4,541 research outputs found
On a discrete-to-continuum convergence result for a two dimensional brittle material in the small displacement regime
We consider a two-dimensional atomic mass spring system and show that in the
small displacement regime the corresponding discrete energies can be related to
a continuum Griffith energy functional in the sense of Gamma-convergence. We
also analyze the continuum problem for a rectangular bar under tensile boundary
conditions and find that depending on the boundary loading the minimizers are
either homogeneous elastic deformations or configurations that are completely
cracked generically along a crystallographic line. As applications we discuss
cleavage properties of strained crystals and an effective continuum fracture
energy for magnets
An analysis of crystal cleavage in the passage from atomistic models to continuum theory
We study the behavior of atomistic models in general dimensions under
uniaxial tension and investigate the system for critical fracture loads. We
rigorously prove that in the discrete-to-continuum limit the minimal energy
satisfies a particular cleavage law with quadratic response to small boundary
displacements followed by a sharp constant cut-off beyond some critical value.
Moreover, we show that the minimal energy is attained by homogeneous elastic
configurations in the subcritical case and that beyond critical loading
cleavage along specific crystallographic hyperplanes is energetically
favorable. In particular, our results apply to mass spring models with full
nearest and next-to-nearest pair interactions and provide the limiting minimal
energy and minimal configurations.Comment: The final publication is available at springerlink.co
Supersymmetry and eigensurface topology of the planar quantum pendulum
We make use of supersymmetric quantum mechanics (SUSY QM) to find three sets
of conditions under which the problem of a planar quantum pendulum becomes
analytically solvable. The analytic forms of the pendulum's eigenfuntions make
it possible to find analytic expressions for observables of interest, such as
the expectation values of the angular momentum squared and of the orientation
and alignment cosines as well as of the eigenenergy. Furthermore, we find that
the topology of the intersections of the pendulum's eigenenergy surfaces can be
characterized by a single integer index whose values correspond to the sets of
conditions under which the analytic solutions to the quantum pendulum problem
exist
Supersymmetry and eigensurface topology of the spherical quantum pendulum
We undertook a mutually complementary analytic and computational study of the
full-fledged spherical (3D) quantum rotor subject to combined orienting and
aligning interactions characterized, respectively, by dimensionless parameters
and . By making use of supersymmetric quantum mechanics (SUSY
QM), we found two sets of conditions under which the problem of a spherical
quantum pendulum becomes analytically solvable. These conditions coincide with
the loci of the intersections of the eigenenergy
surfaces spanned by the and parameters. The integer topological
index is independent of the eigenstate and thus of the projection quantum
number . These findings have repercussions for rotational spectra and
dynamics of molecules subject to combined permanent and induced dipole
interactions.Comment: arXiv admin note: text overlap with arXiv:1404.224
Topology of surfaces for molecular Stark energy, alignment and orientation generated by combined permanent and induced electric dipole interactions
We show that combined permanent and induced electric dipole interactions of
polar and polarizable molecules with collinear electric fields lead to a sui
generis topology of the corresponding Stark energy surfaces and of other
observables - such as alignment and orientation cosines - in the plane spanned
by the permanent and induced dipole interaction parameters. We find that the
loci of the intersections of the surfaces can be traced analytically and that
the eigenstates as well as the number of their intersections can be
characterized by a single integer index. The value of the index, distinctive
for a particular ratio of the interaction parameters, brings out a close
kinship with the eigenproperties obtained previously for a class of Stark
states via the apparatus of supersymmetric quantum mechanics.Comment: 22 pages, including 2 tables and 8 figure
"weit vor dem Ende abgebrochen [...]" : Kafkas fragmentarisches Schreiben
Der vorliegende Beitrag - die stark überarbeitete Fassung des Vortrages "Lektüren des Unausdeutbaren ", den der Verfasser im Januar 2004 im Rahmen der kulturwissenschaftlichen Vortragsreihe GrenzBereiche des Lesens hielt - ist auch erschienen in: literatur für leser 27 (2004), Heft 4, S. 181-199. Ein Beispiel für die Schwierigkeit der literarischen Lektüre gibt Friedrich Schmidt. Er untersucht Lektüremöglichkeiten für das formale wie semantische "Abgebrochensein" des literarischen Kunstwerks der Moderne, wie es in den Fragmenten Kafkas seinen exponierten Ausdruck findet. In diesen Texten tritt zur äußeren Unabgeschlossenheit des Textkorpus ein brüchiges Sinngefüge: die Endlosigkeit der Reflexionen und Handlungszüge, die Heterogenität der Erzählfiguren, die Inkonsistenz jeder Bedeutungskonstruktion von Seiten des Lesers. Indem überdies der Abbruch, als verlorene Schrift oder verschwiegene Botschaft, in Kafkas Fragmenten explizit zum Thema wird, erhebt sich der Text gleichzeitig zum metareflexiven Kommentar: er vollzieht selbst, wovon er spricht. Insofern handelt er – sprachskeptisch – vom Defizit seines eigenen Ausdrucks, das letztlich auch von Lektüren nie vollständig eingeholt werden kann
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