scholarly journals Weighted integral solvers for elastic scattering by open arcs in two dimensions

2021 ◽  
Author(s):  
Oscar P. Bruno ◽  
Liwei Xu ◽  
Tao Yin
Keyword(s):  
Elastic Scattering ◽  
Two Dimensions ◽  
Weighted Integral

scholarly journals Ambit Field Modelling of Isotropic, Homogeneous, Divergence-Free and Skewed Vector Fields in Two Dimensions

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1265
Author(s):  
Jürgen Schmiegel
Keyword(s):  
Stream Function ◽  
Vector Fields ◽  
Necessary Conditions ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Field Modelling ◽  
Parity Symmetry ◽  
Weighted Integral ◽  
Divergence Free ◽  
Stochastic Vector

We discuss the application of ambit fields to the construction of stochastic vector fields in two dimensions that are divergence-free and statistically homogeneous and isotropic but are not invariant under the parity operation. These vector fields are derived from a stochastic stream function defined as a weighted integral with respect to a Lévy basis. By construction, the stream function is homogeneous and isotropic and the corresponding vector field is, in addition, divergence-free. From a decomposition of the kernel in the Lévy-based integral, necessary conditions for the violation of parity symmetry are inferred. In particular, we focus on such fields that allow for skewness of projected increments, which is one of the cornerstones of the Kraichnan–Leith–Bachelor theory of two-dimensional turbulence.

The tangled web of agency

2018 ◽  
Vol 41 ◽  
Author(s):  
Alain Pe-Curto ◽  
Julien A. Deonna ◽  
David Sander
Keyword(s):  
Two Dimensions ◽  
Bad Company

AbstractWe characterize Doris's anti-reflectivist, collaborativist, valuational theory along two dimensions. The first dimension is socialentanglement, according to which cognition, agency, and selves are socially embedded. The second dimension isdisentanglement, the valuational element of the theory that licenses the anchoring of agency and responsibility in distinct actors. We then present an issue for the account: theproblem of bad company.

Elastic Scattering in Electron Microscopy

1973 ◽  
Vol 31 ◽  
pp. 252-253
Author(s):  
J. Langmore ◽  
M. Isaacson ◽  
J. Wall ◽  
A. V. Crewe
Keyword(s):  
Electron Microscopy ◽  
Elastic Scattering ◽  
Cross Section ◽  
Quantum Noise ◽  
Dark Field ◽  
Elastic Cross Section ◽  
Biological Molecules ◽  
Dark Field Microscopy ◽  
Field Systems ◽  
Effects Of Radiation

High resolution dark field microscopy is becoming an important tool for the investigation of unstained and specifically stained biological molecules. Of primary consideration to the microscopist is the interpretation of image Intensities and the effects of radiation damage to the specimen. Ignoring inelastic scattering, the image intensity is directly related to the collected elastic scattering cross section, σɳ, which is the product of the total elastic cross section, σ and the eficiency of the microscope system at imaging these electrons, η. The number of potentially bond damaging events resulting from the beam exposure required to reduce the effect of quantum noise in the image to a given level is proportional to 1/η. We wish to compare η in three dark field systems.

The Resolution and Contrast in Biological Sections Determined by Inelastic and Elastic Scattering

1973 ◽  
Vol 31 ◽  
pp. 224-225
Author(s):  
D. L. Misell
Keyword(s):  
Electron Microscopy ◽  
Adverse Effect ◽  
Elastic Scattering ◽  
Inelastic Scattering ◽  
Amorphous Carbon ◽  
Polymeric Materials ◽  
Chromatic Aberration ◽  
Image Resolution ◽  
Quantitative Estimates ◽  
Elastic Ratio

In the electron microscopy of biological sections the adverse effect of chromatic aberration on image resolution is well known. In this paper calculations are presented for the inelastic and elastic image intensities using a wave-optical formulation. Quantitative estimates of the deterioration in image resolution as a result of chromatic aberration are presented as an alternative to geometric calculations. The predominance of inelastic scattering in the unstained biological and polymeric materials is shown by the inelastic to elastic ratio, I/E, within an objective aperture of 0.005 rad for amorphous carbon of a thickness, t=50nm, typical of biological sections; E=200keV, I/E=16.

A New Image Processing Technique for STEM

1974 ◽  
Vol 32 ◽  
pp. 432-433
Author(s):  
Yasushi Kokubo ◽  
Hirotami Koike ◽  
Teruo Someya
Keyword(s):  
Electron Microscopy ◽  
Image Processing ◽  
Scanning Electron Microscopy ◽  
Elastic Scattering ◽  
Field Emission ◽  
Processing Technique ◽  
Image Processing Technique ◽  
Energy Analyzer ◽  
Scanning Microscope ◽  
Scanning Electron

One of the advantages of scanning electron microscopy is the capability for processing the image contrast, i.e., the image processing technique. Crewe et al were the first to apply this technique to a field emission scanning microscope and show images of individual atoms. They obtained a contrast which depended exclusively on the atomic numbers of specimen elements (Zcontrast), by displaying the images treated with the intensity ratio of elastically scattered to inelastically scattered electrons. The elastic scattering electrons were extracted by a solid detector and inelastic scattering electrons by an energy analyzer. We noted, however, that there is a possibility of the same contrast being obtained only by using an annular-type solid detector consisting of multiple concentric detector elements.

A Base Specific Single Heavy Atom Stain for Electron Microscopy

1972 ◽  
Vol 30 ◽  
pp. 184-185
Author(s):  
J. P. Langmore ◽  
N. R. Cozzarelli ◽  
A. V. Crewe
Keyword(s):  
Electron Microscopy ◽  
Electron Microscope ◽  
High Resolution ◽  
Elastic Scattering ◽  
Heavy Atom ◽  
High Vacuum ◽  
Heavy Atoms ◽  
Large Movement ◽  
Base Sequencing ◽  
Scanning Electron

A system has been developed to allow highly specific derivatization of the thymine bases of DNA with mercurial compounds wich should be visible in the high resolution scanning electron microscope. Three problems must be completely solved before this staining system will be useful for base sequencing by electron microscopy: 1) the staining must be shown to be highly specific for one base, 2) the stained DNA must remain intact in a high vacuum on a thin support film suitable for microscopy, 3) the arrangement of heavy atoms on the DNA must be determined by the elastic scattering of electrons in the microscope without loss or large movement of heavy atoms.

Electron Scattering in Solids

1990 ◽  
Vol 48 (2) ◽  
pp. 4-5
Author(s):  
Ryuichi Shimizu ◽  
Ze-Jun Ding
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Angular Distribution ◽  
Elastic Scattering ◽  
Electron Scattering ◽  
Cross Sections ◽  
Expansion Method ◽  
Electron Excitation ◽  
Partial Wave Expansion ◽  
Backscattered Electrons

Monte Carlo simulation has been becoming most powerful tool to describe the electron scattering in solids, leading to more comprehensive understanding of the complicated mechanism of generation of various types of signals for microbeam analysis.The present paper proposes a practical model for the Monte Carlo simulation of scattering processes of a penetrating electron and the generation of the slow secondaries in solids. The model is based on the combined use of Gryzinski’s inner-shell electron excitation function and the dielectric function for taking into account the valence electron contribution in inelastic scattering processes, while the cross-sections derived by partial wave expansion method are used for describing elastic scattering processes. An improvement of the use of this elastic scattering cross-section can be seen in the success to describe the anisotropy of angular distribution of elastically backscattered electrons from Au in low energy region, shown in Fig.l. Fig.l(a) shows the elastic cross-sections of 600 eV electron for single Au-atom, clearly indicating that the angular distribution is no more smooth as expected from Rutherford scattering formula, but has the socalled lobes appearing at the large scattering angle.

A transmission electron microscopic study of structural transitions in fast ionic conductors

1987 ◽  
Vol 45 ◽  
pp. 156-157
Author(s):  
R. B. Queenan ◽  
P. K. Davies
Keyword(s):  
Optical Properties ◽  
Ionic Conduction ◽  
Recent Observation ◽  
Ionic Conductivities ◽  
Sodium Aluminate ◽  
Two Dimensions ◽  
Ionic Conductors ◽  
Electron Microscopic ◽  
Transmission Electron ◽  
Trivalent Cations

Na ß“-alumina (Na1.67Mg67Al10.33O17) is a non-stoichiometric sodium aluminate which exhibits fast ionic conduction of the Na+ ions in two dimensions. The Na+ ions can be exchanged with a variety of mono-, di-, and trivalent cations. The resulting exchanged materials also show high ionic conductivities.Considerable interest in the Na+-Nd3+-ß“-aluminas has been generated as a result of the recent observation of lasing in the pulsed and cw modes. A recent TEM investigation on a 100% exchanged Nd ß“-alumina sample found evidence for the intergrowth of two different structure types. Microdiffraction revealed an ordered phase coexisting with an apparently disordered phase, in which the cations are completely randomized in two dimensions. If an order-disorder transition is present then the cooling rates would be expected to affect the microstructures of these materials which may in turn affect the optical properties. The purpose of this work was to investigate the affect of thermal treatments upon the micro-structural and optical properties of these materials.

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