710 research outputs found
Symplectomorphisms and discrete braid invariants
Area and orientation preserving diffeomorphisms of the standard 2-disc,
referred to as symplectomorphisms of , allow decompositions in
terms of positive twist diffeomorphisms. Using the latter decomposition we
utilize the Conley index theory of discrete braid classes as introduced in
[Ghrist et al., C. R. Acad. Sci. Paris S\'er. I Math., 331(11), 2000, Invent.
Math., 152(2), 2003] in order to obtain a Morse type forcing theory of periodic
points: a priori information about periodic points determines a mapping class
which may force additional periodic points.Comment: 31 pages, in print in Journal of Fixed Point Theory and Application
Functoriality and duality in Morse-Conley-Floer homology
In~\cite{rotvandervorst} a homology theory --Morse-Conley-Floer homology--
for isolated invariant sets of arbitrary flows on finite dimensional manifolds
is developed. In this paper we investigate functoriality and duality of this
homology theory. As a preliminary we investigate functoriality in Morse
homology. Functoriality for Morse homology of closed manifolds is
known~\cite{abbondandoloschwarz, aizenbudzapolski,audindamian,
kronheimermrowka, schwarz}, but the proofs use isomorphisms to other homology
theories. We give direct proofs by analyzing appropriate moduli spaces. The
notions of isolating map and flow map allows the results to generalize to local
Morse homology and Morse-Conley-Floer homology. We prove Poincar\'e type
duality statements for local Morse homology and Morse-Conley-Floer homology.Comment: To appear in the Journal of Fixed Point theory and its Application
Morse-Conley-Floer Homology
For Morse-Smale pairs on a smooth, closed manifold the Morse-Smale-Witten
chain complex can be defined. The associated Morse homology is isomorphic to
the singular homology of the manifold and yields the classical Morse relations
for Morse functions. A similar approach can be used to define homological
invariants for isolated invariant sets of flows on a smooth manifold, which
gives an analogue of the Conley index and the Morse-Conley relations. The
approach will be referred to as Morse-Conley-Floer homology
Morse theory on spaces of braids and Lagrangian dynamics
In the first half of the paper we construct a Morse-type theory on certain
spaces of braid diagrams. We define a topological invariant of closed positive
braids which is correlated with the existence of invariant sets of parabolic
flows defined on discretized braid spaces. Parabolic flows, a type of
one-dimensional lattice dynamics, evolve singular braid diagrams in such a way
as to decrease their topological complexity; algebraic lengths decrease
monotonically. This topological invariant is derived from a Morse-Conley
homotopy index and provides a gloablization of `lap number' techniques used in
scalar parabolic PDEs.
In the second half of the paper we apply this technology to second order
Lagrangians via a discrete formulation of the variational problem. This
culminates in a very general forcing theorem for the existence of infinitely
many braid classes of closed orbits.Comment: Revised version: numerous changes in exposition. Slight modification
of two proofs and one definition; 55 pages, 20 figure
The algebra of semi-flows: a tale of two topologies
To capture the global structure of a dynamical system we reformulate dynamics
in terms of appropriately constructed topologies, which we call flow
topologies; we call this process topologization. This yields a description of a
semi-flow in terms of a bi-topological space, with the first topology
corresponding to the (phase) space and the second to the flow topology. A study
of topology is facilitated through discretization, i.e. defining and examining
appropriate finite sub-structures. Topologizing the dynamics provides an
elegant solution to their discretization by discretizing the associated flow
topologies. We introduce Morse pre-orders, an instance of a more general
bi-topological discretization, which synthesize the space and flow topologies,
and encode the directionality of dynamics. We describe how Morse pre-orders can
be augmented with appropriate (co)homological information in order to describe
invariance of the dynamics; this ensemble provides an algebraization of the
semi-flow. An illustration of the main ingredients of the paper is provided by
an application to the theory of discrete parabolic flows. Algebraization yields
a new invariant for positive braids in terms of a bi-graded differential module
which contains Morse theoretic information of parabolic flows
Conductive atomic force microscopy studies of thin SiO[sub 2] layer degradation
The dielectric degradation of ultrathin 2 nm silicon dioxide SiO2 layers has been investigated
by constant and ramped voltage stresses with the conductive atomic force microscopy CAFM.
CAFM imaging shows clearly the lateral degradation propagation and its saturation. Current-voltage
characteristics, performed at nanometer scale, show the trap creation rate in function of the stress
condition. The critical trap density has been found
Phase formation and thermal stability of ultrathin nickel-silicides on Si(100)
The solid-state reaction and agglomeration of thin nickel-silicide films was investigated from sputter deposited nickel films (1-10 nm) on silicon-on-insulator (100) substrates. For typical anneals at a ramp rate of 3 degrees C/s, 5-10 nm Ni films react with silicon and form NiSi, which agglomerates at 550-650 degrees C, whereas films with a thickness of 3.7 nm of less were found to form an epitaxylike nickel-silicide layer. The resulting films show an increased thermal stability with a low electrical resistivity up to 800 degrees C
- …