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Microscopic Study of Two Band Superconductivity in Magnesium Diboride Superconductor (MgB2)
Basanta Kumar Sahoo,
Biswa Ranjan Mishra,
Subhalaxmi Das,
Santosh Kumar Barik,
Padmaja Patnaik,
Ranjan Kumar Bhuyan,
Bibekananda Panda
Issue:
Volume 9, Issue 2, March 2021
Pages:
29-33
Received:
15 March 2021
Accepted:
7 April 2021
Published:
26 April 2021
Abstract: We formulate a Model Hamiltonian of two band superconductivity for Magnesium Diboride superconductors (MgB2). It is a conventional BCS type metallic superconductor which has the highest critical temperature Tc=39K. It is assumed that the superconductivity in MgB2 arises due to metallic nature of the 2D sheets. From band structure calculations, it is observed that two types of bands i.e. σ and π bands are located at Fermi surface. Here, we consider phonon mediated superconductivity in which σ band is dominant over π band i.e. σ band is more coupled to a superconductor with much higher coupling. We consider a model Hamiltonian with mean field approach and solve this by calculating equations of motion of Green functions for a single particle. We determine the quasi-particle energy from the poles of the Green functions. We derive the single particle correlation functions and determine the two SC order parameters for both σ and π band. Here, the two SC order parameters for the bands are solved self- consistently and numerically. The conduction bandwidth (W) is considered as W=8t0, where t0 is the hopping integral. To make all the physical quantities dimensionless, we divide 2t0 in each of the physical quantities. We then calculate the gap ratio 2∆(0)/KBTc for both the bands. It is seen form our theoretical model that the two bands of MgB2 superconductors have two different SC gaps with the same critical temperature. We also observe the variation of dispersion curves of quasi-particles for different temperature parameters for both σ and π band.
Abstract: We formulate a Model Hamiltonian of two band superconductivity for Magnesium Diboride superconductors (MgB2). It is a conventional BCS type metallic superconductor which has the highest critical temperature Tc=39K. It is assumed that the superconductivity in MgB2 arises due to metallic nature of the 2D sheets. From band structure calculations, it i...
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The Wheel – Vehicle Considered as a Material Point: An Approximate Theory of Automobiles
Issue:
Volume 9, Issue 2, March 2021
Pages:
34-41
Received:
2 February 2021
Accepted:
24 February 2021
Published:
26 April 2021
Abstract: The objective of the article is the mathematical description of the car motion in the most possible general form using Newton’s second law and the forces that act on it when they are known. In the first section, the forces that act on the vehicle are described and the normal (usual) conditions of driving are considered. Secondly the dynamical equation of motion baced on Newton’s second law is introduced which is in general a non-linear second order ordinary differential equation. Various cases are discussed such as going uphill, downhill, accelerating, decelerating etc. In Section 3, the energy consumption of the fuel is discussed and it is stated that it is consisted of two parts this of the “idle” worke and this of the sustainment of the motion. Besides it is shown that for a certain space “s” there is one unique speed that minimizes the consumption of fuel. In Section 4, the basic “defect” of the equation of motion which is the inclusion in the equation of the unknown driving force F(t) it is shown that it can be “circumvented” with energetic considerations leading to an equation having at the right – hand side the speed in the denominator and the excess revolutions per minute in the numerator. The resulting equation is such that a knowledge of δr(t)=(rpm)(t) – (rpm)0 can, by the numerical solution of the equation, lead to the function of speed and so a relation is established detween the velocity (u(t)) and the excess (rpm) which can be cheched as true or false by the aposteriori resister of the tachograph (u(t)) and rotation – counter (rpm(t)). Finally, in Section 5, we calculate, using the decelerating motion of a car in a flat road (when somebody leaves the throttle) all the kinematical and “energetical” constants that are introduced in the previous sections for sixth gear such as Fc, 6, b6, σ6, λ6 which can be used, post – hoc, to examine together with δr(t) if the real velocityof a vehicle coincides with the prediction that a computer can make. Besides for a flat road, the power of a car can be estimated for instance when it has u=120 km/h at rpm=3000 and in the 6th gear, giving for power -45HP which is a very reasonable estimate in order of magnitude.
Abstract: The objective of the article is the mathematical description of the car motion in the most possible general form using Newton’s second law and the forces that act on it when they are known. In the first section, the forces that act on the vehicle are described and the normal (usual) conditions of driving are considered. Secondly the dynamical equat...
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Estimation of Concentration of Naturally Occurring Radioactivity and Radiation Hazards, in Iron Ore Deposit Soil from Wag-Himra Zone, Ethiopia
Tadesse Gebeyehu,
Baye Zinabe,
Teshager Akalie
Issue:
Volume 9, Issue 2, March 2021
Pages:
42-47
Received:
3 April 2021
Accepted:
6 May 2021
Published:
21 May 2021
Abstract: The current study looked at the concentration of naturally occurring radioactivity and radiation hazards in iron ore deposited in soil. The aim of this study was to identify the dose of radiation which is emitted from rocks, soil and some building materials, the radiation dose and the effect in the area. In this work, analyses of the sample soils were performed with a computer-based gamma-spectrometry system with software of G-2000 for qualitative and quantitative determination of gamma-emitting radionuclide of natural occurrence of radioactive materials. The quantitative investigation of natural radioactive materials of 238U, 232Th and 40K were 11.688±0.42Bq/kg, 23.505±0.925Bq/kg and 141.48±4.403Bq/kg respectively. In addition to this, the results of absorbed dose rate, annual effective dose equivalent, radium equivalent activity and representative gamma index of the sample were much less as compared to recommended international values by UNSCEAR-2000. At low activity concentrations of the radionuclides produce low background radiation to the environment. The value obtained from the experiment reveals that the radiation hazards emitted by natural radionuclides in the soil cause insignificant harm to the public from the Wag-himra iron ore deposit soil. The concentration of natural radioactive elements in this area's soil could be used for construction purposes without causing any significant radiological hazards to humans for the time being.
Abstract: The current study looked at the concentration of naturally occurring radioactivity and radiation hazards in iron ore deposited in soil. The aim of this study was to identify the dose of radiation which is emitted from rocks, soil and some building materials, the radiation dose and the effect in the area. In this work, analyses of the sample soils w...
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Evaluation of Natural Radioactive Elements and Hazardous Indexes Using High Pure Germanium Gamma Ray Spectroscopy in Sekota, Waghimra, Zone, Ethiopia
Baye Zinabe Kebede,
Tadesse Gebeyehu
Issue:
Volume 9, Issue 2, March 2021
Pages:
48-52
Received:
8 May 2021
Accepted:
30 June 2021
Published:
9 July 2021
Abstract: This research paper desired to illustrate the presence of naturally occurring radioactive minerals concentration and the way how naturally occurring radioactive minerals were identified in Wag-himra iron ore deposit soil site. The deposit area covers five Kebelles of the border of Sekota, Ziquale and Abergelle districts. We were used high pure germanium detector to identify the presence of natural occurring radioactivity concentration in iron ore/alloy deposit soil, and applied appropriate research methodology particularly experimental design were more preferable. The researcher was collected samples from ten places across iron ore deposit area by using judgmental sampling techniques and prepared as a desirable manner. The chosen sample was sealed for four weeks in order to obtain secular equilibrium, wherein the rate of decay of the daughter’s equivalent that of the parent. Radium equivalent activity, external hazard index and representative gamma index of the sample were 56.19, 0.1515, 0.804, 0.408, 0.00011 (Bq/kg) respectively. However, internal hazard index was slightly approaching to recommended value and it may cause the significant radiation hazard through long dwelling to the area. This study NORM was analysis from sample of soil from at mineral/iron ore deposit area. The natural occurrence of radioactive materials identified in the samples were 238U, 232Th and 40K. The radiation hazardous were external and internal index.
Abstract: This research paper desired to illustrate the presence of naturally occurring radioactive minerals concentration and the way how naturally occurring radioactive minerals were identified in Wag-himra iron ore deposit soil site. The deposit area covers five Kebelles of the border of Sekota, Ziquale and Abergelle districts. We were used high pure germ...
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