LEADER 03962nam 2200637 a 450 001 9910437900903321 005 20250609110843.0 010 $a1-283-93548-1 010 $a3-642-35245-6 024 7 $a10.1007/978-3-642-35245-4 035 $a(CKB)2670000000317408 035 $a(EBL)1082888 035 $a(OCoLC)823728201 035 $a(SSID)ssj0000879852 035 $a(PQKBManifestationID)11458749 035 $a(PQKBTitleCode)TC0000879852 035 $a(PQKBWorkID)10853698 035 $a(PQKB)11202704 035 $a(DE-He213)978-3-642-35245-4 035 $a(MiAaPQ)EBC1082888 035 $a(MiAaPQ)EBC4976497 035 $a(Au-PeEL)EBL4976497 035 $a(CaONFJC)MIL424798 035 $a(OCoLC)1027160769 035 $a(PPN)168328305 035 $a(MiAaPQ)EBC4419247 035 $a(EXLCZ)992670000000317408 100 $a20121031d2013 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aTopological derivatives in shape optimization /$fAntonio Andre Novotny and Jan Sokoowski 205 $a1st ed. 2013. 210 $aNew York $cSpringer$d2013 215 $a1 online resource (422 p.) 225 1 $aInteraction of mechanics and mathematics,$x1860-6245 300 $aDescription based upon print version of record. 311 08$a3-642-35244-8 320 $aIncludes bibliographical references and index. 327 $aDomain Derivation in Continuum Mechanics -- Material and Shape Derivatives for Boundary Value Problems -- Singular Perturbations of Energy Functionals -- Configurational Perturbations of Energy Functionals -- Topological Derivative Evaluation with Adjoint States -- Topological Derivative for Steady-State Orthotropic Heat Diffusion Problems -- Topological Derivative for Three-Dimensional Linear Elasticity Problems -- Compound Asymptotic Expansions for Spectral Problems -- Topological Asymptotic Analysis for Semilinear Elliptic Boundary Value Problems -- Topological Derivatives for Unilateral Problems. 330 $aThe topological derivative is defined as the first term (correction) of the asymptotic expansion of a given shape functional with respect to a small parameter that measures the size of singular domain perturbations, such as holes, inclusions, defects, source-terms and cracks. Over the last decade, topological asymptotic analysis has become a broad, rich and fascinating research area from both theoretical and numerical standpoints. It has applications in many different fields such as shape and topology optimization, inverse problems, imaging processing and mechanical modeling including synthesis and/or optimal design of microstructures, sensitivity analysis in fracture mechanics and damage evolution modeling. Since there is no monograph on the subject at present, the authors provide here the first account of the theory which combines classical sensitivity analysis in shape optimization with asymptotic analysis by means of compound asymptotic expansions for elliptic boundary value problems. This book is intended for researchers and graduate students in applied mathematics and computational mechanics interested in any aspect of topological asymptotic analysis. In particular, it can be adopted as a textbook in advanced courses on the subject and shall be useful for readers interested in the mathematical aspects of topological asymptotic analysis as well as in applications of topological derivatives in computational mechanics. 410 0$aInteraction of mechanics and mathematics series. 606 $aShape theory (Topology) 615 0$aShape theory (Topology) 676 $a005.4/3 700 $aNovotny$b Antonio Andre$00 701 $aSokoowski$b Jan$059815 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910437900903321 996 $aTopological derivatives in shape optimization$94194416 997 $aUNINA LEADER 03854nam 22006135 450 001 9910996495003321 005 20250411151520.0 010 $a9789819616435 010 $a9819616433 024 7 $a10.1007/978-981-96-1643-5 035 $a(CKB)38429305600041 035 $a(DE-He213)978-981-96-1643-5 035 $a(MiAaPQ)EBC32007522 035 $a(Au-PeEL)EBL32007522 035 $a(EXLCZ)9938429305600041 100 $a20250411d2025 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aHigher-Form Symmetry and Eigenstate Thermalization Hypothesis /$fby Osamu Fukushima 205 $a1st ed. 2025. 210 1$aSingapore :$cSpringer Nature Singapore :$cImprint: Springer,$d2025. 215 $a1 online resource (XIV, 75 p. 14 illus., 13 illus. in color.) 225 1 $aSpringer Theses, Recognizing Outstanding Ph.D. Research,$x2190-5061 311 08$a9789819616428 311 08$a9819616425 327 $a -- 1 Introduction. -- 2 Thermalization in isolated quantum systems. -- 3 Violation of the ETH in QFTs with higher-form symmetry. -- 4 Effects of projective phase on the ETH. -- 5 Conclusion and discussion. -- 6 Appendices. 330 $aThe eigenstate thermalization hypothesis (ETH) provides a successful framework for understanding thermalization in isolated quantum systems. While extensive numerical and theoretical studies support ETH as a key mechanism for thermalization, determining whether specific systems satisfy ETH analytically remains a challenge. In quantum many-body systems and quantum field theories, ETH violations signal nontrivial thermalization processes and are gaining attention. This book explores how higher-form symmetries affect thermalization dynamics in isolated quantum systems. It analytically shows that a p-form symmetry in a $(d+1)$-dimensional quantum field theory can cause ETH breakdown for certain nontrivial $(d-p)$-dimensional observables. For discrete higher-form symmetries (i.e., $p\geq 1$), thermalization fails for observables that are non-local yet much smaller than the system size, despite the absence of local conserved quantities. Numerical evidence is provided for the $(2+1)$-dimensional $\mathbb{Z}_2$ lattice gauge theory, where local observables thermalize, but non-local ones, such as those exciting a magnetic dipole, relax to a generalized Gibbs ensemble incorporating the $\mathbb{Z}_2$ 1-form symmetry. The ETH violation mechanism here involves the mixing of symmetry sectors within an energy shell?a rather difficult condition to verify. To address this, the book introduces a projective phase framework for $\mathbb{Z}_N$-symmetric theories, supported by numerical analyses of spin chains and lattice gauge theories. 410 0$aSpringer Theses, Recognizing Outstanding Ph.D. Research,$x2190-5061 606 $aQuantum theory 606 $aStatistical physics 606 $aParticles (Nuclear physics) 606 $aQuantum field theory 606 $aFundamental concepts and interpretations of QM 606 $aStatistical Physics 606 $aElementary Particles, Quantum Field Theory 615 0$aQuantum theory. 615 0$aStatistical physics. 615 0$aParticles (Nuclear physics) 615 0$aQuantum field theory. 615 14$aFundamental concepts and interpretations of QM. 615 24$aStatistical Physics. 615 24$aElementary Particles, Quantum Field Theory. 676 $a530.12 700 $aFukushima$b Osamu$4aut$4http://id.loc.gov/vocabulary/relators/aut$0474853 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910996495003321 996 $aHigher-Form Symmetry and Eigenstate Thermalization Hypothesis$94375205 997 $aUNINA