{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,26]],"date-time":"2025-03-26T16:09:05Z","timestamp":1743005345807,"version":"3.40.3"},"publisher-location":"Cham","reference-count":22,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783030802080"},{"type":"electronic","value":"9783030802097"}],"license":[{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021]]},"DOI":"10.1007\/978-3-030-80209-7_33","type":"book-chapter","created":{"date-parts":[[2021,7,14]],"date-time":"2021-07-14T00:02:40Z","timestamp":1626220960000},"page":"292-301","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Metriplectic Integrators for Dissipative Fluids"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7637-3979","authenticated-orcid":false,"given":"Michael","family":"Kraus","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,7,14]]},"reference":[{"key":"33_CR1","unstructured":"Beris, A.N., Edwards, B.J.: Thermodynamics of Flowing Systems. Oxford University Press, Oxford (1994)"},{"key":"33_CR2","doi-asserted-by":"publisher","first-page":"835860302","DOI":"10.1017\/S0022377820000392","volume":"86","author":"B Coquinot","year":"2020","unstructured":"Coquinot, B., Morrison, P.J.: A general metriplectic framework with application to dissipative extended magnetohydrodynamics. J. Plasma Phys. 86, 835860302 (2020)","journal-title":"J. Plasma Phys."},{"key":"33_CR3","doi-asserted-by":"crossref","unstructured":"Eldred, C., Gay-Balmaz, F.: Single and double generator bracket formulations of multicomponent fluids with irreversible processes. J. Phys. A Math. Theor. 53, 395701 (2020)","DOI":"10.1088\/1751-8121\/ab91d3"},{"key":"33_CR4","doi-asserted-by":"crossref","unstructured":"Gay-Balmaz, F., Yoshimura, H.: From variational to bracket formulations in nonequilibrium thermodynamics of simple systems. J. Geom. Phys. 158, 103812 (2020)","DOI":"10.1016\/j.geomphys.2020.103812"},{"key":"33_CR5","doi-asserted-by":"publisher","unstructured":"Giaquinta, M., Hildebrandt, S.: Calculus of Variations I. Springer, Dordrecht (2004). https:\/\/doi.org\/10.1007\/978-3-662-03278-7","DOI":"10.1007\/978-3-662-03278-7"},{"issue":"8","key":"33_CR6","doi-asserted-by":"publisher","first-page":"355","DOI":"10.1016\/0375-9601(84)90297-4","volume":"102","author":"M Grmela","year":"1984","unstructured":"Grmela, M.: Bracket formulation of dissipative fluid mechanics equations. Phys. Lett. A 102(8), 355\u2013358 (1984)","journal-title":"Phys. Lett. A"},{"key":"33_CR7","doi-asserted-by":"crossref","unstructured":"Grmela, M.: Particle and bracket formulations of kinetic equations. In: Fluids and Plasmas: Geometry and Dynamics, pp. 125\u2013132. American Mathematical Society, Providence (1984)","DOI":"10.1090\/conm\/028\/751978"},{"issue":"1\u20132","key":"33_CR8","doi-asserted-by":"publisher","first-page":"36","DOI":"10.1016\/0375-9601(85)90797-2","volume":"111","author":"M Grmela","year":"1985","unstructured":"Grmela, M.: Bracket formulation of dissipative time evolution equations. Phys. Lett. A 111(1\u20132), 36\u201340 (1985)","journal-title":"Phys. Lett. A"},{"key":"33_CR9","doi-asserted-by":"crossref","unstructured":"Grmela, M., \u00d6ttinger, H.C.: Dynamics and thermodynamics of complex fluids. I. Development of a general formalism. Phys. Rev. E 56, 6620\u20136632 (1997)","DOI":"10.1103\/PhysRevE.56.6620"},{"issue":"1","key":"33_CR10","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0370-1573(85)90028-6","volume":"123","author":"DD Holm","year":"1985","unstructured":"Holm, D.D., Marsden, J.E., Ratiu, T., Weinstein, A.: Nonlinear stability of fluid and plasma equilibria. Phys. Rep. 123(1), 1\u2013116 (1985)","journal-title":"Phys. Rep."},{"issue":"8","key":"33_CR11","doi-asserted-by":"publisher","first-page":"419","DOI":"10.1016\/0375-9601(84)90634-0","volume":"100","author":"AN Kaufman","year":"1984","unstructured":"Kaufman, A.N.: Dissipative Hamiltonian systems: a unifying principle. Phys. Lett. A 100(8), 419\u2013422 (1984)","journal-title":"Phys. Lett. A"},{"issue":"8","key":"33_CR12","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1016\/0375-9601(82)90664-8","volume":"88","author":"AN Kaufman","year":"1982","unstructured":"Kaufman, A.N., Morrison, P.J.: Algebraic structure of the plasma quasilinear equations. Phys. Lett. A 88(8), 405\u2013406 (1982)","journal-title":"Phys. Lett. A"},{"key":"33_CR13","doi-asserted-by":"crossref","unstructured":"Kraus, M., Hirvijoki, E.: Metriplectic integrators for the landau collision operator. Phys. Plasmas 24, 102311 (2017)","DOI":"10.1063\/1.4998610"},{"issue":"8","key":"33_CR14","doi-asserted-by":"publisher","first-page":"423","DOI":"10.1016\/0375-9601(84)90635-2","volume":"100","author":"PJ Morrison","year":"1984","unstructured":"Morrison, P.J.: Bracket formulation for irreversible classical fields. Phys. Lett. A 100(8), 423\u2013427 (1984)","journal-title":"Phys. Lett. A"},{"key":"33_CR15","unstructured":"Morrison, P.J.: Some observations regarding brackets and dissipation. Tech. rep., Center for Pure and Applied Mathematics Report PAM-228, University of California, Berkeley (1984)"},{"key":"33_CR16","doi-asserted-by":"publisher","first-page":"410","DOI":"10.1016\/0167-2789(86)90209-5","volume":"18","author":"PJ Morrison","year":"1986","unstructured":"Morrison, P.J.: A paradigm for joined Hamiltonian and dissipative systems. Phys. D Nonlinear Phenom. 18, 410\u2013419 (1986)","journal-title":"Phys. D Nonlinear Phenom."},{"issue":"2","key":"33_CR17","doi-asserted-by":"publisher","first-page":"467","DOI":"10.1103\/RevModPhys.70.467","volume":"70","author":"PJ Morrison","year":"1998","unstructured":"Morrison, P.J.: Hamiltonian description of the ideal fluid. Rev. Mod. Phys. 70(2), 467\u2013521 (1998)","journal-title":"Rev. Mod. Phys."},{"key":"33_CR18","doi-asserted-by":"publisher","first-page":"790","DOI":"10.1103\/PhysRevLett.45.790","volume":"45","author":"PJ Morrison","year":"1980","unstructured":"Morrison, P.J., Greene, J.M.: Noncanonical Hamiltonian density formulation of hydrodynamics and ideal magnetohydrodynamics. Phys. Rev. Lett. 45, 790\u2013794 (1980)","journal-title":"Phys. Rev. Lett."},{"key":"33_CR19","doi-asserted-by":"crossref","unstructured":"\u00d6ttinger, H.C.: Beyond Equilibrium Thermodynamics. John Wiley & Sons, New York(2005)","DOI":"10.1002\/0471727903"},{"key":"33_CR20","doi-asserted-by":"crossref","unstructured":"\u00d6ttinger, H.C., Grmela, M.: Dynamics and thermodynamics of complex fluids. II. Illustrations of a general formalism. Phys. Rev. E 56, 6633\u20136655 (1997)","DOI":"10.1103\/PhysRevE.56.6633"},{"key":"33_CR21","doi-asserted-by":"crossref","unstructured":"Suzuki, Y.: A GENERIC formalism for Korteweg-type fluids: I. A comparison with classical theory. Fluid Dyn. Res. 52, 015516 (2020)","DOI":"10.1088\/1873-7005\/ab6f47"},{"key":"33_CR22","doi-asserted-by":"crossref","unstructured":"Suzuki, Y.: A GENERIC formalism for Korteweg-type fluids: II. Higher-order models and relation to microforces. Fluid Dyn. Res. 52, 025510 (2020)","DOI":"10.1088\/1873-7005\/ab7ff6"}],"container-title":["Lecture Notes in Computer Science","Geometric Science of Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-80209-7_33","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,7,14]],"date-time":"2021-07-14T00:06:24Z","timestamp":1626221184000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-030-80209-7_33"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021]]},"ISBN":["9783030802080","9783030802097"],"references-count":22,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-80209-7_33","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2021]]},"assertion":[{"value":"14 July 2021","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"GSI","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Geometric Science of Information","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Paris","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"France","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2021","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"21 July 2021","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"23 July 2021","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"5","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"gsi2021","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/www.see.asso.fr\/en\/GSI2021?screen_check=done&Width=1280&Height=720","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Single-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"EasyChair","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"125","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"98","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"0","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"78% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"The conference was held virtually.","order":10,"name":"additional_info_on_review_process","label":"Additional Info on Review Process","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}