scholarly journals On coefficient of mutual inductance between solenoid and coiled circuit with parallel axes

2021 ◽  
Vol 2 (396) ◽  
pp. 93-98
Author(s):  
G. Tsitsikyan ◽  
Keyword(s):  
Numerical Integration ◽  
Computational Methods ◽  
Mutual Inductance ◽  
Axial Displacement ◽  
Written Expression ◽  
Numerical Estimation ◽  
Limiting Case

Object and purpose of research. Current recommendations on calculation of mutual inductance between solenoids and coiled circuits with parallel axes are shown and compared. Advisability of such verification for a limiting case when the axes are aligned is revealed. Materials and methods. Verification of these recommendations for cases of zero axial displacement is performed on the basis of well-tested expressions. For this purpose alternative expressions for the mutual inductance of the coaxial circuit and solenoid and two circuits. Main results. A number of significant discrepancies are identified between numerical values including difference in signs for the case of a solenoid and a circuit with parallel axes. For circuits with parallel axes, attention is focused on the necessity to use auxiliary tables, which confirms the complexity of numerical estimation in this case either. Conclusion. In terms of the identified flaws, the conclusion was drawn about the advisability of using computational methods for configurations with parallel axes. For circuits with parallel axes, as follows from the written expression, it is sufficient to apply a single numerical integration.

scholarly journals Fluence Rate in UV Photoreactor for Disinfection of Water: Isotropically Radiating Cylinder

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Roman Ilinsky ◽  
Andrey Ulyanov
Keyword(s):  
Numerical Integration ◽  
Light Source ◽  
Uv Radiation ◽  
Infinite Length ◽  
Fluence Rate ◽  
Chebyshev Method ◽  
Limiting Case

The calculation of fluence rate in the photochemical reactor using ultraviolet (UV) radiation for disinfection of water for the case, when a cylinder of infinite length is used as a light source, has been considered. Such a cylinder is filled with an isotropically radiating medium. The dependence of the fluent rate on the diameter of the radiating cylinder has been analytically analyzed. The limiting case when the diameter of the radiating cylinder tends to zero has been considered and the notion of “effective interval” has been introduced. Based on this notion, the comparison of fluence rates for the cylinders of finite and infinite lengths has been performed. In the calculations of fluence rate, it is advisable to use the Chebyshev method for the operations of numerical integration.

scholarly journals Vector Potential, Magnetic Field, Mutual Inductance, Magnetic Force, Torque and Stiffness Calculation between Current-Carrying Arc Segments with Inclined Axes in Air

2021 ◽  
Author(s):  
Slobodan Babic
Keyword(s):  
Magnetic Field ◽  
Numerical Integration ◽  
Vector Potential ◽  
Magnetic Force ◽  
Analytical Form ◽  
Mutual Inductance ◽  
Magnetic Vector Potential ◽  
Magnetic Vector ◽  
Special Cases ◽  
Incomplete Elliptic Integrals

In this paper we give the improved and new analytical and semi-analytical expression for calcu-lating the magnetic vector potential, magnetic field, magnetic force, mutual inductance, torque, and stiffness between two inclined current-carrying arc segments in air. The expressions are ob-tained either in the analytical form over the incomplete elliptic integrals of the first and the sec-ond time or by the single numerical integration of some elliptical integrals of the first and the second kind. The validity of the presented formulas is proved from the special cases when the inclined circular loops are treated. We mention that all formulas are obtain by the integral ap-proach except the stiffness which is found by the derivative of the magnetic force.

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

Freeze fracture imaging and computer simulation of liposome structure: Membrane geometry and defects

1983 ◽  
Vol 41 ◽  
pp. 646-647
Author(s):  
Joseph A. Zasadzinski
Keyword(s):  
Liquid Crystalline ◽  
Freeze Fracture ◽  
Continuum Theory ◽  
Closed Surfaces ◽  
Straight Line ◽  
Low Weight ◽  
Concentric Spheres ◽  
Membrane Geometry ◽  
Dupin Cyclides ◽  
Limiting Case

At low weight fractions, many surfactant and biological amphiphiles form dispersions of lamellar liquid crystalline liposomes in water. Amphiphile molecules tend to align themselves in parallel bilayers which are free to bend. Bilayers must form closed surfaces to separate hydrophobic and hydrophilic domains completely. Continuum theory of liquid crystals requires that the constant spacing of bilayer surfaces be maintained except at singularities of no more than line extent. Maxwell demonstrated that only two types of closed surfaces can satisfy this constraint: concentric spheres and Dupin cyclides. Dupin cyclides (Figure 1) are parallel closed surfaces which have a conjugate ellipse (r1) and hyperbola (r2) as singularities in the bilayer spacing. Any straight line drawn from a point on the ellipse to a point on the hyperbola is normal to every surface it intersects (broken lines in Figure 1). A simple example, and limiting case, is a family of concentric tori (Figure 1b).To distinguish between the allowable arrangements, freeze fracture TEM micrographs of representative biological (L-α phosphotidylcholine: L-α PC) and surfactant (sodium heptylnonyl benzenesulfonate: SHBS)liposomes are compared to mathematically derived sections of Dupin cyclides and concentric spheres.

Suppression of γ’ Precipitation in a Laser-Melted Nickel-Base Alloy

1977 ◽  
Vol 35 ◽  
pp. 270-271
Author(s):  
J. M. Walsh ◽  
J. C. Whittles ◽  
B. H. Kear ◽  
E. M. Breinan
Keyword(s):  
Cooling Rate ◽  
Base Alloy ◽  
Material Surface ◽  
Intimate Contact ◽  
Absorbed Power ◽  
Perfect Contact ◽  
Nickel Base ◽  
Rapidly Solidified ◽  
Limiting Case ◽  
The Heat Transfer Coefficient

Conventionally cast γ’ precipitation hardened nickel-base superalloys possess well-defined dendritic structures and normally exhibit pronounced segregation. Splat quenched, or rapidly solidified alloys, on the other hand, show little or no evidence for phase decomposition and markedly reduced segregation. In what follows, it is shown that comparable results have been obtained in superalloys processed by the LASERGLAZE™ method.In laser glazing, a sharply focused laser beam is traversed across the material surface at a rate that induces surface localized melting, while avoiding significant surface vaporization. Under these conditions, computations of the average cooling rate can be made with confidence, since intimate contact between the melt and the self-substrate ensures that the heat transfer coefficient is reproducibly constant (h=∞ for perfect contact) in contrast to the variable h characteristic of splat quenching. Results of such computations for pure nickel are presented in Fig. 1, which shows that there is a maximum cooling rate for a given absorbed power density, corresponding to the limiting case in which melt depth approaches zero.

Sign in / Sign up

Export Citation Format

Share Document