Covalently Interconnected Three- Dimensional Graphene Oxide Solids

The creation of three-dimensionally engineered nanoporous architectures via covalently interconnected nanoscale building blocks remains one of the fundamental challenges in nanotechnology. Here we report the synthesis of ordered, stacked macroscopic three-dimensional (3D) solid scaffolds of graphene oxide (GO) fabricated via chemical cross-linking of two-dimensional GO building blocks. The resulting 3D GO network solids form highly porous interconnected structures, and the controlled reduction of these structures leads to formation of 3D conductive graphene scaffolds. These 3D architectures show promise for potential applications such as gas storage; CO2 gas adsorption measurements carried out under ambient conditions show high sorption capacity, demonstrating the possibility of creating new functional carbon solids starting with two-dimensional carbon layers

Dielectric studies of polyvinyl-acetate-based phantom for applications in microwave medical imaging

Phantoms that exhibit complex dielectric properties similar to low water content biological tissues over the electromagnetic spectrum of 2–3 GHz have been synthesized from carbon black powder, graphite powder and polyvinyl-acetate-based adhesive. The materials overcome various problems that are inherent in conventional phantoms such as decomposition and deterioration due to the invasion of bacteria or mold. The absorption coefficients of the materials for various compositions of carbon black and graphite powder are studied. A combination of 50% polyvinylacetate- based adhesive, 20% carbon black powder and 30% graphite powder exhibits high absorption coefficient, which suggests another application of the material as good microwave absorber for interior lining of tomographic chamber in microwave imaging. Cavity perturbation technique is adopted to study the dielectric properties of the material.

Dielectric Studies of Corn Syrup for Applications in Microwave Breast Imaging

Permittivity and conductivity studies of corn syrup in various concentrations are performed using coaxial cavity perturbation technique over a frequency range of 250 MHz–3000 MHz. The results are utilized to estimate relaxation time and dipole moments of the samples. The stability of the material over the variations of time is studied. The measured specific absorption rate of the material complies with the microwave power absorption rate of biological tissues. This suggests the feasibility of using corn syrup as a suitable, cost effective coupling medium for microwave breast imaging. The material can also be used as an efficient breast phantom in microwave breast imaging studies.

Topological Invariants in Hydrodynamics and Hydromagnetics

In this thesis we are studying possible invariants in hydrodynamics and hydromagnetics. The concept of flux preservation and line preservation of vector fields, especially vorticity vector fields, have been studied from the very beginning of the study of fluid mechanics by Helmholtz and others. In ideal magnetohydrodynamic flows the magnetic fields satisfy the same conservation laws as that of vorticity field in ideal hydrodynamic flows. Apart from these there are many other fields also in ideal hydrodynamic and magnetohydrodynamic flows which preserves flux across a surface or whose vector lines are preserved. A general study using this analogy had not been made for a long time. Moreover there are other physical quantities which are also invariant under the flow, such as Ertel invariant. Using the calculus of differential forms Tur and Yanovsky classified the possible invariants in hydrodynamics. This mathematical abstraction of physical quantities to topological objects is needed for an elegant and complete analysis of invariants.Many authors used a four dimensional space-time manifold for analysing fluid flows. We have also used such a space-time manifold in obtaining invariants in the usual three dimensional flows.In chapter one we have discussed the invariants related to vorticity field using vorticity field two form w2 in E4. Corresponding to the invariance of four form w2 ^ w2 we have got the invariance of the quantity E. w. We have shown that in an isentropic flow this quantity is an invariant over an arbitrary volume.In chapter three we have extended this method to any divergence-free frozen-in field. In a four dimensional space-time manifold we have defined a closed differential two form and its potential one from corresponding to such a frozen-in field. Using this potential one form w1 , it is possible to define the forms dw1 , w1 ^ dw1 and dw1 ^ dw1 . Corresponding to the invariance of the four form we have got an additional invariant in the usual hydrodynamic flows, which can not be obtained by considering three dimensional space.In chapter four we have classified the possible integral invariants associated with the physical quantities which can be expressed using one form or two form in a three dimensional flow. After deriving some general results which hold for an arbitrary dimensional manifold we have illustrated them in the context of flows in three dimensional Euclidean space JR3. If the Lie derivative of a differential p-form w is not vanishing,then the surface integral of w over all p-surfaces need not be constant of flow. Even then there exist some special p-surfaces over which the integral is a constant of motion, if the Lie derivative of w satisfies certain conditions. Such surfaces can be utilised for investigating the qualitative properties of a flow in the absence of invariance over all p-surfaces. We have also discussed the conditions for line preservation and surface preservation of vector fields. We see that the surface preservation need not imply the line preservation. We have given some examples which illustrate the above results. The study given in this thesis is a continuation of that started by Vedan et.el. As mentioned earlier, they have used a four dimensional space-time manifold to obtain invariants of flow from variational formulation and application of Noether's theorem. This was from the point of view of hydrodynamic stability studies using Arnold's method. The use of a four dimensional manifold has great significance in the study of knots and links. In the context of hydrodynamics, helicity is a measure of knottedness of vortex lines. We are interested in the use of differential forms in E4 in the study of vortex knots and links. The knowledge of surface invariants given in chapter 4 may also be utilised for the analysis of vortex and magnetic reconnections.