scholarly journals Using of Parallel Coordinates in Finding Minimum Distance in Time-Space

2019 ◽  
Vol 21 (3) ◽  
pp. 3-7
Author(s):  
Olga Blazekova ◽  
Maria Vojtekova
Keyword(s):  
Coordinate System ◽  
Minimum Distance ◽  
Three Dimensional ◽  
Multidimensional Data ◽  
Fourth Dimension ◽  
Geometric Representation ◽  
Two Dimensional ◽  
Parallel Coordinates ◽  
Time Space ◽  
Cartesian Coordinate

Airspace domain may be represented by a time-space consisting of a three-dimensional Cartesian coordinate system and time as the fourth dimension. A coordinate system provides a scheme for locating points given its coordinates and vice versa. The choice of coordinate system is important, as it transforms data to geometric representation. Visualization of the three and more dimensional data on the two-dimensional drawing - computer monitor is usually done by projection, which often can restrict the amount of information presented at a time. Using the parallel coordinate system is one of possibilities to present multidimensional data. The aim of this article is to describe basics of parallel coordinate system and to investigate lines and their characteristics in time-space.

On the Flexural-Torsional Behavior of a Straight Elastic Beam Subject to Terminal Moments

1993 ◽  
Vol 60 (2) ◽  
pp. 498-505 ◽  
Author(s):  
Z. Tan ◽  
J. A. Witz
Keyword(s):  
Coordinate System ◽  
Cross Section ◽  
Equilibrium Equation ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Elastic Beam ◽  
Cartesian Coordinate System ◽  
Kinematic Constraints ◽  
Torsional Behavior ◽  
Cartesian Coordinate

This paper discusses the large-displacement flexural-torsional behavior of a straight elastic beam with uniform circular cross-section subject to arbitrary terminal bending and twisting moments. The beam is assumed to be free from any kinematic constraints at both ends. The equilibrium equation is solved analytically with the full expression for curvature to obtain the deformed configuration in a three-dimensional Cartesian coordinate system. The results show the influence of the terminal moments on the beam’s deflected configuration.

scholarly journals New insights into the suitability of the third dimension for visualizing multivariate/multidimensional data: A study based on loss of quality quantification

2014 ◽  
Vol 15 (1) ◽  
pp. 3-30 ◽  
Author(s):  
Antonio Gracia ◽  
Santiago González ◽  
Víctor Robles ◽  
Ernestina Menasalvas ◽  
Tatiana von Landesberger
Keyword(s):  
Analytical Approach ◽  
Distance Perception ◽  
Statistical Tests ◽  
Three Dimensional ◽  
Multidimensional Data ◽  
Two Dimensional ◽  
Dimensional Representation ◽  
The Third ◽  
Quality Degradation ◽  
Third Dimension

Most visualization techniques have traditionally used two-dimensional, instead of three-dimensional representations to visualize multidimensional and multivariate data. In this article, a way to demonstrate the underlying superiority of three-dimensional, with respect to two-dimensional, representation is proposed. Specifically, it is based on the inevitable quality degradation produced when reducing the data dimensionality. The problem is tackled from two different approaches: a visual and an analytical approach. First, a set of statistical tests (point classification, distance perception, and outlier identification) using the two-dimensional and three-dimensional visualization are carried out on a group of 40 users. The results indicate that there is an improvement in the accuracy introduced by the inclusion of a third dimension; however, these results do not allow to obtain definitive conclusions on the superiority of three-dimensional representation. Therefore, in order to draw further conclusions, a deeper study based on an analytical approach is proposed. The aim is to quantify the real loss of quality produced when the data are visualized in two-dimensional and three-dimensional spaces, in relation to the original data dimensionality, to analyze the difference between them. To achieve this, a recently proposed methodology is used. The results obtained by the analytical approach reported that the loss of quality reaches significantly high values only when switching from three-dimensional to two-dimensional representation. The considerable quality degradation suffered in the two-dimensional visualization strongly suggests the suitability of the third dimension to visualize data.

Three-dimensional quantum mechanics in a curved space based on the q-addition

2019 ◽  
Vol 34 (29) ◽  
pp. 1950177
Author(s):  
Won Sang Chung ◽  
Hassan Hassanabadi
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Coordinate System ◽  
Three Dimensional ◽  
One Dimension ◽  
Cartesian Coordinate System ◽  
Spherical Coordinate ◽  
Curved Space ◽  
Dimension Formula ◽  
Cartesian Coordinate

In this paper, we extend the theory of the [Formula: see text]-deformed quantum mechanics in one dimension[Formula: see text] into three-dimensional case. We relate the [Formula: see text]-deformed quantum theory to the quantum theory in a curved space. We discuss the diagonal metric based on [Formula: see text]-addition in the Cartesian coordinate system and core radius of neutron star. We also discuss the diagonal metric based on [Formula: see text]-addition in the spherical coordinate system and [Formula: see text]-deformed Heisenberg atom model.

A Quasi-Generalized-Coordinate Approach for Numerical Simulation of Complex Flows

2006 ◽  
Vol 128 (6) ◽  
pp. 1394-1399 ◽  
Author(s):  
Donghyun You ◽  
Meng Wang ◽  
Rajat Mittal ◽  
Parviz Moin
Keyword(s):  
Coordinate System ◽  
Stokes Equations ◽  
Computational Cost ◽  
Three Dimensional ◽  
Cost Effective ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Curvilinear Coordinate ◽  
Generalized Coordinate

A novel structured grid approach which provides an efficient way of treating a class of complex geometries is proposed. The incompressible Navier-Stokes equations are formulated in a two-dimensional, generalized curvilinear coordinate system complemented by a third quasi-curvilinear coordinate. By keeping all two-dimensional planes defined by constant third coordinate values parallel to one another, the proposed approach significantly reduces the memory requirement in fully three-dimensional geometries, and makes the computation more cost effective. The formulation can be easily adapted to an existing flow solver based on a two-dimensional generalized coordinate system coupled with a Cartesian third direction, with only a small increase in computational cost. The feasibility and efficiency of the present method have been assessed in a simulation of flow over a tapered cylinder.

scholarly journals Maximum Allowable Pressure Calculation of Water Tube Boiler during Operation

2021 ◽  
Vol 2 (3) ◽  
pp. 27-33
Author(s):  
Abdlmanam Elmaryami ◽  
Mahmoud Abdelrazek Ahmida ◽  
Walid Saleh Muhammad
Keyword(s):  
Temperature Distribution ◽  
Three Dimensional ◽  
Industrial Sector ◽  
Limiting Factors ◽  
Steam Boiler ◽  
Two Dimensional ◽  
Water Tube ◽  
Steady State Temperature ◽  
Cartesian Coordinate ◽  
Tube Life

In the steam boiler industrial sector, pressure and temperature of the water tube are the two main factors that affect the safety and efficiency of a steam boiler.  Explosions may be occurring because of a sudden drop in pressure without a corresponding drop in temperature.  Therefore, understanding the temperature distribution of the water tube boiler is essential to control the failure and explosion of the boiler.  Once the temperature distribution is known than the limiting factors that affect the water tube life such as the maximum allowable pressure can be determined.  ANSYS software will be used to determine the temperature distribution in the water tube of a utility boiler during operation at elevated inlet water and furnace temperature.  The theory of axisymmetric has been utilized since the water- tube is cylindrical in shape.  In axisymmetric theory, a three-dimensional cylindrical problem like a water tube can be reduced to two-dimensional by ignoring the circumferential Ө, while the r-axis and z-axis became x-axis and y-axis or Cartesian coordinate.  Then two-dimensional rectangular elements meshing for the profile cross-section along the water tube in r and z axes were implemented in a computerized simulation using ANSYS 10 to find out the steady-state temperature distribution of the water tube.

A Comparison of Three Visual Representations of Complex Multidimensional Accounting Information

1999 ◽  
Vol 13 (2) ◽  
pp. 117-131 ◽  
Author(s):  
Richard B. Dull ◽  
David P. Tegarden
Keyword(s):  
Computer Program ◽  
Three Dimensional ◽  
Accounting Information ◽  
Visual Representations ◽  
Multidimensional Data ◽  
Accounting System ◽  
Two Dimensional ◽  
Interactive Computer Program ◽  
Data Output ◽  
The Relationship

This study investigates the relationship between three visual representations (two-dimensional, three-dimensional fixed, and three-dimensional rotatable) of multidimensional data, and the subjects' ability to make predictions based on the data. Output of a momentum accounting system was simulated and graphics were rendered based on that information. An interactive computer program was developed and used to administer the laboratory experiment and collect results. Subjects made prediction decisions based on the graphics produced for four companies. Each subject made predictions for one type of graphics representation for each of the four companies. Subjects using three-dimensional data that could be rotated provided the most accurate predictions. This finding is significant in a systems environment where visualizations and graphics are steadily increasing. The results should be considered when developing systems to provide accounting system users with information for making decisions, especially when the information to be presented is multidimensional in nature.

Textual Topography

2020 ◽  
pp. 83-101
Author(s):  
Ciaran McMorran
Keyword(s):  
Coordinate System ◽  
James Joyce ◽  
Fourth Dimension ◽  
Structural Level ◽  
Cartesian Coordinate System ◽  
Nonlinear Form ◽  
Cartesian Coordinate ◽  
Definition Of ◽  
Narrative Framework

This chapter examines how the branching narrative framework of “Wandering Rocks” reflects the structure of the manneristic maze and emulates the nonlinear visual structures which are traced by the characters of Ulysses as they wander through Dublin’s streets. In light of Henri Poincaré’s definition of geometry as “the summary of the laws by which images succeed each other,” it explores how James Joyce presents time presented as the fourth dimension of space in his construction of a textual “picture of Dublin” which follows the movement of wandering bodies. This chapter provides a schema of the narrative network in “Wandering Rocks,” illustrating how Joyce’s textual remapping of Dublin involves the structural emulation of fundamental geometric constructs and related topographical concepts which involve the coincident meeting of lines (as in triangulation, parallax, and the Cartesian coordinate system). In light of the parallactic perspectives which are facilitated by the episode’s branching structure, this chapter demonstrates how the labyrinthine “Wandering Rocks” narrative epitomizes Joyce’s Brunonian perversion of unidirectional rectilinearity on a structural level, disrupting “wider manifestations […] of ‘conceptual and behavioral rectilinearity’” in its nonlinear form.

scholarly journals Controlling the dual cascade of two-dimensional turbulence

2010 ◽  
Vol 668 ◽  
pp. 202-222 ◽  
Author(s):  
M. M. FARAZMAND ◽  
N. K.-R. KEVLAHAN ◽  
B. PROTAS
Keyword(s):  
Reynolds Number ◽  
Energy Spectrum ◽  
Three Dimensional ◽  
Careful Analysis ◽  
Space Structure ◽  
Inertial Range ◽  
Two Dimensional ◽  
Control Approach ◽  
Time Space ◽  
Moderate Reynolds Number

The Kraichnan–Leith–Batchelor (KLB) theory of statistically stationary forced homogeneous isotropic two-dimensional turbulence predicts the existence of two inertial ranges: an energy inertial range with an energy spectrum scaling of k−5/3, and an enstrophy inertial range with an energy spectrum scaling of k−3. However, unlike the analogous Kolmogorov theory for three-dimensional turbulence, the scaling of the enstrophy range in the two-dimensional turbulence seems to be Reynolds-number-dependent: numerical simulations have shown that as Reynolds number tends to infinity, the enstrophy range of the energy spectrum converges to the KLB prediction, i.e. E ~ k−3. The present paper uses a novel optimal control approach to find a forcing that does produce the KLB scaling of the energy spectrum in a moderate Reynolds number flow. We show that the time–space structure of the forcing can significantly alter the scaling of the energy spectrum over inertial ranges. A careful analysis of the optimal forcing suggests that it is unlikely to be realized in nature, or by a simple numerical model.

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