On Algorithms of Graphical Plotting of Geodesic Line on a Ruled Surface

2015 ◽  
Vol 3 (4) ◽  
pp. 15-18 ◽  
Author(s):  
Умбетов ◽  
Nurlan Umbetov ◽  
Джанабаев ◽  
Zh. Dzhanabaev
Keyword(s):  
Initial Point ◽  
Intersection Point ◽  
Ruled Surface ◽  
Engineering Practice ◽  
Geodesic Line ◽  
Axis Of Rotation ◽  
Characteristic Lines ◽  
Geodesic Lines ◽  
Internal Properties

Geodesic lines find interesting applications when solving many tasks of fundamental sciences (mathematicians, physics, etc.) and engineering practice. In differential geometry geodesic lines are characteristic lines for determination of internal properties of surface. However, the construction of geodesic line on a surface presents certain complications, mainly solved by the methods of calculating mathematics and descriptive geometry. In this article the development of a simple and comfortable algorithm of construction of geodesic line is considered on linear surfaces. In general case, the spatial model of algorithm of construction of geodesic line on a ruled surface is expressed in the following: a ruled surface we replace with averged surface, and at any side of the viewed verge, the intersection point of the geodesic with the rib of fracture (line of bending of dihedral angle) will be determined as the intersection of contiguous generatrix with the surface of cone of rotation – the congruence of directions of geodesic laying with the top at initial point, axis of rotation, incident to the considered generatrix, and the corner at the top of cone, equal to the doubled corner between the axis of rotation and direction of the geodesic laying. Next, as an initial parameters the contiguous with reviewed generatrix are accepted, determined higher point, lying on it, and the direction of geodesic is a corner between a segment obtained from geodesic and contiguous generatrix. Thus, repeatedly reiterating the described cycle, we will get the multitude number of points, making the required geodesic line.

scholarly journals Solar structure and evolution

2021 ◽  
Vol 18 (1) ◽  
Author(s):  
Jørgen Christensen-Dalsgaard
Keyword(s):  
Solar Surface ◽  
Solar Neutrinos ◽  
Solar Interior ◽  
Stellar Structure ◽  
The Sun ◽  
Physical Processes ◽  
Solar Evolution ◽  
Internal Properties ◽  
Atmospheric Phenomena

AbstractThe Sun provides a critical benchmark for the general study of stellar structure and evolution. Also, knowledge about the internal properties of the Sun is important for the understanding of solar atmospheric phenomena, including the solar magnetic cycle. Here I provide a brief overview of the theory of stellar structure and evolution, including the physical processes and parameters that are involved. This is followed by a discussion of solar evolution, extending from the birth to the latest stages. As a background for the interpretation of observations related to the solar interior I provide a rather extensive analysis of the sensitivity of solar models to the assumptions underlying their calculation. I then discuss the detailed information about the solar interior that has become available through helioseismic investigations and the detection of solar neutrinos, with further constraints provided by the observed abundances of the lightest elements. Revisions in the determination of the solar surface abundances have led to increased discrepancies, discussed in some detail, between the observational inferences and solar models. I finally briefly address the relation of the Sun to other similar stars and the prospects for asteroseismic investigations of stellar structure and evolution.

Fast Determination of Phosphorus Concentration in Phosphogypsum Waste Using Calibration-Free LIBS in Air and Helium

2021 ◽  
Author(s):  
Khaled Elsayed ◽  
Walid Tawfik ◽  
Ashraf E M Khater ◽  
Tarek S Kayed ◽  
Mohamed Fikry
Keyword(s):  
Complete Analysis ◽  
Phosphorus Concentration ◽  
Stark Broadening ◽  
Breakdown Spectroscopy ◽  
P Concentration ◽  
Characteristic Lines ◽  
Laser Induced Breakdown ◽  
Novel Method ◽  
Calibration Free

Abstract This work represents a novel method to determine phosphorus (P) concentration in phosphogypsum (PG) waste samples using calibration-free laser-induced breakdown spectroscopy (LIBS). A 50 mJ Q-switched Nd: YAG laser has generated the PG LIBS spectrum. Spectroscopic analysis of plasma evolution has been characterized by electron density Ne and electron temperature Te using the emission intensity and stark broadening for P I characteristic lines 213.61, 214.91, and 215.40 nm under non-purged (air) and purged (helium) conditions. It was found that both Te and Ne have significant changes linearly with P concentrations 4195, 5288, 6293, and 6905 ppm. The values of plasma Te and Ne increased from about 6900 to 10000 K and 1.1×1017 to 3.4×1017 cm− 3, respectively, for the non-purged PG. On the other hand, Te and Ne ranged from 8200 to 11000 K and 1.4×1017 to 3.5×1017 cm− 3, respectively, for the PG purged with helium. It is concluded that Te and Ne values represent a fingerprint plasma characterization for a given P concentration in PG samples, which can be used to identify P concentration without a PG's complete analysis. These results demonstrate a new achievement in the field of spectrochemical analysis of environmental applications.

scholarly journals Determination of Equivalent Mohr-Coulomb Criterion from Generalised Hoek-Brown Criterion

2021 ◽  
Author(s):  
Qingqing Yang ◽  
Fei Cai
Keyword(s):  
Principal Stress ◽  
Least Squares Method ◽  
Method Comparison ◽  
Friction Angle ◽  
Engineering Practice ◽  
Shear Strength Parameters ◽  
Strength Parameters ◽  
Coulomb Criterion ◽  
Minor Principal Stress

Abstract A new analytical solution is presented for determining equivalent Mohr-Coulomb (MC) shear strength parameters over an arbitrary interval of minor principal stress σ3 from the generalised Hoek-Brown (HB) criterion using least squares method. Comparison with several published examples demonstrates that the proposed solution had a capacity to accurately determine equivalent MC parameters over a given interval of σ3, as well as instantaneous MC parameters by using a very small interval of σ3. EMC parameters depended heavily on the interval of σ3, which highlighted the importance of intervals of σ3. A calculation case shows that the equivalent internal friction angle and cohesion over the interval of σ3 from tension cut-off σcut−off to maximum minor principal stress σ3max were approximately 12% smaller and 10.3% larger than those over an interval from tensile strength to σ3max, respectively. The proposed solution offers great flexibility for the application of the HB criterion with existing methods based on the MC criterion for rock engineering practice.

scholarly journals Effect of the New Equinox Definition on the Zero-Point of Longitude of the Indian Calendar

1990 ◽  
Vol 141 ◽  
pp. 186-186
Author(s):  
A. K. Bhatnagar
Keyword(s):  
Initial Point ◽  
Zero Point ◽  
The Mean ◽  
Image Position ◽  
Calendar Reform

Indian calendars follow a sidereal system of astronomy taking a fixed initial point on the ecliptic as the origin from which the longitudes are measured. Its position for the official Indian Calendar has been defined by the Calendar Reform Committee (1955) as the point on the ecliptic whose true tropical longitude was 23°15′00″ as on 21 March 1956, 0h UT. Its position was determined upto the year 1984 in accordance with Newcomb's value for general precession using the relation where T is in centuries of 36525 ephemeris days from 1900 January 0.5 ET. Recent changes in the location and the motion of the equinox with reference to the epoch J2000.0 have necessitated corresponding changes to be included in the determination of the mean and true positions of the above initial point. The new algorithm worked out is where T is in Julian centuries of 36525 days from J2000.0.

scholarly journals The use of dilatometer test for the determination of undrained shear strength in organic soils

2008 ◽  
Vol 40 (1) ◽  
pp. 97-105
Author(s):  
Simon Rabarijoely
Keyword(s):  
Shear Strength ◽  
Undrained Shear Strength ◽  
Organic Soils ◽  
Engineering Practice ◽  
Empirical Correlations ◽  
Empirical Formulas ◽  
Geotechnical Design ◽  
Design Calculations ◽  
Undrained Shear

The use of dilatometer test for the determination of undrained shear strength in organic soils The use of dilatometer test for the determination of undrained shear strength in organic soils. In engineering practice the empirical correlations or charts are often use to determine soil properties for design calculations. The DMT tests results are analysed on the basis of the empirical formulas proposed by Marchetti (1980). In this paper the new chart to determine the τfu of organic mud was proposed. The chart presents the relationships between dilatometer readings (p0 - u0), (p1 - u0), σ'v0 and τfu. The chart will be helpful in geotechnical design of embankments constructed on organic subsoil.

scholarly journals Middle Rules and Rhumb-Line Sailing

2017 ◽  
Vol 24 (2) ◽  
pp. 13-16
Author(s):  
Miljenko Petrović
Keyword(s):  
Intrinsic Property ◽  
Middle Latitude ◽  
Iterative Solution ◽  
Transcendental Equation ◽  
Intersection Point ◽  
System Of Nonlinear Equations ◽  
Incremental Value ◽  
Novel Concept ◽  
Raphson Method

Abstract This work tackles the problem of misconception when using sophisticated mathematical tools, nonlinear optimization in this particular case, to solve a navigational problem. Namely, to reach the Great Circle vertex with two rhumb line legs ensuing the optimized distance, an initial rhumb line course equal to the orthodromic course at middle latitude may be used. The initial course is thereupon optimized by the incremental value steps. The optimized distance is achieved if the rhumb line course is altered towards the vertex at the orthodrome-loxodrome intersection point. As determination of this point cannot be formulated in a closed form, an iterative solution is to be applied. The derived transcendental equation forms a basis for an iterative solution of intersection using the Newton-Raphson method. To the contrary, finding solutions to a system of nonlinear equations can mislead a researcher unable to comprehend and grasp the mathematical meanings of the algorithm. The gist of this essay is a novel concept showing an intrinsic property i.e. orthodrome-loxodrome correlation using a well-known formula.

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