Analysis on the Deflection Angle of Columnar Dendrites of Continuous Casting Steel Billets Under the Influence of Mold Electromagnetic Stirring

To better evaluate the spatial steering effect of directional perforation hydraulic fractures, evaluation indexes for the spatial steering effect are first proposed in this paper. Then, these indexes are used to quantitatively evaluate existing physical experimental results. Finally, with the help of RFPA2D-Flow software, the influence of perforation length and azimuth on the spatial steering process of hydraulic fracture are quantitatively analysed using four evaluation indexes. It is shown by the results that the spatial deflection trajectory, deflection distance, deflection angle and initiation pressure of hydraulic fractures can be used as quantitative evaluation indexes for the spatial steering effect of hydraulic fractures. The deflection paths of directional perforation hydraulic fractures are basically the same. They all gradually deflect to the maximum horizontal principal stress direction from the perforation hole and finally represent a double-wing bending fracture. The deflection distance, deflection angle and initiation pressure of hydraulic fractures increase gradually with increasing perforation azimuth, and the sensitivity of the deflection angle to the perforation azimuth of hydraulic fractures also increases. With increasing perforation length, the deflection distance of hydraulic fractures increases gradually. However, the deflection angle and initiation pressure decrease gradually, as does the sensitivity.

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Fluid flow phenomena in the electromagnetic stirring of continuous casting systems, part 1: the behaviour of a cylindrically shaped laboratory scale installation

Steel Research ◽

10.1002/srin.199000378 ◽

1990 ◽

Vol 61 (10) ◽

pp. 455-466 ◽

Cited By ~ 2

Author(s):

Navtej S. Saluja ◽

Olusegun Johnson Ilegbusi ◽

Julian Szekely

Keyword(s):

Fluid Flow ◽

Continuous Casting ◽

Laboratory Scale ◽

Electromagnetic Stirring ◽

Flow Phenomena

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OPERATOR-PRODUCT EXPANSION AND ANALYTICITY

International Journal of Modern Physics A ◽

10.1142/s0217751x9900227x ◽

1999 ◽

Vol 14 (30) ◽

pp. 4819-4840

Author(s):

JAN FISCHER ◽

IVO VRKOČ

Keyword(s):

Operator Product Expansion ◽

Deflection Angle ◽

Vacuum Expectation ◽

Vacuum Expectation Value ◽

Operator Product ◽

Coupling Constant ◽

Expectation Value ◽

Euclidean Region ◽

The Deflection Angle ◽

Class Of Functions

We discuss the current use of the operator-product expansion in QCD calculations. Treating the OPE as an expansion in inverse powers of an energy-squared variable (with possible exponential terms added), approximating the vacuum expectation value of the operator product by several terms and assuming a bound on the remainder along the Euclidean region, we observe how the bound varies with increasing deflection from the Euclidean ray down to the cut (Minkowski region). We argue that the assumption that the remainder is constant for all angles in the cut complex plane down to the Minkowski region is not justified. Making specific assumptions on the properties of the expanded function, we obtain bounds on the remainder in explicit form and show that they are very sensitive both to the deflection angle and to the class of functions considered. The results obtained are discussed in connection with calculations of the coupling constant αs from the τ decay.

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Influence of the configuration of the submerged entry nozzle inner channel and electromagnetic effect within its length on the qualitative distribution of metal flows during continuous casting of steel

Chernye Metally ◽

10.17580/chm.2021.01.03 ◽

2021 ◽

pp. 17-22

Author(s):

A. Yu. Tretyak ◽

◽

Qiang Wang ◽

Chun-Lei Wu ◽

E. I. Shifrin ◽

...

Keyword(s):

Quality Control ◽

Continuous Casting ◽

Submerged Entry Nozzle ◽

Electromagnetic Stirring ◽

Continuous Casting Of Steel ◽

Electromagnetic Effect ◽

Inner Surface ◽

Continuously Cast ◽

Inner Channel ◽

Research Show

Today, the most promising and effective method of quality control of the continuously cast billets is electromagnetic stirring of the melt. In this case, an important component is the effect of the stirring on the jet in the nozzle. Moreover, as research has shown, this method is highly dependent on the configuration of the inner channel of the nozzle. Research have shown that positive or negative taper of the inner surface of the nozzle allows to obtain different results after applying EMS. Taper control completely changes the pattern of the melt flow and its deceleration in the mold, especially when it is casting of large billets. The results of the research show that minor changes in the taper of the nozzle significantly increase the effect of EMS implementation, which is observed already at 0.27 % of positive the taper and increases to 0.54%.

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The precise calculations of the constant terms in the equations of motions of planets and photons of general relativity

Physics Essays ◽

10.4006/0836-1398-34.2.183 ◽

2021 ◽

Vol 34 (2) ◽

pp. 183-192

Author(s):

Mei Xiaochun

Keyword(s):

General Relativity ◽

Gravitational Field ◽

Deflection Angle ◽

Constant Term ◽

Equation Of Motion ◽

Time Dependent ◽

Newtonian Gravity ◽

Newtonian Theory ◽

The Deflection Angle ◽

Equations Of Motions

In general relativity, the values of constant terms in the equations of motions of planets and light have not been seriously discussed. Based on the Schwarzschild metric and the geodesic equations of the Riemann geometry, it is proved in this paper that the constant term in the time-dependent equation of motion of planet in general relativity must be equal to zero. Otherwise, when the correction term of general relativity is ignored, the resulting Newtonian gravity formula would change its basic form. Due to the absence of this constant term, the equation of motion cannot describe the elliptical and the hyperbolic orbital motions of celestial bodies in the solar gravitational field. It can only describe the parabolic orbital motion (with minor corrections). Therefore, it becomes meaningless to use general relativity calculating the precession of Mercury's perihelion. It is also proved that the time-dependent orbital equation of light in general relativity is contradictory to the time-independent equation of light. Using the time-independent orbital equation to do calculation, the deflection angle of light in the solar gravitational field is <mml:math display="inline"> <mml:mrow> <mml:mn>1.7</mml:mn> <mml:msup> <mml:mn>5</mml:mn> <mml:mo>″</mml:mo> </mml:msup> </mml:mrow> </mml:math> . But using the time-dependent equation to do calculation, the deflection angle of light is only a small correction of the prediction value <mml:math display="inline"> <mml:mrow> <mml:mn>0.87</mml:mn> <mml:msup> <mml:mn>5</mml:mn> <mml:mo>″</mml:mo> </mml:msup> </mml:mrow> </mml:math> of the Newtonian gravity theory with a magnitude order of <mml:math display="inline"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> . The reason causing this inconsistency was the Einstein's assumption that the motion of light satisfied the condition <mml:math display="inline"> <mml:mrow> <mml:mi>d</mml:mi> <mml:mi>s</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> in gravitational field. It leads to the absence of constant term in the time-independent equation of motion of light and destroys the uniqueness of geodesic in curved space-time. Meanwhile, light is subjected to repulsive forces in the gravitational field, rather than attractive forces. The direction of deflection of light is opposite, inconsistent with the predictions of present general relativity and the Newtonian theory of gravity. Observing on the earth surface, the wavelength of light emitted by the sun is violet shifted. This prediction is obviously not true. Practical observation is red shift. Finally, the practical significance of the calculation of the Mercury perihelion's precession and the existing problems of the light's deflection experiments of general relativity are briefly discussed. The conclusion of this paper is that general relativity cannot have consistence with the Newtonian theory of gravity for the descriptions of motions of planets and light in the solar system. The theory itself is not self-consistent too.

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Gauging the earth

The Mathematical Gazette ◽

10.1017/s0025557200000140 ◽

2013 ◽

Vol 97 (540) ◽

pp. 413-420

Author(s):

John D. Mahony

Keyword(s):

Approximate Formula ◽

Deflection Angle ◽

School Science ◽

Science Department ◽

Measurement Apparatus ◽

The Earth ◽

Interesting Discussion ◽

Simple Measurement ◽

The Deflection Angle

In an earlier note by W. J. A. Colman [1], the reader was treated to an interesting discussion concerning a BBC programme about the earth's radius in the context of endeavours to determine it by an 11th century Persian mathematician, Al-Biruni. At the same time a modem but approximate formula that might not have been available to the ancients was proposed for the radius and, following that account, it is the purpose here to explore just how accurately one might determine the earth's radius using this formula together with a simple measurement apparatus (not a sophisticated astrolabe) that might be constructed from materials found in the garage of any DIY handyman, or indeed, in the laboratory of any school science department. A schematic for the configuration of an observer P at a height h above the earth (of radius R) where the deflection angle to the horizon is denoted by θ, is shown in Figure 1. Also shown in the figure is a ‘sighting tube’ of length L about which more will be said later.

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SPECIAL VEHICLE MOTION STABILIZATION SYSTEM

IZVESTIA VOLGOGRAD STATE TECHNICAL UNIVERSITY ◽

10.35211/1990-5297-2021-9-256-37-41 ◽

2021 ◽

pp. 37-41

Author(s):

M. V. Lyashenko ◽

V. V. Shekhovtsov ◽

P. V. Potapov ◽

A. A. Shvedunenko

Keyword(s):

Pid Controller ◽

Deflection Angle ◽

Angular Displacement ◽

Dynamic Equations ◽

Engine Torque ◽

Special Vehicle ◽

Vehicle Motion ◽

Motion Stabilization ◽

The Deflection Angle ◽

The Mathematical Model

The system of special vehicle (SV) motion stabilization during moving on a straight surface is modeled on the base of dynamic equations of the mathematical model. The movement is stabilized by using a PID controller, the angular displacement of the mass is selected to ensure a given speed of movement, and the deflection angle is stabilized by controlling the engine torque.

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Values estimation of deflection angle of a floating sensor for various objects (to the resistance to measuring the water surface rate)

Bulletin of Science and Practice ◽

10.33619/2414-2948/39/25 ◽

2019 ◽

Vol 5 (2) ◽

pp. 181-196

Author(s):

K. Presnyakov ◽

G. Kerimkulova ◽

G. Askalieva

Keyword(s):

Water Surface ◽

Deflection Angle ◽

Surface Velocity ◽

Informative Parameter ◽

The Deflection Angle

A device is proposed for measuring the surface velocity of water, the use of which is based on the use of a new informative parameter — the deflection angle of the movable float sensor (together with the guide slide) from the vertical in the direction of the dynamic axis of the flow, allowing you to simply and reliably measure the surface velocity of water.

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