scholarly journals On New Families of Integrals in Analytical Studies of Superconductors within the Conformal Transformation Method

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Ryszard Gonczarek ◽  
Mateusz Krzyzosiak ◽  
Adam Gonczarek ◽  
Lucjan Jacak
Keyword(s):  
Conformal Transformation ◽  
Mathematical Structure ◽  
Transformation Method ◽  
Variable Density ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Quantitative Characteristics ◽  
Analytical Formulas ◽  
Fundamental Equations ◽  
New Generation

We show that, by applying the conformal transformation method, strongly correlated superconducting systems can be discussed in terms of the Fermi liquid with a variable density of states function. Within this approach, it is possible to formulate and carry out purely analytical study based on a set of fundamental equations. After presenting the mathematical structure of thes-wave superconducting gap and other quantitative characteristics of superconductors, we evaluate and discuss integrals inherent in fundamental equations describing superconducting systems. The results presented here extend the approach formulated by Abrikosov and Maki, which was restricted to the first-order expansion. A few infinite families of integrals are derived and allow us to express the fundamental equations by means of analytical formulas. They can be then exploited in order to find quantitative characteristics of superconducting systems by the method of successive approximations. We show that the results can be applied in studies of high-Tcsuperconductors and other superconducting materials of the new generation.

New classes of integrals inherent in the mathematical structure of extended equations describing superconducting systems

2015 ◽  
Vol 29 (17) ◽  
pp. 1550117 ◽  
Author(s):  
Ryszard Gonczarek ◽  
Mateusz Krzyzosiak ◽  
Adam Gonczarek ◽  
Lucjan Jacak
Keyword(s):  
Mathematical Structure ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Superconducting Gap ◽  
S Wave ◽  
First Order ◽  
Order Expansion ◽  
Quantitative Characteristics ◽  
Fundamental Equations ◽  
New Generation

In this paper, we discuss the mathematical structure of the s-wave superconducting gap and other quantitative characteristics of superconducting systems. In particular, we evaluate and discuss integrals inherent in fundamental equations describing superconducting systems. The results presented here extend the approach formulated by Abrikosov and Maki, which was restricted to the first-order expansion. A few infinite families of integrals are derived and allow us to express the fundamental equations by means of analytic formulas. They can be then exploited in order to find some quantitative characteristics of superconducting systems by the method of successive approximations. We show that the results can be applied to some modern formalisms in order to study high-Tc superconductors and other superconducting materials of the new generation.

scholarly journals The cascade theory of electronic showers

1938 ◽  
Vol 166 (925) ◽  
pp. 213-228 ◽  
Keyword(s):  
Fast Electron ◽  
Nuclear Charge ◽  
Critical Energy ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Cascade Theory ◽  
Nuclear Field ◽  
Order Of Magnitude ◽  
Fundamental Equations ◽  
Fundamental Physical

1. Bhabha and Heitler (1937) and also Carlson and Oppenheimer (1937) have recently proposed a very ingenious theory of showers which explains nearly all the observed phenomena; both these treatments, however, contain approximations the validity of which cannot always be justified. The calculations of the first two authors make use of the method of successive approximations whose exactness is difficult to estimate, while the second authors replace one of the fundamental equations by a different one, and it is impossible to see how this replacement may distort the final result. Consequently, we have thought it useful to make the calculation in a more rigorous way; the fundamental physical ideas, however, are exactly the same as those of the authors mentioned above. 2. Consider a fast electron penetrating into a layer of matter; as long as its energy is below a certain order of magnitude, the loss of energy of the electron will be determined mainly by ionization; for higher energies, however, loss of energy by radiation (Bremsstrahlung) becomes more important. This critical energy lies in the region of about ϵ = 750/ Z̅ million volts, where Z̅ denotes a certain average nuclear charge (there may be several nuclei of different kinds present). Since the collision radiation, which is determined by the interaction between the electron and the nuclear field, increases as Z 2 , while the ionization is approximately pro­portional to the number of electrons in the material.

Numerical Methods for Solving Physically Nonlinear Problems for Inhomogeneous Thick-Walled Shells

2017 ◽  
Vol 865 ◽  
pp. 325-330 ◽  
Author(s):  
Vladimir I. Andreev ◽  
Lyudmila S. Polyakova
Keyword(s):  
Numerical Method ◽  
Nonlinear Problems ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Deformation Diagram ◽  
Method Of Solution ◽  
Properties Of Materials ◽  
Physical Fields ◽  
Cylinders And Spheres ◽  
Numerical Method Of Solution

The paper proposes the numerical method of solution the problems of calculation the stress state in thick-walled cylinders and spheres from physically nonlinear inhomogeneous material. The urgency of solved problem due to the change of mechanical properties of materials under the influence of different physical fields (temperature, humidity, radiation, etc.). The deformation diagram describes the three-parameter formula. The numerical method used the method of successive approximations. The results of numerical calculation are compared with the test analytical solutions obtaining the authors with some restrictions on diagram parameters. The obtained results can be considered quite satisfactory.

On a sphere performing linear and torsional oscillations in a viscous fluid

1988 ◽  
Vol 66 (7) ◽  
pp. 576-579
Author(s):  
G. T. Karahalios ◽  
C. Sfetsos
Keyword(s):  
Boundary Layer ◽  
Viscous Fluid ◽  
Secondary Flow ◽  
Small Amplitude ◽  
Equations Of Motion ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Time Varying ◽  
Torsional Oscillations

A sphere executes small-amplitude linear and torsional oscillations in a fluid at rest. The equations of motion of the fluid are solved by the method of successive approximations. Outside the boundary layer, a steady secondary flow is induced in addition to the time-varying motion.

scholarly journals Green’s Function In Free Axisymmetric Vibration Analysis Of Annular Thin Plates With Different Boundary Conditions

2015 ◽  
Vol 20 (4) ◽  
pp. 939-951
Author(s):  
K.K. Żur
Keyword(s):  
Power Series ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Thin Plates ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Axisymmetric Vibration ◽  
Annular Plates ◽  
The Core ◽  
Analytical Frequency

Abstract Free vibration analysis of homogeneous and isotropic annular thin plates by using Green’s functions is considered. The formula of the influence function for uniform thin circular and annular plates is presented in closed-form. The limited independent solutions of differential Euler equation were expanded in the Neumann power series based on properties of integral equations. The analytical frequency equations as power series were obtained using the method of successive approximations. The natural axisymmetric frequencies for singularities when the core radius approaches zero are calculated. The results are compared with selected results presented in the literature.

scholarly journals A new method of successive approximations when calculating elements of electromechanical machines

2020 ◽  
Vol 5 (2) ◽  
pp. 168-172
Author(s):  
K. Ismayilov ◽  
◽  
S.T. Suleymanov ◽  
S.T. Ruziev ◽  
M.B. Aripjanova ◽  
...  
Keyword(s):  
New Method ◽  
Successive Approximations ◽  
Method Of Successive Approximations

scholarly journals Fuzzy Volterra integral equations with in-finite delay

2009 ◽  
Vol 40 (1) ◽  
pp. 19-29 ◽  
Author(s):  
P. Prakash ◽  
V. Kalaiselvi
Keyword(s):  
Integral Equations ◽  
Existence And Uniqueness ◽  
Infinite Delay ◽  
Volterra Integral Equations ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Uniqueness Of Solutions ◽  
Finite Delay

In this paper, we study the existence and uniqueness of solutions for a class of fuzzy Volterra integral equations with infinite delay by using the method of successive approximations.

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