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Convergence analysis of a finite element approximation of minimum action methods

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arXiv 2017年

作者： Wan, Xiaoliang Yu, Haijun Zhai, Jiayu Department of Mathematics and Center for Computation and Technology Louisiana State University Baton Rouge70803 United States School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China NCMIS and LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Beijing100190 China

In this work, we address the convergence of a finite element approximation of the minimizer of the Freidlin-Wentzell (F-W) action functional for non-gradient dynamical systems perturbed by small noise. The F-W theory of large deviations is a rigorous mathematical tool to study small-noise-induced transitions in a dynamical system. The central task in the application of F-W theory of large deviations is to seek the minimizer and minimum of the F-W action functional. We discretize the F-W action functional using linearfinite elements, and establish the convergence of the approximation through Γ-convergence.65M60, 65P40, 65K10 Copyright © 2017, The Authors. All rights reserved.

关键词： Dynamical systems

A note on optimal decay rates for the axisymmetric D-solutions to the steady Navier-Stokes equations

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arXiv 2017年

作者： Weng, Shangkun Xie, Chunjing School of Mathematics and Statistics Computational Science Hubei Key Laboratory Wuhan University Wuhan Hubei Province430072 China Department of Mathematics Institute of Natural Sciences Ministry of Education Key Laboratory of Scientific and Engineering Computing Shanghai Jiao Tong University Shanghai200240 China

In this paper, we investigate the decay properties of an axisymmetric D-solutions to stationary incompressible Navier-Stokes systems in R3. We obtain the optimal decay rate |u(x)| | xC|+1 for axisymmetric flows without swirl. Furthermore, we find a dichotomy for the decay rates of the swirl component ua, that is, either O(+11) +1or |ue(r,z)| (C1r)3, where p = Vr2+ z2. In the latter case, we can further deduce that the other two components of the velocity field also attain the optimal decay rates: |ur(r, z)| + |uz(r, z)| C+1-. We do not require any small assumptions on the forcing *** Codes 76D05 Copyright © 2017, The Authors. All rights reserved.

关键词： Navier Stokes equations

Application of Bayesian networks for estimation of individual psychological characteristics

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arXiv 2017年

作者： Litvinenko, Alexander Litvinenko, Natalya Mamyrbayev, Orken Extreme Computing Research Center Center for Uncertainty Quantification in Computational Science & Engineering King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia Applied research department Institute of Mathematics and Mathematical Modeling CS MES RK Almaty Kazakhstan Institute of information and computational technologies CS MES RK Almaty Kazakhstan

An accurate qualitative and comprehensive assessment of human potential is one of the most important challenges in any company or collective. We apply Bayesian networks for developing more accurate overall estimations of psychological characteristics of an individual, based on psychological test results, which identify how much an individual possesses a certain trait. Examples of traits could be a stress resistance, the readiness to take a risk, the ability to concentrate on certain complicated work. The most common way of studying psychological characteristics of each individual is testing. Additionally, the overall estimation is usually based on personal experiences and the subjective perception of a psychologist or a group of psychologists about the investigated psychological personality traits.62C10, 62C12 Copyright © 2017, The Authors. All rights reserved.

关键词： Bayesian networks

From atomistic model to the Peierls-Nabarro model with g-surface for dislocations

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arXiv 2017年

作者： Luo, Tao Ming, Pingbing Xiang, Yang Department of Mathematics Hong Kong University of Science and Technology Clear Water Bay Kowloon Hong Kong LSEC Institute of Computational Mathematics and Scientific/Engineering Computing AMSS Chinese Academy of Sciences No. 55 East Road Zhong-Guan-Cun Beijing100190 China

The Peierls-Nabarro (PN) model for dislocations is a hybrid model that incorporates the atomistic information of the dislocation core structure into the continuum theory. In this paper, we study the convergence from a full atomisticmodel to the PNmodel with g-surface for the dislocation in a bilayer system (e.g. bilayer graphene). We prove that the displacement field of and the total energy of the dislocation solution of the PN model are asymptotically close to those of the full atomistic model. Our work can be considered as a generalization of the analysis of the convergence from atomistic model to Cauchy-Born rule for crystals without defects in the literature. Copyright © 2017, The Authors. All rights reserved.

关键词： Continuum mechanics

On the ideal interpolation operator in algebraic multigrid methods

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arXiv 2017年

作者： Xu, Xuefeng Zhang, Chen-Song LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China LSEC & NCMIS Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

Various algebraic multigrid algorithms have been developed for solving problems in scientific and engineering computation over the past decades. They have been shown to be well-suited for solving discretized partial differential equations on unstructured girds in practice. One key ingredient of algebraic multigrid algorithms is a strategy for constructing an effective prolongation operator. Among many questions on constructing a prolongation, an important question is how to evaluate its quality. In this paper, we establish new characterizations (including sufficient condition, necessary condition, and equivalent condition) of the so-called ideal interpolation operator. Our result suggests that, compared with common wisdom, one has more room to construct an ideal interpolation, which can provide new insights for designing algebraic multigrid algorithms. Moreover, we derive a new expression for a class of ideal interpolation operators.65F10, 65F15, 65N55 Copyright © 2017, The Authors. All rights reserved.

关键词： Coarsening

All-sky search for continuous gravitational waves from isolated neutron stars using Advanced LIGO and Advanced Virgo O3 data

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Physical Review D 2022年第10期106卷 102008-102008页

作者： R. Abbott H. Abe F. Acernese K. Ackley N. Adhikari R. X. Adhikari V. K. Adkins V. B. Adya C. Affeldt D. Agarwal M. Agathos K. Agatsuma N. Aggarwal O. D. Aguiar L. Aiello A. Ain P. Ajith T. Akutsu S. Albanesi R. A. Alfaidi A. Allocca P. A. Altin A. Amato C. Anand S. Anand A. Ananyeva S. B. Anderson W. G. Anderson M. Ando T. Andrade N. Andres M. Andrés-Carcasona T. Andrić S. V. Angelova S. Ansoldi J. M. Antelis S. Antier T. Apostolatos E. Z. Appavuravther S. Appert S. K. Apple K. Arai A. Araya M. C. Araya J. S. Areeda M. Arène N. Aritomi N. Arnaud M. Arogeti S. M. Aronson H. Asada Y. Asali G. Ashton Y. Aso M. Assiduo S. Assis de Souza Melo S. M. Aston P. Astone F. Aubin K. AultONeal C. Austin S. Babak F. Badaracco M. K. M. Bader C. Badger S. Bae Y. Bae A. M. Baer S. Bagnasco Y. Bai J. Baird R. Bajpai T. Baka M. Ball G. Ballardin S. W. Ballmer A. Balsamo G. Baltus S. Banagiri B. Banerjee D. 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 S. Basak R. Bassiri A. Basti M. Bawaj J. C. Bayley M. Bazzan B. R. Becher B. Bécsy V. M. Bedakihale F. Beirnaert M. Bejger I. Belahcene V. Benedetto D. Beniwal M. G. Benjamin T. F. Bennett J. D. Bentley M. BenYaala S. Bera M. Berbel F. Bergamin B. K. Berger S. Bernuzzi D. Bersanetti A. Bertolini J. Betzwieser D. Beveridge R. Bhandare A. V. Bhandari U. Bhardwaj R. Bhatt D. Bhattacharjee S. Bhaumik A. Bianchi I. A. Bilenko G. Billingsley S. Bini R. Birney O. Birnholtz S. Biscans M. Bischi S. Biscoveanu A. Bisht B. Biswas M. Bitossi M.-A. Bizouard J. K. Blackburn C. D. Blair D. G. Blair R. M. Blair F. Bobba N. Bode M. Boër G. Bogaert M. Boldrini G. N. Bolingbroke L. D. Bonavena 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 LIGO Laboratory California Institute of Technology Pasadena California 91125 USA Graduate School of Science Tokyo Institute of Technology Meguro-ku Tokyo 152-8551 Japan 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 University of Wisconsin-Milwaukee Milwaukee Wisconsin 53201 USA Louisiana State University Baton Rouge Louisiana 70803 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 Inter-University Centre for Astronomy and Astrophysics Pune 411007 India 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 Northwestern University Evanston Illinois 60208 USA Instituto Nacional de Pesquisas Espaciais 12227-010 São José dos Campos São Paulo Brazil Cardiff University Cardiff CF24 3AA United Kingdom INFN Sezione 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 Dipartimento di Fisica Università degli Studi di Torino I-10125 Torino Italy INFN Sezione di Torino I-10125 Torino Italy SUPA University of Glasgow Glasgow G12 8QQ United Kingdom Università di Napoli “Federico II ” Complesso Universitario di Monte S. Angelo I-80126 Napoli Italy Université de Lyon Université Claude Bernard Lyon 1

We present results of an all-sky search for continuous gravitational waves which can be produced by spinning neutron stars with an asymmetry around their rotation axis, using data from the third observing run of the Advanced LIGO and Advanced Virgo detectors. Four different analysis methods are used to search in a gravitational-wave frequency band from 10 to 2048 Hz and a first frequency derivative from −10−8 to 10−9 Hz/s. No statistically significant periodic gravitational-wave signal is observed by any of the four searches. As a result, upper limits on the gravitational-wave strain amplitude h0 are calculated. The best upper limits are obtained in the frequency range of 100 to 200 Hz and they are ∼1.1×10−25 at 95% confidence level. The minimum upper limit of 1.10×10−25 is achieved at a frequency 111.5 Hz. We also place constraints on the rates and abundances of nearby planetary- and asteroid-mass primordial black holes that could give rise to continuous gravitational-wave signals.

关键词： Gravitational wave sources Neutron stars & pulsars Gravitational wave detection

All-sky search for gravitational wave emission from scalar boson clouds around spinning black holes in LIGO O3 data

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Physical Review D 2022年第10期105卷 102001-102001页

作者： R. Abbott H. Abe F. Acernese K. Ackley N. Adhikari R. X. Adhikari V. K. Adkins V. B. Adya C. Affeldt D. Agarwal M. Agathos K. Agatsuma N. Aggarwal O. D. Aguiar L. Aiello A. Ain P. Ajith T. Akutsu S. Albanesi R. A. Alfaidi A. Allocca P. A. Altin A. Amato C. Anand S. Anand A. Ananyeva S. B. Anderson W. G. Anderson M. Ando T. Andrade N. Andres M. Andrés-Carcasona T. Andrić S. V. Angelova S. Ansoldi J. M. Antelis S. Antier T. Apostolatos E. Z. Appavuravther S. Appert S. K. Apple K. Arai A. Araya M. C. Araya J. S. Areeda M. Arène N. Aritomi N. Arnaud M. Arogeti S. M. Aronson K. G. Arun H. Asada Y. Asali G. Ashton Y. Aso M. Assiduo S. Assis de Souza Melo S. M. Aston P. Astone F. Aubin K. AultONeal C. Austin S. Babak F. Badaracco M. K. M. Bader C. Badger S. Bae Y. Bae A. M. Baer S. Bagnasco Y. Bai J. Baird R. Bajpai T. Baka M. Ball G. Ballardin S. W. Ballmer A. Balsamo G. Baltus S. Banagiri B. Banerjee D. 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 S. Basak R. Bassiri A. Basti M. Bawaj J. C. Bayley M. Bazzan B. R. Becher B. Bécsy V. M. Bedakihale F. Beirnaert M. Bejger I. Belahcene V. Benedetto D. Beniwal M. G. Benjamin T. F. Bennett J. D. Bentley M. BenYaala S. Bera M. Berbel F. Bergamin B. K. Berger S. Bernuzzi D. Bersanetti A. Bertolini J. Betzwieser D. Beveridge R. Bhandare A. V. Bhandari U. Bhardwaj R. Bhatt D. Bhattacharjee S. Bhaumik A. Bianchi I. A. Bilenko G. Billingsley S. Bini R. Birney O. Birnholtz S. Biscans M. Bischi S. Biscoveanu A. Bisht B. Biswas M. Bitossi M.-A. Bizouard J. K. Blackburn C. D. Blair D. G. Blair R. M. Blair F. Bobba N. Bode M. Boër G. Bogaert M. Boldrini G. N. Bolingbroke L. D. Bonavena 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 LIGO Laboratory California Institute of Technology Pasadena California 91125 USA Graduate School of Science Tokyo Institute of Technology Meguro-ku Tokyo 152-8551 Japan 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 University of Wisconsin-Milwaukee Milwaukee Wisconsin 53201 USA Louisiana State University Baton Rouge Louisiana 70803 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 Inter-University Centre for Astronomy and Astrophysics Pune 411007 India 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 Northwestern University Evanston Illinois 60208 USA Instituto Nacional de Pesquisas Espaciais 12227-010 São José dos Campos São Paulo Brazil Cardiff University Cardiff CF24 3AA United Kingdom INFN Sezione 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 Dipartimento di Fisica Università degli Studi di Torino I-10125 Torino Italy INFN Sezione di Torino I-10125 Torino Italy SUPA University of Glasgow Glasgow G12 8QQ United Kingdom Università di Napoli “Federico II” Complesso Universitario di Monte S. Angelo I-80126 Napoli Italy Université de Lyon Université Claude Bernard Lyon 1

This paper describes the first all-sky search for long-duration, quasimonochromatic gravitational-wave signals emitted by ultralight scalar boson clouds around spinning black holes using data from the third observing run of Advanced LIGO. We analyze the frequency range from 20 to 610 Hz, over a small frequency derivative range around zero, and use multiple frequency resolutions to be robust towards possible signal frequency wanderings. Outliers from this search are followed up using two different methods, one more suitable for nearly monochromatic signals, and the other more robust towards frequency fluctuations. We do not find any evidence for such signals and set upper limits on the signal strain amplitude, the most stringent being ≈10−25 at around 130 Hz. We interpret these upper limits as both an “exclusion region” in the boson mass/black hole mass plane and the maximum detectable distance for a given boson mass, based on an assumption of the age of the black hole/boson cloud system.

关键词： Classical black holes Gravitational wave detection Gravitational wave sources Particle astrophysics Particle dark matter

Sample Approximation-Based Deflation Approaches for Chance SINR-Constrained Joint Power and Admission Control

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Sample Approximation-Based Deflation Approaches for Chance S...

作者： Liu, Ya-Feng Hong, Mingyi Song, Enbin State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Chinese Academy of Sciences Beijing100190 China Iowa State University AmesIA50011 United States Department of Mathematics Sichuan University Chengdu610064 China

Consider the joint power and admission control (JPAC) problem for a multiuser single-input single-output (SISO) interference channel. Most existing works on JPAC assume the perfect instantaneous channel state information (CSI). In this paper, we consider the JPAC problem with the imperfect CSI, i.e., we assume that only the channel distribution information (CDI) is available. We formulate the JPAC problem into a chance (probabilistic)-constrained program, where each link's SINR outage probability is enforced to be less than or equal to a specified tolerance. To circumvent the computational difficulty of the chance SINR constraints, we propose to use the sample (scenario) approximation scheme to convert them into finitely many simple linear constraints. Furthermore, we reformulate the sample approximation of the chance SINR-constrained JPAC problem as a composite group sparse minimization problem and then approximate it by a second-order cone program (SOCP). The solution of the SOCP approximation can be used to check the simultaneous supportability of all links in the network and to guide an iterative link removal procedure (the deflation approach). We exploit the special structure of the SOCP approximation and custom-design an efficient algorithm for solving it. Finally, we illustrate the effectiveness and efficiency of the proposed sample approximation-based deflation approaches by simulations. © 2016 IEEE.

关键词： Channel state information

Search for gravitational waves from Scorpius X-1 with a hidden Markov model in O3 LIGO data

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Physical Review D 2022年第6期106卷 062002-062002页

Results are presented for a semicoherent search for continuous gravitational waves from the low-mass x-ray binary Scorpius X-1, using a hidden Markov model (HMM) to allow for spin wandering. This search improves on previous HMM-based searches of Laser Interferometer Gravitational-Wave Observatory data by including the orbital period in the search template grid, and by analyzing data from the latest (third) observing run. In the frequency range searched, from 60 to 500 Hz, we find no evidence of gravitational radiation. This is the most sensitive search for Scorpius X-1 using a HMM to date. For the most sensitive subband, starting at 256.06 Hz, we report an upper limit on gravitational wave strain (at 95% confidence) of h095%=6.16×10−26, assuming the orbital inclination angle takes its electromagnetically restricted value ι=44°. The upper limits on gravitational wave strain reported here are on average a factor of ∼3 lower than in the second observing run HMM search. This is the first Scorpius X-1 HMM search with upper limits that reach below the indirect torque-balance limit for certain subbands, assuming ι=44°.

关键词： Gravitational waves Binary stars Neutron stars & pulsars