Tensor-valued random fields for continuum physics /:
Many areas of continuum physics pose a challenge to physicists. What are the most general, admissible statistically homogeneous and isotropic tensor-valued random fields (TRFs)? Previously, only the TRFs of rank 0 were completely described. This book assembles a complete description of such fields i...
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| Hauptverfasser: | , |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY :
Cambridge University Press,
2019.
|
| Schriftenreihe: | Cambridge monographs on mathematical physics.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | Many areas of continuum physics pose a challenge to physicists. What are the most general, admissible statistically homogeneous and isotropic tensor-valued random fields (TRFs)? Previously, only the TRFs of rank 0 were completely described. This book assembles a complete description of such fields in terms of one- and two-point correlation functions for tensors of ranks 1 through 4. Working from the standpoint of invariance of physical laws with respect to the choice of a coordinate system, spatial domain representations, as well as their wavenumber domain counterparts are rigorously given in full detail. The book also discusses, an introduction to a range of continuum theories requiring TRFs, an introduction to mathematical theories necessary for the description of homogeneous and isotropic TRFs, and a range of applications including a strategy for simulation of TRFs, ergodic TRFs, scaling laws of stochastic constitutive responses, and applications to stochastic partial differential equations. It is invaluable for mathematicians looking to solve problems of continuum physics, and for physicists aiming to enrich their knowledge of the relevant mathematical tools. |
| Beschreibung: | 1 online resource : illustrations |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9781108567800 1108567800 |
Internformat
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| 520 | |a Many areas of continuum physics pose a challenge to physicists. What are the most general, admissible statistically homogeneous and isotropic tensor-valued random fields (TRFs)? Previously, only the TRFs of rank 0 were completely described. This book assembles a complete description of such fields in terms of one- and two-point correlation functions for tensors of ranks 1 through 4. Working from the standpoint of invariance of physical laws with respect to the choice of a coordinate system, spatial domain representations, as well as their wavenumber domain counterparts are rigorously given in full detail. The book also discusses, an introduction to a range of continuum theories requiring TRFs, an introduction to mathematical theories necessary for the description of homogeneous and isotropic TRFs, and a range of applications including a strategy for simulation of TRFs, ergodic TRFs, scaling laws of stochastic constitutive responses, and applications to stochastic partial differential equations. It is invaluable for mathematicians looking to solve problems of continuum physics, and for physicists aiming to enrich their knowledge of the relevant mathematical tools. | ||
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| illustrated | Illustrated |
| indexdate | 2024-10-25T15:50:02Z |
| institution | BVB |
| isbn | 9781108567800 1108567800 |
| language | English |
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| publishDate | 2019 |
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| series | Cambridge monographs on mathematical physics. |
| series2 | Cambridge monographs on mathematical physics |
| spelling | Malyarenko, Anatoliy, author. http://id.loc.gov/authorities/names/no2013115399 Tensor-valued random fields for continuum physics / Anatoliy Malyarenko and Martin Ostoja-Starzewski. New York, NY : Cambridge University Press, 2019. 1 online resource : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Cambridge monographs on mathematical physics Includes bibliographical references and index. Online resource; title from PDF title page (EBSCO, viewed November 30, 2018). Introduction to continuum theories -- Mathematical preliminaries -- Mathematical results -- Tensor random fields in continuum theories. Many areas of continuum physics pose a challenge to physicists. What are the most general, admissible statistically homogeneous and isotropic tensor-valued random fields (TRFs)? Previously, only the TRFs of rank 0 were completely described. This book assembles a complete description of such fields in terms of one- and two-point correlation functions for tensors of ranks 1 through 4. Working from the standpoint of invariance of physical laws with respect to the choice of a coordinate system, spatial domain representations, as well as their wavenumber domain counterparts are rigorously given in full detail. The book also discusses, an introduction to a range of continuum theories requiring TRFs, an introduction to mathematical theories necessary for the description of homogeneous and isotropic TRFs, and a range of applications including a strategy for simulation of TRFs, ergodic TRFs, scaling laws of stochastic constitutive responses, and applications to stochastic partial differential equations. It is invaluable for mathematicians looking to solve problems of continuum physics, and for physicists aiming to enrich their knowledge of the relevant mathematical tools. Random fields. http://id.loc.gov/authorities/subjects/sh85111347 Tensor fields. http://id.loc.gov/authorities/subjects/sh2012001399 Field theory (Physics) http://id.loc.gov/authorities/subjects/sh85048117 Champs aléatoires. Champs tensoriels. Théorie des champs (Physique) MATHEMATICS Applied. bisacsh MATHEMATICS Probability & Statistics General. bisacsh Field theory (Physics) fast Random fields fast Tensor fields fast Ostoja-Starzewski, Martin, author. http://id.loc.gov/authorities/names/no94033588 has work: Tensor-valued random fields for continuum physics (Text) https://id.oclc.org/worldcat/entity/E39PCGhjGWCXbHBRGvpB3xhRw3 https://id.oclc.org/worldcat/ontology/hasWork Print version: Malyarenko, Anatoliy. Tensor-valued random fields for continuum physics. New York, NY : Cambridge University Press, 2019 1108429858 9781108429856 (OCoLC)1045177336 Cambridge monographs on mathematical physics. http://id.loc.gov/authorities/names/n42005691 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=1917146 Volltext CBO01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=1917146 Volltext |
| spellingShingle | Malyarenko, Anatoliy Ostoja-Starzewski, Martin Tensor-valued random fields for continuum physics / Cambridge monographs on mathematical physics. Introduction to continuum theories -- Mathematical preliminaries -- Mathematical results -- Tensor random fields in continuum theories. Random fields. http://id.loc.gov/authorities/subjects/sh85111347 Tensor fields. http://id.loc.gov/authorities/subjects/sh2012001399 Field theory (Physics) http://id.loc.gov/authorities/subjects/sh85048117 Champs aléatoires. Champs tensoriels. Théorie des champs (Physique) MATHEMATICS Applied. bisacsh MATHEMATICS Probability & Statistics General. bisacsh Field theory (Physics) fast Random fields fast Tensor fields fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85111347 http://id.loc.gov/authorities/subjects/sh2012001399 http://id.loc.gov/authorities/subjects/sh85048117 |
| title | Tensor-valued random fields for continuum physics / |
| title_auth | Tensor-valued random fields for continuum physics / |
| title_exact_search | Tensor-valued random fields for continuum physics / |
| title_full | Tensor-valued random fields for continuum physics / Anatoliy Malyarenko and Martin Ostoja-Starzewski. |
| title_fullStr | Tensor-valued random fields for continuum physics / Anatoliy Malyarenko and Martin Ostoja-Starzewski. |
| title_full_unstemmed | Tensor-valued random fields for continuum physics / Anatoliy Malyarenko and Martin Ostoja-Starzewski. |
| title_short | Tensor-valued random fields for continuum physics / |
| title_sort | tensor valued random fields for continuum physics |
| topic | Random fields. http://id.loc.gov/authorities/subjects/sh85111347 Tensor fields. http://id.loc.gov/authorities/subjects/sh2012001399 Field theory (Physics) http://id.loc.gov/authorities/subjects/sh85048117 Champs aléatoires. Champs tensoriels. Théorie des champs (Physique) MATHEMATICS Applied. bisacsh MATHEMATICS Probability & Statistics General. bisacsh Field theory (Physics) fast Random fields fast Tensor fields fast |
| topic_facet | Random fields. Tensor fields. Field theory (Physics) Champs aléatoires. Champs tensoriels. Théorie des champs (Physique) MATHEMATICS Applied. MATHEMATICS Probability & Statistics General. Random fields Tensor fields |
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