a non-overlapping patch technique and Chebyshev discretizations) for efficient solution of problems of acoustic and electromagnetic scattering by open surfaces. Our integral equation formulations (1) Incorporate, as ansatz, the singular nature of open-surface integral-equation solutions, and (2) For the Electric Field Integral Equation (EFIE), use analytical regularizes that effectively reduce the number of iterations required by iterative linear-algebra solution based on Krylov-subspace iterative solvers.

On the complete and partial integrability of non-Hamiltonian systems

NASA Astrophysics Data System (ADS)

Bountis, T. C.; Ramani, A.; Grammaticos, B.; Dorizzi, B.

1984-11-01

The methods of singularity analysis are applied to several third order non-Hamiltonian systems of physical significance including the Lotka-Volterra equations, the three-wave interaction and the Rikitake dynamo model. Complete integrability is defined and new completely integrable systems are discovered by means of the Painlevé property. In all these cases we obtain integrals, which reduce the equations either to a final quadrature or to an irreducible second order ordinary differential equation (ODE) solved by Painlevé transcendents. Relaxing the Painlevé property we find many partially integrable cases whose movable singularities are poles at leading order, with In( t- t0) terms entering at higher orders. In an Nth order, generalized Rössler model a precise relation is established between the partial fulfillment of the Painlevé conditions and the existence of N - 2 integrals of the motion.

Explicit integration of Friedmann's equation with nonlinear equations of state

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

Chen, Shouxin; Gibbons, Gary W.; Yang, Yisong, E-mail: chensx@henu.edu.cn, E-mail: gwg1@damtp.cam.ac.uk, E-mail: yisongyang@nyu.edu

2015-05-01

In this paper we study the integrability of the Friedmann equations, when the equation of state for the perfect-fluid universe is nonlinear, in the light of the Chebyshev theorem. A series of important, yet not previously touched, problems will be worked out which include the generalized Chaplygin gas, two-term energy density, trinomial Friedmann, Born-Infeld, two-fluid models, and Chern-Simons modified gravity theory models. With the explicit integration, we are able to understand exactly the roles of the physical parameters in various models play in the cosmological evolution which may also offer clues to a profound understanding of the problems in generalmore » settings. For example, in the Chaplygin gas universe, a few integrable cases lead us to derive a universal formula for the asymptotic exponential growth rate of the scale factor, of an explicit form, whether the Friedmann equation is integrable or not, which reveals the coupled roles played by various physical sectors and it is seen that, as far as there is a tiny presence of nonlinear matter, conventional linear matter makes contribution to the dark matter, which becomes significant near the phantom divide line. The Friedmann equations also arise in areas of physics not directly related to cosmology. We provide some examples ranging from geometric optics and central orbits to soap films and the shape of glaciated valleys to which our results may be applied.« less

Integrability of systems of two second-order ordinary differential equations admitting four-dimensional Lie algebras

PubMed Central

Gazizov, R. K.

2017-01-01

We suggest an algorithm for integrating systems of two second-order ordinary differential equations with four symmetries. In particular, if the admitted transformation group has two second-order differential invariants, the corresponding system can be integrated by quadratures using invariant representation and the operator of invariant differentiation. Otherwise, the systems reduce to partially uncoupled forms and can also be integrated by quadratures. PMID:28265184

Integrability of systems of two second-order ordinary differential equations admitting four-dimensional Lie algebras.

PubMed

Gainetdinova, A A; Gazizov, R K

2017-01-01

We suggest an algorithm for integrating systems of two second-order ordinary differential equations with four symmetries. In particular, if the admitted transformation group has two second-order differential invariants, the corresponding system can be integrated by quadratures using invariant representation and the operator of invariant differentiation. Otherwise, the systems reduce to partially uncoupled forms and can also be integrated by quadratures.

A multi-domain spectral method for time-fractional differential equations

NASA Astrophysics Data System (ADS)

Chen, Feng; Xu, Qinwu; Hesthaven, Jan S.

2015-07-01

This paper proposes an approach for high-order time integration within a multi-domain setting for time-fractional differential equations. Since the kernel is singular or nearly singular, two main difficulties arise after the domain decomposition: how to properly account for the history/memory part and how to perform the integration accurately. To address these issues, we propose a novel hybrid approach for the numerical integration based on the combination of three-term-recurrence relations of Jacobi polynomials and high-order Gauss quadrature. The different approximations used in the hybrid approach are justified theoretically and through numerical examples. Based on this, we propose a new multi-domain spectral method for high-order accurate time integrations and study its stability properties by identifying the method as a generalized linear method. Numerical experiments confirm hp-convergence for both time-fractional differential equations and time-fractional partial differential equations.

Differential Galois theory and non-integrability of planar polynomial vector fields

NASA Astrophysics Data System (ADS)

Acosta-Humánez, Primitivo B.; Lázaro, J. Tomás; Morales-Ruiz, Juan J.; Pantazi, Chara

2018-06-01

We study a necessary condition for the integrability of the polynomials vector fields in the plane by means of the differential Galois Theory. More concretely, by means of the variational equations around a particular solution it is obtained a necessary condition for the existence of a rational first integral. The method is systematic starting with the first order variational equation. We illustrate this result with several families of examples. A key point is to check whether a suitable primitive is elementary or not. Using a theorem by Liouville, the problem is equivalent to the existence of a rational solution of a certain first order linear equation, the Risch equation. This is a classical problem studied by Risch in 1969, and the solution is given by the "Risch algorithm". In this way we point out the connection of the non integrability with some higher transcendent functions, like the error function.

Complex quantum Hamilton-Jacobi equation with Bohmian trajectories: Application to the photodissociation dynamics of NOCl

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

Chou, Chia-Chun, E-mail: ccchou@mx.nthu.edu.tw

2014-03-14

The complex quantum Hamilton-Jacobi equation-Bohmian trajectories (CQHJE-BT) method is introduced as a synthetic trajectory method for integrating the complex quantum Hamilton-Jacobi equation for the complex action function by propagating an ensemble of real-valued correlated Bohmian trajectories. Substituting the wave function expressed in exponential form in terms of the complex action into the time-dependent Schrödinger equation yields the complex quantum Hamilton-Jacobi equation. We transform this equation into the arbitrary Lagrangian-Eulerian version with the grid velocity matching the flow velocity of the probability fluid. The resulting equation describing the rate of change in the complex action transported along Bohmian trajectories is simultaneouslymore » integrated with the guidance equation for Bohmian trajectories, and the time-dependent wave function is readily synthesized. The spatial derivatives of the complex action required for the integration scheme are obtained by solving one moving least squares matrix equation. In addition, the method is applied to the photodissociation of NOCl. The photodissociation dynamics of NOCl can be accurately described by propagating a small ensemble of trajectories. This study demonstrates that the CQHJE-BT method combines the considerable advantages of both the real and the complex quantum trajectory methods previously developed for wave packet dynamics.« less

A novel approach to solve nonlinear Fredholm integral equations of the second kind.

PubMed

Li, Hu; Huang, Jin

2016-01-01

In this paper, we present a novel approach to solve nonlinear Fredholm integral equations of the second kind. This algorithm is constructed by the integral mean value theorem and Newton iteration. Convergence and error analysis of the numerical solutions are given. Moreover, Numerical examples show the algorithm is very effective and simple.

A Note on ;New Hierarchies of Integrable Lattice Equations and Associated Properties: Darboux Transformation Conservation Laws and Integrable Coupling; [Rep. Math. Phys. 67 (2011), 259

NASA Astrophysics Data System (ADS)

Xu, Xi-Xiang

2016-12-01

We prove that two new hierarchies of integrable lattice equations in [Rep. Math. Phys.67 (2011), 259] can be respectively changed into the famous relativistic Toda lattice hierarchies in the polynomial and the rational forms by means of a simple transformation.

Proceedings of the 1993 Scientific Conference on Obscuration and Aerosol Research Held in Aberdeen Proving Ground on 22-24 Jun 1993

DTIC Science & Technology

1994-03-01

equation (4.1.27) is not a finite rank integral equation, it suggests that an approxi- mate finite rank integral equation Pf" = Pg + APL(K~p) Pfa 4 \\PNPfa...Harry Salem Richard Farrell Mark Seaver Dennis F Flanigan George Sehmel David Freund Jungshik Shin Robert H Frickel Orazio I Sindoni Edward Fry Michael

Variational iteration method — a promising technique for constructing equivalent integral equations of fractional order

NASA Astrophysics Data System (ADS)

Wang, Yi-Hong; Wu, Guo-Cheng; Baleanu, Dumitru

2013-10-01

The variational iteration method is newly used to construct various integral equations of fractional order. Some iterative schemes are proposed which fully use the method and the predictor-corrector approach. The fractional Bagley-Torvik equation is then illustrated as an example of multi-order and the results show the efficiency of the variational iteration method's new role.

Boundary regularized integral equation formulation of the Helmholtz equation in acoustics.

PubMed

Sun, Qiang; Klaseboer, Evert; Khoo, Boo-Cheong; Chan, Derek Y C

2015-01-01

A boundary integral formulation for the solution of the Helmholtz equation is developed in which all traditional singular behaviour in the boundary integrals is removed analytically. The numerical precision of this approach is illustrated with calculation of the pressure field owing to radiating bodies in acoustic wave problems. This method facilitates the use of higher order surface elements to represent boundaries, resulting in a significant reduction in the problem size with improved precision. Problems with extreme geometric aspect ratios can also be handled without diminished precision. When combined with the CHIEF method, uniqueness of the solution of the exterior acoustic problem is assured without the need to solve hypersingular integrals.

Boundary regularized integral equation formulation of the Helmholtz equation in acoustics

PubMed Central

Sun, Qiang; Klaseboer, Evert; Khoo, Boo-Cheong; Chan, Derek Y. C.

2015-01-01

A boundary integral formulation for the solution of the Helmholtz equation is developed in which all traditional singular behaviour in the boundary integrals is removed analytically. The numerical precision of this approach is illustrated with calculation of the pressure field owing to radiating bodies in acoustic wave problems. This method facilitates the use of higher order surface elements to represent boundaries, resulting in a significant reduction in the problem size with improved precision. Problems with extreme geometric aspect ratios can also be handled without diminished precision. When combined with the CHIEF method, uniqueness of the solution of the exterior acoustic problem is assured without the need to solve hypersingular integrals. PMID:26064591

Integrability of the one dimensional Schrödinger equation

NASA Astrophysics Data System (ADS)

Combot, Thierry

2018-02-01

We present a definition of integrability for the one-dimensional Schrödinger equation, which encompasses all known integrable systems, i.e., systems for which the spectrum can be explicitly computed. For this, we introduce the class of rigid functions, built as Liouvillian functions, but containing all solutions of rigid differential operators in the sense of Katz, and a notion of natural of boundary conditions. We then make a complete classification of rational integrable potentials. Many new integrable cases are found, some of them physically interesting.

Fractional calculus in hydrologic modeling: A numerical perspective

PubMed Central

Benson, David A.; Meerschaert, Mark M.; Revielle, Jordan

2013-01-01

Fractional derivatives can be viewed either as handy extensions of classical calculus or, more deeply, as mathematical operators defined by natural phenomena. This follows the view that the diffusion equation is defined as the governing equation of a Brownian motion. In this paper, we emphasize that fractional derivatives come from the governing equations of stable Lévy motion, and that fractional integration is the corresponding inverse operator. Fractional integration, and its multi-dimensional extensions derived in this way, are intimately tied to fractional Brownian (and Lévy) motions and noises. By following these general principles, we discuss the Eulerian and Lagrangian numerical solutions to fractional partial differential equations, and Eulerian methods for stochastic integrals. These numerical approximations illuminate the essential nature of the fractional calculus. PMID:23524449

Traveling wave solutions to a reaction-diffusion equation

NASA Astrophysics Data System (ADS)

Feng, Zhaosheng; Zheng, Shenzhou; Gao, David Y.

2009-07-01

In this paper, we restrict our attention to traveling wave solutions of a reaction-diffusion equation. Firstly we apply the Divisor Theorem for two variables in the complex domain, which is based on the ring theory of commutative algebra, to find a quasi-polynomial first integral of an explicit form to an equivalent autonomous system. Then through this first integral, we reduce the reaction-diffusion equation to a first-order integrable ordinary differential equation, and a class of traveling wave solutions is obtained accordingly. Comparisons with the existing results in the literature are also provided, which indicates that some analytical results in the literature contain errors. We clarify the errors and instead give a refined result in a simple and straightforward manner.

Improving multilevel Monte Carlo for stochastic differential equations with application to the Langevin equation

PubMed Central

Müller, Eike H.; Scheichl, Rob; Shardlow, Tony

2015-01-01

This paper applies several well-known tricks from the numerical treatment of deterministic differential equations to improve the efficiency of the multilevel Monte Carlo (MLMC) method for stochastic differential equations (SDEs) and especially the Langevin equation. We use modified equations analysis as an alternative to strong-approximation theory for the integrator, and we apply this to introduce MLMC for Langevin-type equations with integrators based on operator splitting. We combine this with extrapolation and investigate the use of discrete random variables in place of the Gaussian increments, which is a well-known technique for the weak approximation of SDEs. We show that, for small-noise problems, discrete random variables can lead to an increase in efficiency of almost two orders of magnitude for practical levels of accuracy. PMID:27547075

Soliton solutions for ABS lattice equations: I. Cauchy matrix approach

NASA Astrophysics Data System (ADS)

Nijhoff, Frank; Atkinson, James; Hietarinta, Jarmo

2009-10-01

In recent years there have been new insights into the integrability of quadrilateral lattice equations, i.e. partial difference equations which are the natural discrete analogues of integrable partial differential equations in 1+1 dimensions. In the scalar (i.e. single-field) case, there now exist classification results by Adler, Bobenko and Suris (ABS) leading to some new examples in addition to the lattice equations 'of KdV type' that were known since the late 1970s and early 1980s. In this paper, we review the construction of soliton solutions for the KdV-type lattice equations and use those results to construct N-soliton solutions for all lattice equations in the ABS list except for the elliptic case of Q4, which is left to a separate treatment.

Improving multilevel Monte Carlo for stochastic differential equations with application to the Langevin equation.

PubMed

Müller, Eike H; Scheichl, Rob; Shardlow, Tony

2015-04-08

This paper applies several well-known tricks from the numerical treatment of deterministic differential equations to improve the efficiency of the multilevel Monte Carlo (MLMC) method for stochastic differential equations (SDEs) and especially the Langevin equation. We use modified equations analysis as an alternative to strong-approximation theory for the integrator, and we apply this to introduce MLMC for Langevin-type equations with integrators based on operator splitting. We combine this with extrapolation and investigate the use of discrete random variables in place of the Gaussian increments, which is a well-known technique for the weak approximation of SDEs. We show that, for small-noise problems, discrete random variables can lead to an increase in efficiency of almost two orders of magnitude for practical levels of accuracy.

Reaction formulation for radiation and scattering from plates, corner reflectors and dielectric-coated cylinders

NASA Technical Reports Server (NTRS)

Wang, N. N.

1974-01-01

The reaction concept is employed to formulate an integral equation for radiation and scattering from plates, corner reflectors, and dielectric-coated conducting cylinders. The surface-current density on the conducting surface is expanded with subsectional bases. The dielectric layer is modeled with polarization currents radiating in free space. Maxwell's equation and the boundary conditions are employed to express the polarization-current distribution in terms of the surface-current density on the conducting surface. By enforcing reaction tests with an array of electric test sources, the moment method is employed to reduce the integral equation to a matrix equation. Inversion of the matrix equation yields the current distribution, and the scattered field is then obtained by integrating the current distribution. The theory, computer program and numerical results are presented for radiation and scattering from plates, corner reflectors, and dielectric-coated conducting cylinders.

Plane elasto-plastic analysis of v-notched plate under bending by boundary integral equation method. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Rzasnicki, W.

1973-01-01

A method of solution is presented, which, when applied to the elasto-plastic analysis of plates having a v-notch on one edge and subjected to pure bending, will produce stress and strain fields in much greater detail than presently available. Application of the boundary integral equation method results in two coupled Fredholm-type integral equations, subject to prescribed boundary conditions. These equations are replaced by a system of simultaneous algebraic equations and solved by a successive approximation method employing Prandtl-Reuss incremental plasticity relations. The method is first applied to number of elasto-static problems and the results compared with available solutions. Good agreement is obtained in all cases. The elasto-plastic analysis provides detailed stress and strain distributions for several cases of plates with various notch angles and notch depths. A strain hardening material is assumed and both plane strain and plane stress conditions are considered.

Bending of Euler-Bernoulli nanobeams based on the strain-driven and stress-driven nonlocal integral models: a numerical approach

NASA Astrophysics Data System (ADS)

Oskouie, M. Faraji; Ansari, R.; Rouhi, H.

2018-04-01

Eringen's nonlocal elasticity theory is extensively employed for the analysis of nanostructures because it is able to capture nanoscale effects. Previous studies have revealed that using the differential form of the strain-driven version of this theory leads to paradoxical results in some cases, such as bending analysis of cantilevers, and recourse must be made to the integral version. In this article, a novel numerical approach is developed for the bending analysis of Euler-Bernoulli nanobeams in the context of strain- and stress-driven integral nonlocal models. This numerical approach is proposed for the direct solution to bypass the difficulties related to converting the integral governing equation into a differential equation. First, the governing equation is derived based on both strain-driven and stress-driven nonlocal models by means of the minimum total potential energy. Also, in each case, the governing equation is obtained in both strong and weak forms. To solve numerically the derived equations, matrix differential and integral operators are constructed based upon the finite difference technique and trapezoidal integration rule. It is shown that the proposed numerical approach can be efficiently applied to the strain-driven nonlocal model with the aim of resolving the mentioned paradoxes. Also, it is able to solve the problem based on the strain-driven model without inconsistencies of the application of this model that are reported in the literature.

Elliptic Euler-Poisson-Darboux equation, critical points and integrable systems

NASA Astrophysics Data System (ADS)

Konopelchenko, B. G.; Ortenzi, G.

2013-12-01

The structure and properties of families of critical points for classes of functions W(z,{\\overline{z}}) obeying the elliptic Euler-Poisson-Darboux equation E(1/2, 1/2) are studied. General variational and differential equations governing the dependence of critical points in variational (deformation) parameters are found. Explicit examples of the corresponding integrable quasi-linear differential systems and hierarchies are presented. There are the extended dispersionless Toda/nonlinear Schrödinger hierarchies, the ‘inverse’ hierarchy and equations associated with the real-analytic Eisenstein series E(\\beta ,{\\overline{\\beta }};1/2) among them. The specific bi-Hamiltonian structure of these equations is also discussed.

Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (4).

PubMed

Murase, Kenya

2016-01-01

Partial differential equations are often used in the field of medical physics. In this (final) issue, the methods for solving the partial differential equations were introduced, which include separation of variables, integral transform (Fourier and Fourier-sine transforms), Green's function, and series expansion methods. Some examples were also introduced, in which the integral transform and Green's function methods were applied to solving Pennes' bioheat transfer equation and the Fourier series expansion method was applied to Navier-Stokes equation for analyzing the wall shear stress in blood vessels.Finally, the author hopes that this series will be helpful for people who engage in medical physics.

VLA Discovers Giant Rings Around Galaxy Cluster

NASA Astrophysics Data System (ADS)

2006-11-01

Astronomers using the National Science Foundation's Very Large Array (VLA) radio telescope have discovered giant, ring-like structures around a cluster of galaxies. The discovery provides tantalizing new information about how such galaxy clusters are assembled, about magnetic fields in the vast spaces between galaxy clusters, and possibly about the origin of cosmic rays. Radio-Optical Image of Cluster Galaxy Cluster Abell 3376 (Radio/Optical) CREDIT: Joydeep Bagchi, IUCAA, NRAO/AUI/NSF Above, a combined radio/optical image shows the galaxy cluster Abell 3376 in visible light (blue) and radio (red) images. The giant radio arcs surrounding the cluster were discovered using the Very Large Array. The visible-light image is from the Digitized Sky survey. Below, an X-ray image of Abell 3376 made using the European Space Agency's XMM-Newton telescope shows a spectacular, bullet-shaped region of X-rays coming from gas heated to 60 million degrees Kelvin. The bullet shape results from the supersonic collision of a smaller smaller galaxy subcluster with the main body of the larger cluster. Click on images for larger version. X-Ray Image of Cluster Galaxy Cluster Abell 3376 (X-Ray) CREDIT: Joydeep Bagchi, IUCAA, ESA "These giant, radio-emitting rings probably are the result of shock waves caused by violent collisions of smaller groups of galaxies within the cluster," said Joydeep Bagchi, of the Inter-University Centre for Astronomy and Astrophysics in Pune, India, who led an international research team. The scientists reported their findings in the November 3 edition of the journal Science. The newly-discovered ring segments, some 6 million light-years across, surround a galaxy cluster called Abell 3376, more than 600 million light-years from Earth. They were revealed because fast-moving electrons emitted radio waves as they spiraled around magnetic field lines in intergalactic space. "Even from this large distance, the feeble radio waves were easily picked up by the VLA, thanks to its very high sensitivity and unique capability to make images of exceedingly faint radio-emitting objects," Bagchi said. The scientists also used the European Space Agency's XMM-Newton, the world's most sensitive X-ray observatory, to observe this extraordinary cluster of galaxies. "The advanced technical capabilities of the orbiting XMM-Newton revealed a spectacular bullet-like region of X-ray emission in this dynamically active cluster," said Gastao B. Lima Neto, of the Institute of Astronomy and Geophysics in Sao Paulo, Brazil, a co-author of the research paper. "Our X-ray observations strongly suggest a recent collision and merger of two or more smaller clusters. Such a phenomenon is among the most energetic events in the Universe after the Big Bang. Only a tiny fraction of the total energy of this collision, if transferred to electrons, would cause them to emit the radio waves observed by the VLA. However, the main question is, how this is achieved," said Florence Durret of the Astrophysical Institute of Paris, France, another of the researchers. The scientists calculated that the total energy of the colliding groups of galaxies would be enough to keep our Sun shining for more than 20 sextillion years (2 followed by 22 zeros)! "We think the shock waves that sped up these electrons came from the collision of a smaller group of galaxies with the main body of the larger cluster. When two such massive objects crash into each other at supersonic speed, gigantic ripple-like shock waves are created in the surrounding gas, which race out to the outer regions of the forming cluster at a speed of thousands of kilometers per second," Bagchi said. "You can imagine that each cluster is like a supersonic aircraft, moving faster than the speed of sound in the surrounding gas, and just as you hear a sonic boom when shock waves from an airplane pass by you, we believe that the situation in the Abell 3376 cluster is similar, with ringlike radio structures tracing out the shock waves," Bagchi explained. Such a scenario also is supported by images of the cluster made with the XMM-Newton and ROSAT X-ray satellites, as well as by computer simulations, Bagchi added. The exact mechanism for producing the shock waves is still open to question, the scientists said. "This is the first observational evidence for this type of shock wave around a massive galaxy cluster," Bagchi said. "This discovery will help us understand more about the thin gas between the galaxies, and also about the magnetic fields in the outskirts of such clusters -- magnetic fields whose origin still is unknown," he said. In addition, the scientists speculate that violent regions like those in Abell 3376 may be sites from which cosmic rays originate. Cosmic rays are protons or atomic nuclei accelerated to nearly the speed of light, and shocks such as those found in the collisions of galaxy groups may be energetic enough to provide the required amount of "kick." "Some of the most energetic cosmic ray particles detected on Earth may contain about 100 million times more energy than the highest energy achieved so far in any man-made particle accelerator. Where do these cosmic rays come from and exactly what process kicks them to such stupendous energy is still a fascinating unsolved problem of physics," said graduate student Surajit Paul of the Institute for Theoretical Physics and Astrophysisc at Wuerzburg University in Germany, who was on the research team. "A cosmic accelerator source containing powerful shock waves and magnetic fields extending over millions of light years in length is capable of accelerating a proton or nucleus to such enormous energies. Although our observations do not conclusively show the evidence for such particles, our VLA radio image does show clearly that such structures are indeed present in this galaxy cluster. Only future cosmic ray observations can tell if Abell 3376 is an ultra-high-energy cosmic ray source. We will continue to explore this fascinating cosmic laboratory in the future, employing some of the world's most sensitive radio, X-ray and gamma-ray telescopes to reveal its mysteries," Bagchi said. The National Radio Astronomy Observatory is a facility of the National Science Foundation, operated under cooperative agreement by Associated Universities, Inc.

A Bifurcation Problem for a Nonlinear Partial Differential Equation of Parabolic Type,

DTIC Science & Technology

NONLINEAR DIFFERENTIAL EQUATIONS, INTEGRATION), (*PARTIAL DIFFERENTIAL EQUATIONS, BOUNDARY VALUE PROBLEMS), BANACH SPACE , MAPPING (TRANSFORMATIONS), SET THEORY, TOPOLOGY, ITERATIONS, STABILITY, THEOREMS

Integrability of the coupled cubic-quintic complex Ginzburg-Landau equations and multiple-soliton solutions via mathematical methods

NASA Astrophysics Data System (ADS)

Selima, Ehab S.; Seadawy, Aly R.; Yao, Xiaohua; Essa, F. A.

2018-02-01

This paper is devoted to study the (1+1)-dimensional coupled cubic-quintic complex Ginzburg-Landau equations (cc-qcGLEs) with complex coefficients. This equation can be used to describe the nonlinear evolution of slowly varying envelopes of periodic spatial-temporal patterns in a convective binary fluid. Dispersion relation and properties of cc-qcGLEs are constructed. Painlevé analysis is used to check the integrability of cc-qcGLEs and to establish the Bäcklund transformation form. New traveling wave solutions and a general form of multiple-soliton solutions of cc-qcGLEs are obtained via the Bäcklund transformation and simplest equation method with Bernoulli, Riccati and Burgers’ equations as simplest equations.

Integral Equations and Scattering Solutions for a Square-Well Potential.

ERIC Educational Resources Information Center

Bagchi, B.; Seyler, R. G.

1979-01-01

Derives Green's functions and integral equations for scattering solutions subject to a variety of boundary conditions. Exact solutions are obtained for the case of a finite spherical square-well potential, and properties of these solutions are discussed. (Author/HM)

The statistical theory of the fracture of fragile bodies. Part 2: The integral equation method

NASA Technical Reports Server (NTRS)

Kittl, P.

1984-01-01

It is demonstrated how with the aid of a bending test, the Weibull fracture risk function can be determined - without postulating its analytical form - by resolving an integral equation. The respective solutions for rectangular and circular section beams are given. In the first case the function is expressed as an algorithm and in the second, in the form of series. Taking into account that the cumulative fracture probability appearing in the solution to the integral equation must be continuous and monotonically increasing, any case of fabrication or selection of samples can be treated.

The Use of ICT Tools in Mathematics: A Case-Control Study of Best Practice in 9th Grade Classrooms

ERIC Educational Resources Information Center

Thorvaldsen, Steinar; Vavik, Lars; Salomon, Gavriel

2012-01-01

Results are reported from a study in which teachers' views of highly achieving ninth grade classes in Norway (KappAbel national competition winners) were compared with teachers' views of average achievement classes with regard to the use of information and communication technologies (ICT) and pedagogical practices. The main purpose of the study…

Sending out an S.O.S. for SES (Supplemental Educational Services). The Abell Report. Volume 24, No.5

ERIC Educational Resources Information Center

Jacobson, Joan

2011-01-01

Each year, under the federal program called Supplemental Educational Services (SES), the Baltimore City Public School System (City Schools) pays educational vendors millions of public dollars to tutor thousands of its poorest students in its lowest achieving schools. Established in 2002 by the federal No Child Left Behind Act, SES was created to…

U.S. EPA, Pesticide Product Label, DREXEL SIMAZINE 80WP, 07/05/1995

EPA Pesticide Factsheets

2011-04-21

... Jo~( tclu4~t tot shl~~.nt of tn. p(Od~ct cgnatitut.~ .cc~~t.nc. ot t~.56 c~ndlttoA •• A .taAr.o copy cf •• cb ot tn •• e lAbel. ia .Del ••• d to, yo~c r.cocQa. ...

"Chartering" Maryland's Future: Is There an Expanded Role for National Charter Management Organizations in Our Schools? The Abell Report. Volume 28, No. 1

ERIC Educational Resources Information Center

Abell Foundation, 2015

2015-01-01

Over the past decade, a handful of high performing public charter schools have developed in Baltimore, but the need for high quality educational offerings, particularly for low-income students, remains high. "'Chartering' Maryland's Future: Is There an Expanded Role for National Charter Management Organizations in Our Schools?" considers…

Galaxy luminosity profiles of SARS clusters

NASA Astrophysics Data System (ADS)

Coenda, V.; Donzelli, C.; Muriel, H.; Quintana, H.; Infante, L.

We have analyzed CCD images in the R filter of 14 Abell clusters of the SARS survey, with cz<40000 km/s. We have obtained the luminosity profiles of 507 galaxies and we have studied several relations between the photometric and structural parameters. In the present contributed paper we analyze the following relations: the Kormendy relation and the correlations among the Sérsic parameters.

KSC-04pd1253

NASA Image and Video Library

2004-06-09

KENNEDY SPACE CENTER, FLA. - At Cape Canaveral Air Force Station, KSC Firefighter Chris Maupin (left) takes equipment from Lt. Keith Abell. They and other KSC firefighters teamed up with task forces from Satellite Beach, Malabar, Melbourne, Palm Bay, Patrick Air Force Base and Brevard County to help fight wildfires in the Palm Bay and Malabar areas that threatened homes and property during the Memorial Day holiday weekend.

Discovery of Ram-pressure Stripped Gas around an Elliptical Galaxy in Abell 2670

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

Sheen, Yun-Kyeong; Kim, Minjin; Smith, Rory

Studies of cluster galaxies are increasingly finding galaxies with spectacular one-sided tails of gas and young stars, suggestive of intense ram-pressure stripping. These so-called “jellyfish” galaxies typically have late-type morphology. In this paper, we present Multi Unit Spectroscopic Explorer (MUSE) observations of an elliptical galaxy in Abell 2670 with long tails of material visible in the optical spectra, as well as blobs with tadpole-like morphology. The spectra in the central part of the galaxy reveal a stellar component as well as ionized gas. The stellar component does not have significant rotation, while the ionized gas defines a clear star-forming gasmore » disk. We argue, based on deep optical images of the galaxy, that the gas was most likely acquired during a past wet merger. It is possible that the star-forming blobs are also remnants of the merger. In addition, the direction and kinematics of the one-sided ionized tails, combined with the tadpole morphology of the star-forming blobs, strongly suggests that the system is undergoing ram pressure from the intracluster medium. In summary, this paper presents the discovery of a post-merger elliptical galaxy undergoing ram-pressure stripping.« less

Diffuse radio emission in the complex merging galaxy cluster Abell2069

NASA Astrophysics Data System (ADS)

Drabent, A.; Hoeft, M.; Pizzo, R. F.; Bonafede, A.; van Weeren, R. J.; Klein, U.

2015-03-01

Context. Galaxy clusters with signs of a recent merger in many cases show extended diffuse radio features. This emission originates from relativistic electrons that suffer synchrotron losses due to the intracluster magnetic field. The mechanisms of particle acceleration and the properties of the magnetic field are still poorly understood. Aims: We search for diffuse radio emission in galaxy clusters. Here, we study the complex galaxy cluster Abell 2069, for which X-ray observations indicate a recent merger. Methods: We investigate the cluster's radio continuum emission by deep Westerbork Synthesis Radio Telescope (WSRT) observations at 346 MHz and Giant Metrewave Radio Telescope (GMRT) observations at 322 MHz. Results: We find an extended diffuse radio feature roughly coinciding with the main component of the cluster. We classify this emission as a radio halo and estimate its lower limit flux density at 25 ± 9 mJy. Moreover, we find a second extended diffuse source located at the cluster's companion and estimate its flux density at 15 ± 2 mJy. We speculate that this is a small halo or a mini-halo. If true, this cluster is the first example of a double-halo in a single galaxy cluster.

Simulations of galaxy cluster collisions with a dark plasma component

NASA Astrophysics Data System (ADS)

Spethmann, Christian; Veermäe, Hardi; Sepp, Tiit; Heikinheimo, Matti; Deshev, Boris; Hektor, Andi; Raidal, Martti

2017-12-01

Context. Dark plasma is an intriguing form of self-interacting dark matter with an effective fluid-like behavior, which is well motivated by various theoretical particle physics models. Aims: We aim to find an explanation for an isolated mass clump in the Abell 520 system, which cannot be explained by traditional models of dark matter, but has been detected in weak lensing observations. Methods: We performed N-body smoothed particle hydrodynamics simulations of galaxy cluster collisions with a two component model of dark matter, which is assumed to consist of a predominant non-interacting dark matter component and a 10-40% mass fraction of dark plasma. Results: The mass of a possible dark clump was calculated for each simulation in a parameter scan over the underlying model parameters. In two higher resolution simulations shock-waves and Mach cones were observed to form in the dark plasma halos. Conclusions: By choosing suitable simulation parameters, the observed distributions of dark matter in both the Bullet cluster (1E 0657-558) and Abell 520 (MS 0451.5+0250) can be qualitatively reproduced. Movies associated to Figs. A.1 and A.2 are available at http://www.aanda.org

Discovery of Ram-pressure Stripped Gas around an Elliptical Galaxy in Abell 2670

NASA Astrophysics Data System (ADS)

Sheen, Yun-Kyeong; Smith, Rory; Jaffé, Yara; Kim, Minjin; Yi, Sukyoung K.; Duc, Pierre-Alain; Nantais, Julie; Candlish, Graeme; Demarco, Ricardo; Treister, Ezequiel

2017-05-01

Studies of cluster galaxies are increasingly finding galaxies with spectacular one-sided tails of gas and young stars, suggestive of intense ram-pressure stripping. These so-called “jellyfish” galaxies typically have late-type morphology. In this paper, we present Multi Unit Spectroscopic Explorer (MUSE) observations of an elliptical galaxy in Abell 2670 with long tails of material visible in the optical spectra, as well as blobs with tadpole-like morphology. The spectra in the central part of the galaxy reveal a stellar component as well as ionized gas. The stellar component does not have significant rotation, while the ionized gas defines a clear star-forming gas disk. We argue, based on deep optical images of the galaxy, that the gas was most likely acquired during a past wet merger. It is possible that the star-forming blobs are also remnants of the merger. In addition, the direction and kinematics of the one-sided ionized tails, combined with the tadpole morphology of the star-forming blobs, strongly suggests that the system is undergoing ram pressure from the intracluster medium. In summary, this paper presents the discovery of a post-merger elliptical galaxy undergoing ram-pressure stripping.

Mass Mapping Abell 2261 with Kinematic Weak Lensing: A Pilot Study for NASAs WFIRST mission

NASA Astrophysics Data System (ADS)

Eifler, Tim

2015-02-01

We propose to investigate a new method to extract cosmological information from weak gravitational lensing in the context of the mission design and requirements of NASAs Wide-Field Infrared Survey Telescope (WFIRST). In a recent paper (Huff, Krause, Eifler, George, Schlegel 2013) we describe a new method for reducing the shape noise in weak lensing measurements by an order of magnitude. Our method relies on spectroscopic measurements of disk galaxy rotation and makes use of the well-established Tully-Fisher (TF) relation in order to control for the intrinsic orientations of galaxy disks. Whereas shape noise is one of the major limitations for current weak lensing experiments it ceases to be an important source of statistical error in our new proposed technique. Specifically, we propose a pilot study that maps the projected mass distribution in the massive cluster Abell 2261 (z=0.225) to infer whether this promising technique faces systematics that prohibit its application to WFIRST. In addition to the cosmological weak lensing prospects, these measurements will also allow us to test kinematic lensing in the context of cluster mass reconstruction with a drastically improved signal-to-noise (S/N) per galaxy.

Medusa spectroscopy of A400, A576, A1767, and A2124

NASA Technical Reports Server (NTRS)

Hintzen, P.; Hill, J. M.; Lindley, D.; Scott, J. S.; Angel, J. R. P.

1982-01-01

Galaxy velocity data taken with the Steward Observatory multiple aperture fiber optic spectrograph are presented for four Abell clusters. The root-mean-square external errors in these velocities are about 100 km/s; accuracy which compares favorably with that obtained from single-object observations. It is expected that the recent adoption of a CCD detector should decrease external errors to about 50 km/s. All four of the clusters observed are known X-ray sources and the present data agree well with empirically derived velocity dispersion-X-ray luminosity relations for clusters of galaxies. Abell 400 is interesting in this regard, since both its X-ray luminosity and its velocity dispersion are quite small. Such objects are particularly important in determining the slope of the velocity dispersion-X-ray luminosity relation. The large microwave decrement observed in A576 was initially interpreted as due to Compton scattering of the microwave background by the X-ray-emitting intracluster gas. White and Silk have presented Einstein X-ray data which indicate that A576 contains too little gas to produce the observed microwave decrement by Compton scattering. The velocity dispersion obtained here for 47 members of this cluster strengthens their conclusion.

Asian International Students at an Australian University: Mapping the Paths between Integrative Motivation, Competence in L2 Communication, Cross-Cultural Adaptation and Persistence with Structural Equation Modelling

ERIC Educational Resources Information Center

Yu, Baohua

2013-01-01

This study examined the interrelationships of integrative motivation, competence in second language (L2) communication, sociocultural adaptation, academic adaptation and persistence of international students at an Australian university. Structural equation modelling demonstrated that the integrative motivation of international students has a…

Development of volume equations using data obtained by upper stem dendrometry with Monte Carlo integration: preliminary results for eastern redcedar

Treesearch

Thomas B. Lynch; Rodney E. Will; Rider Reynolds

2013-01-01

Preliminary results are given for development of an eastern redcedar (Juniperus virginiana) cubic-volume equation based on measurements of redcedar sample tree stem volume using dendrometry with Monte Carlo integration. Monte Carlo integration techniques can be used to provide unbiased estimates of stem cubic-foot volume based on upper stem diameter...

PREFACE: Symmetries and integrability of difference equations Symmetries and integrability of difference equations

NASA Astrophysics Data System (ADS)

Levi, Decio; Olver, Peter; Thomova, Zora; Winternitz, Pavel

2009-11-01

The concept of integrability was introduced in classical mechanics in the 19th century for finite dimensional continuous Hamiltonian systems. It was extended to certain classes of nonlinear differential equations in the second half of the 20th century with the discovery of the inverse scattering transform and the birth of soliton theory. Also at the end of the 19th century Lie group theory was invented as a powerful tool for obtaining exact analytical solutions of large classes of differential equations. Together, Lie group theory and integrability theory in its most general sense provide the main tools for solving nonlinear differential equations. Like differential equations, difference equations play an important role in physics and other sciences. They occur very naturally in the description of phenomena that are genuinely discrete. Indeed, they may actually be more fundamental than differential equations if space-time is actually discrete at very short distances. On the other hand, even when treating continuous phenomena described by differential equations it is very often necessary to resort to numerical methods. This involves a discretization of the differential equation, i.e. a replacement of the differential equation by a difference one. Given the well developed and understood techniques of symmetry and integrability for differential equations a natural question to ask is whether it is possible to develop similar techniques for difference equations. The aim is, on one hand, to obtain powerful methods for solving `integrable' difference equations and to establish practical integrability criteria, telling us when the methods are applicable. On the other hand, Lie group methods can be adapted to solve difference equations analytically. Finally, integrability and symmetry methods can be combined with numerical methods to obtain improved numerical solutions of differential equations. The origin of the SIDE meetings goes back to the early 1990s and the first meeting with the name `Symmetries and Integrability of Discrete Equations (SIDE)' was held in Estérel, Québec, Canada. This was organized by D Levi, P Winternitz and L Vinet. After the success of the first meeting the scientific community decided to hold bi-annual SIDE meetings. They were held in 1996 at the University of Kent (UK), 1998 in Sabaudia (Italy), 2000 at the University of Tokyo (Japan), 2002 in Giens (France), 2004 in Helsinki (Finland) and in 2006 at the University of Melbourne (Australia). In 2008 the SIDE 8 meeting was again organized near Montreal, in Ste-Adèle, Québec, Canada. The SIDE 8 International Advisory Committee (also the SIDE steering committee) consisted of Frank Nijhoff, Alexander Bobenko, Basil Grammaticos, Jarmo Hietarinta, Nalini Joshi, Decio Levi, Vassilis Papageorgiou, Junkichi Satsuma, Yuri Suris, Claude Vialet and Pavel Winternitz. The local organizing committee consisted of Pavel Winternitz, John Harnad, Véronique Hussin, Decio Levi, Peter Olver and Luc Vinet. Financial support came from the Centre de Recherches Mathématiques in Montreal and the National Science Foundation (through the University of Minnesota). Proceedings of the first three SIDE meetings were published in the LMS Lecture Note series. Since 2000 the emphasis has been on publishing selected refereed articles in response to a general call for papers issued after the conference. This allows for a wider author base, since the call for papers is not restricted to conference participants. The SIDE topics thus are represented in special issues of Journal of Physics A: Mathematical and General 34 (48) and Journal of Physics A: Mathematical and Theoretical, 40 (42) (SIDE 4 and SIDE 7, respectively), Journal of Nonlinear Mathematical Physics 10 (Suppl. 2) and 12 (Suppl. 2) (SIDE 5 and SIDE 6 respectively). The SIDE 8 meeting was organized around several topics and the contributions to this special issue reflect the diversity presented during the meeting. The papers presented at the SIDE 8 meeting were organized into the following special sessions: geometry of discrete and continuous Painlevé equations; continuous symmetries of discrete equations—theory and computational applications; algebraic aspects of discrete equations; singularity confinement, algebraic entropy and Nevanlinna theory; discrete differential geometry; discrete integrable systems and isomonodromy transformations; special functions as solutions of difference and q-difference equations. This special issue of the journal is organized along similar lines. The first three articles are topical review articles appearing in alphabetical order (by first author). The article by Doliwa and Nieszporski describes the Darboux transformations in a discrete setting, namely for the discrete second order linear problem. The article by Grammaticos, Halburd, Ramani and Viallet concentrates on the integrability of the discrete systems, in particular they describe integrability tests for difference equations such as singularity confinement, algebraic entropy (growth and complexity), and analytic and arithmetic approaches. The topical review by Konopelchenko explores the relationship between the discrete integrable systems and deformations of associative algebras. All other articles are presented in alphabetical order (by first author). The contributions were solicited from all participants as well as from the general scientific community. The contributions published in this special issue can be loosely grouped into several overlapping topics, namely: •Geometry of discrete and continuous Painlevé equations (articles by Spicer and Nijhoff and by Lobb and Nijhoff). •Continuous symmetries of discrete equations—theory and applications (articles by Dorodnitsyn and Kozlov; Levi, Petrera and Scimiterna; Scimiterna; Ste-Marie and Tremblay; Levi and Yamilov; Rebelo and Winternitz). •Yang--Baxter maps (article by Xenitidis and Papageorgiou). •Algebraic aspects of discrete equations (articles by Doliwa and Nieszporski; Konopelchenko; Tsarev and Wolf). •Singularity confinement, algebraic entropy and Nevanlinna theory (articles by Grammaticos, Halburd, Ramani and Viallet; Grammaticos, Ramani and Tamizhmani). •Discrete integrable systems and isomonodromy transformations (article by Dzhamay). •Special functions as solutions of difference and q-difference equations (articles by Atakishiyeva, Atakishiyev and Koornwinder; Bertola, Gekhtman and Szmigielski; Vinet and Zhedanov). •Other topics (articles by Atkinson; Grünbaum Nagai, Kametaka and Watanabe; Nagiyev, Guliyeva and Jafarov; Sahadevan and Uma Maheswari; Svinin; Tian and Hu; Yao, Liu and Zeng). This issue is the result of the collaboration of many individuals. We would like to thank the authors who contributed and everyone else involved in the preparation of this special issue.

Solving modal equations of motion with initial conditions using MSC/NASTRAN DMAP. Part 1: Implementing exact mode superposition

NASA Technical Reports Server (NTRS)

Abdallah, Ayman A.; Barnett, Alan R.; Ibrahim, Omar M.; Manella, Richard T.

1993-01-01

Within the MSC/NASTRAN DMAP (Direct Matrix Abstraction Program) module TRD1, solving physical (coupled) or modal (uncoupled) transient equations of motion is performed using the Newmark-Beta or mode superposition algorithms, respectively. For equations of motion with initial conditions, only the Newmark-Beta integration routine has been available in MSC/NASTRAN solution sequences for solving physical systems and in custom DMAP sequences or alters for solving modal systems. In some cases, one difficulty with using the Newmark-Beta method is that the process of selecting suitable integration time steps for obtaining acceptable results is lengthy. In addition, when very small step sizes are required, a large amount of time can be spent integrating the equations of motion. For certain aerospace applications, a significant time savings can be realized when the equations of motion are solved using an exact integration routine instead of the Newmark-Beta numerical algorithm. In order to solve modal equations of motion with initial conditions and take advantage of efficiencies gained when using uncoupled solution algorithms (like that within TRD1), an exact mode superposition method using MSC/NASTRAN DMAP has been developed and successfully implemented as an enhancement to an existing coupled loads methodology at the NASA Lewis Research Center.

Matrix Methods for Solving Hartree-Fock Equations in Atomic Structure Calculations and Line Broadening

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

Gomez, Thomas; Nagayama, Taisuke; Fontes, Chris

Atomic structure of N-electron atoms is often determined by solving the Hartree-Fock equations, which are a set of integro-differential equations. The integral part of the Hartree-Fock equations treats electron exchange, but the Hartree-Fock equations are not often treated as an integro-differential equation. The exchange term is often approximated as an inhomogeneous or an effective potential so that the Hartree-Fock equations become a set of ordinary differential equations (which can be solved using the usual shooting methods). Because the Hartree-Fock equations are an iterative-refinement method, the inhomogeneous term relies on the previous guess of the wavefunction. In addition, there are numericalmore » complications associated with solving inhomogeneous differential equations. This work uses matrix methods to solve the Hartree-Fock equations as an integro-differential equation. It is well known that a derivative operator can be expressed as a matrix made of finite-difference coefficients; energy eigenvalues and eigenvectors can be obtained by using linear-algebra packages. The integral (exchange) part of the Hartree-Fock equation can be approximated as a sum and written as a matrix. The Hartree-Fock equations can be solved as a matrix that is the sum of the differential and integral matrices. We compare calculations using this method against experiment and standard atomic structure calculations. This matrix method can also be used to solve for free-electron wavefunctions, thus improving how the atoms and free electrons interact. Here, this technique is important for spectral line broadening in two ways: it improves the atomic structure calculations, and it improves the motion of the plasma electrons that collide with the atom.« less

Matrix Methods for Solving Hartree-Fock Equations in Atomic Structure Calculations and Line Broadening

DOE PAGES

Gomez, Thomas; Nagayama, Taisuke; Fontes, Chris; ...

2018-04-23

Atomic structure of N-electron atoms is often determined by solving the Hartree-Fock equations, which are a set of integro-differential equations. The integral part of the Hartree-Fock equations treats electron exchange, but the Hartree-Fock equations are not often treated as an integro-differential equation. The exchange term is often approximated as an inhomogeneous or an effective potential so that the Hartree-Fock equations become a set of ordinary differential equations (which can be solved using the usual shooting methods). Because the Hartree-Fock equations are an iterative-refinement method, the inhomogeneous term relies on the previous guess of the wavefunction. In addition, there are numericalmore » complications associated with solving inhomogeneous differential equations. This work uses matrix methods to solve the Hartree-Fock equations as an integro-differential equation. It is well known that a derivative operator can be expressed as a matrix made of finite-difference coefficients; energy eigenvalues and eigenvectors can be obtained by using linear-algebra packages. The integral (exchange) part of the Hartree-Fock equation can be approximated as a sum and written as a matrix. The Hartree-Fock equations can be solved as a matrix that is the sum of the differential and integral matrices. We compare calculations using this method against experiment and standard atomic structure calculations. This matrix method can also be used to solve for free-electron wavefunctions, thus improving how the atoms and free electrons interact. Here, this technique is important for spectral line broadening in two ways: it improves the atomic structure calculations, and it improves the motion of the plasma electrons that collide with the atom.« less

Evaluating Feynman integrals by the hypergeometry

NASA Astrophysics Data System (ADS)

Feng, Tai-Fu; Chang, Chao-Hsi; Chen, Jian-Bin; Gu, Zhi-Hua; Zhang, Hai-Bin

2018-02-01

The hypergeometric function method naturally provides the analytic expressions of scalar integrals from concerned Feynman diagrams in some connected regions of independent kinematic variables, also presents the systems of homogeneous linear partial differential equations satisfied by the corresponding scalar integrals. Taking examples of the one-loop B0 and massless C0 functions, as well as the scalar integrals of two-loop vacuum and sunset diagrams, we verify our expressions coinciding with the well-known results of literatures. Based on the multiple hypergeometric functions of independent kinematic variables, the systems of homogeneous linear partial differential equations satisfied by the mentioned scalar integrals are established. Using the calculus of variations, one recognizes the system of linear partial differential equations as stationary conditions of a functional under some given restrictions, which is the cornerstone to perform the continuation of the scalar integrals to whole kinematic domains numerically with the finite element methods. In principle this method can be used to evaluate the scalar integrals of any Feynman diagrams.

Design and Operation of a Two-Color Interferometer to Measure Plasma and Neutral Gas Densities in a Laser-Triggered Spark Gap Switch

NASA Astrophysics Data System (ADS)

Camacho, J. F.; Ruden, E. L.; Domonkos, M. T.; Schmitt-Sody, A.; Lucero, A.

2014-10-01

A Mach-Zehnder imaging interferometer, operating with 1064-nm and 532-nm wavelength beams from a short-pulse laser and a frequency-doubled branch, respectively, has been designed and built to simultaneously measure plasma free electron and neutral gas densities profiles within a laser-triggered spark gap switch with a 5-mm gap. The switch will be triggered by focusing a separate 532-nm or 1064-nm laser pulse along the gap's axis to trigger low-jitter breakdown. Illuminating the gap transverse to this axis, the diagnostic will generate interferograms for each wavelength, which will then be numerically converted to phase-shift maps. These will be used to calculate independent line-integrated free electron and neutral density profiles by exploiting their different frequency dispersion curves. The density profiles themselves, then, will be calculated by Abel inversion. Details of the interferometer's design will be presented along with density data obtained using a variety of fill gasses at various pressures. Other switch parameters will be varied as well in order to characterize more fully the performance of the switch.

ROSAT observations of clusters with wide-angle tailed radio sources

NASA Technical Reports Server (NTRS)

Burns, Jack O.

1993-01-01

The goal of these ROSAT PSPC pointed observations was to understand the nature of X-ray emission associated clusters that contain luminous wide-angle tailed (WAT) radio sources identified with the centrally dominant cluster galaxies. These 500 kpc diameter radio sources are strongly affected by confinement and interaction with the intracluster medium. So, a complete picture of the origin and evolution of these radio sources is not possible without detailed X-ray observations which sample the distribution and temperature of the surrounding hot gas. Two WAT clusters have been observed with the ROSAT PSPC to date. The first is Abell 2634 which contains the WAT 3C 465 and was approved for observations in AO-1. Unfortunately, these observations were broken into two widely separated pieces in time. The first data set containing about 9000 sec of integration arrived in mid-March, 1992. The second data set containing about 10,500 sec arrived just recently in early April (after a first tape was destroyed in the mail). The second cluster is 1919+479 which was approved for observations in AO-2. These ROSAT data arrived in October 1992.

Orphan Stars Found in Long Galaxy Tail

NASA Astrophysics Data System (ADS)

2007-09-01

Astronomers have found evidence that stars have been forming in a long tail of gas that extends well outside its parent galaxy. This discovery suggests that such "orphan" stars may be much more prevalent than previously thought. The comet-like tail was observed in X-ray light with NASA's Chandra X-ray Observatory and in optical light with the Southern Astrophysical Research (SOAR) telescope in Chile. The feature extends for more than 200,000 light years and was created as gas was stripped from a galaxy called ESO 137-001 that is plunging toward the center of Abell 3627, a giant cluster of galaxies. "This is one of the longest tails like this we have ever seen," said Ming Sun of Michigan State University, who led the study. "And, it turns out that this is a giant wake of creation, not of destruction." Chandra X-ray Image of ESO 137-001 and Tail in Abell 3627 Chandra X-ray Image of ESO 137-001 and Tail in Abell 3627 The observations indicate that the gas in the tail has formed millions of stars. Because the large amounts of gas and dust needed to form stars are typically found only within galaxies, astronomers have previously thought it unlikely that large numbers of stars would form outside a galaxy. "This isn't the first time that stars have been seen to form between galaxies," said team member Megan Donahue, also of MSU. "But the number of stars forming here is unprecedented." The evidence for star formation in this tail includes 29 regions of ionized hydrogen glowing in optical light, thought to be from newly formed stars. These regions are all downstream of the galaxy, located in or near the tail. Two Chandra X-ray sources are near these regions, another indication of star formation activity. The researchers believe the orphan stars formed within the last 10 million years or so. The stars in the tail of this fast-moving galaxy, which is some 220 million light years away, would be much more isolated than the vast majority of stars in galaxies. H-alpha Image of ESO 137-001 and Tail in Abell 3627 H-alpha Image of ESO 137-001 and Tail in Abell 3627 "By our galactic standards, these are extremely lonely stars," said Mark Voit, another team member from MSU. "If life was to form out there on a planet a few billion years from now, they would have very dark skies." The gas that formed the orphan stars was stripped out of its parent galaxy by the pressure induced by the motion of the galaxy through the multimillion degree gas that pervades the intergalactic space of the galaxy cluster. Eventually most of the gas will be scoured from the galaxy, depleting the raw material for new stars, and effectively stopping further star formation in the galaxy. This process may represent an important but short-lived stage in the transformation of a galaxy. Although apparently rare in the present-day universe, galactic tails of gas and orphan stars may have been more common billions of years ago when galaxies were younger and richer in star-forming gas. These results will appear in the December 10th issue of The Astrophysical Journal. NASA's Marshall Space Flight Center, Huntsville, Ala., manages the Chandra program for the agency's Science Mission Directorate. The Smithsonian Astrophysical Observatory controls science and flight operations from the Chandra X-ray Center in Cambridge, Mass. The SOAR (Southern Astrophysical Research Telescope) is a joint project of Michigan State University, Conselho Nacional de Pesquisas Científicas e Tecnológicas (CNPq-Brazil), The University of North Carolina at Chapel Hill, and the National Optical Astronomy Observatory.

On the Formulation of Weakly Singular Displacement/Traction Integral Equations; and Their Solution by the MLPG Method

NASA Technical Reports Server (NTRS)

Atluri, Satya N.; Shen, Shengping

2002-01-01

In this paper, a very simple method is used to derive the weakly singular traction boundary integral equation based on the integral relationships for displacement gradients. The concept of the MLPG method is employed to solve the integral equations, especially those arising in solid mechanics. A moving Least Squares (MLS) interpolation is selected to approximate the trial functions in this paper. Five boundary integral Solution methods are introduced: direct solution method; displacement boundary-value problem; traction boundary-value problem; mixed boundary-value problem; and boundary variational principle. Based on the local weak form of the BIE, four different nodal-based local test functions are selected, leading to four different MLPG methods for each BIE solution method. These methods combine the advantages of the MLPG method and the boundary element method.

The geometric approach to sets of ordinary differential equations and Hamiltonian dynamics

NASA Technical Reports Server (NTRS)

Estabrook, F. B.; Wahlquist, H. D.

1975-01-01

The calculus of differential forms is used to discuss the local integration theory of a general set of autonomous first order ordinary differential equations. Geometrically, such a set is a vector field V in the space of dependent variables. Integration consists of seeking associated geometric structures invariant along V: scalar fields, forms, vectors, and integrals over subspaces. It is shown that to any field V can be associated a Hamiltonian structure of forms if, when dealing with an odd number of dependent variables, an arbitrary equation of constraint is also added. Families of integral invariants are an immediate consequence. Poisson brackets are isomorphic to Lie products of associated CT-generating vector fields. Hamilton's variational principle follows from the fact that the maximal regular integral manifolds of a closed set of forms must include the characteristics of the set.

High-order solution methods for grey discrete ordinates thermal radiative transfer

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

Maginot, Peter G., E-mail: maginot1@llnl.gov; Ragusa, Jean C., E-mail: jean.ragusa@tamu.edu; Morel, Jim E., E-mail: morel@tamu.edu

This work presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation ismore » accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.« less

High-order solution methods for grey discrete ordinates thermal radiative transfer

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

Maginot, Peter G.; Ragusa, Jean C.; Morel, Jim E.

This paper presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation ismore » accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.« less

High-order solution methods for grey discrete ordinates thermal radiative transfer

DOE PAGES

Maginot, Peter G.; Ragusa, Jean C.; Morel, Jim E.

2016-09-29

This paper presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation ismore » accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.« less

AKNS hierarchy, Darboux transformation and conservation laws of the 1D nonautonomous nonlinear Schroedinger equations

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

Zhao Dun; Center for Interdisciplinary Studies, Lanzhou University, Lanzhou 730000; Zhang Yujuan

2011-04-15

By constructing nonisospectral Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy, we investigate the nonautonomous nonlinear Schroedinger (NLS) equations which have been used to describe the Feshbach resonance management in matter-wave solitons in Bose-Einstein condensate and the dispersion and nonlinearity managements for optical solitons. It is found that these equations are some special cases of a new integrable model of nonlocal nonautonomous NLS equations. Based on the Lax pairs, the Darboux transformation and conservation laws are explored. It is shown that the local external potentials would break down the classical infinite number of conservation laws. The result indicates that the integrability of the nonautonomous NLSmore » systems may be nontrivial in comparison to the conventional concept of integrability in the canonical case.« less

Particle connectedness and cluster formation in sequential depositions of particles: integral-equation theory.

PubMed

Danwanichakul, Panu; Glandt, Eduardo D

2004-11-15

We applied the integral-equation theory to the connectedness problem. The method originally applied to the study of continuum percolation in various equilibrium systems was modified for our sequential quenching model, a particular limit of an irreversible adsorption. The development of the theory based on the (quenched-annealed) binary-mixture approximation includes the Ornstein-Zernike equation, the Percus-Yevick closure, and an additional term involving the three-body connectedness function. This function is simplified by introducing a Kirkwood-like superposition approximation. We studied the three-dimensional (3D) system of randomly placed spheres and 2D systems of square-well particles, both with a narrow and with a wide well. The results from our integral-equation theory are in good accordance with simulation results within a certain range of densities.

Particle connectedness and cluster formation in sequential depositions of particles: Integral-equation theory

NASA Astrophysics Data System (ADS)

Danwanichakul, Panu; Glandt, Eduardo D.

2004-11-01

We applied the integral-equation theory to the connectedness problem. The method originally applied to the study of continuum percolation in various equilibrium systems was modified for our sequential quenching model, a particular limit of an irreversible adsorption. The development of the theory based on the (quenched-annealed) binary-mixture approximation includes the Ornstein-Zernike equation, the Percus-Yevick closure, and an additional term involving the three-body connectedness function. This function is simplified by introducing a Kirkwood-like superposition approximation. We studied the three-dimensional (3D) system of randomly placed spheres and 2D systems of square-well particles, both with a narrow and with a wide well. The results from our integral-equation theory are in good accordance with simulation results within a certain range of densities.

Integrable particle systems vs solutions to the KP and 2D Toda equations

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

Ruijsenaars, S.N.

Starting from the relation between integrable relativistic N-particle systems with hyperbolic interactions and elementary N-soliton solutions to the KP and 2D Toda equations, we show how fusion properties of the soliton solutions are mirrored by fusion properties of the Poisson commuting particle dynamics. We also obtain previously known relations between elliptic solutions and integrable N-particle systems with elliptic interactions, without invoking finite-gap integration theory. {copyright} 1997 Academic Press, Inc.

Theoretical Investigation of Thermo-Mechanical Behavior of Carbon Nanotube-Based Composites Using the Integral Transform Method

NASA Technical Reports Server (NTRS)

Pawloski, Janice S.

2001-01-01

This project uses the integral transform technique to model the problem of nanotube behavior as an axially symmetric system of shells. Assuming that the nanotube behavior can be described by the equations of elasticity, we seek a stress function x which satisfies the biharmonic equation: del(exp 4) chi = [partial deriv(r(exp 2)) + partial deriv(r) + partial deriv(z(exp 2))] chi = 0. The method of integral transformations is used to transform the differential equation. The symmetry with respect to the z-axis indicates that we only need to consider the sine transform of the stress function: X(bar)(r,zeta) = integral(from 0 to infinity) chi(r,z)sin(zeta,z) dz.

Dusty Pair Plasma—Wave Propagation and Diffusive Transition of Oscillations

NASA Astrophysics Data System (ADS)

Atamaniuk, Barbara; Turski, Andrzej J.

2011-11-01

The crucial point of the paper is the relation between equilibrium distributions of plasma species and the type of propagation or diffusive transition of plasma response to a disturbance. The paper contains a unified treatment of disturbance propagation (transport) in the linearized Vlasov electron-positron and fullerene pair plasmas containing charged dust impurities, based on the space-time convolution integral equations. Electron-positron-dust/ion (e-p-d/i) plasmas are rather widespread in nature. Space-time responses of multi-component linearized Vlasov plasmas on the basis of multiple integral equations are invoked. An initial-value problem for Vlasov-Poisson/Ampère equations is reduced to the one multiple integral equation and the solution is expressed in terms of forcing function and its space-time convolution with the resolvent kernel. The forcing function is responsible for the initial disturbance and the resolvent is responsible for the equilibrium velocity distributions of plasma species. By use of resolvent equations, time-reversibility, space-reflexivity and the other symmetries are revealed. The symmetries carry on physical properties of Vlasov pair plasmas, e.g., conservation laws. Properly choosing equilibrium distributions for dusty pair plasmas, we can reduce the resolvent equation to: (i) the undamped dispersive wave equations, (ii) and diffusive transport equations of oscillations.

All Source Sensor Integration Using an Extended Kalman Filter

DTIC Science & Technology

2012-03-22

Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 All...Positioning System . . . . . . . . . . . . . . . . . . 1 ASPN All Source Positioning Navigation . . . . . . . . . . . . . . 2 DARPA Defense Advanced...equations are developed for sensor preprocessed mea- 1 surements, and these navigation equations are not dependent upon the integrating filter. That is

Multi-Hamiltonian structure of Plebanski's second heavenly equation

NASA Astrophysics Data System (ADS)

Neyzi, F.; Nutku, Y.; Sheftel, M. B.

2005-09-01

We show that Plebanski's second heavenly equation, when written as a first-order nonlinear evolutionary system, admits multi-Hamiltonian structure. Therefore by Magri's theorem it is a completely integrable system. Thus it is an example of a completely integrable system in four dimensions.

Time-dependent spectral renormalization method

NASA Astrophysics Data System (ADS)

Cole, Justin T.; Musslimani, Ziad H.

2017-11-01

The spectral renormalization method was introduced by Ablowitz and Musslimani (2005) as an effective way to numerically compute (time-independent) bound states for certain nonlinear boundary value problems. In this paper, we extend those ideas to the time domain and introduce a time-dependent spectral renormalization method as a numerical means to simulate linear and nonlinear evolution equations. The essence of the method is to convert the underlying evolution equation from its partial or ordinary differential form (using Duhamel's principle) into an integral equation. The solution sought is then viewed as a fixed point in both space and time. The resulting integral equation is then numerically solved using a simple renormalized fixed-point iteration method. Convergence is achieved by introducing a time-dependent renormalization factor which is numerically computed from the physical properties of the governing evolution equation. The proposed method has the ability to incorporate physics into the simulations in the form of conservation laws or dissipation rates. This novel scheme is implemented on benchmark evolution equations: the classical nonlinear Schrödinger (NLS), integrable PT symmetric nonlocal NLS and the viscous Burgers' equations, each of which being a prototypical example of a conservative and dissipative dynamical system. Numerical implementation and algorithm performance are also discussed.

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

Fang, Dongfan, E-mail: fangdongfan1208@126.com; Sun, Qizhi; Zhao, Xiaoming

A 633 nm laser interferometer has been designed based on a novel concept, which, without the acousto-optic modulator or the demodulator circuit, adopts the fibers to connect all elements except photodetectors and oscilloscope in this system to make it more compact, portable, and efficient. The noteworthy feature is to mathematically compare the two divided interference signals, which have the same phase-shift caused by the electron density but possess the different initial phase and low angular frequencies. It is possible to read the plasma density directly on the oscilloscope by our original mathematic demodulation method without a camera. Based on themore » Abel inversion algorithm, the radial electron density profiles versus time can be obtained by using the multi-chord system. The designed measurable phase shift ranges from 0 to 2π rad corresponding to the maximum line integral of electron density less than 3.5 × 10{sup 17} cm{sup −2}, and the phase accuracy is about 0.017 rad corresponding to the line integral of electron density accuracy of 1 × 10{sup 15} cm{sup −2}. After the construction of eight-chord interferometer, it will provide the detailed time resolved information of the spatial distribution of the electron density in the field-reversed configuration (FRC) plasma target produced by the “Yingguang-1” programmed-discharge device, which is being constructed in the Key Laboratory of Pulsed Power, China Academy of Engineering Physics.« less

The Atacama Cosmology Telescope: High-Resolution Sunyaev-Zel'dovich Array Observations of ACT SZE-Selected Clusters from the Equatorial Strip

NASA Technical Reports Server (NTRS)

Reese, Erik D.; Mroczkowski, Tony; Menanteau, Felipe; Hilton, Matt; Sievers, Jonathan; Aguirre, Paula; Appel, John William; Baker, Andrew J.; Bond, J. Richard; Das, Sudeep;

The Atacama Cosmology Telescope: High-Resolution Sunyaev-Zeldovich Array Observations of ACT SZE-Selected Clusters from the Equatorial Strip

NASA Technical Reports Server (NTRS)

Reese, Erik; Mroczkowski, Tony; Menateau, Felipe; Hilton, Matt; Sievers, Jonathan; Aguirre, Paula; Appel, John William; Baker, Andrew J.; Bond, J. Richard; Das, Sudeep;

Numerical integration of KPZ equation with restrictions

NASA Astrophysics Data System (ADS)

Torres, M. F.; Buceta, R. C.

2018-03-01

In this paper, we introduce a novel integration method of Kardar–Parisi–Zhang (KPZ) equation. It is known that if during the discrete integration of the KPZ equation the nearest-neighbor height-difference exceeds a critical value, instabilities appear and the integration diverges. One way to avoid these instabilities is to replace the KPZ nonlinear-term by a function of the same term that depends on a single adjustable parameter which is able to control pillars or grooves growing on the interface. Here, we propose a different integration method which consists of directly limiting the value taken by the KPZ nonlinearity, thereby imposing a restriction rule that is applied in each integration time-step, as if it were the growth rule of a restricted discrete model, e.g. restricted-solid-on-solid (RSOS). Taking the discrete KPZ equation with restrictions to its dimensionless version, the integration depends on three parameters: the coupling constant g, the inverse of the time-step k, and the restriction constant ε which is chosen to eliminate divergences while keeping all the properties of the continuous KPZ equation. We study in detail the conditions in the parameters’ space that avoid divergences in the 1-dimensional integration and reproduce the scaling properties of the continuous KPZ with a particular parameter set. We apply the tested methodology to the d-dimensional case (d = 3, 4 ) with the purpose of obtaining the growth exponent β, by establishing the conditions of the coupling constant g under which we recover known values reached by other authors, particularly for the RSOS model. This method allows us to infer that d  =  4 is not the critical dimension of the KPZ universality class, where the strong-coupling phase disappears.

Integrability in AdS/CFT correspondence: quasi-classical analysis

NASA Astrophysics Data System (ADS)

Gromov, Nikolay

2009-06-01

In this review, we consider a quasi-classical method applicable to integrable field theories which is based on a classical integrable structure—the algebraic curve. We apply it to the Green-Schwarz superstring on the AdS5 × S5 space. We show that the proposed method reproduces perfectly the earlier results obtained by expanding the string action for some simple classical solutions. The construction is explicitly covariant and is not based on a particular parameterization of the fields and as a result is free from ambiguities. On the other hand, the finite size corrections in some particularly important scaling limit are studied in this paper for a system of Bethe equations. For the general superalgebra \\su(N|K) , the result for the 1/L corrections is obtained. We find an integral equation which describes these corrections in a closed form. As an application, we consider the conjectured Beisert-Staudacher (BS) equations with the Hernandez-Lopez dressing factor where the finite size corrections should reproduce quasi-classical results around a general classical solution. Indeed, we show that our integral equation can be interpreted as a sum of all physical fluctuations and thus prove the complete one-loop consistency of the BS equations. We demonstrate that any local conserved charge (including the AdS energy) computed from the BS equations is indeed given at one loop by the sum of the charges of fluctuations with an exponential precision for large S5 angular momentum of the string. As an independent result, the BS equations in an \\su(2) sub-sector were derived from Zamolodchikovs's S-matrix. The paper is based on the author's PhD thesis.

Elimination of secular terms from the differential equations for the elements of perturbed two-body motion

NASA Technical Reports Server (NTRS)

Bond, Victor R.; Fraietta, Michael F.

1991-01-01

In 1961, Sperling linearized and regularized the differential equations of motion of the two-body problem by changing the independent variable from time to fictitious time by Sundman's transformation (r = dt/ds) and by embedding the two-body energy integral and the Laplace vector. In 1968, Burdet developed a perturbation theory which was uniformly valid for all types of orbits using a variation of parameters approach on the elements which appeared in Sperling's equations for the two-body solution. In 1973, Bond and Hanssen improved Burdet's set of differential equations by embedding the total energy (which is a constant when the potential function is explicitly dependent upon time.) The Jacobian constant was used as an element to replace the total energy in a reformulation of the differential equations of motion. In the process, another element which is proportional to a component of the angular momentum was introduced. Recently trajectories computed during numerical studies of atmospheric entry from circular orbits and low thrust beginning in near-circular orbits exhibited numerical instability when solved by the method of Bond and Gottlieb (1989) for long time intervals. It was found that this instability was due to secular terms which appear on the righthand sides of the differential equations of some of the elements. In this paper, this instability is removed by the introduction of another vector integral called the delta integral (which replaces the Laplace Vector) and another scalar integral which removes the secular terms. The introduction of these integrals requires a new derivation of the differential equations for most of the elements. For this rederivation, the Lagrange method of variation of parameters is used, making the development more concise. Numerical examples of this improvement are presented.

Does the supersymmetric integrability imply the integrability of Bosonic sector

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

Popowicz, Ziemowit

2010-03-08

The answer is no. This is demonstrated for two equations that belong to the supersymmetric Manin-Radul N = 1 Kadomtsev-Petviashvili (MRSKP) hierarchy. The first one is the N = 1 supersymmetric Sawada-Kotera equation recently considered by Tian and Liu. We define the bi-Hamiltonian structure for this equation which however does not reduce in the bosonic limit to the known bi-Hamiltonian structure. The second equation is obtained from the Lax operator of the fifth order in the supersymmetric derivatives which in the bosonic sector reduces to the system of interacted two KdV equations discovered by Drinfeld and Sokolov in 1981 andmore » later rediscovered by Sakovich and Foursov.« less

Solution of steady and unsteady transonic-vortex flows using Euler and full-potential equations

NASA Technical Reports Server (NTRS)

Kandil, Osama A.; Chuang, Andrew H.; Hu, Hong

1989-01-01

Two methods are presented for inviscid transonic flows: unsteady Euler equations in a rotating frame of reference for transonic-vortex flows and integral solution of full-potential equation with and without embedded Euler domains for transonic airfoil flows. The computational results covered: steady and unsteady conical vortex flows; 3-D steady transonic vortex flow; and transonic airfoil flows. The results are in good agreement with other computational results and experimental data. The rotating frame of reference solution is potentially efficient as compared with the space fixed reference formulation with dynamic gridding. The integral equation solution with embedded Euler domain is computationally efficient and as accurate as the Euler equations.

Connectivity as an alternative to boundary integral equations: Construction of bases

PubMed Central

Herrera, Ismael; Sabina, Federico J.

1978-01-01

In previous papers Herrera developed a theory of connectivity that is applicable to the problem of connecting solutions defined in different regions, which occurs when solving partial differential equations and many problems of mechanics. In this paper we explain how complete connectivity conditions can be used to replace boundary integral equations in many situations. We show that completeness is satisfied not only in steady-state problems such as potential, reduced wave equation and static and quasi-static elasticity, but also in time-dependent problems such as heat and wave equations and dynamical elasticity. A method to obtain bases of connectivity conditions, which are independent of the regions considered, is also presented. PMID:16592522

Subprograms for integrating the equations of motion of satellites. FORTRAN 4

NASA Technical Reports Server (NTRS)

Prokhorenko, V. I.

1980-01-01

The subprograms for the formation of the right members of the equations of motion of artificial Earth satellites (AES), integration of systems of differential equations by Adams' method, and the calculation of the values of various functions from the AES parameters of motion are described. These subprograms are written in the FORTRAN 4 language and constitute an essential part of the package of applied programs for the calculation of navigational parameters AES.

Student Solution Manual for Essential Mathematical Methods for the Physical Sciences

NASA Astrophysics Data System (ADS)

Riley, K. F.; Hobson, M. P.

2011-02-01

1. Matrices and vector spaces; 2. Vector calculus; 3. Line, surface and volume integrals; 4. Fourier series; 5. Integral transforms; 6. Higher-order ODEs; 7. Series solutions of ODEs; 8. Eigenfunction methods; 9. Special functions; 10. Partial differential equations; 11. Solution methods for PDEs; 12. Calculus of variations; 13. Integral equations; 14. Complex variables; 15. Applications of complex variables; 16. Probability; 17. Statistics.

Essential Mathematical Methods for the Physical Sciences

NASA Astrophysics Data System (ADS)

Riley, K. F.; Hobson, M. P.

2011-02-01

1. Matrices and vector spaces; 2. Vector calculus; 3. Line, surface and volume integrals; 4. Fourier series; 5. Integral transforms; 6. Higher-order ODEs; 7. Series solutions of ODEs; 8. Eigenfunction methods; 9. Special functions; 10. Partial differential equations; 11. Solution methods for PDEs; 12. Calculus of variations; 13. Integral equations; 14. Complex variables; 15. Applications of complex variables; 16. Probability; 17. Statistics; Appendices; Index.

General pulsed-field gradient signal attenuation expression based on a fractional integral modified-Bloch equation

NASA Astrophysics Data System (ADS)

Lin, Guoxing

2018-10-01

Anomalous diffusion has been investigated in many polymer and biological systems. The analysis of PFG anomalous diffusion relies on the ability to obtain the signal attenuation expression. However, the general analytical PFG signal attenuation expression based on the fractional derivative has not been previously reported. Additionally, the reported modified-Bloch equations for PFG anomalous diffusion in the literature yielded different results due to their different forms. Here, a new integral type modified-Bloch equation based on the fractional derivative for PFG anomalous diffusion is proposed, which is significantly different from the conventional differential type modified-Bloch equation. The merit of the integral type modified-Bloch equation is that the original properties of the contributions from linear or nonlinear processes remain unchanged at the instant of the combination. From the modified-Bloch equation, the general solutions are derived, which includes the finite gradient pulse width (FGPW) effect. The numerical evaluation of these PFG signal attenuation expressions can be obtained either by the Adomian decomposition, or a direct integration method that is fast and practicable. The theoretical results agree with the continuous-time random walk (CTRW) simulations performed in this paper. Additionally, the relaxation effect in PFG anomalous diffusion is found to be different from that in PFG normal diffusion. The new modified-Bloch equations and their solutions provide a fundamental tool to analyze PFG anomalous diffusion in nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI).

Solution of differential equations by application of transformation groups

NASA Technical Reports Server (NTRS)

Driskell, C. N., Jr.; Gallaher, L. J.; Martin, R. H., Jr.

1968-01-01

Report applies transformation groups to the solution of systems of ordinary differential equations and partial differential equations. Lies theorem finds an integrating factor for appropriate invariance group or groups can be found and can be extended to partial differential equations.

The XMM Cluster Outskirts Project (X-COP): Thermodynamic properties of the intracluster medium out to R200 in Abell 2319

NASA Astrophysics Data System (ADS)

Ghirardini, V.; Ettori, S.; Eckert, D.; Molendi, S.; Gastaldello, F.; Pointecouteau, E.; Hurier, G.; Bourdin, H.

2018-06-01

Aims: We present the joint analysis of the X-ray and Sunyaev-Zel'dovich (SZ) signals in Abell 2319, the galaxy cluster with the highest signal-to-noise ratio in SZ Planck maps and that has been surveyed within our XMM-Newton Cluster Outskirts Project (X-COP), a very large program which aims to grasp the physical condition in 12 local (z < 0.1) and massive (M200 > 3 × 1014 M⊙) galaxy clusters out to R200 and beyond. Methods: We recover the profiles of the thermodynamic properties by the geometrical deprojection of the X-ray surface brightness, of the SZ Comptonization parameter, and accurate and robust spectroscopic measurements of the gas temperature out to 3.2 Mpc (1.6 R200), 4 Mpc (2 R200), and 1.6 Mpc (0.8 R200), respectively. We resolve the clumpiness of the gas density to be below 20% over the entire observed volume. We also demonstrate that most of this clumpiness originates from the ongoing merger and can be associated with large-scale inhomogeneities (the "residual" clumpiness). We estimate the total mass through the hydrostatic equilibrium equation. This analysis is done both in azimuthally averaged radial bins and in eight independent angular sectors, enabling us to study in detail the azimuthal variance of the recovered properties. Results: Given the exquisite quality of the X-ray and SZ datasets, their radial extension, and their complementarity, we constrain at R200 the total hydrostatic mass, modelled with a Navarro-Frenk-White profile at very high precision (M200 = 10.7 ± 0.5stat. ± 0.9syst. × 1014 M⊙). We identify the ongoing merger and how it is affecting differently the gas properties in the resolved azimuthal sectors. We have several indications that the merger has injected a high level of non-thermal pressure in this system: the clumping free density profile is above the average profile obtained by stacking Rosat/PSPC observations; the gas mass fraction recovered using our hydrostatic mass profile exceeds the expected cosmic gas fraction beyond R500; the pressure profile is flatter than the fit obtained by the Planck Collaboration; the entropy profile is flatter than the mean profile predicted from non-radiative simulations; the analysis in azimuthal sectors has revealed that these deviations occur in a preferred region of the cluster. All these tensions are resolved by requiring a relative support of about 40% from non-thermal to the total pressure at R200.

On the solubility of certain classes of non-linear integral equations in p-adic string theory

NASA Astrophysics Data System (ADS)

Khachatryan, Kh. A.

2018-04-01

We study classes of non-linear integral equations that have immediate application to p-adic mathematical physics and to cosmology. We prove existence and uniqueness theorems for non-trivial solutions in the space of bounded functions.

Addendum to "Free energies from integral equation theories: enforcing path independence".

PubMed

Kast, Stefan M

2006-01-01

The variational formalism developed for the analysis of the path dependence of free energies from integral equation theories [S. M. Kast, Phys. Rev. E 67, 041203 (2003)] is extended in order to allow for the three-dimensional treatment of arbitrarily shaped solutes.

Numerical analysis of composite STEEL-CONCRETE SECTIONS using integral equation of Volterra

NASA Astrophysics Data System (ADS)

Partov, Doncho; Kantchev, Vesselin

2011-09-01

The paper presents analysis of the stress and deflections changes due to creep in statically determinate composite steel-concrete beam. The mathematical model involves the equation of equilibrium, compatibility and constitutive relationship, i.e. an elastic law for the steel part and an integral-type creep law of Boltzmann — Volterra for the concrete part. On the basis of the theory of the viscoelastic body of Arutyunian-Trost-Bažant for determining the redistribution of stresses in beam section between concrete plate and steel beam with respect to time "t", two independent Volterra integral equations of the second kind have been derived. Numerical method based on linear approximation of the singular kernal function in the integral equation is presented. Example with the model proposed is investigated. The creep functions is suggested by the model CEB MC90-99 and the "ACI 209R-92 model. The elastic modulus of concrete E c (t) is assumed to be constant in time `t'. The obtained results from the both models are compared.

The Application of a Boundary Integral Equation Method to the Prediction of Ducted Fan Engine Noise

NASA Technical Reports Server (NTRS)

Dunn, M. H.; Tweed, J.; Farassat, F.

1999-01-01

The prediction of ducted fan engine noise using a boundary integral equation method (BIEM) is considered. Governing equations for the BIEM are based on linearized acoustics and describe the scattering of incident sound by a thin, finite-length cylindrical duct in the presence of a uniform axial inflow. A classical boundary value problem (BVP) is derived that includes an axisymmetric, locally reacting liner on the duct interior. Using potential theory, the BVP is recast as a system of hypersingular boundary integral equations with subsidiary conditions. We describe the integral equation derivation and solution procedure in detail. The development of the computationally efficient ducted fan noise prediction program TBIEM3D, which implements the BIEM, and its utility in conducting parametric noise reduction studies are discussed. Unlike prediction methods based on spinning mode eigenfunction expansions, the BIEM does not require the decomposition of the interior acoustic field into its radial and axial components which, for the liner case, avoids the solution of a difficult complex eigenvalue problem. Numerical spectral studies are presented to illustrate the nexus between the eigenfunction expansion representation and BIEM results. We demonstrate BIEM liner capability by examining radiation patterns for several cases of practical interest.

Yang-Baxter maps, discrete integrable equations and quantum groups

NASA Astrophysics Data System (ADS)

Bazhanov, Vladimir V.; Sergeev, Sergey M.

2018-01-01

For every quantized Lie algebra there exists a map from the tensor square of the algebra to itself, which by construction satisfies the set-theoretic Yang-Baxter equation. This map allows one to define an integrable discrete quantum evolution system on quadrilateral lattices, where local degrees of freedom (dynamical variables) take values in a tensor power of the quantized Lie algebra. The corresponding equations of motion admit the zero curvature representation. The commuting Integrals of Motion are defined in the standard way via the Quantum Inverse Problem Method, utilizing Baxter's famous commuting transfer matrix approach. All elements of the above construction have a meaningful quasi-classical limit. As a result one obtains an integrable discrete Hamiltonian evolution system, where the local equation of motion are determined by a classical Yang-Baxter map and the action functional is determined by the quasi-classical asymptotics of the universal R-matrix of the underlying quantum algebra. In this paper we present detailed considerations of the above scheme on the example of the algebra Uq (sl (2)) leading to discrete Liouville equations, however the approach is rather general and can be applied to any quantized Lie algebra.

A new method for true and spurious eigensolutions of arbitrary cavities using the combined Helmholtz exterior integral equation formulation method.

PubMed

Chen, I L; Chen, J T; Kuo, S R; Liang, M T

2001-03-01

Integral equation methods have been widely used to solve interior eigenproblems and exterior acoustic problems (radiation and scattering). It was recently found that the real-part boundary element method (BEM) for the interior problem results in spurious eigensolutions if the singular (UT) or the hypersingular (LM) equation is used alone. The real-part BEM results in spurious solutions for interior problems in a similar way that the singular integral equation (UT method) results in fictitious solutions for the exterior problem. To solve this problem, a Combined Helmholtz Exterior integral Equation Formulation method (CHEEF) is proposed. Based on the CHEEF method, the spurious solutions can be filtered out if additional constraints from the exterior points are chosen carefully. Finally, two examples for the eigensolutions of circular and rectangular cavities are considered. The optimum numbers and proper positions for selecting the points in the exterior domain are analytically studied. Also, numerical experiments were designed to verify the analytical results. It is worth pointing out that the nodal line of radiation mode of a circle can be rotated due to symmetry, while the nodal line of the rectangular is on a fixed position.

On the integrable elliptic cylindrical Kadomtsev-Petviashvili equation.

PubMed

Khusnutdinova, K R; Klein, C; Matveev, V B; Smirnov, A O

2013-03-01

There exist two versions of the Kadomtsev-Petviashvili (KP) equation, related to the Cartesian and cylindrical geometries of the waves. In this paper, we derive and study a new version, related to the elliptic cylindrical geometry. The derivation is given in the context of surface waves, but the derived equation is a universal integrable model applicable to generic weakly nonlinear weakly dispersive waves. We also show that there exist nontrivial transformations between all three versions of the KP equation associated with the physical problem formulation, and use them to obtain new classes of approximate solutions for water waves.

Open groups of constraints. Integrating arbitrary involutions

NASA Astrophysics Data System (ADS)

Batalin, Igor; Marnelius, Robert

1998-11-01

A new type of quantum master equation is presented which is expressed in terms of a recently introduced quantum antibracket. The equation involves only two operators: an extended nilpotent BFV-BRST charge and an extended ghost charge. It is proposed to determine the generalized quantum Maurer-Cartan equations for arbitrary open groups. These groups are the integration of constraints in arbitrary involutions. The only condition for this is that the constraint operators may be embedded in an odd nilpotent operator, the BFV-BRST charge. The proposal is verified at the quasigroup level. The integration formulas are also used to construct a generating operator for quantum antibrackets of operators in arbitrary involutions.

Pseudodynamic systems approach based on a quadratic approximation of update equations for diffuse optical tomography.

PubMed

Biswas, Samir Kumar; Kanhirodan, Rajan; Vasu, Ram Mohan; Roy, Debasish

2011-08-01

We explore a pseudodynamic form of the quadratic parameter update equation for diffuse optical tomographic reconstruction from noisy data. A few explicit and implicit strategies for obtaining the parameter updates via a semianalytical integration of the pseudodynamic equations are proposed. Despite the ill-posedness of the inverse problem associated with diffuse optical tomography, adoption of the quadratic update scheme combined with the pseudotime integration appears not only to yield higher convergence, but also a muted sensitivity to the regularization parameters, which include the pseudotime step size for integration. These observations are validated through reconstructions with both numerically generated and experimentally acquired data.

A study of numerical methods of solution of the equations of motion of a controlled satellite under the influence of gravity gradient torque

NASA Technical Reports Server (NTRS)

Thompson, J. F.; Mcwhorter, J. C.; Siddiqi, S. A.; Shanks, S. P.

1973-01-01

Numerical methods of integration of the equations of motion of a controlled satellite under the influence of gravity-gradient torque are considered. The results of computer experimentation using a number of Runge-Kutta, multi-step, and extrapolation methods for the numerical integration of this differential system are presented, and particularly efficient methods are noted. A large bibliography of numerical methods for initial value problems for ordinary differential equations is presented, and a compilation of Runge-Kutta and multistep formulas is given. Less common numerical integration techniques from the literature are noted for further consideration.

A numerical scheme to solve unstable boundary value problems

NASA Technical Reports Server (NTRS)

Kalnay Derivas, E.

1975-01-01

A new iterative scheme for solving boundary value problems is presented. It consists of the introduction of an artificial time dependence into a modified version of the system of equations. Then explicit forward integrations in time are followed by explicit integrations backwards in time. The method converges under much more general conditions than schemes based in forward time integrations (false transient schemes). In particular it can attain a steady state solution of an elliptical system of equations even if the solution is unstable, in which case other iterative schemes fail to converge. The simplicity of its use makes it attractive for solving large systems of nonlinear equations.

Integrable discretisations for a class of nonlinear Schrödinger equations on Grassmann algebras

NASA Astrophysics Data System (ADS)

Grahovski, Georgi G.; Mikhailov, Alexander V.

2013-12-01

Integrable discretisations for a class of coupled (super) nonlinear Schrödinger (NLS) type of equations are presented. The class corresponds to a Lax operator with entries in a Grassmann algebra. Elementary Darboux transformations are constructed. As a result, Grassmann generalisations of the Toda lattice and the NLS dressing chain are obtained. The compatibility (Bianchi commutativity) of these Darboux transformations leads to integrable Grassmann generalisations of the difference Toda and NLS equations. The resulting systems will have discrete Lax representations provided by the set of two consistent elementary Darboux transformations. For the two discrete systems obtained, initial value and initial-boundary problems are formulated.

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

Thompson, S.

This report describes the use of several subroutines from the CORLIB core mathematical subroutine library for the solution of a model fluid flow problem. The model consists of the Euler partial differential equations. The equations are spatially discretized using the method of pseudo-characteristics. The resulting system of ordinary differential equations is then integrated using the method of lines. The stiff ordinary differential equation solver LSODE (2) from CORLIB is used to perform the time integration. The non-stiff solver ODE (4) is used to perform a related integration. The linear equation solver subroutines DECOMP and SOLVE are used to solve linearmore » systems whose solutions are required in the calculation of the time derivatives. The monotone cubic spline interpolation subroutines PCHIM and PCHFE are used to approximate water properties. The report describes the use of each of these subroutines in detail. It illustrates the manner in which modules from a standard mathematical software library such as CORLIB can be used as building blocks in the solution of complex problems of practical interest. 9 refs., 2 figs., 4 tabs.« less

The aerodynamics of propellers and rotors using an acoustic formulation in the time domain

NASA Technical Reports Server (NTRS)

Long, L. N.

1983-01-01

The aerodynamics of propellers and rotors is especially complicated because of the highly three-dimensional and compressible nature of the flow field. However, in linearized theory the problem is governed by the wave equation, and a numerically-efficient integral formulation can be derived. This reduces the problem from one in space to one over a surface. Many such formulations exist in the aeroacoustics literature, but these become singular integral equations if one naively tries to use them to predict surface pressures, i.e., for aerodynamics. The present paper illustrates how one must interpret these equations in order to obtain nonambiguous results. After the regularized form of the integral equation is derived, a method for solving it numerically is described. This preliminary computer code uses Legendre-Gaussian quadrature to solve the equation. Numerical results are compared to experimental results for ellipsoids, wings, and rotors, including effects due to lift. Compressibility and the farfield boundary conditions are satisfied automatically using this method.

Numerical solution of the quantum Lenard-Balescu equation for a non-degenerate one-component plasma

DOE PAGES

Scullard, Christian R.; Belt, Andrew P.; Fennell, Susan C.; ...

2016-09-01

We present a numerical solution of the quantum Lenard-Balescu equation using a spectral method, namely an expansion in Laguerre polynomials. This method exactly conserves both particles and kinetic energy and facilitates the integration over the dielectric function. To demonstrate the method, we solve the equilibration problem for a spatially homogeneous one-component plasma with various initial conditions. Unlike the more usual Landau/Fokker-Planck system, this method requires no input Coulomb logarithm; the logarithmic terms in the collision integral arise naturally from the equation along with the non-logarithmic order-unity terms. The spectral method can also be used to solve the Landau equation andmore » a quantum version of the Landau equation in which the integration over the wavenumber requires only a lower cutoff. We solve these problems as well and compare them with the full Lenard-Balescu solution in the weak-coupling limit. Finally, we discuss the possible generalization of this method to include spatial inhomogeneity and velocity anisotropy.« less

K(m, n) equations with fifth order symmetries and their integrability

NASA Astrophysics Data System (ADS)

Tian, Kai

2018-03-01

For K(m, n) equation ut =Dx3(un) + αDx(um) , all non-degenerate (n ≠ 0) cases admitting fifth order symmetries are identified, including K(m1, 1), K(m2 , - 1 / 2) and K(m3 , - 2) , where m1 = 0 , 1 , 2 , 3 , m2 = - 1 / 2 , 0 , 1 , 3 / 2 and m3 = - 2 , - 1 , 0 , 1 . For five less studied cases, namely K(0 , - 2) , K(- 1 , - 2) , K(- 2 , - 2) , K(- 1 / 2 , - 1 / 2) and K(3 / 2 , - 1 / 2) , bi-Hamiltonian structures are established through their invertible links with some famous integrable equations. Hence, all cases, having fifth order symmetries, of K(m, n) equation are integrable in the bi-Hamiltonian sense. As an interesting observation, their Hamiltonian operators are linearly combinations of Dx, Dx3 , uDx +Dx u and Dx u Dx-1uDx, basic ingredients in the bi-Hamiltonian theory of Korteweg-de Vries and modified Korteweg-de Vries equations.

Vertically Integrated Models for Carbon Storage Modeling in Heterogeneous Domains

NASA Astrophysics Data System (ADS)

Bandilla, K.; Celia, M. A.

2017-12-01

Numerical modeling is an essential tool for studying the impacts of geologic carbon storage (GCS). Injection of carbon dioxide (CO2) into deep saline aquifers leads to multi-phase flow (injected CO2 and resident brine), which can be described by a set of three-dimensional governing equations, including mass-balance equation, volumetric flux equations (modified Darcy), and constitutive equations. This is the modeling approach on which commonly used reservoir simulators such as TOUGH2 are based. Due to the large density difference between CO2 and brine, GCS models can often be simplified by assuming buoyant segregation and integrating the three-dimensional governing equations in the vertical direction. The integration leads to a set of two-dimensional equations coupled with reconstruction operators for vertical profiles of saturation and pressure. Vertically-integrated approaches have been shown to give results of comparable quality as three-dimensional reservoir simulators when applied to realistic CO2 injection sites such as the upper sand wedge at the Sleipner site. However, vertically-integrated approaches usually rely on homogeneous properties over the thickness of a geologic layer. Here, we investigate the impact of general (vertical and horizontal) heterogeneity in intrinsic permeability, relative permeability functions, and capillary pressure functions. We consider formations involving complex fluvial deposition environments and compare the performance of vertically-integrated models to full three-dimensional models for a set of hypothetical test cases consisting of high permeability channels (streams) embedded in a low permeability background (floodplains). The domains are randomly generated assuming that stream channels can be represented by sinusoidal waves in the plan-view and by parabolas for the streams' cross-sections. Stream parameters such as width, thickness and wavelength are based on values found at the Ketzin site in Germany. Results from the vertically-integrated approach are compared to results using TOUGH2, both in terms of depth-averaged saturation and vertical saturation profiles.

Integral equation methods for computing likelihoods and their derivatives in the stochastic integrate-and-fire model.

PubMed

Paninski, Liam; Haith, Adrian; Szirtes, Gabor

2008-02-01

We recently introduced likelihood-based methods for fitting stochastic integrate-and-fire models to spike train data. The key component of this method involves the likelihood that the model will emit a spike at a given time t. Computing this likelihood is equivalent to computing a Markov first passage time density (the probability that the model voltage crosses threshold for the first time at time t). Here we detail an improved method for computing this likelihood, based on solving a certain integral equation. This integral equation method has several advantages over the techniques discussed in our previous work: in particular, the new method has fewer free parameters and is easily differentiable (for gradient computations). The new method is also easily adaptable for the case in which the model conductance, not just the input current, is time-varying. Finally, we describe how to incorporate large deviations approximations to very small likelihoods.

Hamiltonian structure of real Monge - Ampère equations

NASA Astrophysics Data System (ADS)

Nutku, Y.

1996-06-01

The variational principle for the real homogeneous Monge - Ampère equation in two dimensions is shown to contain three arbitrary functions of four variables. There exist two different specializations of this variational principle where the Lagrangian is degenerate and furthermore contains an arbitrary function of two variables. The Hamiltonian formulation of these degenerate Lagrangian systems requires the use of Dirac's theory of constraints. As in the case of most completely integrable systems the constraints are second class and Dirac brackets directly yield the Hamiltonian operators. Thus the real homogeneous Monge - Ampère equation in two dimensions admits two classes of infinitely many Hamiltonian operators, namely a family of local, as well as another family non-local Hamiltonian operators and symplectic 2-forms which depend on arbitrary functions of two variables. The simplest non-local Hamiltonian operator corresponds to the Kac - Moody algebra of vector fields and functions on the unit circle. Hamiltonian operators that belong to either class are compatible with each other but between classes there is only one compatible pair. In the case of real Monge - Ampère equations with constant right-hand side this compatible pair is the only pair of Hamiltonian operators that survives. Then the complete integrability of all these real Monge - Ampère equations follows by Magri's theorem. Some of the remarkable properties we have obtained for the Hamiltonian structure of the real homogeneous Monge - Ampère equation in two dimensions turn out to be generic to the real homogeneous Monge - Ampère equation and the geodesic flow for the complex homogeneous Monge - Ampère equation in arbitrary number of dimensions. Hence among all integrable nonlinear evolution equations in one space and one time dimension, the real homogeneous Monge - Ampère equation is distinguished as one that retains its character as an integrable system in multiple dimensions.

AN INTEGRAL EQUATION REPRESENTATION OF WIDE-BAND ELECTROMAGNETIC SCATTERING BY THIN SHEETS

EPA Science Inventory

An efficient, accurate numerical modeling scheme has been developed, based on the integral equation solution to compute electromagnetic (EM) responses of thin sheets over a wide frequency band. The thin-sheet approach is useful for simulating the EM response of a fracture system ...

Separation of variables in the special diagonal Hamilton-Jacobi equation: Application to the dynamical problem of a particle constrained on a moving surface

NASA Technical Reports Server (NTRS)

Blanchard, D. L.; Chan, F. K.

1973-01-01

For a time-dependent, n-dimensional, special diagonal Hamilton-Jacobi equation a necessary and sufficient condition for the separation of variables to yield a complete integral of the form was established by specifying the admissible forms in terms of arbitrary functions. A complete integral was then expressed in terms of these arbitrary functions and also the n irreducible constants. As an application of the results obtained for the two-dimensional Hamilton-Jacobi equation, analysis was made for a comparatively wide class of dynamical problems involving a particle moving in Euclidean three-dimensional space under the action of external forces but constrained on a moving surface. All the possible cases in which this equation had a complete integral of the form were obtained and these are tubulated for reference.

The Baseball Hall of Fame Is Not the Kiss of Death

ERIC Educational Resources Information Center

Smith, Gary

2011-01-01

E. Abel and M. Kruger (2005) reported that the median life expectancy of Major League Baseball players after election to the Baseball Hall of Fame is 5 years shorter than that of players of the same age who are not elected to the Hall of Fame. This conclusion is surprising because there is no compelling explanation for such a dramatic reduction in…

A Cross-Cultural Assessment of Three Theories of Pro-Environmental Behavior: A Comparison between Business Students of Chile and the United States

ERIC Educational Resources Information Center

Cordano, Mark; Welcomer, Stephanie; Scherer, Robert F.; Pradenas, Lorena; Parada, Victor

2011-01-01

We surveyed business students in the United States (n = 256) and Chile (n = 310) to compare three theories of pro-environmental behavior.We examined Ajzen and Fishbein's theory of reasoned action, Schawartz's norm activation theory, and the values-beliefs-norms theory created by Stern, Dietz, Abel, Guagnano, and Kalof. We produced reliable…