scholarly journals Global cross sections for Anosov flows

2015 ◽  
Vol 36 (8) ◽  
pp. 2661-2674
Author(s):  
SLOBODAN N. SIMIĆ
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Anosov Flow ◽  
Anosov Flows ◽  
New Criterion ◽  
Volume Preserving

We provide a new criterion for the existence of a global cross section to a volume-preserving Anosov flow. The criterion is expressed in terms of expansion and contraction rates of the flow and generalizes known results of this type.

Codimension one Anosov flows and a conjecture of Verjovsky

1997 ◽  
Vol 17 (5) ◽  
pp. 1211-1231 ◽  
Author(s):  
SLOBODAN SIMIĆ
Keyword(s):  
Cross Section ◽  
Compact Riemannian Manifold ◽  
Positive Answer ◽  
Stable Bundle ◽  
Anosov Flow ◽  
Hölder Continuous ◽  
Codimension One ◽  
Higher Dimensional ◽  
Anosov Flows ◽  
Volume Preserving

Let $ \Phi $ be a $C^2$ codimension one Anosov flow on a compact Riemannian manifold $M$ of dimension greater than three. Verjovsky conjectured that $ \Phi $ admits a global cross-section and we affirm this conjecture when $ \Phi $ is volume preserving in the following two cases: (1) if the sum of the strong stable and strong unstable bundle of $\Phi$ is $ \theta $-Hölder continuous for all $ \theta < 1 $; (2) if the center stable bundle of $ \Phi $ is of class $ C^{1 + \theta} $ for all $ \theta < 1 $. We also show how certain transitive Anosov flows (those whose center stable bundle is $C^1$ and transversely orientable) can be ‘synchronized’, that is, reparametrized so that the strong unstable determinant of the time $t$ map (for all $t$) of the synchronized flow is identically equal to $ e^t $. Several applications of this method are given, including vanishing of the Godbillon–Vey class of the center stable foliation of a codimension one Anosov flow (when $ \dim M > 3 $ and that foliation is $ C^{1 + \theta} $ for all $ \theta < 1 $), and a positive answer to a higher-dimensional analog to Problem 10.4 posed by Hurder and Katok in [HK].

Electron Irradiation Effects in Polyoxymethylene Crystals Grown Inside Trioxane Crystals

1971 ◽  
Vol 29 ◽  
pp. 78-79
Author(s):  
J. P. Colson ◽  
D. H. Reneker
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Detailed Examination ◽  
The Other ◽  
Electron Micrograph ◽  
Irradiation Effects ◽  
Threefold Axis ◽  
Typical Sample ◽  
Polymer Crystals ◽  
Chain Axis

Polyoxymethylene (POM) crystals grow inside trioxane crystals which have been irradiated and heated to a temperature slightly below their melting point. Figure 1 shows a low magnification electron micrograph of a group of such POM crystals. Detailed examination at higher magnification showed that three distinct types of POM crystals grew in a typical sample. The three types of POM crystals were distinguished by the direction that the polymer chain axis in each crystal made with respect to the threefold axis of the trioxane crystal. These polyoxymethylene crystals were described previously.At low magnifications the three types of polymer crystals appeared as slender rods. One type had a hexagonal cross section and the other two types had rectangular cross sections, that is, they were ribbonlike.

A quantitative approach to inner shell losses

1978 ◽  
Vol 36 (1) ◽  
pp. 526-527 ◽  
Author(s):  
R.D. Leapman ◽  
P. Rez ◽  
D.F. Mayers
Keyword(s):  
Energy Transfer ◽  
Cross Section ◽  
Cross Sections ◽  
Accurate Determination ◽  
Background Intensity ◽  
Core Excitation ◽  
Quantitative Basis ◽  
Cross Section Differential ◽  
Bound Electrons

Microanalysis by EELS has been developing rapidly and though the general form of the spectrum is now understood there is a need to put the technique on a more quantitative basis (1,2). Certain aspects important for microanalysis include: (i) accurate determination of the partial cross sections, σx(α,ΔE) for core excitation when scattering lies inside collection angle a and energy range ΔE above the edge, (ii) behavior of the background intensity due to excitation of less strongly bound electrons, necessary for extrapolation beneath the signal of interest, (iii) departures from the simple hydrogenic K-edge seen in L and M losses, effecting σx and complicating microanalysis. Such problems might be approached empirically but here we describe how computation can elucidate the spectrum shape.The inelastic cross section differential with respect to energy transfer E and momentum transfer q for electrons of energy E0 and velocity v can be written as

Oxygen K near edge structures studied with multiple scattering calculations

1988 ◽  
Vol 46 ◽  
pp. 504-505
Author(s):  
Xudong Weng ◽  
Peter Rez
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Partial Cross Section ◽  
Energy Window ◽  
Edge Structure ◽  
Fine Structures ◽  
Hydrogenic Model ◽  
Electron Energy Loss ◽  
Quantitative Chemical

In electron energy loss spectroscopy, quantitative chemical microanalysis is performed by comparison of the intensity under a specific inner shell edge with the corresponding partial cross section. There are two commonly used models for calculations of atomic partial cross sections, the hydrogenic model and the Hartree-Slater model. Partial cross sections could also be measured from standards of known compositions. These partial cross sections are complicated by variations in the edge shapes, such as the near edge structure (ELNES) and extended fine structures (ELEXFS). The role of these solid state effects in the partial cross sections, and the transferability of the partial cross sections from material to material, has yet to be fully explored. In this work, we consider the oxygen K edge in several oxides as oxygen is present in many materials. Since the energy window of interest is in the range of 20-100 eV, we limit ourselves to the near edge structures.

Absolute inner-shell cross section determination for EELS analysis

1988 ◽  
Vol 46 ◽  
pp. 534-535
Author(s):  
P.A. Crozier
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Absolute Cross Section ◽  
Specimen Thickness ◽  
Mass Thickness ◽  
Scattering Cross ◽  
Before And After ◽  
Estimated Error ◽  
Scattering Cross Sections ◽  
Electron Microscopist

Absolute inelastic scattering cross sections or mean free paths are often used in EELS analysis for determining elemental concentrations and specimen thickness. In most instances, theoretical values must be used because there have been few attempts to determine experimental scattering cross sections from solids under the conditions of interest to electron microscopist. In addition to providing data for spectral quantitation, absolute cross section measurements yields useful information on many of the approximations which are frequently involved in EELS analysis procedures. In this paper, experimental cross sections are presented for some inner-shell edges of Al, Cu, Ag and Au.Uniform thin films of the previously mentioned materials were prepared by vacuum evaporation onto microscope cover slips. The cover slips were weighed before and after evaporation to determine the mass thickness of the films. The estimated error in this method of determining mass thickness was ±7 x 107g/cm2. The films were floated off in water and mounted on Cu grids.

A technique for preparing semiconductor cross sections for both TEM and SEM analysis

1989 ◽  
Vol 47 ◽  
pp. 712-713
Author(s):  
Stanley J. Klepeis ◽  
J.P. Benedict ◽  
R.M Anderson
Keyword(s):  
Sample Preparation ◽  
Cross Section ◽  
Cross Sections ◽  
Sem Analysis ◽  
Preparation Technique ◽  
Ion Milling ◽  
Tem Analysis ◽  
Polished Cross Section ◽  
Area Of Interest ◽  
Polished Side

The ability to prepare a cross-section of a specific semiconductor structure for both SEM and TEM analysis is vital in characterizing the smaller, more complex devices that are now being designed and manufactured. In the past, a unique sample was prepared for either SEM or TEM analysis of a structure. In choosing to do SEM, valuable and unique information was lost to TEM analysis. An alternative, the SEM examination of thinned TEM samples, was frequently made difficult by topographical artifacts introduced by mechanical polishing and lengthy ion-milling. Thus, the need to produce a TEM sample from a unique,cross-sectioned SEM sample has produced this sample preparation technique.The technique is divided into an SEM and a TEM sample preparation phase. The first four steps in the SEM phase: bulk reduction, cleaning, gluing and trimming produces a reinforced sample with the area of interest in the center of the sample. This sample is then mounted on a special SEM stud. The stud is inserted into an L-shaped holder and this holder is attached to the Klepeis polisher (see figs. 1 and 2). An SEM cross-section of the sample is then prepared by mechanically polishing the sample to the area of interest using the Klepeis polisher. The polished cross-section is cleaned and the SEM stud with the attached sample, is removed from the L-shaped holder. The stud is then inserted into the ion-miller and the sample is briefly milled (less than 2 minutes) on the polished side. The sample on the stud may then be carbon coated and placed in the SEM for analysis.

Experimental Studies Of Multilayer Glass Structures On Compression, Compression With Bending And Simple Bending

2019 ◽  
pp. 22-30
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Applied Load ◽  
Experimental Studies ◽  
Strength Properties ◽  
Research Topic ◽  
Normative Values ◽  
Laminated Glass ◽  
The Cross ◽  
Experimental Values

The work of multilayer glass structures for central and eccentric compression and bending are considered. The substantiation of the chosen research topic is made. The description and features of laminated glass for the structures investigated, their characteristics are presented. The analysis of the results obtained when testing for compression, compression with bending, simple bending of models of columns, beams, samples of laminated glass was made. Overview of the types and nature of destruction of the models are presented, diagrams of material operation are constructed, average values of the resistance of the cross-sections of samples are obtained, the table of destructive loads is generated. The need for development of a set of rules and guidelines for the design of glass structures, including laminated glass, for bearing elements, as well as standards for testing, rules for assessing the strength, stiffness, crack resistance and methods for determining the strength of control samples is emphasized. It is established that the strength properties of glass depend on the type of applied load and vary widely, and significantly lower than the corresponding normative values of the strength of heat-strengthened glass. The effect of the connecting polymeric material and manufacturing technology of laminated glass on the strength of the structure is also shown. The experimental values of the elastic modulus are different in different directions of the cross section and in the direction perpendicular to the glass layers are two times less than along the glass layers.

Cross Section Analysis of Cu Filled TSVs Based on High Throughput Plasma-FIB Milling

2012 ◽  
Author(s):  
Frank Altmann ◽  
Jens Beyersdorfer ◽  
Jan Schischka ◽  
Michael Krause ◽  
German Franz ◽  
...  
Keyword(s):  
High Resolution ◽  
Cross Section ◽  
High Throughput ◽  
Cross Sections ◽  
Electron Backscatter Diffraction ◽  
Grain Structure ◽  
Electron Backscatter ◽  
Section Surface ◽  
Backscatter Diffraction ◽  
Section Analysis

Abstract In this paper the new Vion™ Plasma-FIB system, developed by FEI, is evaluated for cross sectioning of Cu filled Through Silicon Via (TSV) interconnects. The aim of the study presented in this paper is to evaluate and optimise different Plasma-FIB (P-FIB) milling strategies in terms of performance and cross section surface quality. The sufficient preservation of microstructures within cross sections is crucial for subsequent Electron Backscatter Diffraction (EBSD) grain structure analyses and a high resolution interface characterisation by TEM.

Automated 3D measurement of fiber cross section morphology in handsheets

2012 ◽  
Vol 27 (2) ◽  
pp. 264-269 ◽  
Author(s):  
Christian Lorbach ◽  
Ulrich Hirn ◽  
Johannes Kritzinger ◽  
Wolfgang Bauer
Keyword(s):  
Image Analysis ◽  
Cross Section ◽  
Cross Sections ◽  
Image Plane ◽  
3D Measurement ◽  
Cross Sectional ◽  
Fiber Cross Section ◽  
Fiber Wall ◽  
Sectional Shape ◽  
Cross Section Geometry

Abstract We present a method for 3D measurement of fiber cross sectional morphology from handsheets. An automated procedure is used to acquire 3D datasets of fiber cross sectional images using an automated microtome and light microscopy. The fiber cross section geometry is extracted using digital image analysis. Simple sample preparation and highly automated image acquisition and image analysis are providing an efficient tool to analyze large samples. It is demonstrated that if fibers are tilted towards the image plane the images of fiber cross sections are always larger than the true fiber cross section geometry. In our analysis the tilting angles of the fibers to the image plane are measured. The resulting fiber cross sectional images are distorted to compensate the error due to fiber tilt, restoring the true fiber cross sectional shape. We use an approximated correction, the paper provides error estimates of the approximation. Measurement results for fiber wall thickness, fiber coarseness and fiber collapse are presented for one hardwood and one softwood pulp.

scholarly journals Collinear expansion for color singlet cross sections

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Markus A. Ebert ◽  
Bernhard Mistlberger ◽  
Gherardo Vita
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Production Cross ◽  
Gluon Fusion ◽  
Building Blocks ◽  
Color Singlet ◽  
Final State ◽  
Beam Function ◽  
Kinematic Limit ◽  
State Radiation

Abstract We demonstrate how to efficiently expand cross sections for color-singlet production at hadron colliders around the kinematic limit of all final state radiation being collinear to one of the incoming hadrons. This expansion is systematically improvable and applicable to a large class of physical observables. We demonstrate the viability of this technique by obtaining the first two terms in the collinear expansion of the rapidity distribution of the gluon fusion Higgs boson production cross section at next-to-next-to leading order (NNLO) in QCD perturbation theory. Furthermore, we illustrate how this technique is used to extract universal building blocks of scattering cross section like the N-jettiness and transverse momentum beam function at NNLO.

Sign in / Sign up

Export Citation Format

Share Document