scholarly journals A Universal Generating Algorithm of the Polyhedral Discrete Grid Based on Unit Duplication

2019 ◽  
Vol 8 (3) ◽  
pp. 146 ◽  
Author(s):  
Li Meng ◽  
Xiaochong Tong ◽  
Shuaibo Fan ◽  
Chengqi Cheng ◽  
Bo Chen ◽  
...  
Keyword(s):  
Coordinate System ◽  
Grid Cell ◽  
Triangular Grid ◽  
Grid System ◽  
Rectangular Coordinate System ◽  
Factors Affecting ◽  
Grid Systems ◽  
Starting Point ◽  
Rectangular Coordinates ◽  
Discrete Grid

Based on the analysis of the problems in the generation algorithm of discrete grid systems domestically and abroad, a new universal algorithm for the unit duplication of a polyhedral discrete grid is proposed, and its core is “simple unit replication + effective region restriction”. First, the grid coordinate system and the corresponding spatial rectangular coordinate system are established to determine the rectangular coordinates of any grid cell node. Then, the type of the subdivision grid system to be calculated is determined to identify the three key factors affecting the grid types, which are the position of the starting point, the length of the starting edge, and the direction of the starting edge. On this basis, the effective boundary of a multiscale grid can be determined and the grid coordinates of a multiscale grid can be obtained. A one-to-one correspondence between the multiscale grids and subdivision types can be established. Through the appropriate rotation, translation and scaling of the multiscale grid, the node coordinates of a single triangular grid system are calculated, and the relationships between the nodes of different levels are established. Finally, this paper takes a hexagonal grid as an example to carry out the experiment verifications by converting a single triangular grid system (plane) directly to a single triangular grid with a positive icosahedral surface to generate a positive icosahedral surface grid. The experimental results show that the algorithm has good universality and can generate the multiscale grid of an arbitrary grid configuration by adjusting the corresponding starting transformation parameters.

scholarly journals Complete coverage of space favors modularity of the grid system in the brain

2016 ◽  
Author(s):  
A. Sanzeni ◽  
V. Balasubramanian ◽  
G. Tiana ◽  
M. Vergassola
Keyword(s):  
Statistical Physics ◽  
Physical Space ◽  
Grid Cell ◽  
Triangular Grid ◽  
Grid System ◽  
Grid Cells ◽  
Scaling Relation ◽  
Complete Coverage ◽  
Space Experiments ◽  
The Brain

Grid cells in the entorhinal cortex fire when animals that are exploring a certain region of space occupy the vertices of a triangular grid that spans the environment. Different neurons feature triangular grids that differ in their properties of periodicity, orientation and ellipticity. Taken together, these grids allow the animal to maintain an internal, mental representation of physical space. Experiments show that grid cells are modular, i.e. there are groups of neurons which have grids with similar periodicity, orientation and ellipticity. We use statistical physics methods to derive a relation between variability of the properties of the grids within a module and the range of space that can be covered completely (i.e. without gaps) by the grid system with high probability. Larger variability shrinks the range of representation, providing a functional rationale for the experimentally observed co-modularity of grid cell periodicity, orientation and ellipticity. We obtain a scaling relation between the number of neurons and the period of a module, given the variability and coverage range. Specifically, we predict how many more neurons are required at smaller grid scales than at larger ones.

scholarly journals A New Coordinate System for Constructing Spherical Grid Systems

2020 ◽  
Vol 10 (2) ◽  
pp. 655
Author(s):  
Kin Lei ◽  
Dongxu Qi ◽  
Xiaolin Tian
Keyword(s):  
Coordinate System ◽  
Spatial Data ◽  
Spherical Surface ◽  
Planetary Science ◽  
Barycentric Coordinates ◽  
Global Coordinate System ◽  
Simple Relationship ◽  
Grid System ◽  
Grid Systems ◽  
Spherical Data

In astronomy, physics, climate modeling, geoscience, planetary science, and many other disciplines, the mass of data often comes from spherical sampling. Therefore, establishing an efficient and distortion-free representation of spherical data is essential. This paper introduces a novel spherical (global) coordinate system that is free of singularity. Contrary to classical coordinates, such as Cartesian or spherical polar systems, the proposed coordinate system is naturally defined on the spherical surface. The basic idea of this coordinate system originated from the classical planar barycentric coordinates that describe the positions of points on a plane concerning the vertices of a given planar triangle; analogously, spherical area coordinates (SACs) describe the positions of points on a sphere concerning the vertices of a given spherical triangle. In particular, the global coordinate system is obtained by decomposing the globe into several identical triangular regions, constructing local coordinates for each region, and then combining them. Once the SACs have been established, the coordinate isolines form a new class of global grid systems. This kind of grid system has some useful properties: the grid cells exhaustively cover the globe without overlapping and have the same shape, and the grid system has a congruent hierarchical structure and simple relationship with traditional coordinates. These beneficial characteristics are suitable for organizing, representing, and analyzing spatial data.

Technology of determining the Earth’s gravitational field parameters using gradiometric measurements Part 6. Calculation the components of the gravitational potential tensor in the earth’s spatial rectangular coordinate system

2021 ◽  
Vol 973 (7) ◽  
pp. 2-8
Author(s):  
A.A. Kluykov
Keyword(s):  
Gravitational Field ◽  
Coordinate System ◽  
Gravitational Potential ◽  
Rectangular Coordinate System ◽  
Gradient Tensor ◽  
Gravitational Gradient ◽  
Earth’S Gravitational Field ◽  
Second Derivatives ◽  
Rectangular Coordinates ◽  
Potential Tensor

This is the sixth one in a series of articles describing the technology of determining the Earth’s gravitational field parameters through gradiometric measurements performed with an onboard satellite electrostatic gradiometer. It provides formulas for calculating the components of the gravitational potential tensor in a geocentric spatial rectangular earth coordinate system in order to convert them into a gradiometric one and obtain a free term for the equations of correcting gradiometric measurements when determining the parameters of the Earth’s gravitational field. The components of the gravitational gradient tensor are functions of test masses accelerations measured by accelerometers and relate to the gradiometer coordinate system, while the desired parameters of the Earth’s gravitational field model relate to the Earth’s coordinate one. The components of the gravitational gradient tensor are the second derivatives of the gravitational potential in rectangular coordinates. The calculated values of the gravitational potential tensor components in the earth’s spatial rectangular coordinate system are obtained through double differentiation of the gravitational potential formula. Basing on the obtained formulas, an algorithm and a program in the Fortran algorithmic language were developed. Using this program, experimental calculations were performed, the results of which were compared with the data of the EGG_TRF_2 product.

Earth's gravity field parameters determination by the space geodesy dynamical approach

2017 ◽  
Vol 919 (1) ◽  
pp. 7-12
Author(s):  
N.A Sorokin
Keyword(s):  
Coordinate System ◽  
Gravitational Potential ◽  
Coefficient Matrix ◽  
Measured Quantity ◽  
Second Derivative ◽  
Measured Variable ◽  
Second Derivatives ◽  
Rectangular Coordinates ◽  
Cartesian Coordinate ◽  
Derivatives Of

The method of the geopotential parameters determination with the use of the gradiometry data is considered. The second derivative of the gravitational potential in the correction equation on the rectangular coordinates x, y, z is used as a measured variable. For the calculated value of the measured quantity required for the formation of a free member of the correction equation, the the Cunningham polynomials were used. We give algorithms for computing the second derivatives of the Cunningham polynomials on rectangular coordinates x, y, z, which allow to calculate the second derivatives of the geopotential at the rectangular coordinates x, y, z.Then we convert derivatives obtained from the Cartesian coordinate system in the coordinate system of the gradiometer, which allow to calculate the free term of the correction equation. Afterwards the correction equation coefficients are calculated by differentiating the formula for calculating the second derivative of the gravitational potential on the rectangular coordinates x, y, z. The result is a coefficient matrix of the correction equations and corrections vector of the free members of equations for each component of the tensor of the geopotential. As the number of conditional equations is much more than the number of the specified parameters, we go to the drawing up of the system of normal equations, from which solutions we determine the required corrections to the harmonic coefficients.

The characteristics of transforming coordinates from the geocentric system WGS-84 for the Mercator projection under low latitudes conditions

2018 ◽  
Vol 940 (10) ◽  
pp. 2-6
Author(s):  
J.A. Younes ◽  
M.G. Mustafin
Keyword(s):  
Coordinate System ◽  
Satellite System ◽  
Programming Algorithm ◽  
Low Latitude ◽  
Model Calculations ◽  
Mercator Projection ◽  
Low Latitudes ◽  
Rectangular Coordinates ◽  
Global Navigation Satellite ◽  
Coordination Methods

The issue of calculating the plane rectangular coordinates using the data obtained by the satellite observations during the creation of the geodetic networks is discussed in the article. The peculiarity of these works is in conversion of the coordinates into the Mercator projection, while the plane coordinate system on the base of Gauss-Kruger projection is used in Russia. When using the technology of global navigation satellite system, this task is relevant for any point (area) of the Earth due to a fundamentally different approach in determining the coordinates. The fact is that satellite determinations are much more precise than the ground coordination methods (triangulation and others). In addition, the conversion to the zonal coordinate system is associated with errors; the value at present can prove to be completely critical. The expediency of using the Mercator projection in the topographic and geodetic works production at low latitudes is shown numerically on the basis of model calculations. To convert the coordinates from the geocentric system with the Mercator projection, a programming algorithm which is widely used in Russia was chosen. For its application under low-latitude conditions, the modification of known formulas to be used in Saudi Arabia is implemented.

scholarly journals Vector Arithmetic in the Triangular Grid

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 373
Author(s):  
Khaled Abuhmaidan ◽  
Monther Aldwairi ◽  
Benedek Nagy
Keyword(s):  
Coordinate System ◽  
Triangular Grid ◽  
Vector Addition ◽  
Plane Space ◽  
Physical Simulations ◽  
Rectangular Grids ◽  
Cartesian Coordinate ◽  
Zero Sum ◽  
Coordinate Geometry ◽  
Point Lattice

Vector arithmetic is a base of (coordinate) geometry, physics and various other disciplines. The usual method is based on Cartesian coordinate-system which fits both to continuous plane/space and digital rectangular-grids. The triangular grid is also regular, but it is not a point lattice: it is not closed under vector-addition, which gives a challenge. The points of the triangular grid are represented by zero-sum and one-sum coordinate-triplets keeping the symmetry of the grid and reflecting the orientations of the triangles. This system is expanded to the plane using restrictions like, at least one of the coordinates is an integer and the sum of the three coordinates is in the interval [−1,1]. However, the vector arithmetic is still not straightforward; by purely adding two such vectors the result may not fulfill the above conditions. On the other hand, for various applications of digital grids, e.g., in image processing, cartography and physical simulations, one needs to do vector arithmetic. In this paper, we provide formulae that give the sum, difference and scalar product of vectors of the continuous coordinate system. Our work is essential for applications, e.g., to compute discrete rotations or interpolations of images on the triangular grid.

Integrity Management of Ground Movement Hazards

2016 ◽  
Author(s):  
Yong-Yi Wang ◽  
Don West ◽  
Douglas Dewar ◽  
Alex McKenzie-Johnson ◽  
Millan Sen
Keyword(s):  
Management Program ◽  
Ground Movement ◽  
Tensile Failure ◽  
Weld Strength ◽  
Factors Affecting ◽  
Ground Movements ◽  
Decision Points ◽  
Starting Point ◽  
Integrity Management ◽  
Girth Welds

Ground movements, such as landslides and subsidence/settlement, can pose serious threats to pipeline integrity. The consequence of these incidents can be severe. In the absence of systematic integrity management, preventing and predicting incidents related to ground movements can be difficult. A ground movement management program can reduce the potential of those incidents. Some basic concepts and terms relevant to the management of ground movement hazards are introduced first. A ground movement management program may involve a long segment of a pipeline that may have a threat of failure in unknown locations. Identifying such locations and understanding the potential magnitude of the ground movement is often the starting point of a management program. In other cases, management activities may start after an event is known to have occurred. A sample response process is shown to illustrate key considerations and decision points after the evidence of an event is discovered. Such a process can involve fitness-for-service (FFS) assessment when appropriate information is available. The framework and key elements of FFS assessment are explained, including safety factors on strain capacity. The use of FFS assessment is illustrated through the assessment of tensile failure mode. Assessment models are introduced, including key factors affecting the outcome of an assessment. The unique features of girth welds in vintage pipelines are highlighted because the management of such pipelines is a high priority in North America and perhaps in other parts of the worlds. Common practice and appropriate considerations in a pipeline replacement program in areas of potential ground movement are highlighted. It is advisable to replace pipes with pipes of similar strength and stiffness so the strains can be distributed as broadly as possible. The chemical composition of pipe steels and the mechanical properties of the pipes should be such that the possibility of HAZ softening and weld strength undermatching is minimized. In addition, the benefits and cost of using the workmanship flaw acceptance criteria of API 1104 or equivalent standards in making repair and cutout decisions of vintage pipelines should be evaluated against the possible use of FFS assessment procedures. FFS assessment provides a quantifiable performance target which is not available through the workmanship criteria. However, necessary inputs to perform FFS assessment may not be readily available. Ongoing work intended to address some of the gaps is briefly described.

scholarly journals Innovation in education: problems and ways of their solution

2020 ◽  
Vol 210 ◽  
pp. 18054
Author(s):  
Uliana Milhaleva
Keyword(s):  
Education System ◽  
New Technologies ◽  
Innovative Development ◽  
New Approach ◽  
Factors Affecting ◽  
Modern Education ◽  
Professional Activities ◽  
Innovation In Education ◽  
Starting Point ◽  
The Individual

This article analyzes the problems of modern education, and on the basis of this analysis, a search for a new approach to the formation of not only necessary knowledge, but also skills in the learning process is conducted. It will be about contextual, cross-contextual and existential skills, their improvement and transformation. Such skills should be developed in modern educational centers, which, in turn, should become the starting point of an individual educational route. It is the individual approach and new technologies that will help to form a personality adapted to professional activities in a rapidly changing world. The article also classifies the factors affecting the modern education system, they are divided into three main groups: social, technological and geopolitical. This classification, in turn, is used to study the strategies of innovative development of the educational system in Russia.

Axisymmetric Isothermal Forging

1989 ◽  
Author(s):  
Shiro Kobayashi ◽  
Soo-Ik Oh ◽  
Taylan Altan
Keyword(s):  
Finite Element ◽  
Coordinate System ◽  
Three Dimensions ◽  
Cold Forging ◽  
Axially Symmetric ◽  
Rectangular Coordinate System ◽  
Complex Deformation ◽  
Fem Method ◽  
Natural Coordinate System ◽  
Main Dimension

According to Spies, the majority of forgings can be classified into three main groups. The first group consists of compact shapes that have approximately the same dimensions in all three directions. The second group consists of disk shapes that have two of the three dimensions (length and width) approximately equal and larger than the height. The third group consists of the long shapes that have one main dimension significantly larger than the two others. All axially symmetric forgings belong to the second group, which includes approximately 30% of all commonly used forgings. A basic axisymmetric forging process is compression of cylinders. It is a relatively simple operation and thus it is often used as a property test and as a preforming operation in hot and cold forging. The apparent simplicity, however, turns into a complex deformation when friction is present at the die–workpiece interface. With the finite-element method, this complex deformation mode can be examined in detail. In this chapter, compression of cylinders and related forming operations are discussed. Since friction at the tool–workpiece interface is an important factor in the analysis of metal-forming processes, this aspect is also given particular consideration. Further, applications of the FEM method for complex-shaped dies are shown in the examples of forging and cabbaging. Finite-element discretization with a quadrilateral element is similar to that given in Chap. 8. The cylindrical coordinate system (r, ϑ, z) is used instead of the rectangular coordinate system. The element is a ring element with a quadrilateral cross-section, as shown in Fig. 9.1. The ξ and η of the natural coordinate system vary from −1 to 1 within each element.

A SIMPLIFIED TEXTURAL CLASSIFICATION DIAGRAM

1958 ◽  
Vol 38 (1) ◽  
pp. 54-55 ◽  
Author(s):  
J. A. Toogood
Keyword(s):  
Coordinate System ◽  
Rectangular Coordinate System

A textural diagram based on per cent clay and per cent sand is proposed. With a standard rectangular coordinate system it is easier to use than currently suggested triangles.

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