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APPLICATIONS TO PROBLEMS IN POLYMER PHYSICS AND RHEOLOGY

2000; World Scientific; Linguagem: Inglês

10.1142/9789812817747_0007

Helmut Schiessel, Chr. Friedrich, A. Blumen,

Polymer Nanocomposites and Properties

Applications of Fractional Calculus in Physics, pp. 331-376 (2000) No AccessAPPLICATIONS TO PROBLEMS IN POLYMER PHYSICS AND RHEOLOGYH. SCHIESSEL, CHR. FRIEDRICH, and A. BLUMENH. SCHIESSELTheoretical Polymer Physics, Freiburg University, Rheinstr. 12, 79104, Freiburg, GermanyMaterials Research Laboratory, University of California, Santa Barbara, CA 93106-5130, USA, CHR. FRIEDRICHFreiburg Materials' Research Center, Freiburg University, Stefan-Meier-Str. 21, 70104 Freiburg, Germany, and A. BLUMENTheoretical Polymer Physics, Freiburg University, Rheinstr. 12, 79104, Freiburg, Germanyhttps://doi.org/10.1142/9789812817747_0007Cited by:37 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail Abstract: The following sections are included: Introduction Applications to Microscopic Models of Polymer Dynamics Pulling a Rouse Chain at One of its Ends Pulling One Monomer of a Fractal Network Polyampholytes in External Electrical Fields Polyampholytic Networks in External Electrical Fields Rouse Dynamics of Generalized Gaussian Structures: Connection to Macroscopic Properties Applications to Rheological Constitutive Equations Viscoelasticity: Classical Approach and its Fractional Generalization Mechanical Analogues to Fractional Rheological Equations Overview over Exactly Solvable Fractional Models Fractional Element Fractional Maxwell Model Fractional Kelvin-Voigt Model Fractional Zener Model Fractional Poynting-Thomson Model Application to Experimental Data Conclusion Acknowledgments References FiguresReferencesRelatedDetailsCited By 37IntroductionWen Chen, HongGuang Sun and Xicheng Li26 February 2022Soft Matter Characterization From Ultrasonic Microrheology and Fractional CalculusVincent Gauthier, Emmanuel Caplain, Stephane Serfaty, Magalie Michiel and Pascal Griesmar et al.1 Jan 2022 | IEEE Sensors Journal, Vol. 22, No. 1Fractional relaxation noises, motions and the fractional energy balance equationShaun Lovejoy25 February 2022 | Nonlinear Processes in Geophysics, Vol. 29, No. 1Modeling the rheological properties of four commercially available composite core build-up materialsIvan Šarčev, Branislava Petronijević Šarčev, Veljko Krstonošić, Marko Janev and Teodor M Atanacković25 August 2020 | Polymers and Polymer Composites, Vol. 29, No. 7Large and Infinite Mass–Spring–Damper NetworksKevin Leyden, Mihir Sen and Bill Goodwine21 February 2019 | Journal of Dynamic Systems, Measurement, and Control, Vol. 141, No. 6Justification for Power Laws and Fractional ModelsSverre Holm16 April 2019Identification of main steam temperature of power plant using fractional-order transfer function based on Lévy flights — Artificial bee colony algorithmMing Sun, Ze Dong and Qin Zhang1 Jul 2017Viscoelasticity and pattern formations in stock market indicesGüngör Gündüz and Aydın Gündüz5 June 2017 | The European Physical Journal B, Vol. 90, No. 6Dynamic Stability of Axially Loaded Nonlocal Rod on Generalized Pasternak FoundationDušan Zorica, Teodor M. Atanacković, Zora Vrcelj and Branislava Novaković1 May 2017 | Journal of Engineering Mechanics, Vol. 143, No. 5Hysteresis behaviour modelling of woven composite using a collaborative elastoplastic damage model with fractional derivativesAlina Krasnobrizha, Patrick Rozycki, Laurent Gornet and Pascal Cosson1 Dec 2016 | Composite Structures, Vol. 158Review of methods and approaches for mechanical problem solutions based on fractional calculusMichael A Zhuravkov and Natalie S Romanova5 May 2014 | Mathematics and Mechanics of Solids, Vol. 21, No. 5Bibliography21 February 2014Hydrodynamic effects on scale-free polymer networks in external fieldsM. Galiceanu21 Jan 2014 | The Journal of Chemical Physics, Vol. 140, No. 3Generalized Algorithm for Estimating Non-Commensurate Fractional-Order ModelsA. Taskinen, T. Roinila and M. Vilkko30 October 2012 | Asian Journal of Control, Vol. 15, No. 3Dynamics of semiflexible regular hyperbranched polymersFlorian Fürstenberg, Maxim Dolgushev and Alexander Blumen21 Jan 2013 | The Journal of Chemical Physics, Vol. 138, No. 3SelfsimilarityVladimir V. Uchaikin1 Jan 2013Equations and SolutionsVladimir V. Uchaikin1 Jan 2013Generalized Kubo relations and conditions for anomalous diffusion: Physical insights from a mathematical theoremGerald R. Kneller14 Jun 2011 | The Journal of Chemical Physics, Vol. 134, No. 22Molecular dynamics of ionic liquids as probed by rheologyN. V. Pogodina, M. Nowak, J. Läuger, C. O. Klein and M. Wilhelm et al.1 Mar 2011 | Journal of Rheology, Vol. 55, No. 2Thermodynamical Restrictions and Wave Propagation for a Class of Fractional Order Viscoelastic RodsTeodor M. Atanacković, Sanja Konjik, Ljubica Oparnica and Dušan Zorica1 Jan 2011 | Abstract and Applied Analysis, Vol. 2011Modern Rheology on a Stock Market: Fractional Dynamics of IndicesM. Kozłowska and R. Kutner1 Oct 2010 | Acta Physica Polonica A, Vol. 118, No. 4Relaxation of polymers modeled by generalized Husimi cactiM Galiceanu28 June 2010 | Journal of Physics A: Mathematical and Theoretical, Vol. 43, No. 30Rheological representation of fractional order viscoelastic material modelsKaterina D. Papoulia, Vassilis P. Panoskaltsis, Nishu V. Kurup and Igor Korovajchuk20 February 2010 | Rheologica Acta, Vol. 49, No. 4Singular Dynamics of Various Macroeconomic SectorsM. Kozłowska and R. Kutner1 Apr 2010 | Acta Physica Polonica A, Vol. 117, No. 4Exact solution on unsteady Couette flow of generalized Maxwell fluid with fractional derivativeW. Shaowei and X. Mingyu14 April 2006 | Acta Mechanica, Vol. 187, No. 1-4Intermediate processes and critical phenomena: Theory, method and progress of fractional operators and their applications to modern mechanicsMingyu Xu and Wenchang Tan1 Jun 2006 | Science in China Series G, Vol. 49, No. 3Generalized Gaussian Structures: Models for Polymer Systems with ComplexTopologiesAndrey A. Gurtovenko and Alexander Blumen5 July 2005Counter-ions dynamics in highly plastic and conducting compounds of poly(aniline). A quasi-elastic neutron scattering studyDavid Djurado, Marc Bée, Maciej Sniechowski, Spencer Howells and Patrice Rannou et al.1 January 2005 | Phys. Chem. Chem. Phys., Vol. 7, No. 6Generalized Vicsek Fractals: Regular Hyperbranched PolymersA. Blumen, Ch. von Ferber, A. Jurjiu and Th. Koslowski24 December 2003 | Macromolecules, Vol. 37, No. 2Anomalous diffusion, nonlinear fractional Fokker–Planck equation and solutionsE.K. Lenzi, L.C. Malacarne, R.S. Mendes and I.T. Pedron1 Mar 2003 | Physica A: Statistical Mechanics and its Applications, Vol. 319Viscoelastic Relaxation of Cross-Linked, Alternating Copolymers in the Free-Draining LimitCristian Satmarel, Andrew A. Gurtovenko and Alexander Blumen28 December 2002 | Macromolecules, Vol. 36, No. 2Rouse Dynamics of Polymer Networks Bearing Dendritic WedgesAndrew A. Gurtovenko, Yuli Ya. Gotlib and Alexander Blumen8 August 2002 | Macromolecules, Vol. 35, No. 19Dynamics of dendrimers and of randomly built branched polymersC. von Ferber and A. Blumen1 Jan 2002 | The Journal of Chemical Physics, Vol. 116, No. 19Anomalous dynamics of model polymer systemsA. Blumen, A.A. Gurtovenko and S. Jespersen1 Dec 2001 | Journal of Luminescence, Vol. 94-95Dynamics of annealed systems under external fields: CTRW and the fractional Fokker-Planck equationsI. M Sokolov, A Blumen and J Klafter2 January 2007 | Europhysics Letters (EPL), Vol. 56, No. 2Anomalous diffusion of particles with internal degrees of freedomAlexander Blumen25 August 2009 | Philosophical Magazine B, Vol. 81, No. 9Fractional Diffusion Based on Riemann-Liouville Fractional DerivativesR. Hilfer4 April 2000 | The Journal of Physical Chemistry B, Vol. 104, No. 16 Applications of Fractional Calculus in PhysicsMetrics History PDF download