LEADER 00955nam a22002531i 4500 001 991000111839707536 005 20230307122020.0 008 040802s1971 fr |||||||||||||||||fre 035 $ab13178623-39ule_inst 035 $aARCHE-113123$9ExL 040 $aBibl. Interfacoltà T. Pellegrino$bita$cA.t.i. Arché s.c.r.l. Pandora Sicilia s.r.l. 082 04$a794.1 100 1 $aAlekhine, Alexander$0489968 245 10$aTestament d'Alekhine :$bcommentaires : Alekhine selon Alekhine /$cpar A. Baratz 260 $aParis :$bPresses du Temps present,$c[1971] 300 $a182 p. ;$c24 cm 650 4$aScacchi 700 1 $aBaratz, A. 907 $a.b13178623$b02-04-14$c05-08-04 912 $a991000111839707536 945 $aLE002 Fondo Giudici S 561$g1$i2002000391520$lle002$nC. 1$o-$pE0.00$q-$rn$so$t0$u0$v0$w0$x0$y.i13819343$z05-08-04 996 $aTestament d'Alekhine$9313110 997 $aUNISALENTO 998 $ale002$b05-08-04$cm$da$e-$ffre$gfr$h0$i1 LEADER 02540nam 22004573a 450 001 9910557635903321 005 20230124202330.0 024 8 $ahttps://doi.org/10.30819/5378 035 $a(CKB)5400000000045055 035 $a(ScCtBLL)a7e6ac82-a206-4fd4-a3e4-7c4cdacb3f5c 035 $a(oapen)https://directory.doabooks.org/handle/20.500.12854/75074 035 $a(oapen)doab77421 035 $a(EXLCZ)995400000000045055 100 $a20220504i20212022 uu 101 0 $aeng 135 $auru|||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 00$aOn the Stability of Objective Structures$fMartin Steinbach$hVolume 38 210 $aBerlin$cLogos Verlag Berlin$d2021 210 1$a[s.l.] :$cLogos Verlag Berlin,$d2021. 215 $a1 online resource (174 p.) 225 1 $aAugsburger Schriften zur Mathematik, Physik und Informatik 311 08$a9783832553784 311 08$a3832553789 330 $aThe main focus of this thesis is the discussion of stability of an objective (atomic) structure consisting of single atoms which interact via a potential. We define atomistic stability using a second derivative test. More precisely, atomistic stability is equivalent to a vanishing first derivative of the configurational energy (at the corresponding point) and the coerciveness of the second derivative of the configurational energy with respect to an appropriate semi-norm. Atomistic stability of a lattice is well understood, see, e.,g., [40]. The aim of this thesis is to generalize the theory to objective structures. In particular, we first investigate discrete subgroups of the Euclidean group, then define an appropriate seminorm and the atomistic stability for a given objective structure, and finally provide an efficient algorithm to check its atomistic stability. The algorithm particularly checks the validity of the Cauchy-Born rule for objective structures. To illustrate our results, we prove numerically the stability of a carbon nanotube by applying the algorithm. 410 $aAugsburger Schriften zur Mathematik, Physik und Informatik 606 $aScience / Physics$2bisacsh 606 $aMathematics$2bisacsh 606 $aMathematics 615 7$aScience / Physics 615 7$aMathematics 615 0$aMathematics. 700 $aSteinbach$b Martin$01229891 801 0$bScCtBLL 801 1$bScCtBLL 906 $aBOOK 912 $a9910557635903321 996 $aOn the Stability of Objective Structures$92854906 997 $aUNINA