The True Size Distribution of Ain Particles Obtained from Extraction Replicas

1990 ◽  
Vol 48 (1) ◽  
pp. 588-589
Author(s):  
Ö.N. Doğan ◽  
H.W. Kwon ◽  
G.M. Michal
Keyword(s):  
Size Distribution ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Thin Foil ◽  
Spherical Particles ◽  
Two Dimensional ◽  
Extraction Replica ◽  
Tem Analysis ◽  
Planar Section ◽  
Thin Foils

Determination of the morphology and size distribution of particles in a multiple phase material can be accomplished using opaque planar section optical microscopy or thin foil and extraction replica TEM analysis. In all cases, measurements are obtained using two-dimensional information from a planar section or through a projection of three-dimensional space. The two-dimensional size and morphology data obtained must be converted into the true three-dimensional data to be of further use. For spherical particles, methods of two- to three-dimensional size distribution conversion have been developed for planar sections, thin foils and extraction replicas. However, A1N particles precipitated in FCC iron are rod-shaped with a square cross section. To analyze these particles, an iterative method has been developed to determine the true three-dimensional size distribution of rod-shaped particles from their projected images obtained from extraction replicas. This method assumes that the particles are randomly oriented in the matrix phase and that they have a common aspect ratio.

scholarly journals Derivation of Equations for a Size Distribution of Spherical Particles in Non-Transparent Materials

2021 ◽  
Vol 5 (4) ◽  
pp. 53-60
Author(s):  
Daniel Gurgul ◽  
Andriy Burbelko ◽  
Tomasz Wiktor
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Size Distribution ◽  
Density Function ◽  
Cross Section ◽  
Three Dimensional ◽  
Spherical Particles ◽  
Two Dimensional ◽  
Mathematical Formulas ◽  
Transparent Materials

This paper presents a new proposition on how to derive mathematical formulas that describe an unknown Probability Density Function (PDF3) of the spherical radii (r3) of particles randomly placed in non-transparent materials. We have presented two attempts here, both of which are based on data collected from a random planar cross-section passed through space containing three-dimensional nodules. The first attempt uses a Probability Density Function (PDF2) the form of which is experimentally obtained on the basis of a set containing two-dimensional radii (r2). These radii are produced by an intersection of the space by a random plane. In turn, the second solution also uses an experimentally obtained Probability Density Function (PDF1). But the form of PDF1 has been created on the basis of a set containing chord lengths collected from a cross-section.The most important finding presented in this paper is the conclusion that if the PDF1 has proportional scopes, the PDF3 must have a constant value in these scopes. This fact allows stating that there are no nodules in the sample space that have particular radii belonging to the proportional ranges the PDF1.

Study on Porous Structure of Porous Media in Geotechnical Materials

2021 ◽  
Vol 871 ◽  
pp. 363-370
Author(s):  
Yong Xin Wang ◽  
Chun Hui Lan ◽  
Hai Tian
Keyword(s):  
Pore Size Distribution ◽  
Pore Size ◽  
Size Distribution ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Structural Materials ◽  
Two Dimensional ◽  
Complex Materials ◽  
Structural Problems ◽  
Porosity Model

Geotechnical materials are complex materials with very strong structures, but their structural problems have always been difficult problems in this field. In this paper, by studying the structural problems of geotechnical materials, we understand and master this kind of structural materials. Methods for describing complex materials, as well as the nature, characteristics, and changes of the material after being affected by the environment, especially the influence of the structure of the material on the macroscopic properties of the material. Starting from the basis of the material-material particles, fully consider the particle Geometry, surface characteristics and material characteristics, further analysis of the mechanical and geometric characteristics of structural materials composed of particles, a porosity model describing the pore size distribution is proposed, and the two-dimensional and three-dimensional The experimental data of pores in the space shows that the predicted value of the porosity model agrees well with the measured value in the three-dimensional space.In two-dimensional space, the validity of the model is closely related to the corresponding number of pores and the fractal dimension of the pore size distribution.

scholarly journals Three-Dimensional Thematic Map Imaging of the Yacht Port on the Example of the Polish National Sailing Centre Marina in Gdańsk

2021 ◽  
Vol 11 (15) ◽  
pp. 7016
Author(s):  
Pawel S. Dabrowski ◽  
Cezary Specht ◽  
Mariusz Specht ◽  
Artur Makar
Keyword(s):  
Spatial Data ◽  
Convex Surface ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Future Research ◽  
Two Dimensional ◽  
Thematic Maps ◽  
Research Directions ◽  
Future Research Directions ◽  
The Many

The theory of cartographic projections is a tool which can present the convex surface of the Earth on the plane. Of the many types of maps, thematic maps perform an important function due to the wide possibilities of adapting their content to current needs. The limitation of classic maps is their two-dimensional nature. In the era of rapidly growing methods of mass acquisition of spatial data, the use of flat images is often not enough to reveal the level of complexity of certain objects. In this case, it is necessary to use visualization in three-dimensional space. The motivation to conduct the study was the use of cartographic projections methods, spatial transformations, and the possibilities offered by thematic maps to create thematic three-dimensional map imaging (T3DMI). The authors presented a practical verification of the adopted methodology to create a T3DMI visualization of the marina of the National Sailing Centre of the Gdańsk University of Physical Education and Sport (Poland). The profiled characteristics of the object were used to emphasize the key elements of its function. The results confirmed the increase in the interpretative capabilities of the T3DMI method, relative to classic two-dimensional maps. Additionally, the study suggested future research directions of the presented solution.

Symbol recognition system based on 3D stereo vision

2020 ◽  
pp. 1-10
Author(s):  
Linlin Wang
Keyword(s):  
Camera Calibration ◽  
Stereo Vision ◽  
Stereo Matching ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Recognition System ◽  
Symbol Recognition ◽  
Two Dimensional ◽  
Measuring Machine ◽  
Left And Right

With the continuous development of computer science and technology, symbol recognition systems may be converted from two-dimensional space to three-dimensional space. Therefore, this article mainly introduces the symbol recognition system based on 3D stereo vision. The three-dimensional image is taken by the visual coordinate measuring machine in two places on the left and right. Perform binocular stereo matching on the edge of the feature points of the two images. A corner detection algorithm combining SUSAN and Harris is used to detect the left and right camera calibration templates. The two-dimensional coordinate points of the object are determined by the image stereo matching module, and the three-dimensional discrete coordinate points of the object space can be obtained according to the transformation relationship between the image coordinates and the actual object coordinates. Then draw the three-dimensional model of the object through the three-dimensional drawing software. Experimental data shows that the logic resources and memory resources occupied by image preprocessing account for 30.4% and 27.4% of the entire system, respectively. The results show that the system can calibrate the internal and external parameters of the camera. In this way, the camera calibration result will be more accurate and the range will be wider. At the same time, it can effectively make up for the shortcomings of traditional modeling techniques to ensure the measurement accuracy of the detection system.

scholarly journals FOUR-DIMENSIONAL BALL IN A GRAPHIC REPRESENTATION

2021 ◽  
pp. 37-46
Author(s):  
Helena Bidnichenko
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Geometric Modelling ◽  
Vector Model ◽  
Original Position ◽  
Two Dimensional ◽  
Axis Of Rotation ◽  
Dimensional Ball ◽  
Three Dimensional Space ◽  
Horizontal Vector

The paper presents a method for geometric modelling of a four-dimensional ball. For this, the regularities of the change in the shape of the projections of simple geometric images of two-dimensional and three-dimensional spaces during rotation are considered. Rotations of a segment and a circle around an axis are considered; it is shown that during rotation the shape of their projections changes from the maximum value to the degenerate projection. It was found that the set of points of the degenerate projection belongs to the axis of rotation, and each n-dimensional geometric image during rotation forms a body of a higher dimension, that is, one that belongs to (n + 1) -dimensional space. Identified regularities are extended to the four-dimensional space in which the ball is placed. It is shown that the axis of rotation of the ball will be a degenerate projection in the form of a circle, and the ball, when rotating, changes its size from a volumetric object to a flat circle, then increases again, but in the other direction (that is, it turns out), and then in reverse order to its original position. This rotation is more like a deformation, and such a ball of four-dimensional space is a hypersphere. For geometric modelling of the hypersphere and the possibility of its projection image, the article uses the vector model proposed by P.V. Filippov. The coordinate system 0xyzt is defined. The algebraic equation of the hypersphere is given by analogy with the three-dimensional space along certain coordinates of the center a, b, c, d. A variant of hypersection at t = 0 is considered, which confirms by equations obtaining a two-dimensional ball of three-dimensional space, a point (a ball of zero radius), which coincides with the center of the ball, or an imaginary ball. For the variant t = d, the equation of a two-dimensional ball is obtained, in which the radius is equal to R and the coordinates of all points along the 0t axis are equal to d. The variant of hypersection t = k turned out to be interesting, in which the equation of a two-dimensional sphere was obtained, in which the coordinates of all points along the 0t axis are equal to k, and the radius is . Horizontal vector projections of hypersection are constructed for different values of k. It is concluded that the set of horizontal vector projections of hypersections at t = k defines an ellipse.  

scholarly journals Optimization of the multidimensional signal interpolator in a lower dimensional space

2019 ◽  
Vol 43 (4) ◽  
pp. 653-660 ◽  
Author(s):  
M.V. Gashnikov
Keyword(s):  
Experimental Study ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Multidimensional Signals ◽  
Multidimensional Signal ◽  
Signal Sample ◽  
Lower Dimensional Space ◽  
Lower Dimensional ◽  
Selection Of

Adaptive multidimensional signal interpolators are developed. These interpolators take into account the presence and direction of boundaries of flat signal regions in each local neighborhood based on the automatic selection of the interpolating function for each signal sample. The selection of the interpolating function is performed by a parameterized rule, which is optimized in a parametric lower dimensional space. The dimension reduction is performed using rank filtering of local differences in the neighborhood of each signal sample. The interpolating functions of adaptive interpolators are written for the multidimensional, three-dimensional and two-dimensional cases. The use of adaptive interpolators in the problem of compression of multidimensional signals is also considered. Results of an experimental study of adaptive interpolators for real multidimensional signals of various types are presented.

scholarly journals Capacity of Inhomogeneous Hybrid Wireless Networks in Three-Dimensional Space

2015 ◽  
Vol 11 (9) ◽  
pp. 47
Author(s):  
Feng Wu ◽  
Jiang Zhu ◽  
Yilong Tian ◽  
Zhipeng Xi
Keyword(s):  
Sensor Node ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Network Capacity ◽  
Throughput Capacity ◽  
Two Dimensional ◽  
Hybrid Wireless Networks ◽  
Node Distribution ◽  
Analytical Expressions ◽  
Three Dimensional Space

Network capacity has been widely studied in recent years. However, most of the literatures focus on the networks where nodes are distributed in a two-dimensional space. In this paper, we propose a 3D hybrid sensor network model. By setting different sensor node distribution probabilities for cells, we divide all the cells in the network into dense cells and sparse cells. Analytical expressions of the aggregate throughput capacity are obtained. We also find that suitable inhomogeneity can increase the network throughput capacity.

Non-Spheric Colloidal Suspensions in Three-Dimensional Space

1997 ◽  
Vol 08 (04) ◽  
pp. 985-997 ◽  
Author(s):  
Dewei Qi
Keyword(s):  
Reynolds Number ◽  
Dimensional Space ◽  
Low Reynolds Number ◽  
Paper Industry ◽  
Three Dimensional ◽  
Colloidal Suspensions ◽  
Solid Particles ◽  
Spherical Particles ◽  
Dynamic Simulations ◽  
Low Reynolds

The translation and rotation of non-spherical particles, such as ellipsoidal, cylindric or disk-like pigment particles, in a Couette flow system similar to a blade coating system in the paper industry6 have been successfully simulated by using the lattice-Boltzmann method combined with Newtonian dynamic simulations. Hydrodynamic forces and torques are obtained by the use of boundary conditions which match the moving surface of solid particles. Then Euler equations have been integrated to include three-dimensional rotations of the suspensions by using four quaternion parameters as generalized coordinates. The three-dimensional rotations have been clearly observed. Consequently, the motion of the particles suspended in fluids of both low-Reynolds-number and finite-Reynolds-number, up to several hundreds, has been studied. It appears that the 3D translation and rotation of the non-spherical particles are more clearly observed in a high-Reynolds-number fluid than in a low-Reynolds-number fluid.

Map fragmentation in two- and three-dimensional environments

2013 ◽  
Vol 36 (5) ◽  
pp. 569-570 ◽  
Author(s):  
Homare Yamahachi ◽  
May-Britt Moser ◽  
Edvard I. Moser
Keyword(s):  
Small Area ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Brain Circuits ◽  
Three Dimensional Space

AbstractThe suggestion that three-dimensional space is represented by a mosaic of neural map fragments, each covering a small area of space in the plane of locomotion, receives support from studies in complex two-dimensional environments. How map fragments are linked, which brain circuits are involved, and whether metric is preserved across fragments are questions that remain to be determined.

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