LEADER 00872nam a2200253 i 4500 001 991001255279707536 005 20020502185751.0 008 950612s1993 it ||| | ita 020 $a888598861X 035 $ab11486004-39ule_inst 035 $aPRUMB57625$9ExL 040 $aDip. di SSSC - Teatro$bita 100 1 $aSpoto, Donald$0527431 245 10$aLaurence Olivier :$bUna biografia /$cDonald Spoto 260 $aMilano :$bBaldini & Castoldi,$cc1993 300 $a519 p. ;$c25 cm. 490 0 $aSaggi [Baldini & Castoldi] ;$v23 650 4$aOlivier, Laurence 907 $a.b11486004$b01-03-17$c01-07-02 912 $a991001255279707536 945 $aLE021 C34C15$g1$i2021000155031$lle021$o-$pE0.00$q-$rl$so $t0$u1$v1$w1$x0$y.i11677351$z01-07-02 996 $aLaurence Olivier$9812343 997 $aUNISALENTO 998 $ale021$b01-01-95$cm$da $e-$fita$git $h0$i1 LEADER 03933nam 22007935 450 001 9910300254203321 005 20250717140300.0 010 $a94-6239-154-8 024 7 $a10.2991/978-94-6239-154-3 035 $a(CKB)3710000000515995 035 $a(EBL)4098364 035 $a(SSID)ssj0001585298 035 $a(PQKBManifestationID)16264952 035 $a(PQKBTitleCode)TC0001585298 035 $a(PQKBWorkID)14865724 035 $a(PQKB)10694555 035 $a(DE-He213)978-94-6239-154-3 035 $a(MiAaPQ)EBC4098364 035 $z(PPN)258862440 035 $a(PPN)190523344 035 $a(EXLCZ)993710000000515995 100 $a20151119d2015 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aMean Field Theories and Dual Variation - Mathematical Structures of the Mesoscopic Model /$fby Takashi Suzuki 205 $a2nd ed. 2015. 210 1$aParis :$cAtlantis Press :$cImprint: Atlantis Press,$d2015. 215 $a1 online resource (450 p.) 225 1 $aAtlantis Studies in Mathematics for Engineering and Science,$x2467-9631 ;$v11 300 $aDescription based upon print version of record. 311 08$a94-6239-153-X 320 $aIncludes bibliographical references and index. 327 $aChemotaxis -- Time Relaxization -- Toland Duality -- Phenomenology -- Phase Transition -- Critical Phenomena of Isolated Systems -- Self-Interacting Fluids -- Magnetic Fields -- Boltzmann-Poisson Equation -- Particle Kinetics -- Parabolic Equations -- Gauge Fields -- Higher- Dimensional Blowup. 330 $aMean field approximation has been adopted to describe macroscopic phenomena from microscopic overviews. It is still in progress; fluid mechanics, gauge theory, plasma physics, quantum chemistry, mathematical oncology, non-equilibirum thermodynamics.  spite of such a wide range of scientific areas that are concerned with the mean field theory, a unified study of its mathematical structure has not been discussed explicitly in the open literature.  The benefit of this point of view on nonlinear problems should have significant impact on future research, as will be seen from the underlying features of self-assembly or bottom-up self-organization which is to be illustrated in a unified way. The aim of this book is to formulate the variational and hierarchical aspects of the equations that arise in the mean field theory from macroscopic profiles to microscopic principles, from dynamics to equilibrium, and from biological models to models that arise from chemistry and physics. 410 0$aAtlantis Studies in Mathematics for Engineering and Science,$x2467-9631 ;$v11 606 $aMathematical analysis 606 $aMathematical optimization 606 $aCalculus of variations 606 $aMathematical physics 606 $aPopulation genetics 606 $aBiomathematics 606 $aAnalysis 606 $aCalculus of Variations and Optimization 606 $aMathematical Physics 606 $aPopulation Genetics 606 $aMathematical and Computational Biology 615 0$aMathematical analysis. 615 0$aMathematical optimization. 615 0$aCalculus of variations. 615 0$aMathematical physics. 615 0$aPopulation genetics. 615 0$aBiomathematics. 615 14$aAnalysis. 615 24$aCalculus of Variations and Optimization. 615 24$aMathematical Physics. 615 24$aPopulation Genetics. 615 24$aMathematical and Computational Biology. 676 $a510 700 $aSuzuki$b Takashi$4aut$4http://id.loc.gov/vocabulary/relators/aut$0224044 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300254203321 996 $aMean field theories and dual variation - mathematical structures of the mesoscopic model$92440615 997 $aUNINA