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Beltrami States in Three Component Plasmas

Thesis Info

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Author

Gondal, Saba Majeed

Program

PhD

Institute

University of Engineering and Technology

Institute Type

Public

City

Lahore

Province

Punjab

Country

Pakistan

Thesis Completing Year

2018

Thesis Completion Status

Completed

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/12119/1/Saba%20Majeed%20Gondal%20Physics%202018.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676728108149

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A static and stationary relaxed state of a single fluid MHD plasma appears as a consequence of the minimization of magnetic energy while the magnetic helicity remains conserved. The relaxed state is known as Beltrami state and represented by eigenvalue equation of the curl operator. The Beltrami state is a force-free equilibrium state and characterized by a single scale parameter. There exists no pressure gradient in ideal MHD self-organized state.On the other hand, selforganized states of multi component plasmas composed of multi Beltrami states are characterized by strong flow and pressure gradients which are the important features of practical plasmas found in laboratory and space environments. The self-organized states of multi component plasmas are investigated and analyzed. It is shown that self-organized state of electronegative dusty plasma comprising of one positive ion, two negative ions and immobile heavy dust grains can be cast as a superposition of three Beltrami states characterized by three scale parameters. This state is called as Triple Beltrami state and has a wide range of solutions covering paramagnetic as well as diamagnetic self-organized states. The relaxed equilibrium state of three component plasmas is found to be composed of four Beltrami states when all the inertial and non-inertial forces are taken into account. Two of the components constitute a pair while other one is taken to be a singly ionized positive ion. The self-organized state is called as Quadruple Beltrami state and governed by four eigenvalues. It is found that density of ions plays a significant role in the formation of relaxed structures. It is also shown that the relaxed state of three component plasmas can be cast in terms of double Beltrami state which is the superposition of two Beltrami states. The loss of equilibrium in a slowly varying double Beltrami state is investigated by changing control parameter.The equilibrium state is analyzed to observe the effects of magnetic helicity, generalized helicity, ratio of magnetic field to positron flow, density of components and energy of the system. The critical values of energy and control parameter are derived and the results are applied to model the eruptive events occurring in solar coronal loops.
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ضبط نے وحشتوں کو باندھا ہے

ضبط نے وحشتوں کو باندھا ہے
یعنی پھر آنسوئوں کو باندھا ہے

کس نے سب زندگی کی کڑیوں میں
درد کے سلسلوں کو باندھا ہے

تیرے باعث ہی دیکھ غزلوں میں
درد کے قافیوں کو باندھا ہے

یوں ہی روشن نہیں ہے دل اس میں
آس کے جگنوئوں کو باندھا ہے

درد نے ساز پھر سے چھیڑے ہیں
ہم نے بھی گھنگھروئوں کو باندھا ہے

دل کی باتیں سمجھ نہ پائے تم
ہم نے کب فلسفوں کو باندھا ہے

تیری زلفوں کی ڈور سے ہم نے
اپنے سب رتجگوں کو باندھا ہے

مسيحيت اور اسلام ميں تصور گناہ

God has given us two kinds of commandments "al-awaamir wan-nawaahi" i.e. Biddings and forbiddings whose violation is called "sin”. Christianity and Islam both are divine religions and their teachings are God-gifted. Their followers are required to lead their lives according to the commandments of God in order to succeed. But with the passage of time, Christians started distortions within their law. They, therefore, promoted the belief that every man is a sinner by birth. Christians believe that Adam (PBUH) committed sin. Islam teaches that every child is innocent by birth. The holy Prophet (BPBUM) said: “Every child is born on Islamic nature and his parents cause him to be Christian, Jew or Magian". Despite being distorted, Christianity does possess yet such teachings that resemble Islamic teachings. If these teachings are followed the mankind can be reformed though these teachings have its limitations. Islam is a final and ultimate religion and its teachings are, valid up to the day of resurrection. Also, these teachings have not been distorted. Islam has described each and every sin in detail more than the Christianity. If one follows Islamic teachings be can achieve success and salvation.

Pr Roduction Potential of Maize As a Affected D by Interc Cropping, Planting Geomet Try, Popul Lation Dyn Amics and D Fertilizer R Managem Ment

Investigations into production potential of maize (Zea maize L. cv. Pioneer 30-Y- 87) as affected by intercropping, planting geometry, population dynamics and fertilizer management was carried out at the Agronomic Research Farm, University of Agriculture, Faisalabad, in two field experiments during Kharif 2006 and 2007. Both experiments were carried out in randomized complete block design with split arrangements. First experiment consisted of three nitrogen levels (150, 200 and 250 kg ha -1 ), two zinc levels (0 and 15 kg ha -1 ) and three population densities (57100, 71400, and 999000 plants ha -1 ). Fertilizers were kept in main plots and plant densities in sub-plots. Second experiment comprised of three intercropping systems i.e. maize alone, maize + mungbean (Vigna radiate L.) and maize + mashbean (Vigna mungo L.) and three planting geometries (70 cm apart single row planting, 105/35 cm apart paired row planting, and 140/35 cm apart three row planting, respectively), keeping planting geometries in main plots while intercropping systems in sub-plots. Sowing was done with the help of a dibbler to ensure desired plant population. The results of the experiments are briefly described as under. In the first experiment, growth and development of maize crop was maximum with increase in nitrogen from 150 to 250 kg ha + 15 kg Zn ha -1 and consequently, yield (24 %) and yield components increased. LAI, LAD, and CGR increased with increasing plant populations. Although, yield components decreased with elevated plant densities yet grain yield increased due to more number of plants per unit area. In the second experiment, maize crop sown in double row strips proved superior to other planting geometries in terms of yield and yield components. Although intercropping of legumes in maize reduced growth and development, yield components and finally the grain yield of maize, however additional benefits obtained from intercrops compensated more than the losses in maize production. The effect of planting geometries and intercropping systems was non-significant on grain quality of maize.