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Zh. Vychisl. Mat. Mat. Fiz., 2011, Volume 51, Number 3, Pages 480–491 (Mi zvmmf8085)  

This article is cited in 12 scientific papers (total in 13 papers)

Model of real-time active noise shielding of a given subdomain subject to external noise sources

V. S. Ryaben'kii

Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, Moscow, 125047 Russia

Abstract: A linear one-dimensional problem is considered, which is interpreted as a mathematical model of sound propagation. Additional sound sources are constructed that shield a given subdomain from sound sources localized in an additional subdomain without changing the solution in the additional subdomain. A complicating point in the problem is that the desired shielding sources can be constructed at the current time as based only on information about the shielded process that has become available by this current time. In an important special case, information in a convenient form is derived via noise exploration introduced in this work.

Key words: nonstationary problems, noise shielding, control of sound propagation, difference potential method.

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English version:
Computational Mathematics and Mathematical Physics, 2011, 51:3, 444–454

Bibliographic databases:

UDC: 519.63
Received: 05.02.2010

Citation: V. S. Ryaben'kii, “Model of real-time active noise shielding of a given subdomain subject to external noise sources”, Zh. Vychisl. Mat. Mat. Fiz., 51:3 (2011), 480–491; Comput. Math. Math. Phys., 51:3 (2011), 444–454

Citation in format AMSBIB
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\pages 480--491
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. S. Ryaben'kii, “Synchronous exploration for the control of real-time external noise suppression in a three-dimensional subdomain”, Comput. Math. Math. Phys., 51:10 (2011), 1777–1791  mathnet  crossref  mathscinet  isi
    2. V. S. Ryabenkii, “Upravlenie v realnom vremeni aktivnym umensheniem shuma v trekhmernoi podoblasti s pomoschyu sinkhronnoi razvedki shumom”, Preprinty IPM im. M. V. Keldysha, 2011, 003, 24 pp.  mathnet
    3. V. S. Ryaben'kii, “Difference potentials analogous to Cauchy integrals”, Russian Math. Surveys, 67:3 (2012), 541–567  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. Ryabenkii V.S., “Potentsialy dlya abstraktnykh raznostnykh skhem”, Preprinty IPM im. M.V. Keldysha, 2012, no. 10, 1–30  elib
    5. Ryabenkii V.S., “Teoriya upravleniya resheniyami lineinykh raznostnykh skhem v sostavnykh oblastyakh”, Preprinty IPM im. M.V. Keldysha, 2012, no. 11, 1–32  elib
    6. V. S. Ryaben'kii, “Mathematical model of device for quietizing external noise in subregion of space”, Math. Models Comput. Simul., 5:2 (2013), 103–121  mathnet  crossref  mathscinet  elib
    7. V. S. Ryabenkii, “Potentsialy dlya abstraktnykh raznostnykh skhem”, Preprinty IPM im. M. V. Keldysha, 2012, 010, 30 pp.  mathnet
    8. Utyuzhnikov S.V., “Real-Time Active Wave Control With Preservation of Wanted Field”, IMA J. Appl. Math., 79:6 (2014), 1126–1138  crossref  mathscinet  zmath  isi  elib  scopus
    9. S. K. Godunov, V. T. Zhukov, M. I. Lazarev, I. L. Sofronov, V. I. Turchaninov, A. S. Kholodov, S. V. Tsynkov, B. N. Chetverushkin, Ye. Yu. Epshteyn, “Viktor Solomonovich Ryaben'kii and his school (on his 90th birthday)”, Russian Math. Surveys, 70:6 (2015), 1183–1210  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    10. V. S. Ryabenkii, “Aktivnaya zaschita akusticheskogo polya zhelatelnykh istochnikov ot vneshnego shuma v realnom vremeni”, Preprinty IPM im. M. V. Keldysha, 2016, 027, 21 pp.  mathnet
    11. Gilman M. Smith E. Tsynkov S., “Transionospheric Synthetic Aperture Imaging”, Transionospheric Synthetic Aperture Imaging, Applied and Numerical Harmonic Analysis, Birkhauser Boston, 2017, 1–458  crossref  mathscinet  zmath  isi
    12. Utyuzhnikov S.V., “A Practical Algorithm For Real-Time Active Sound Control With Preservation of Interior Sound”, Comput. Fluids, 157 (2017), 175–181  crossref  mathscinet  zmath  isi  scopus
    13. Utyuzhnikov S.V., “A Practical Algorithm For Real-Time Active Sound Control With Preservation of Interior Sound”, Comput. Fluids, 169:SI (2018), 373–379  crossref  mathscinet  zmath  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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