Studies on the dynamics and rheology of dilute suspensions of Brownian particles in simple shear flow under the action of an external force

We present a novel approach to computing the orientation moments and rheological properties of a dilute suspension of spheroids in a simple shear flow at arbitrary Peclct number based on a generalised Langevin equation method. This method differs from the diffusion equation method which is commonly used to model similar systems in that the actual equations of motion for the orientations of the individual particles are used in the computations, instead of a solution of the diffusion equation of the system. It also differs from the method of 'Brownian dynamics simulations' in that the equations used for the simulations are deterministic differential equations even in the presence of noise, and not stochastic differential equations as in Brownian dynamics simulations. One advantage of the present approach over the Fokker-Planck equation formalism is that it employs a common strategy that can be applied across a wide range of shear and diffusion parameters. Also, since deterministic differential equations are easier to simulate than stochastic differential equations, the Langevin equation method presented in this work is more efficient and less computationally intensive than Brownian dynamics simulations.We derive the Langevin equations governing the orientations of the particles in the suspension and evolve a procedure for obtaining the equation of motion for any orientation moment. A computational technique is described for simulating the orientation moments dynamically from a set of time-averaged Langevin equations, which can be used to obtain the moments when the governing equations are harder to solve analytically. The results obtained using this method are in good agreement with those available in the literature.The above computational method is also used to investigate the effect of rotational Brownian motion on the rheology of the suspension under the action of an external force field. The force field is assumed to be either constant or periodic. In the case of con- I stant external fields earlier results in the literature are reproduced, while for the case of periodic forcing certain parametric regimes corresponding to weak Brownian diffusion are identified where the rheological parameters evolve chaotically and settle onto a low dimensional attractor. The response of the system to variations in the magnitude and orientation of the force field and strength of diffusion is also analyzed through numerical experiments. It is also demonstrated that the aperiodic behaviour exhibited by the system could not have been picked up by the diffusion equation approach as presently used in the literature.The main contributions of this work include the preparation of the basic framework for applying the Langevin method to standard flow problems, quantification of rotary Brownian effects by using the new method, the paired-moment scheme for computing the moments and its use in solving an otherwise intractable problem especially in the limit of small Brownian motion where the problem becomes singular, and a demonstration of how systems governed by a Fokker-Planck equation can be explored for possible chaotic behaviour.

Educational rights of the minorities under article 30 of the Indian Constitution

This thesis entitled “ Educational rights of the minorities under article 30 of the indian constitution.The study is divided into nine chapters.The object of the present study is to explore whether the judiciary has been successful in balancing the conflicting rights of the minorities and the state. The study also seeks to bring forth those judicial principles which have governed the operation of these rights and determined the limits of their application. Article 30 confers a special right on minorities to establish educational institutions of their own choice.This is an expression of the liberal and tolerent culture of our nation which is reflected in the Constitution. The idea is to foster unity' in diversity, ea unique characteristic of the Indian way of life.This study suggested that where a minority is a minority’ in the historical or national context and its claim is based on religion it must be defined and ascertained in terms of the population of the whole country irrespective of its being a numerical majority' in any particular State and the minority status. of linguistic group has to be ascertained in terms of the population of any particular State irrespective of its being a numerical minority in terms of the population of the whole country.A religious denomination also can be treated as a religion within the meaning of Article 30(1) provided it is having a separate organisation with doctrines and tenets and rites and practices of its own.

The power of taxation under the indian constitution

The Power Of Taxation Under The lndian Constitution, the subject of the present thesis has a wide ambit covering the entire federal field end deep constitutional significance traversing many of the principles like pith and substance, colourability, severebility etc. However, considerations of time, space and areas already investigated have indicated that the present study may be confined to the fundamental constitutional limitations end the federal problem. Thus the effect of fundamental rights, the commerce clause, immunity of instrumentalitis and the principle limiting the power of legislative delegation on the power of taxation has been studied. The distribution of taxes between the Union and units of the Indian federation leans so much over to the former and that part of this study has been directed to discover what devices can help the units to gain economic viability

"Right to Personal Liberty Under the Indian Constitution - With Special Reference to Judicial Process"

The nature and extent of protection secured to personal liberty has been a subject matter of great controversy and debate. The expression "procedure established by law" as a standard of protection for personal liberty has been looked upon as highly unsatisfactory and inadequate. For, unlike the specific attributes of liberty that are separately guaranteed under Art.19, ‘personal liberty‘ as guaranteed by Art.21 does not obligate the .Legislature to comply with the requirements of justice and reasonableness as and when it enchroaches upon that right. Though the concept of ‘personal liberty‘ has received an evolutive and expansive meaning through judicial process, the standard of protection which the judicial process could secure to personal liberty through the interpretation of Art.21 has been far from satisfactory Even after four decades of judicial process in the interpretation of Art.21 the problem of evolving a just and adequate standard of protection for personal liberty in that Article continues to be 21 crucial constitutional issue, craving for a. satisfactory solution. And the present study is a humble attempt to unravel this problem and to Search for a reasonable solution.

Comparative efficacy of MS-222 and benzocaine as anaesthetics under simulated transport conditions of a tropical ornamental fish Puntius filamentosus(Valenciennes)

There is a growing commercial interest in the ¢sh, Puntius ¢lamentosus, in the ornamental ¢sh trade in India and elsewhere.The trade is, however, hampered by severe mortalities during transport of the ¢sh owing to insu⁄cient data available on the use of anaesthetics. To resolve this problem, we evaluated the e⁄cacy of two anaesthetics, MS-222 and benzocaine, in sedating P. ¢lamentosus in simulated transportation experiments and used stress response parameters such as cortisol and blood glucose levels to perform assessments. We observed that MS-222 at 40 mg L 1 and benzocaine at 20mg L 1 were su⁄- cient to induce sedation for 48 h. Above these concentrations, both the anaesthetics adversely a¡ected the ¢sh and resulted inmortalities. Both anaesthetics signi¢cantly lowered the blood cortisol and glucose levels compared with the unsedated controls. Importantly, the anaesthetics treatment signi¢cantly lowered the post-transport mortality in the ¢sh. The results of the study show that MS-222 and benzocaine could be used as sedatives to alleviate transport- related stress in P. ¢lamentosus to improve their post-transport survival and hence reduce economic loss.