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Sixth-order Compact Extended Trapezoidal Rules for 2D Schr(o)dinger Equation

数学研究 2015年第1期48卷 30-52页

作者： Xiao-Hui Liu Yu-Jiang Wu Jin-Yun Yuan Raimundo J.B.de Sampaio Yan-Tao Wang School of Mathematics and Statistics Lanzhou University Lanzhou 730000 GansuP.R.China School of Mathematics and Statistics Lanzhou University Lanzhou 730000 GansuP.R.China Key Laboratory of Applied Mathematics and Complex Systems Lanzhou 730000Gansu P.R.China Department of Mathematics Federal University of Paraná Centro Politecnico CP:19.081 81531-980 Curitiba PR Brazil Graduate Program in Production and Systems Engineering Pontifical Catholic University of Paraná CEP: 81611-970 Curitiba PR Brazil

Based on high-order linear multistep methods (LMMs), we use the class of extended trapezoidal rules (ETRs) to solve boundary value problems of ordinary differential equations (ODEs), whose numerical solutions can be approximated by boundary value methods (BVMs). Then we combine this technique with fourth-order Padé compact approximation to discrete 2D Schrödinger equation. We propose a scheme with sixth-order accuracy in time and fourth-order accuracy in space. It is unconditionally stable due to the favourable property of BVMs and ETRs. Furthermore, with Richardson extrapolation, we can increase the scheme to order 6 accuracy both in time and space. Numerical results are presented to illustrate the accuracy of our scheme.

关键词： Schr(o)dinger equation BVMs ETRs compact scheme Richardson extrapolation

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Absolute change pivot rule for the simplex algorithm

Absolute change pivot rule for the simplex algorithm

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International MultiConference of Engineers and Computer Scientists, IMECS 2014

作者： Chankong, Kittiphong Intiyot, Boonyarit Sinapiromsaran, Krung Applied Mathematics and Computational Science Program Department of Mathematics and Computer Science Faculty of Science Chulalongkorn University Bangkok Thailand

ISBN: (纸本)9789881925336

The simplex algorithm is a widely used method for solving a linear programming problem (LP) which is first presented by George B. Dantzig. One of the important steps of the simplex algorithm is applying an appropriate pivot rule, the rule to select the entering variable. An effective pivot rule can lead to the optimal solution of LP with the small number of iterations. In a minimization problem, Dantzig's pivot rule selects an entering variable corresponding to the most negative reduced cost. The concept is to have the maximum improvement in the objective value per unit step of the entering variable. However, in some problems, Dantzig's rule may visit a large number of extreme points before reaching the optimal solution. In this paper, we propose a pivot rule that could reduce the number of such iterations over the Dantzig's pivot rule. The idea is to have the maximum improvement in the objective value function by trying to block a leaving variable that makes a little change in the objective function value as much as possible. Then we test and compare the efficacy of this rule with Dantzig' original rule.

关键词： Linear programming

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Upper limits on the isotropic gravitational-wave background from Advanced LIGO and Advanced Virgo’s third observing run

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Physical Review D 2021年第2期104卷 022004-022004页

作者： R. Abbott T. D. Abbott S. Abraham F. Acernese K. Ackley A. Adams C. Adams R. X. Adhikari V. B. Adya C. Affeldt D. Agarwal M. Agathos K. Agatsuma N. Aggarwal O. D. Aguiar L. Aiello A. Ain T. Akutsu K. M. Aleman G. Allen A. Allocca P. A. Altin A. Amato S. Anand A. Ananyeva S. B. Anderson W. G. Anderson M. Ando S. V. Angelova S. Ansoldi J. M. Antelis S. Antier S. Appert Koya Arai Koji Arai Y. Arai S. Araki A. Araya M. C. Araya J. S. Areeda M. Arène N. Aritomi N. Arnaud S. M. Aronson H. Asada Y. Asali G. Ashton Y. Aso S. M. Aston P. Astone F. Aubin P. Aufmuth K. AultONeal C. Austin S. Babak F. Badaracco M. K. M. Bader S. Bae Y. Bae A. M. Baer S. Bagnasco Y. Bai L. Baiotti J. Baird R. Bajpai M. Ball G. Ballardin S. W. Ballmer M. Bals A. Balsamo G. Baltus S. Banagiri D. Bankar R. S. Bankar J. C. Barayoga C. Barbieri B. C. Barish D. Barker P. Barneo S. Barnum F. Barone B. Barr L. Barsotti M. Barsuglia D. Barta J. Bartlett M. A. Barton I. Bartos R. Bassiri A. Basti M. Bawaj J. C. Bayley A. C. Baylor M. Bazzan B. Bécsy V. M. Bedakihale M. Bejger I. Belahcene V. Benedetto D. Beniwal M. G. Benjamin T. F. Bennett J. D. Bentley M. BenYaala F. Bergamin B. K. Berger S. Bernuzzi D. Bersanetti A. Bertolini J. Betzwieser R. Bhandare A. V. Bhandari D. Bhattacharjee S. Bhaumik J. Bidler I. A. Bilenko G. Billingsley R. Birney O. Birnholtz S. Biscans M. Bischi S. Biscoveanu A. Bisht B. Biswas M. Bitossi M.-A. Bizouard J. K. Blackburn J. Blackman C. D. Blair D. G. Blair R. M. Blair F. Bobba N. Bode M. Boer G. Bogaert M. Boldrini F. Bondu E. Bonilla R. Bonnand P. Booker B. A. Boom R. Bork V. Boschi N. Bose S. Bose V. Bossilkov V. Boudart Y. Bouffanais A. Bozzi C. Bradaschia P. R. Brady A. Bramley A. Branch M. Branchesi J. E. Brau M. Breschi T. Briant J. H. Briggs A. Brillet M. Brinkmann P. Brockill A. F. Brooks J. Brooks D. D. Brown S. Brunett G. Bruno R. Bruntz J. Bryant A. Buikema T. Bulik H. J. Bulten A. Buonanno R. Buscicchio D. Buskulic R. L. Byer L. Cadonati M. Caesar G. Cagnoli C. Cahillane H. W. Cain, III J. Calderón Bustillo J. LIGO Laboratory California Institute of Technology Pasadena California 91125 USA Louisiana State University Baton Rouge Louisiana 70803 USA Inter-University Centre for Astronomy and Astrophysics Pune 411007 India Dipartimento di Farmacia Università di Salerno I-84084 Fisciano Salerno Italy INFN Sezione di Napoli Complesso Universitario di Monte S. Angelo I-80126 Napoli Italy OzGrav School of Physics & Astronomy Monash University Clayton 3800 Victoria Australia Christopher Newport University Newport News Virginia 23606 USA LIGO Livingston Observatory Livingston Louisiana 70754 USA OzGrav Australian National University Canberra Australian Capital Territory 0200 Australia Max Planck Institute for Gravitational Physics (Albert Einstein Institute) D-30167 Hannover Germany Leibniz Universität Hannover D-30167 Hannover Germany University of Cambridge Cambridge CB2 1TN United Kingdom Theoretisch-Physikalisches Institut Friedrich-Schiller-Universität Jena D-07743 Jena Germany University of Birmingham Birmingham B15 2TT United Kingdom Center for Interdisciplinary Exploration & Research in Astrophysics (CIERA) Northwestern University Evanston Illinois 60208 USA Instituto Nacional de Pesquisas Espaciais 12227-010 São José dos Campos São Paulo Brazil Gravity Exploration Institute Cardiff University Cardiff CF24 3AA United Kingdom Gran Sasso Science Institute (GSSI) I-67100 L’Aquila Italy INFN Laboratori Nazionali del Gran Sasso I-67100 Assergi Italy INFN Sezione di Pisa I-56127 Pisa Italy Università di Pisa I-56127 Pisa Italy Gravitational Wave Science Project National Astronomical Observatory of Japan (NAOJ) Mitaka City Tokyo 181-8588 Japan Advanced Technology Center National Astronomical Observatory of Japan (NAOJ) Mitaka City Tokyo 181-8588 Japan California State University Fullerton Fullerton California 92831 USA NCSA University of Illinois at Urbana-Champaign Urbana Illinois 61801 USA Università di Napoli “Federico II” Complesso Universitario

We report results of a search for an isotropic gravitational-wave background (GWB) using data from Advanced LIGO’s and Advanced Virgo’s third observing run (O3) combined with upper limits from the earlier O1 and O2 runs. Unlike in previous observing runs in the advanced detector era, we include Virgo in the search for the GWB. The results of the search are consistent with uncorrelated noise, and therefore we place upper limits on the strength of the GWB. We find that the dimensionless energy density ΩGW≤5.8×10−9 at the 95% credible level for a flat (frequency-independent) GWB, using a prior which is uniform in the log of the strength of the GWB, with 99% of the sensitivity coming from the band 20–76.6 Hz; ΩGW(f)≤3.4×10−9 at 25 Hz for a power-law GWB with a spectral index of 2/3 (consistent with expectations for compact binary coalescences), in the band 20–90.6 Hz; and ΩGW(f)≤3.9×10−10 at 25 Hz for a spectral index of 3, in the band 20–291.6 Hz. These upper limits improve over our previous results by a factor of 6.0 for a flat GWB, 8.8 for a spectral index of 2/3, and 13.1 for a spectral index of 3. We also search for a GWB arising from scalar and vector modes, which are predicted by alternative theories of gravity; we do not find evidence of these, and place upper limits on the strength of GWBs with these polarizations. We demonstrate that there is no evidence of correlated noise of magnetic origin by performing a Bayesian analysis that allows for the presence of both a GWB and an effective magnetic background arising from geophysical Schumann resonances. We compare our upper limits to a fiducial model for the GWB from the merger of compact binaries, updating the model to use the most recent data-driven population inference from the systems detected during O3a. Finally, we combine our results with observations of individual mergers and show that, at design sensitivity, this joint approach may yield stronger constraints on the merger rate of binary black holes at z≳2

关键词： Gravitational wave detection

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All-sky search for continuous gravitational waves from isolated neutron stars in the early O3 LIGO data

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Physical Review D 2021年第8期104卷 082004-082004页

作者： R. Abbott T. D. Abbott S. Abraham F. Acernese K. Ackley A. Adams C. Adams R. X. Adhikari V. B. Adya C. Affeldt D. Agarwal M. Agathos K. Agatsuma N. Aggarwal O. D. Aguiar L. Aiello A. Ain P. Ajith T. Akutsu K. M. Aleman G. Allen A. Allocca P. A. Altin A. Amato S. Anand A. Ananyeva S. B. Anderson W. G. Anderson M. Ando S. V. Angelova S. Ansoldi J. M. Antelis S. Antier S. Appert Koya Arai Koji Arai Y. Arai S. Araki A. Araya M. C. Araya J. S. Areeda M. Arène N. Aritomi N. Arnaud S. M. Aronson H. Asada Y. Asali G. Ashton Y. Aso S. M. Aston P. Astone F. Aubin P. Aufmuth K. AultONeal C. Austin S. Babak F. Badaracco M. K. M. Bader S. Bae Y. Bae A. M. Baer S. Bagnasco Y. Bai L. Baiotti J. Baird R. Bajpai M. Ball G. Ballardin S. W. Ballmer M. Bals A. Balsamo G. Baltus S. Banagiri D. Bankar R. S. Bankar J. C. Barayoga C. Barbieri B. C. Barish D. Barker P. Barneo F. Barone B. Barr L. Barsotti M. Barsuglia D. Barta J. Bartlett M. A. Barton I. Bartos R. Bassiri A. Basti M. Bawaj J. C. Bayley A. C. Baylor M. Bazzan B. Bécsy V. M. Bedakihale M. Bejger I. Belahcene V. Benedetto D. Beniwal M. G. Benjamin T. F. Bennett J. D. Bentley M. BenYaala F. Bergamin B. K. Berger S. Bernuzzi D. Bersanetti A. Bertolini J. Betzwieser R. Bhandare A. V. Bhandari D. Bhattacharjee S. Bhaumik J. Bidler I. A. Bilenko G. Billingsley R. Birney O. Birnholtz S. Biscans M. Bischi S. Biscoveanu A. Bisht B. Biswas M. Bitossi M.-A. Bizouard J. K. Blackburn J. Blackman C. D. Blair D. G. Blair R. M. Blair F. Bobba N. Bode M. Boer G. Bogaert M. Boldrini F. Bondu E. Bonilla R. Bonnand P. Booker B. A. Boom R. Bork V. Boschi N. Bose S. Bose V. Bossilkov V. Boudart Y. Bouffanais A. Bozzi C. Bradaschia P. R. Brady A. Bramley A. Branch M. Branchesi J. E. Brau M. Breschi T. Briant J. H. Briggs A. Brillet M. Brinkmann P. Brockill A. F. Brooks J. Brooks D. D. Brown S. Brunett G. Bruno R. Bruntz J. Bryant A. Buikema T. Bulik H. J. Bulten A. Buonanno R. Buscicchio D. Buskulic R. L. Byer L. Cadonati M. Caesar G. Cagnoli C. Cahillane H. W. Cain, III J. Calderón Bustillo J. LIGO Laboratory California Institute of Technology Pasadena California 91125 USA Louisiana State University Baton Rouge Louisiana 70803 USA Inter-University Centre for Astronomy and Astrophysics Pune 411007 India Dipartimento di Farmacia Università di Salerno I-84084 Fisciano Salerno Italy INFN Sezione di Napoli Complesso Universitario di Monte S.Angelo I-80126 Napoli Italy OzGrav School of Physics and Astronomy Monash University Clayton 3800 Victoria Australia Christopher Newport University Newport News Virginia 23606 USA LIGO Livingston Observatory Livingston Louisiana 70754 USA OzGrav Australian National University Canberra Australian Capital Territory 0200 Australia Max Planck Institute for Gravitational Physics (Albert Einstein Institute) D-30167 Hannover Germany Leibniz Universität Hannover D-30167 Hannover Germany University of Cambridge Cambridge CB2 1TN United Kingdom Theoretisch-Physikalisches Institut Friedrich-Schiller-Universität Jena D-07743 Jena Germany University of Birmingham Birmingham B15 2TT United Kingdom Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA) Northwestern University Evanston Illinois 60208 USA Instituto Nacional de Pesquisas Espaciais 12227-010 São José dos Campos São Paulo Brazil Gravity Exploration Institute Cardiff University Cardiff CF24 3AA United Kingdom Gran Sasso Science Institute (GSSI) I-67100 L’Aquila Italy INFN Laboratori Nazionali del Gran Sasso I-67100 Assergi Italy INFN Sezione di Pisa I-56127 Pisa Italy Università di Pisa I-56127 Pisa Italy International Centre for Theoretical Sciences Tata Institute of Fundamental Research Bengaluru 560089 India Gravitational Wave Science Project National Astronomical Observatory of Japan (NAOJ) Mitaka City Tokyo 181-8588 Japan Advanced Technology Center National Astronomical Observatory of Japan (NAOJ) Mitaka City Tokyo 181-8588 Japan California State University Fullerton Fullerton California 92831 USA NCSA University of Illi

We report on an all-sky search for continuous gravitational waves in the frequency band 20–2000 Hz and with a frequency time derivative in the range of [−1.0,+0.1]×10−8 Hz/s. Such a signal could be produced by a nearby, spinning and slightly nonaxisymmetric isolated neutron star in our Galaxy. This search uses the LIGO data from the first six months of Advanced LIGO’s and Advanced Virgo’s third observational run, O3. No periodic gravitational wave signals are observed, and 95% confidence-level (C.L.) frequentist upper limits are placed on their strengths. The lowest upper limits on worst-case (linearly polarized) strain amplitude h0 are ∼1.7×10−25 near 200 Hz. For a circularly polarized source (most favorable orientation), the lowest upper limits are ∼6.3×10−26. These strict frequentist upper limits refer to all sky locations and the entire range of frequency derivative values. For a population-averaged ensemble of sky locations and stellar orientations, the lowest 95% C.L. upper limits on the strain amplitude are ∼1.4×10−25. These upper limits improve upon our previously published all-sky results, with the greatest improvement (factor of ∼2) seen at higher frequencies, in part because quantum squeezing has dramatically improved the detector noise level relative to the second observational run, O2. These limits are the most constraining to date over most of the parameter space searched.

关键词： Astrophysical studies of gravity Gravitational wave detection Gravitational wave sources Gravitational waves

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Open Data from the Third Observing Run of LIGO, Virgo, KAGRA, and GEO

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Astrophysical Journal, Supplement Series 2023年第2期267卷 29-29页

作者： Abbott, R. Abe, H. Acernese, F. Ackley, K. Adhicary, S. Adhikari, N. Adhikari, R.X. Adkins, V.K. Adya, V.B. Affeldt, C. Agarwal, D. Agathos, M. Aguiar, O.D. Aiello, L. Ain, A. Ajith, P. Akutsu, T. Albanesi, S. Alfaidi, R.A. Al-Jodah, A. Alléné, C. Allocca, A. Almualla, M. Altin, P.A. Amato, A. Amez-Droz, L. Amorosi, A. Anand, S. Ananyeva, A. Andersen, R. Anderson, S.B. Anderson, W.G. Andia, M. Ando, M. Andrade, T. Andres, N. Andrés-Carcasona, M. Andrić, T. Ansoldi, S. Antelis, J.M. Antier, S. Aoumi, M. Apostolatos, T. Appavuravther, E.Z. Appert, S. Apple, S.K. Arai, K. Araya, A. Araya, M.C. Areeda, J.S. Arène, M. Aritomi, N. Arnaud, N. Arogeti, M. Aronson, S.M. Arun, K.G. Asada, H. Ashton, G. Aso, Y. Assiduo, M. Assis de Souza Melo, S. Aston, S.M. Astone, P. Aubin, F. AultONeal, K. Babak, S. Badalyan, A. Badaracco, F. Badger, C. Bae, S. Bagnasco, S. Bai, Y. Baier, J.G. Baiotti, L. Baird, J. Bajpai, R. Baka, T. Ball, M. Ballardin, G. Ballmer, S.W. Baltus, G. Banagiri, S. Banerjee, B. Bankar, D. Baral, P. Barayoga, J.C. Barber, J. Barish, B.C. Barker, D. Barneo, P. Barone, F. Barr, B. Barsotti, L. Barsuglia, M. Barta, D. Barthelmy, S.D. Barton, M.A. Bartos, I. Basak, S. Basalaev, A. Bassiri, R. Basti, A. Bawaj, M. Bayley, J.C. Baylor, A.C. Bazzan, M. Bécsy, B. Bedakihale, V.M. Beirnaert, F. Bejger, M. Bell, A.S. Benedetto, V. Beniwal, D. Benoit, W. Bentley, J.D. Ben Yaala, M. Bera, S. Berbel, M. Bergamin, F. Berger, B.K. Bernuzzi, S. Beroiz, M. Berry, C.P.L. Bersanetti, D. Bertolini, A. Betzwieser, J. Beveridge, D. Bevins, N. Bhandare, R. Bhandari, A.V. Bhardwaj, U. Bhatt, R. Bhattacharjee, D. Bhaumik, S. Bianchi, A. Bilenko, I.A. Bilicki, M. Billingsley, G. Bini, S. Birnholtz, O. Biscans, S. Bischi, M. Biscoveanu, S. Bisht, A. Biswas, B. Bitossi, M. Bizouard, M.-A. Blackburn, J.K. Blair, C.D. Blair, D.G. Blair, R.M. Bobba, F. Bode, N. Boër, M. Bogaert, G. Boileau, G. Boldrini, M. Bolingbroke, G.N. Bonavena, L.D. Bondarescu, R. Bondu, F. Bonilla, E. Bonilla, G.S. Bonnand, R. Booker, P. Bork, R. Boschi, V. Bose, N. LIGO Laboratory California Institute of Technology Pasadena 91125 CA United States Graduate School of Science Tokyo Institute of Technology 2-12-1 Ookayama Meguro-ku Tokyo 152-8551 Japan Dipartimento di Farmacia Università di Salerno Salerno Fisciano I-84084 Italy INFN Sezione di Napoli Napoli I-80126 Italy OzGrav School of Physics & Astronomy Monash University Clayton 3800 VIC Australia The Pennsylvania State University University Park 16802 PA United States University of Wisconsin-Milwaukee Milwaukee 53201 WI United States Louisiana State University Baton Rouge 70803 LA United States OzGrav Australian National University Canberra 0200 ACT Australia Max Planck Institute for Gravitational Physics (Albert Einstein Institute) Hannover D-30167 Germany Leibniz Universität Hannover Hannover D-30167 Germany Inter-University Centre for Astronomy and Astrophysics Pune 411007 India University of Cambridge Cambridge CB2 1TN United Kingdom Instituto Nacional de Pesquisas Espaciais São Paulo São José dos Campos 12227-010 Brazil Cardiff University Cardiff CF24 3AA United Kingdom INFN Sezione di Pisa Pisa I-56127 Italy International Centre for Theoretical Sciences Tata Institute of Fundamental Research Bengaluru 560089 India Gravitational Wave Science Project National Astronomical Observatory of Japan 2-21-1 Osawa Mitaka City Tokyo 181-8588 Japan Advanced Technology Center National Astronomical Observatory of Japan 2-21-1 Osawa Mitaka City Tokyo 181-8588 Japan Dipartimento di Fisica Università degli Studi di Torino Torino I-10125 Italy INFN Sezione di Torino Torino I-10125 Italy SUPA University of Glasgow Glasgow G12 8QQ United Kingdom OzGrav University of Western Australia Crawley 6009 WA Australia Univ. Savoie Mont Blanc CNRS Laboratoire d'Annecy de Physique des Particules - IN2P3 Annecy F-74000 France Università di Napoli “Federico II” Napoli I-80126 Italy University of Minnesota Minneapolis 55455 MN United States M

The global network of gravitational-wave observatories now includes five detectors, namely LIGO Hanford, LIGO Livingston, Virgo, KAGRA, and GEO 600. These detectors collected data during their third observing run, O3, composed of three phases: O3a starting in 2019 April and lasting six months, O3b starting in 2019 November and lasting five months, and O3GK starting in 2020 April and lasting two weeks. In this paper we describe these data and various other science products that can be freely accessed through the Gravitational Wave Open Science Center at https://***. The main data set, consisting of the gravitational-wave strain time series that contains the astrophysical signals, is released together with supporting data useful for their analysis and documentation, tutorials, as well as analysis software packages. © 2023. The Author(s). Published by the American Astronomical Society.

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Single-point kinetic energy density functionals: A pointwise kinetic energy density analysis and numerical convergence investigation

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Physical Review B 2015年第4期91卷 045124-045124页

作者： Junchao Xia Emily A. Carter Department of Mechanical and Aerospace Engineering Princeton University Princeton New Jersey 08544-5263 USA Program in Applied and Computational Mathematics and Andlinger Center for Energy and the Environment Princeton University Princeton New Jersey 08544-5263 USA

We present a comprehensive study of single-point kinetic energy density functionals (KEDFs) to be used in orbital-free density functional theory (DFT) calculations. We first propose a form of KEDFs based on a pointwise Kohn-Sham (KS) kinetic energy density (KED) and electron localization function (ELF) analysis. We find that the ELF and modified enhancement factor have a very strong and transferable correlation with the reduced density in various bulk metals. The non-self-consistent kinetic energy errors predicted by our KEDF models are decreased greatly compared to previously reported generalized gradient approximation (GGA) KEDFs. Second, we perform self-consistent calculations with various single-point KEDFs and investigate their numerical convergence behavior. We find striking numerical instabilities for previous GGA KEDFs; most of the GGA KEDFs fail to converge and show unphysical densities during the optimization. In contrast, our KEDFs demonstrate stable convergence, and their self-consistent results of various bulk properties agree reasonably well with KSDFT. A further detailed KED analysis reveals an interesting bifurcation phenomenon in defective metals and alloys, which may shed light on directions for future KEDF development.

关键词： KINETIC energy DENSITY functionals DENSITY functional theory ELECTRON research BIFURCATION theory

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Reply to “Comment on ‘Single-point kinetic energy density functionals: A pointwise kinetic energy density analysis and numerical convergence investigation’ ”

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Physical Review B 2015年第11期92卷 117102-117102页

We find that the multivalued character of the G factor as a function of the reduced gradient (s) still exists after accounting for pseudopotential artifacts and the kinetic energy global upper bound. We also find that the VT84F functional indeed exhibits stable convergence and more reasonable results for self-consistent bulk properties compared to other generalized gradient approximation (GGA) kinetic energy density functionals (KEDFs) that we tested earlier. However, VT84F generally yields overestimated equilibrium volumes, which may result from its inability (as with all GGAs) to reproduce the G−s multivalued character. The analogous failure to predict the multivalued character of G as a function of the reduced density (d) is also likely to be responsible for the inaccuracy of our vWGTF functionals reported earlier. Our multivaluedness analysis therefore does not impugn any particular GGA KEDF. Instead, it merely confirms the importance of pointwise analysis for improving KEDFs by emphasizing the need to resolve the multivaluedness of G with respect to various density variables.

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A stochastic mechanical model to generate jitter in the production of voiced sounds 1

A stochastic mechanical model to generate jitter in the prod...

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1st ECCOMAS Thematic Conference on Uncertainty Quantification in Computational Sciences and Engineering, UNCECOMP 2015

作者： Cataldo, E. Soize, C. Universidade Federal Fluminense Applied Mathematics Department Graduate Program in Telecommunications Engineering Rua Mário Santos Braga S/N -Centro Niterói-RJ24020-140 Brazil Université Paris-Est Laboratoire Modélisation et Simulation Multi Echelle MSME FRE 3160 CNRS 5 Bd Descartes Marne-la-Vallée77454 France

The quasi-periodic oscillation of the vocal folds causes perturbations in the length of the glottal cycles which are known as jitter. The observation of the glottal cycles variations suggests that jitter is a random phenomenon described by random deviations of the glottal cycle lengths in relation to a corresponding mean value and, in general, its values are expressed as a percentage of the duration of the glottal pulse. The jitter has been the subject for researchers due to its important applications such as identification of pathological voices (nodulus in the vocal folds, paralysis of the vocal folds, or even, the vocal aging, among others). Large values for jitter variation can indicate a pathological characteristic of the voice. The objective of this paper is to construct a stochastic model of jitter using a mechanical model of the vocal folds. This model assumes complete right-left symmetry of the vocal folds and considers motion of the vocal folds only in the horizontal direction. The corresponding stiffness of each vocal fold is considered as a stochastic process and its modelling is proposed. The probability density functions of the fundamental frequency related to the voices produced are constructed and compared for different levels of jitter. Some samples of synthesized voices in these cases are obtained.

关键词： Jitter

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An Evolutionary Beverton-Holt Model

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19th International Conference on Difference Equations and Applications, ICDEA 2013

作者： Cushing, J.M. Department of Mathematics and The Interdisciplinary Program in Applied Mathematics University of Arizona 617 N. Santa Rita Tucson AZ 85721 United States

ISBN: (纸本)9783662441398

The classic Beverton-Holt (discrete logistic) difference equation, which arises in population dynamics, has a globally asymptotically stable equilibrium (for positive initial conditions) if its coefficients are constants. If the coefficients change in time, then the equation becomes nonautonomous and the asymptotic dynamics might not be as simple. One reason the coefficients can change in time is their evolution by natural selection. If the model coefficients are functions of a heritable phenotypic trait subject to natural selection then, by standard methods for modeling evolution, the model becomes a planar system of coupled difference equations, consisting of a Beverton-Holt type equation for the population dynamics and a difference equation for the dynamics of the mean phenotypic trait. We consider a case when the trait equation uncouples from the population dynamic equation and obtain criteria under which the evolutionary system has globally asymptotically stable equilibria or periodic solutions. © Springer-Verlag Berlin Heidelberg 2014.

关键词： Population dynamics

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Secular trends in family dinner frequency among adolescents Public Health

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BMC Research Notes 2016年第1期9卷 1-5页

作者： Walton, Kathryn Kleinman, Ken P. Rifas-Shiman, Sheryl L. Horton, Nicholas J. Gillman, Matthew W. Field, Alison E. Bryn Austin, S. Neumark-Sztainer, Dianne Haines, Jess Department of Family Relations and Applied Nutrition University of Guelph 50 Stone Road East Guelph N1G 2W1 ON Canada Obesity Prevention Program Department of Population Medicine Harvard Medical School Harvard Pilgrim Health Care Institute Boston United States Department of Mathematics and Statistics Amherst College Amherst United States Department of Nutrition Harvard T.H. Chan School of Public Health Boston United States Division of Adolescent and Young Adult Medicine Boston Children's Hospital Boston United States Channing Division of Network Medicine Brigham and Women's Hospital and Harvard Medical School Boston United States Department of Epidemiology Harvard T.H. Chan School of Public Health Boston United States Department of Social and Behavioral Sciences Harvard T.H. Chan School of Public Health Boston United States Division of Epidemiology and Community Health School of Public Health University of Minnesota Minneapolis United States

Background: Eating meals, particularly dinner, with family members has been found to be associated with improved dietary intake, lower prevalence of disordered eating behaviors, lower levels of substance abuse, and improved academic outcomes among adolescents. Limited research has examined how the frequency of family meals has changed over time. The objective of this study was to examine secular trends in family dinner frequency over a 12-year period using a large, nation-wide sample of adolescents. Methods: Using data from two cohorts of the Growing up Today study (GUTS;n = 18,075 observations for 14,79,714 and 15 year olds), we compared family dinner frequency among 14-15-year-olds in 1996 (GUTS1) through 2008 (GUTS2) and rate of change in family dinner frequency from 1996 to 1998 (GUTS1) and 2004-2008 (GUTS2). We fit logistic models using generalized estimating equations with independence working correlation and empirical variance to account for correlation within individual and between siblings. Results: From 1996 to 2008, the number of family dinners per week among males decreased from 5.3 to 4.6 (p = 0.04) and among females from 5.0 to 4.4 (p = 0.03). We found that the rate of decline in frequency of family meals was consistent in GUTS1 (1996-1998) and GUTS2 (2004-2008) among both males and females. Conclusions: From 1996 to 2008, frequency of family dinners decreased among adolescents. Future research should explore reasons for this decline as well as strategies to increase family meals among adolescents. © 2016 Walton et al.

关键词： Adolescents Family meals Longitudinal studies Secular trends

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