On the Stability of Objective Structures
By (author) Martin Steinbach
Paperback (Published)
(November 2021)
ISBN: 9783832553784
5.71 x 8.27 inches
Price: $60.00
Out of stock
The 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.
- By (author) Martin Steinbach
Other Titles in this Series
Connecting Atomistic and Continuum Models of Nonlinear Elasticity Theory
Rigorous Existence and Convergence Results for the Boundary Value Problems
Volume 31
The Lifted Root Number Conjecture for small sets of places and an application to CM-extensions
Volume 12
Effective Theories for Brittle Materials
A Derivation of Cleavage Laws and Linearized Griffith Energies from Atomistic and Continuum Nonlinear Models
Volume 28
Similar Books
![Book cover: Transitive Media [Philosophy]](https://isd.stisonbooks.com/images/books/native/9781804132340.jpg?asset_id=66970)
Care in an Era of New Technologies and Artificial Intelligence
Relationships in a Connected World
Volume 14
Buchblogs zwischen Passion und Profession
Zur Diskursivierung digitaler literaturbezogener Anschlusskommunikation als Arbeit
Die Einführung ins richtige Handeln in der Arithmetik (Madḫal ar-rašad ilā ʿilm al-ʿadad) von al-Qalaṣādī (st. 1486)
Bearbeitung und Einordnung in die maġribinische Mathematikgeschichte
Volume 19
Digitale Medien und Religionsunterricht
Ein domänenspezifischer Beitrag zu einer kritischen Medienbildung unter Berücksichtigung medien-, bildungs- und lerntheoretischer Perspektiven
Ein Glucksritter als Wegbereiter der Motorisierung
Der Basler Kaufmann Eduard Burckhardt (1847-1897)
Partizipative Produktentwicklung in der Modeindustrie
Methoden, Vorgehensmodelle und ihre Anwendung in der Wertschöpfung smarter Outdoorbekleidung
Heterarchical Production Planning and Control Architectures in the Context of Industry 4.0
Complexity-based Selection and Guidance for Implementation
Volume 67
Proceedings of the 7th Symposium of the Hellenic Society for Archaeometry
Archaeology Archaeometry: 30 Years Later
I disegni e i discorsi di Giovanni Antonio Nigrone vol. I
fontanaro e ingegniero de acqua (1585-1609 ca.)
Volume 481
I disegni e i discorsi di Giovanni Antonio Nigrone vol. II
Fontanaro e ingegniero de acqua (1585-1609 ca.)
Volume 497
