Seeing Skin in Reduced Coordinates

The problem of the temperature distribution in the finite cylinder with periodic boundary conditions over all the surfaces is treated analytically and numerically. The solution in the case of steady oscillation and constant thermal properties is presented in reduced coordinates and can be used to correct thermal diffusivity measurements by the Angstrom method or to study, for example, the influence of a destabilized controller which induces a periodic temperature of the sample during thermal treatment.

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Corrigendum to “A representation of the autoacceleration stage of polypropylene thermooxidation in reduced coordinates” [Polym Degrad Stab 2000;67(1):49–56]

Polymer Degradation and Stability ◽

10.1016/s0141-3910(00)00206-8 ◽

2001 ◽

Vol 72 (1) ◽

pp. 187

Author(s):

Pilar Tiemblo ◽

Jose Manuel Gómez-Elvira

Keyword(s):

Reduced Coordinates

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Equidistant map projections of a triaxial ellipsoid with the use of reduced coordinates

Geodesy and Cartography ◽

10.1515/geocart-2017-0021 ◽

2017 ◽

Vol 66 (2) ◽

pp. 271-290 ◽

Cited By ~ 1

Author(s):

Paweł Pędzich

Keyword(s):

Elliptic Integral ◽

Elliptic Functions ◽

New Method ◽

Triaxial Ellipsoid ◽

Polar Regions ◽

Jacobian Elliptic Functions ◽

Map Projections ◽

Basic Properties ◽

Reduced Coordinates

Abstract The paper presents a new method of constructing equidistant map projections of a triaxial ellipsoid as a function of reduced coordinates. Equations for x and y coordinates are expressed with the use of the normal elliptic integral of the second kind and Jacobian elliptic functions. This solution allows to use common known and widely described in literature methods of solving such integrals and functions. The main advantage of this method is the fact that the calculations of x and y coordinates are practically based on a single algorithm that is required to solve the elliptic integral of the second kind. Equations are provided for three types of map projections: cylindrical, azimuthal and pseudocylindrical. These types of projections are often used in planetary cartography for presentation of entire and polar regions of extraterrestrial objects. The paper also contains equations for the calculation of the length of a meridian and a parallel of a triaxial ellipsoid in reduced coordinates. Moreover, graticules of three coordinates systems (planetographic, planetocentric and reduced) in developed map projections are presented. The basic properties of developed map projections are also described. The obtained map projections may be applied in planetary cartography in order to create maps of extraterrestrial objects.

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Optimum Techniques for the Conversion of Space Rectangular and Curvilinear Coordinates

European Journal of Engineering Research and Science ◽

10.24018/ejers.2019.4.10.1588 ◽

2019 ◽

Vol 4 (10) ◽

pp. 147-151

Author(s):

Gafar Suara ◽

Timothy Oluwadare Idowu

Keyword(s):

The Other ◽

Curvilinear Coordinates ◽

High Quality ◽

Order Accuracy ◽

First Order ◽

Optimum Technique ◽

Rectangular Coordinates ◽

Optimum Model ◽

Reduced Coordinates ◽

Coordinate Conversion

Conversion between space rectangular (X, Y, Z) and curvilinear (φ, λ, h) coordinates is an important task in the field of Surveying, geodesy, positioning, navigation, mapping etc. Different techniques which include iterative methods, non-iterative techniques and closed form algebraic methods have been applied over the years to carry out the coordinate conversion. However, the results obtained using these techniques are deficient in one way or the other due to the inherent limitations such as inability to produce results for curvilinear coordinates when the values of X, Y and Z are subsequently or simultaneously equal to zero. Therefore, this study attempts to put forth an optimum coordinate conversion technique between space rectangular and curvilinear coordinates. The data used are coordinates of points which include the space rectangular coordinates and their equivalent curvilinear coordinates. They were observed and processed in Nigeria using Doppler 9 software by African Doppler Survey (ADOS) and they were confirmed to be of first order accuracy and hence of high quality. The data processing involved the design of the optimum techniques equations, coding of the algorithms and necessary computations to obtain results. Analyzing the results obtained, it can be inferred that the designed optimum model has successfully carried out the conversion between space rectangular and curvilinear coordinates. Therefore, the optimum technique model is recommended for use for the conversions from Space rectangular coordinates to Geocentric, Geodetic, Reduced coordinates and vice versa.

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The Solution of Large Time-Dependent Problems Using Reduced Coordinates.

10.21236/ada182618 ◽

1987 ◽

Author(s):

Kyran D. Mish ◽

Leonard R. Herrmann

Keyword(s):

Large Time ◽

Time Dependent ◽

Reduced Coordinates ◽

Time Dependent Problems

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One-axis molecular rotation and phonon scattering in solid C2H6 and C2F6

Open Physics ◽

10.2478/s11534-010-0029-5 ◽

2011 ◽

Vol 9 (1) ◽

Cited By ~ 1

Author(s):

Oleg Pursky ◽

Vyacheslav Konstantinov

Keyword(s):

Heat Transfer ◽

Phonon Scattering ◽

Molecular Crystals ◽

Molecular Rotation ◽

Rotation Effect ◽

Total Thermal Resistance ◽

Transfer Processes ◽

Modified Method ◽

Reduced Coordinates ◽

The One

AbstractUsing solid C2H6 and C2F6 as an example, the one-axis molecular rotation effect on thermal conductivity has been considered in orientationally-ordered (OO) and orientationally-disordered (OD) phases of simple molecular crystals. The influence of molecular rotation on the heat transfer processes has been studied by a modified method of reduced coordinates, which permitted separating phonon-phonon and phonon-rotation contributions to the total thermal resistance.

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