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101 0 $aeng
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181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aOn the Stability of Objective Structures$hVolume 38 /$fMartin Steinbach
210  1$aBerlin :$cLogos Verlag,$d2021.
215   $a1 online resource (174 pages)
225 0 $aAugsburger Schriften zur Mathematik, Physik und Informatik
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.
517   $aOn the Stability of Objective Structures 
606   $aMathematical physics
606   $aMathematics
615  0$aMathematical physics.
615  0$aMathematics.
676   $a530.15
700   $aSteinbach$b Martin$01229891
801  0$bNjHacI
801  1$bNjHacl
906   $aBOOK
912   $a9910774892703321
996   $aOn the Stability of Objective Structures$92854906
997   $aUNINA