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100   $a20121227d2003      u|             0
101 0 $aeng
135   $aurnn#008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aVariational Methods for Crystalline Microstructure - Analysis and Computation$b[electronic resource] /$fby Georg Dolzmann
205   $a1st ed. 2003.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2003.
215   $a1 online resource (XI, 217 p.)
225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1803
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a3-540-00114-X 
327   $aIntroduction -- Semiconvex Hull of Compact Sets -- Macroscopic Energy for Nematic Elastomers -- Uniqueness and Stability of Microstructure -- Applications to Martensitic Transformations -- Algorithmic Aspects -- Bibliographic Remarks -- A. Convexity Conditions and Rank-one Connections -- B. Elements of Crystallography -- C. Notation -- References -- Index.
330   $aPhase transformations in solids typically lead to surprising mechanical behaviour with far reaching technological applications. The mathematical modeling of these transformations in the late 80s initiated a new field of research in applied mathematics, often referred to as mathematical materials science, with deep connections to the calculus of variations and the theory of partial differential equations. This volume gives a brief introduction to the essential physical background, in particular for shape memory alloys and a special class of polymers (nematic elastomers). Then the underlying mathematical concepts are presented with a strong emphasis on the importance of quasiconvex hulls of sets for experiments, analytical approaches, and numerical simulations.
410  0$aLecture Notes in Mathematics,$x0075-8434 ;$v1803
606   $aMathematics
606   $aCondensed matter
606   $aPartial differential equations
606   $aNumerical analysis
606   $aPhysics
606   $aMechanics
606   $aMathematics, general$3https://scigraph.springernature.com/ontologies/product-market-codes/M00009
606   $aCondensed Matter Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P25005
606   $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155
606   $aNumerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M14050
606   $aMathematical Methods in Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19013
606   $aClassical Mechanics$3https://scigraph.springernature.com/ontologies/product-market-codes/P21018
615  0$aMathematics.
615  0$aCondensed matter.
615  0$aPartial differential equations.
615  0$aNumerical analysis.
615  0$aPhysics.
615  0$aMechanics.
615 14$aMathematics, general.
615 24$aCondensed Matter Physics.
615 24$aPartial Differential Equations.
615 24$aNumerical Analysis.
615 24$aMathematical Methods in Physics.
615 24$aClassical Mechanics.
676   $a620.11299
686   $a74N15$2msc
686   $a65M20$2msc
686   $a74B20$2msc
700   $aDolzmann$b Georg$4aut$4http://id.loc.gov/vocabulary/relators/aut$067423
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a996466586303316
996   $aVariational methods for crystalline microstructure$9145757
997   $aUNISA