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.

A simple linear magnetic field sweep generator for magnetic resonance experiments

A simple and inexpensive linear magnetic field sweep generating system suitable for magnetic resonance experiments is described. The circuit, utilising a modified IC bootstrap configuration, generates field sweep over a wide range of sweep durations with excellent sweep linearity.

Studies on Simple and Encapsulated Transition Metal Complexes of Schiff Bases Derived from Diaminonaphthalene

Schiff base complexes of transition metal ions have played a significant role in coordination chemistry.In the present study we have synthesized some new Mn(II),Co(II) and Cu(II) complexes of Schiff bases derived from 1,8-diaminonaphthalene.Even though we could not isolate theses Schiff bases (as they readily cyclise to form the perimidine compounds),we were able to characterize unequivacally the complexes synthesized from these compounds as complexes of Schiff Bases. We Synthesized three perimidine derivatives ,2-(quinoxalin-2-yl)-2,3-dihydro-1H-perimidine,2-(2,3-dihydro-1H-perimidin-2-yl)-6-methoxyphenol and 4-(2,3-dihyro-1H-perimidin-2-yl)-2-methoxyphenol by the condensation of 1,8-diaminonaphthalene with quinoxaline-2-carboxaldehyde,2- hydroxy-3-methoxybenzaldehyde or 4-hydroxy-3-methoxybenzaldehyde respectively.Theses compounds were used as precursor ligands for the preparation of Schiff base complexes.The complexes were characterized by using elemental analysis ,conductance and magnetic susceptibility measuremets ,infrared and UV-Visible spectroscopy ,thermogravimetric analysis and EPR spectroscopy .We also encapsulated the complexes in zeolite Y matrix and these encapsulated complexes were also characterized. We have also tried theses complexes as catalysts in the oxidation of cyclohexanol and decomposition of hydrogen peroxide.

Simple and Encapsulated Transition Metal Complexes of Schiff Bases Derived from Quinoxaline-2-Carboxaldehyde and Diamines: Biological and Catalytic Activity Studies

This thesis is mainly concerned with the synthesis and characterisation of new simple and zeolite encapsulated transition metal (manganese(II),nickel(II),and copper(II)complexes of quinoxaline based double Schiff base ligands.Theses ligands are N,N'-bis(quinoxaline-2-carboxalidene)hydrazine,N,N'-bis(quinoxaline-2-carboxalidene)-1,2-diaminoethane,N,N'-bis(quinoxaline-2-carboxalidene)-1,3-diamonopropane,N,N'-bis(quinoxaline-2-carboxalidene)-1,4-diaminobutane,N,N'-bis(quinoxaline-2-carboxalidene)-1,2-diaminocyclohexane and N,N'-bis(quinoxaline-2-carboxalidene)-1,2-diaminobenzene.The Schiff base ligands have been characterised by spectral and single crystal XRD studies.Theses ligands provide great structural diversity during complexation.Mn(II) and Ni(II) form octahedral with these Schiff bases,whereas Cu(II) forms both octahedral and tetrahedral complexes.Studies on the biological and Catalytic activity of the copper(ll) complexes are also presented in this thesis.

A Study of Closure and Fuzzy Closure Spaces with Reference to H-Closedness and Convexity

Department of Mathematics, Cochin University of Science and Technology.

Closure of the Monte Carlo dynamical equation in the spherical Sherrington-Kirkpatrick model

We study the analytical solution of the Monte Carlo dynamics in the spherical Sherrington-Kirkpatrick model using the technique of the generating function. Explicit solutions for one-time observables (like the energy) and two-time observables (like the correlation and response function) are obtained. We show that the crucial quantity which governs the dynamics is the acceptance rate. At zero temperature, an adiabatic approximation reveals that the relaxational behavior of the model corresponds to that of a single harmonic oscillator with an effective renormalized mass.

Collective dynamic properties in simple crystals: Influence of the structural disorder

Collective dynamic properties in Lennard-Jones crystals are investigated by molecular dynamics simulation. The study is focused on properties such as the dynamic structure factors, the longitudinal and transverse currents and the density of states. The influence on these properties of the structural disorder is analyzed by comparing the results for one-component crystals with those for liquids and supercooled liquids at analogous conditions. The effects of species-disorder on the collective properties of binary crystals are also discussed.

A simple device for the separation of weak larvae of Macrobrachium rosenbergii (De Man)

Larvae of Macrobrachium rosenbergii (De Man) are photopositive (Ling 1969a.b) and negatively rheotactic. While investigating larval diseases of M, rosenbergii it was observed that weak larvae failed to show both these responses. It was felt that this lack of response could be used to develop a device for separating the weak larvae from the apparently healthy ones. Such a device would be a valuable tool for assessing the health of a batch in terms of the percentage of 'healthy' and 'weak' larvae. What follows is a description and mode of operation of the 'photo-flow' device developed by the authors

A simple regulated power supply for characteristics studies of klystron oscillators

A simple and inexpensive power supply suitable for characteristics studies of a klystron is described. The circuit is a modified form of the high voltage adjustable power supply based on LM 317. This provides the necessary cavity and repeller voltages over a wide range, with good regulation. The system is protected aa- ainst short circuits and is ideallv suitable for laboratorv, ex.Deri ments with reflex klystrons.

Simple approach to determine resonant frequencies of microstrip antennas

A simple approach for accurate determination of the resonant frequencies of microstrip antennas of regular geometries is developed and presented. In this approach, a generalised empirical formula for the computation of effective dielectric permittivity is given which takes into account the ratio of the fringing area to the area of the patch. A correction to the equivalent side length of an equilateral triangular patch, previously published, is modified and a new formula is given. A correction to the effective dimensions of an elliptical microstrip antenna is also carried out. Numerical results obtained for the resonant frequencies of elliptical, circular, rectangular and equilateral-triangular microstrip antennas are in good agreement with the available theoretical and experimental results reported by others. The present approach is more efficient, simpler and more accurate

Comments on Simple and Accurate Formula for the Resonant Frequency of the Equilateral Triangular Microstrip Patch Antenna

Antennas and Propagation, IEEE Transactions on,VOL 48,issue 4,pp 636