scholarly journals Study of the Disperse Composition of Suspensions and Sputtered Substances by means of Small-Angle Light Scattering

2021 ◽  
pp. 156-162
Author(s):  
A.Y. Bekshaev ◽  
S.M. Kontush ◽  
A.Y. Popov ◽  
S.S. Rybak
Keyword(s):  
Disperse System ◽  
Small Angle ◽  
Stochastic Systems ◽  
A Priori ◽  
Incident Beam ◽  
Particle Sizes ◽  
System Of Particles ◽  
Small Angle Light Scattering ◽  
The Mean

Spatial distribution of the light scattered by a disperse system of particles depends on their sizes, shapes, positions, etc., which can be used for experimental determination of the parameters mentioned. For stochastic systems with the particles’ sizes exceeding the radiation wavelength, most of the scattered radiation concentrates near the incident beam axis. In this small-angle approximation, the scattering pattern is especially simple and regular, which enables to develop efficient procedures for the disperse system investigation. We describe the algorithm for determination of the mean particle radius in the system with lognormal distribution of the particle sizes and negligible multiple scattering. The algorithm’s performance is demonstrated on the practical example of the “fog” generated by a gasoline injector. The ways are discussed for further algorithm generalization and its extension to a non-parametric analysis of disperse systems with a priori unknown form of the particle sizes’ distribution.

scholarly journals Estimation of the mean normal measure from flat sections

2008 ◽  
Vol 40 (01) ◽  
pp. 31-48
Author(s):  
Markus Kiderlen
Keyword(s):  
A Priori ◽  
The Other ◽  
Consistent Estimator ◽  
Random Set ◽  
Normal Measure ◽  
Mild Assumption ◽  
The Mean ◽  
Vertical Sections ◽  
Almost All

We discuss the determination of the mean normal measure of a stationary random set Z ⊂ ℝ d by taking measurements at the intersections of Z with k-dimensional planes. We show that mean normal measures of sections with vertical planes determine the mean normal measure of Z if k ≥ 3 or if k = 2 and an additional mild assumption holds. The mean normal measures of finitely many flat sections are not sufficient for this purpose. On the other hand, a discrete mean normal measure can be verified (i.e. an a priori guess can be confirmed or discarded) using mean normal measures of intersections with m suitably chosen planes when m ≥ ⌊d / k⌋ + 1. This even holds for almost all m-tuples of k-dimensional planes are viable for verification. A consistent estimator for the mean normal measure of Z, based on stereological measurements in vertical sections, is also presented.

The properties of anisotropic small-angle scattering

1990 ◽  
Vol 23 (2) ◽  
pp. 79-81 ◽  
Author(s):  
D. A. Svetogorsky
Keyword(s):  
Cross Section ◽  
Small Angle ◽  
Symmetric Tensor ◽  
Radius Of Gyration ◽  
Simple Method ◽  
Angle Measurements ◽  
Anisotropic System ◽  
Angle Scattering ◽  
The Mean

It is shown that the cross section of small-angle neutron scattering (SANS) on an anisotropic system of point scatterers is determined by a symmetric tensor (R). The mean square radius of gyration of the system is the trace of R. A simple method is proposed for experimental determination of the tensor R by small-angle measurements with rotation of a sample.

scholarly journals Dynamical Interaction of Electron Waves in a Perfect Single Crystal

1972 ◽  
Vol 27 (3) ◽  
pp. 425-433 ◽  
Author(s):  
G Lehmpfuhl
Keyword(s):  
Single Crystal ◽  
Incident Beam ◽  
Direct Analysis ◽  
Zone Axis ◽  
Perfect Single Crystal ◽  
Dynamical Interaction ◽  
Dispersion Surface ◽  
The Mean ◽  
Beam Interaction

AbstractElectron diffraction from a perfect single crystal shows the influence of many-beam interaction. Investigations with a single crystal wedge allow a direct analysis of the Bloch-waves which are dis-played into their partial waves. The strength of the dynamical interactions in a MgO crystal wedge was investigated by comparing the photographic record of a section through the dispersion surface with many-beam calculations. For a direction of the incident beam near the [110] zone axis the interaction of at least 50 beams has to be taken into account. Using a 50-beam calculation the structure potential V111 was determined to 1.80 volts ±3%. The influence of many-beam interactions on the absorption and the extinction fringe profiles in electron micrographs is discussed. Analysis of extinction fringes on the basis of a 50-beam approximation allowed the determination of the mean absorbing potential V0im of MgO to 0.7 volts ±10%.

scholarly journals Estimation of the mean normal measure from flat sections

2008 ◽  
Vol 40 (1) ◽  
pp. 31-48 ◽  
Author(s):  
Markus Kiderlen
Keyword(s):  
A Priori ◽  
The Other ◽  
Consistent Estimator ◽  
Random Set ◽  
Normal Measure ◽  
Mild Assumption ◽  
The Mean ◽  
Vertical Sections ◽  
Almost All

We discuss the determination of the mean normal measure of a stationary random set Z ⊂ ℝd by taking measurements at the intersections of Z with k-dimensional planes. We show that mean normal measures of sections with vertical planes determine the mean normal measure of Z if k ≥ 3 or if k = 2 and an additional mild assumption holds. The mean normal measures of finitely many flat sections are not sufficient for this purpose. On the other hand, a discrete mean normal measure can be verified (i.e. an a priori guess can be confirmed or discarded) using mean normal measures of intersections with m suitably chosen planes when m ≥ ⌊d / k⌋ + 1. This even holds for almost all m-tuples of k-dimensional planes are viable for verification. A consistent estimator for the mean normal measure of Z, based on stereological measurements in vertical sections, is also presented.

scholarly journals Retrieving Precipitable Water Vapor from Real-Time Precise Point Positioning Using VMF1/VMF3 Forecasting Products

2021 ◽  
Vol 13 (16) ◽  
pp. 3245
Author(s):  
Peng Sun ◽  
Kefei Zhang ◽  
Suqin Wu ◽  
Moufeng Wan ◽  
Yun Lin
Keyword(s):  
Water Vapor ◽  
Real Time ◽  
Precise Point Positioning ◽  
A Priori ◽  
Mapping Function ◽  
Precipitable Water ◽  
The Mean ◽  
Globally Distributed

Real-time precise point positioning (RT-PPP) has become a powerful technique for the determination of the zenith tropospheric delay (ZTD) over a GPS (global positioning system) or GNSS (global navigation satellite systems) station of interest, and the follow-on high-precision retrieval of precipitable water vapor (PWV). The a priori zenith hydrostatic delay (ZHD) and the mapping function used in the PPP approach are the two factors that could affect the accuracy of the PPP-based ZTD significantly. If the in situ atmospheric pressure is available, the Saastamoinen model can be used to determine ZHD values, and the model-predicted ZHD results are of high accuracy. However, not all GPS/GNSS are equipped with an in situ meteorological sensor. In this research, the daily forecasting ZHD and mapping function values from VMF1 forecasting (VMF1_FC) and VMF3 forecasting (VMF3_FC) products were used for the determination of the GPS-derived PWV. The a priori ZHDs derived from VMF1_FC and VMF3_FC were first evaluated by comparing against the reference ZHDs from globally distributed radiosonde stations. GPS observations from 41 IGS stations that have co-located radiosonde stations during the period of the first half of 2020 were used to test the quality of GPS-ZTD and GPS-PWV. Three sets of ZTDs estimated from RT-PPP solutions using the a priori ZHD and mapping function from the following three VMF products were evaluated: (1) VMF1_FC; (2) VMF3_FC (resolution 5° × 5°); (3) VMF3_FC (resolution 1° × 1°). The results showed that, when the ZHDs from 443 globally distributed radiosonde stations from 1 July 2018 to 30 June 2021 were used as the reference, the mean RMSEs of the ZHDs from the three VMF products were 5.9, 5.4, and 4.3 mm, respectively. The ZTDs estimated from RT-PPP at 41 selected IGS stations were compared with those from IGS, and the results showed that the mean RMSEs of the ZTDs of the 41 stations from the three PPP solutions were 8.6, 9.0, and 8.6 mm, respectively, and the mean RMSEs of the PWV converted from their corresponding ZWDs were 1.9, 2.4, and 1.7 mm, respectively, in comparison with the reference PWV from co-located radiosonde stations. The results suggest that the a priori ZHD and mapping function from VMF1_FC and VMF3_FC can be used for the precise determination of real-time GPS/GNSS-PWV in most regions, especially the VMF3_FC (resolution 1° × 1°) product.

Sign in / Sign up

Export Citation Format

Share Document