Corrigenda: The geometry of a Randers rotational surface

2016 ◽  
Vol 88 (3-4) ◽  
pp. 517-519
Author(s):  
RATTANASAK HAMA ◽  
PAKKINEE CHITSAKUL ◽  
SORIN V. SABAU
Keyword(s):  
Rotational Surface

scholarly journals Isometric Deformation of (m,n)-Type Helicoidal Surface in the Three Dimensional Euclidean Space

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 226 ◽  
Author(s):  
Erhan Güler
Keyword(s):  
Euclidean Space ◽  
Three Dimensional ◽  
Beltrami Operator ◽  
Dimensional Euclidean Space ◽  
Natural Numbers ◽  
Rotational Surface ◽  
Isometric Deformation ◽  
Helicoidal Surface

We consider a new kind of helicoidal surface for natural numbers ( m , n ) in the three-dimensional Euclidean space. We study a helicoidal surface of value ( m , n ) , which is locally isometric to a rotational surface of value ( m , n ) . In addition, we calculate the Laplace–Beltrami operator of the rotational surface of value ( 0 , 1 ) .

scholarly journals Near-Field to Far-Field Transformation Techniques with Spiral Scannings: A Comprehensive Review

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Renato Cicchetti ◽  
Francesco D’Agostino ◽  
Flaminio Ferrara ◽  
Claudio Gennarelli ◽  
Rocco Guerriero ◽  
...  
Keyword(s):  
Communication Systems ◽  
Near Field ◽  
Theoretical Background ◽  
Wireless Communication Systems ◽  
Far Field ◽  
Unified Theory ◽  
Transformation Techniques ◽  
Positioning Systems ◽  
Rotational Surface ◽  
Spiral Scanning

An overview of the near-field-far-field (NF-FF) transformation techniques with innovative spiral scannings, useful to derive the radiation patterns of the antennas commonly employed in the modern wireless communication systems, is provided in this paper. The theoretical background and the development of a unified theory of the spiral scannings for quasi-spherical and nonspherical antennas are described, and an optimal sampling interpolation expansion to evaluate the probe response on a quite arbitrary rotational surface from a nonredundant number of its samples, collected along a proper spiral wrapping it, is presented. This unified theory can be applied to spirals wrapping the conventional scanning surfaces and makes it possible to accurately reconstruct the NF data required by the NF-FF transformation employing the corresponding classical scanning. A remarkable reduction of the measurement time is so achieved, due to the use of continuous and synchronized movements of the positioning systems and to the reduced number of needed NF measurements. Some numerical and experimental results relevant to the spherical spiral scanning case when dealing with quasi-planar and electrically long antennas are shown.

scholarly journals The Geometry of a Randers Rotational Surface with an Arbitrary Direction Wind

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2047
Author(s):  
Rattanasak Hama ◽  
Sorin V. Sabau
Keyword(s):  
Arbitrary Direction ◽  
Surfaces Of Revolution ◽  
Killing Field ◽  
Navigation Problem ◽  
Rotational Surface ◽  
Randers Metric ◽  
Global Behaviour

In the present paper, we study the global behaviour of geodesics of a Randers metric, defined on Finsler surfaces of revolution, obtained as the solution of the Zermelo’s navigation problem. Our wind is not necessarily a Killing field. We apply our findings to the case of the topological cylinder R×S1 and describe in detail the geodesics behaviour, the conjugate and cut loci.

On the Formulation of Nonreflecting Boundary Conditions for Turbomachinery Configurations: Part I — Theory and Implementation

2020 ◽  
Author(s):  
Christian Frey ◽  
Daniel Schlüß ◽  
Nina Wolfrum ◽  
Patrick Bechlars ◽  
Maximilian Beck
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Frequency Domain ◽  
Harmonic Balance ◽  
Radial Component ◽  
Rotational Surface ◽  
Nonreflecting Boundary Conditions ◽  
Meridional Velocity ◽  
The Impact ◽  
Rotational Surfaces

Abstract With unsteady flow simulations of industrial turbomachinery configurations becoming more and more affordable there is a growing need for accurate inlet and outlet boundary conditions as numerical reflections alone can lead to incorrect trends in engine efficiency, noise and aeroelastic analysis parameters. This is the first of two papers on the formulation of unsteady boundary conditions which have been implemented for both time-domain and frequency-domain solvers. Giles’ original idea for steady solvers to formulate the boundary condition in terms of characteristics generalizes to frequency-domain solvers. The boundary condition drives the value of the incoming characteristics to ideal values that are computed using the modal decomposition of linearized 2D Euler flows. The present paper explains how to generalize 2D nonreflecting boundary conditions to real 3D annular domains by applying them in certain conical rotational surfaces. For a flow with zero radial component and an annular boundary that is perpendicular to the machine axis, these surfaces are the cylindrical streamsurfaces. For more general flows and geometries, however, there is no natural choice for the rotational surfaces. In this paper, two choices are discussed: the surfaces that are generated by the boundary normals and those that are defined by the circumferentially averaged meridional velocity. The impact of the boundary condition on the stability of the harmonic-balance solver is analyzed by studying the pseudo-time evolution of certain energy integrals. For a model problem which consists of a small disturbance of an inviscid flow, the increase or decrease of this energy integral is shown to be directly related to the normal characteristic variables along the boundary. This shows that the actual boundary condition should be formulated as a control problem for the normal characteristics. Moreover, the application of the harmonic balance solver to a simple duct configuration with prescribed disturbances demonstrates that using the characteristics based on the meridional velocity may prevent the solver from converging. In contrast, the 2D theory can be formulated in a different surface without impairing the robustness of the overall approach. These findings are illustrated by a simple test case. The impact of the choice of the rotational surface for the 2D theory is studied for various duct segments and a low-pressure turbine configuration in the second paper. There it is shown that applying the 2D theory to the meridional-velocity surfaces may be advantageous in that it leads to more accurate results.

Three-DOF Electrostatic Induction Actuator Providing Translational and Rotational Surface-Drive Motion

2016 ◽  
Vol 10 (4) ◽  
pp. 525-532 ◽  
Author(s):  
Norio Yamashita ◽  
◽  
Akio Yamamoto ◽  
Keyword(s):  
Rotational Motion ◽  
Applied Voltage ◽  
Checkerboard Pattern ◽  
Rotational Surface ◽  
Electrostatic Fields ◽  
Electrostatic Induction ◽  
Three Phase ◽  
Rotational Motions ◽  
Regular Manner ◽  
Three Degree Of Freedom

This paper describes the driving characteristics of a three degree-of-freedom (three-DOF) electrostatic induction actuator, which can demonstrate surface-drive characteristics with translational and rotational motions. It consists of a sheet-type slider without electrodes and a planar stator with an array of three-phase driving electrodes. The electrodes with different orientations are aligned in a regular manner to construct a four-by-four checkerboard pattern. Controlling applied voltage patterns can generate translational or rotational patterns of electrostatic fields, which drive the slider. The performance of the three-DOF actuator with regards to translational and rotational motion was investigated.

scholarly journals Timelike rotational surfaces of elliptic, hyperbolic and parabolic types in Minkowski space E41 with pointwise 1-type Gauss map

Filomat ◽  
2015 ◽  
Vol 29 (3) ◽  
pp. 381-392 ◽  
Author(s):  
Burcu Bektaş ◽  
Uğur Dursun
Keyword(s):  
Minkowski Space ◽  
Parabolic Type ◽  
Gauss Map ◽  
Rotational Surface ◽  
Rotational Surfaces

In this work, we focus on a class of timelike rotational surfaces in Minkowski space E41 with 2-dimensional axis. There are three types of rotational surfaces with 2-dimensional axis, called rotational surfaces of elliptic, hyperbolic or parabolic type. We obtain all flat timelike rotational surface of elliptic and hyperbolic types with pointwise 1-type Gauss map of the first and second kind. We also prove that there exists no flat timelike rotational surface of parabolic type in E41 with pointwise 1-type Gauss map.

scholarly journals ON WEAK BIHARMONIC GENERALIZED ROTATIONAL SURFACE IN E⁴

2019 ◽  
Vol 2 (2) ◽  
pp. 166-174
Author(s):  
Kadri Arslan ◽  
Merve Harmanlı ◽  
Betül Bulca
Keyword(s):  
Rotational Surface

scholarly journals The geometry of a Randers rotational surface

2015 ◽  
Vol 87 (3-4) ◽  
pp. 473-502 ◽  
Author(s):  
RATTANASAK HAMA ◽  
PAKKINEE CHITSAKUL ◽  
SORIN V. SABAU
Keyword(s):  
Rotational Surface
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