220 research outputs found
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
Continuation Sheaves in Dynamics: Sheaf Cohomology and Bifurcation
Continuation of algebraic structures in families of dynamical systems is
described using category theory, sheaves, and lattice algebras. Well-known
concepts in dynamics, such as attractors or invariant sets, are formulated as
functors on appropriate categories of dynamical systems mapping to categories
of lattices, posets, rings or abelian groups. Sheaves are constructed from such
functors, which encode data about the continuation of structure as system
parameters vary. Similarly, morphisms for the sheaves in question arise from
natural transformations. This framework is applied to a variety of lattice
algebras and ring structures associated to dynamical systems, whose algebraic
properties carry over to their respective sheaves. Furthermore, the cohomology
of these sheaves are algebraic invariants which contain information about
bifurcations of the parametrized systems
Lateral versus interdigitated diode design for 10 Gb/s low-voltage low-loss silicon ring modulators
Scanning spreading resistance microscopy of two-dimensional diffusion of boron implanted in free-standing silicon nanostructures
B implants of 1keV, 1×10¹⁵at.cm⁻² into 125-nm-wide, free-standing Si nanostructures have been characterized using scanning spreading resistancemicroscopy following a 0s, 1050°Canneal in N₂. A curved diffusion front has been observed. B in the center of the ridge diffuses further than at the sides. A similar effect has been observed in SUPREM-IV simulations. It is attributed to a reduction in transient enhanced diffusion close to the vertical surfaces due to recombination of ion-implantation-induced excess Si self-interstitials
Electrical Characterization of Submicrometer Silicon Devices by Cross-Sectional Contact Mode Atomic Force Microscopy
Two contact mode atomic force microscopic (AFM) techniques under ambient conditions are presented for the electrical evaluation of cross sectioned silicon devices. In the first technique, a conductive AFM tip is used as a voltage probe to determine the local potential distribution on the cross section of a silicon device under operation. The electrical potential is measured simultaneously with the surface topography with nanometer resolution and mV accuracy, offering an easy way of correlating topographic and electrical features. A second method, nanometer spreading resistance profiling (nano-SRP), performs localized spreading resistance measurements to determine the spatial distribution of charge carriers in silicon structures. The conversion of the resistance profiles into charge carrier profiles as well as the applied correction factors are discussed in more detail. Both methods are used to map electrical characteristics of state-of-the-art silicon structures
Thickness dependence of the resistivity of Platinum group metal thin films
We report on the thin film resistivity of several platinum-group metals (Ru,
Pd, Ir, Pt). Platinum-group thin films show comparable or lower resistivities
than Cu for film thicknesses below about 5\,nm due to a weaker thickness
dependence of the resistivity. Based on experimentally determined mean linear
distances between grain boundaries as well as ab initio calculations of the
electron mean free path, the data for Ru, Ir, and Cu were modeled within the
semiclassical Mayadas--Shatzkes model [Phys. Rev. B 1, 1382 (1970)] to assess
the combined contributions of surface and grain boundary scattering to the
resistivity. For Ru, the modeling results indicated that surface scattering was
strongly dependent on the surrounding material with nearly specular scattering
at interfaces with SiO2 or air but with diffuse scattering at interfaces with
TaN. The dependence of the thin film resistivity on the mean free path is also
discussed within the Mayadas--Shatzkes model in consideration of the
experimental findings.Comment: 28 pages, 9 figure
Undoped and in-situ B doped GeSn epitaxial growth on Ge by atmospheric pressure-chemical vapor deposition
- …