scholarly journals Dipole Near Field Analysis – A Closed Form Calculation in Cartesian Coordinates

2013 ◽  
Vol 64 (5) ◽  
pp. 327-330 ◽  
Author(s):  
René Harťanský ◽  
Jozef Slížik ◽  
Lukáš Maršálka
Keyword(s):  
Coordinate System ◽  
Closed Form ◽  
Numerical Method ◽  
Electric Dipole ◽  
Near Field ◽  
Analytical Calculation ◽  
Field Analysis ◽  
Cartesian Coordinate System ◽  
Cartesian Coordinates ◽  
Cartesian Coordinate

Abstract This article deals with analytical calculation of the near-field of an electric dipole in Cartesian coordinate system in a closed form. Results of the analytical calculation are verified by numerical method.

scholarly journals Semiotic Insights into Aristotle’s Theory of Being: Definition and Model of Sign

2012 ◽  
Vol 61 ◽  
pp. 113-135
Author(s):  
Algirdas Budrevičius
Keyword(s):  
Coordinate System ◽  
Initial Part ◽  
Cartesian Coordinate System ◽  
Fundamental Theory ◽  
Cartesian Coordinates ◽  
Surface Maps ◽  
Proposed Model ◽  
Cartesian Coordinate ◽  
Definition Of

This paper is aimed to develop a model of the sign as homomorphism (i.e. similarity of form) as the initial part of a strict and fundamental theory of sign. Many various signs—photographs, pictures, sculptures, diagrams, surface maps, etc.—might be viewed in terms of homomorphism. The proposed model of sign as a homomorphism is derived using Aristotle’s theory of being. Two principles of Aristotle’s theory—form and matter—are used as elementary ideas in the model of sign. The main peculiarity of the undertaken approach to semiotics is treating a sign and a signified object as derivative ideas; they are constructed as compounds of form and matter. To achieve more strictness, the model of sign is treated in terms of the system of Cartesian coordinates modified for the articulation of being. Intentionality is viewed as the key idea in the model of sign. The approach to the definition of sign presented in this paper can be viewed as an ontological alternative to Peirce’s one.Keywords: sign as homomorphism, Aristotle, hylomorphism, Cartesian coordinate system, ontology.Aristotelio esaties teorijos semiotinės įžvalgosAlgirdas BudrevičiusSantraukaPagrindinis šio straipsnio tyrimo dalykas yra ženklas kaip žymimojo objekto homomorfizmas – tai yra ženklas kaip formos panašumas. Pagrindinis tikslas – sukurti ženklo kaip homomorfizmo modelį, kuris būtų griežtos, pamatinės ženklo teorijos pradinė dalis. Daug įvairių ženklų gali būti nagrinėjami kaip homomorfizmai: fotografijos, paveikslai, skulptūros, diagramos, žemėlapiai ir kt. Pasiūlytas homomorfinio ženklo modelis išvestas naudojant Aristotelio esaties teoriją. Kaip elementariosios sąvokos jame naudojami du Aristotelio esaties teorijos principai – forma ir materija (medžiaga). Dėstomo požiūrio ypatumas semiotikos atžvilgiu yra tas, kad ženklas ir žymimasis objektas traktuojami kaip išvestinės sąvokos; jos konstruojamos kaip formos ir materijos junginiai. Siekiant, kad modelis būtų griežtesnis, jam sudaryti naudojama Dekarto koordinačių sistema, pritaikyta esaties artikuliavimui. Homomorfinio ženklo apibrėžimo kertine laikoma intencionalumo sąvoka. Straipsnyje pateiktas požiūris į ženklo apibrėžimą gali būti laikomas ontologine alternatyva Peirce’o požiūriui.

Representation of Reservoir Geometry for Numerical Simulation

1970 ◽  
Vol 10 (04) ◽  
pp. 393-404 ◽  
Author(s):  
G.J. Hirasaki ◽  
P.M. O'Dell
Keyword(s):  
Coordinate System ◽  
Curvilinear Coordinates ◽  
Reference Plane ◽  
Cartesian Coordinate System ◽  
Curvilinear Coordinate System ◽  
Coordinate Systems ◽  
Cartesian Coordinates ◽  
Curvilinear Coordinate ◽  
Reservoir Geometry ◽  
Cartesian Coordinate

Abstract For most reservoirs the reservoir thickness and dip vary with position. For such reservoirs, the use of a Cartesian coordinate system is awkward as the coordinate surfaces are planes and the finite-difference grid elements are rectangular parallepipeds. However, these reservoirs may be efficiently parallepipeds. However, these reservoirs may be efficiently modeled with a curvilinear coordinate system that has coordinate surfaces that coincide with the reservoir surfaces. A procedure is presented that may be used to determine a curvilinear coordinate system that will conform with the geometry of the reservoir. The reservoir geometry is described by the depth of the top of the reservoir and the thickness. The mass conservation equations are presented in curvilinear coordinates. The finite-difference equations differ from the usual Cartesian coordinate formulation by a factor multiplying the pore volume and transmissibilities. A numerical example is presented to illustrate the magnitude of the error that may occur in the computed oil recovery if the Cartesian coordinate system is simply modified to yield the correct depth and pore volumes. Introduction Many reservoirs have a shape that is inconvenient and possibly inaccurate to model with Cartesian coordinates. The use of a curvilinear coordinate system that follows the shape of the reservoir can be advantageous for such reservoirs. The formulation discussed here will have the greatest advantage in modeling thin reservoirs but will have little advantage in modeling a reservoir whose thickness is greater than its radius of curvature, such as a pinnacle reef. pinnacle reef. In this paper the reader is introduced to various grid systems used to model reservoirs. A brief discussion of some concepts of differential geometry contrasts differences between Cartesian coordinates and curvilinear coordinates. A curvilinear coordinate system for modeling reservoir geometry is presented. Formulation of the conservation equations in curvilinear coordinates and the necessary modifications to pore volume and transmissibility are discussed. A numerical example illustrates the magnitude of the error that may result from some coordinate systems. COORDINATE SYSTEMS AND RESERVOIR GRID NETWORKS A reservoir is usually described with the depth, thickness, boundaries, etc., shown on a structure map with sea level as a reference plane. For example, the subsea depth may be shown as a contour map on the reference plane with a Cartesian coordinate grid superimposed on the reference plane as shown on Fig. 1. The Cartesian coordinates, plane as shown on Fig. 1. The Cartesian coordinates, (y1, y2), have been defined as the coordinates for the reference plane. If the reservoir surfaces are parallel planes, Cartesian coordinates may be used. The Cartesian coordinate may be rotated such that the coordinate surfaces coincide with the reservoir surfaces. SPEJ P. 393

scholarly journals Classification of All Non-Isomorphic Regular and Cuspidal Arm Anatomies in an Orthogonal Metamorphic Manipulator

Robotics ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 20 ◽  
Author(s):  
Christos Koukos-Papagiannis ◽  
Vassilis Moulianitis ◽  
Nikos Aspragathos
Keyword(s):  
Coordinate System ◽  
Closed Form ◽  
Inverse Kinematics ◽  
Design Space ◽  
Polynomial Equation ◽  
Cartesian Coordinate System ◽  
Parametric Solution ◽  
Symbolic Algebra ◽  
Cartesian Coordinate

This paper proposes a classification of all non-isomorphic anatomies of an orthogonal metamorphic manipulator according to the topology of workspace considering cusps and nodes. Using symbolic algebra, a general kinematics polynomial equation is formulated, and the closed-form parametric solution of the inverse kinematics is obtained for the coming anatomies. The metamorphic design space was disjointed into eight distinct subspaces with the same number of cusps and nodes plotting the bifurcating and strict surfaces in a cartesian coordinate system { θ π 1 , θ π 2 , d 4 } . In addition, several non-singular, smooth and continuous trajectories are simulated to show the importance of this classification.

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 A Lattice Boltzmann Scheme for Diffusion Equation in Spherical Coordinate

2018 ◽  
Vol 1 (4) ◽  
Author(s):  
Debabrata Datta ◽  
T K Pal
Keyword(s):  
Diffusion Equation ◽  
Coordinate System ◽  
Lattice Boltzmann ◽  
Spherical Coordinate System ◽  
Cartesian Coordinate System ◽  
Spherical Coordinate ◽  
Cartesian Coordinate ◽  
Lattice Boltzmann Models ◽  
Boltzmann Method ◽  
Good Agreement

Lattice Boltzmann models for diffusion equation are generally in Cartesian coordinate system. Very few researchers have attempted to solve diffusion equation in spherical coordinate system. In the lattice Boltzmann based diffusion model in spherical coordinate system extra term, which is due to variation of surface area along radial direction, is modeled as source term. In this study diffusion equation in spherical coordinate system is first converted to diffusion equation which is similar to that in Cartesian coordinate system by using proper variable. The diffusion equation is then solved using standard lattice Boltzmann method. The results obtained for the new variable are again converted to the actual variable. The numerical scheme is verified by comparing the results of the simulation study with analytical solution. A good agreement between the two results is established.

Geometrical Optics

2019 ◽  
pp. 188-214
Author(s):  
B. D. Guenther
Keyword(s):  
Coordinate System ◽  
Ray Tracing ◽  
Geometrical Optics ◽  
Paraxial Approximation ◽  
Cartesian Coordinate System ◽  
Lens System ◽  
Thin Lens ◽  
Aperture Stop ◽  
Sign Convention ◽  
Cartesian Coordinate

Discuss the limits imposed by the paraxial approximation. Define the sign convention based on the cartesian coordinate system, the foiundation of analytic geometery. Demonstrate ray tracing technique to derive the ABCD maxtrix which will generate both the gaussian and Newtonian form of the thin lens equation and the lens maker’s equation. The cardinal points of a lens are also derived. The ABCD matrix is used to explore the methods used in ray tracing to locate the aperture stop of a Cooke’s triplet lens system. In the problem set, the student is asked to use the aperture stop to locate the entrance and exit pupil of a Cooke’s triplet.

scholarly journals Approximate Inertial Coordinate System Selections for Rotation Problems - The Gravitational Field of the Celestial Body Higher than the Object Being Rotated

2015 ◽  
Vol 8 (1) ◽  
pp. 102
Author(s):  
Zifeng Li
Keyword(s):  
Gravitational Field ◽  
Coordinate System ◽  
Celestial Body ◽  
Angular Speed ◽  
Calculation Error ◽  
Cartesian Coordinate System ◽  
Inertial Coordinate System ◽  
The Earth ◽  
The Galaxy ◽  
Cartesian Coordinate

<p class="1Body">Selection of the coordinate system is essential for rotation problems. Otherwise, mistakes may occur due to inaccurate measurement of angular speed. Approximate inertial coordinate system selections for rotation problems should be the gravitational field of the celestial body higher than the object being rotated: (1) the Earth fixed Cartesian coordinate system for normal rotation problem; (2) heliocentric - geocentric Cartesian coordinate system for satellites orbiting the Earth; (3) the Galaxy Heart - heliocentric Cartesian coordinates for Earth's rotation around the Sun. In astrophysics, mass calculation error and angular velocity measurement error lead to a black hole conjecture.</p>

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