02230nam 2200385 450 991077489270332120230223222915.010.30819/5378(CKB)5670000000197671(NjHacI)995670000000197671(EXLCZ)99567000000019767120230223d2021 uy 0engur|||||||||||txtrdacontentcrdamediacrrdacarrierOn the Stability of Objective StructuresVolume 38 /Martin SteinbachBerlin :Logos Verlag,2021.1 online resource (174 pages)Augsburger Schriften zur Mathematik, Physik und InformatikThe 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.On the Stability of Objective Structures Mathematical physicsMathematicsMathematical physics.Mathematics.530.15Steinbach Martin1229891NjHacINjHaclBOOK9910774892703321On the Stability of Objective Structures2854906UNINA