STUDIES ON THE STRESS FLUCTUATIONS IN SHEARED STOKESIAN SUSPENSIONS USING CHAOS THEORY AND NONLINEAR DYNAMICS

The thesis report results obtained from a detailed analysis of the fluctuations of the rheological parameters viz. shear and normal stresses, simulated by means of the Stokesian Dynamics method, of a macroscopically homogeneous sheared suspension of neutrally buoyant non-Brownian suspension of identical spheres in the Couette gap between two parallel walls in the limit of vanishingly small Reynolds numbers using the tools of non-linear dynamics and chaos theory for a range of particle concentration and Couette gaps. The thesis used the tools of nonlinear dynamics and chaos theory viz. average mutual information, space-time separation plots, visual recurrence analysis, principal component analysis, false nearest-neighbor technique, correlation integrals, computation of Lyapunov exponents for a range of area fraction of particles and for different Couette gaps. The thesis observed that one stress component can be predicted using another stress component at the same area fraction. This implies a type of synchronization of one stress component with another stress component. This finding suggests us to further analysis of the synchronization of stress components with another stress component at the same or different area fraction of particles. The different model equations of stress components for different area fraction of particles hints at the possible existence a general formula for stress fluctuations with area fraction of particle as a parameter

Ultrasonic Study Of The Elastic Properties And Phase Transitions In Selected Mixed Sulphate Crystals

The thesis investigated the elastic properties and phase transitions in selected mixed sulphate crystals – Lithium Hydrazinium Sulphate [LiN2H2SO4], Lithium Ammonium Sulphate [LiNH4SO4] and Lithium Potassium Sulphate [LiKSO4] – using ultrasonic technique. The pulse echo overlap technique has been used for measuring ultrasonic velocity and its dependence on temperature along different directions with waves of longitudinal and transverse polarizations. Two major numerical techniques and the corresponding computer programs developed as part of present work are presented in this thesis. All the 9 elastic constants of LHS are determined accurately from ultrasonic measurements and applying misorientation correction refines the constants. Ultrasonic measurements are performed in LAS to determine the elastic constants and to study the low temperature phase transitions. Temperature variation studies of elastic constant of LAS are performed for 6 different modes of propagation for heating and cooling at low temperatures. All the 5 independent elastic constants of LPS is determined using ultrasonic measurements. It is concluded that LPS crystal does not undergo a phase transition near this temperature. A comparison of the three crystals studied shows that LPS has maximum number of phase transitions and LHS has the least number. It is interesting to note that LPS has the simplest formula unit among the three. There is considerable scope for the future work on these crystals and others belonging to the sulphate family.

Elastic Constants And Structural Parameters Of Selected Polycrystalline Ceramics By Ultrasonic Technique

The present work is an attempt to probe the elastic properties in some dielectric ceramics, by using ultrasonic pulse echo overlap technique. The base Ba6-xSm8+2xTi18O54 and Ca5Nb2TiO12 are very important dielectrics ceramics used for microwave communication as well as for substrate materials. Ultrasonic is one of the most widely used and powerful techniques to measure elastic properties of solids. The ultrasonic technique is nondestructive in nature and the measurements are relatively straightforward to perform. One unique advantantage of the ultrasonic technique is that both static and dynamic properties can be measured simultaneously. The velocity and attenuation coefficients of the ultrasonic waves propagating through a medium are related to the microscopic structure of the material and they provide valuable information about the structural changes in the system. Among the various ultrasonic techniques, the pulse echo overlap method is the most accurate and precise one. In the present case the decreased elastic properties of Cas-XMg,Nb2TiO12 and Cas-,ZnNb2TiO12 ceramics can be attributed to their mixture phases beyond x = 1. Moreover, the abrupt change in elastic properties observed for x >1 can also be correlated to the structural transformation of the materials from their phase pure form to mixture phases for higher extent of substitution of the concerned material . Ca4(ANb2Ti)012 (A = Mg, Zn) is the strongest compound with the maximum values for elastic properties . This could be due to the possible substitution of Mg/Zn ions with lesser radius [25] than Ca2+ in perovskite B-site of Ca(Cali4Nb2i4Tili4) O3 material to contribute more ordering and symmetry to the system [20]. All other compositions (x > 1) contain mixed-phases and for such mixed-phase samples, the mechanical properties are difficult to explain.

Theory of Breaking of a Potyrner Molecule under Tension

The thesis presents the dynamics of a polymer chain under tension. It includes existing theories of polymer fracture, important theories of reaction rates, the rate using multidimensional transition state theory and apply it to the case of polyethylene etc. The main findings of the study are; the life time of the bond is somewhat sensitive to the potential lead to rather different answers, for a given potential a rough estimate of the rate can be obtained by a simples approximation that considers the dynamics of only the bond that breaks and neglects the coupling to neighboring bonds. Dynamics of neighboring bonds would decrease the rate, but usually not more than by one order of magnitude, for the breaking of polyethylene, quantum effects are important only for temperatures below 150K, the lifetime strongly depends on the strain and as the strain varies over a narrow range, the life varies rapidly from 105 seconds to 10_5 seconds, if we change one unit of the polymer by a foreign atom, say by one sulphure atom, in the main chain itself, by a weaker bond, the rate is found to increase by orders of magnitude etc.

Ultrasonic measurement of the elastic constants of selected nonlinear optical /semiorganic crystals with orthorhombic symmetry

Ultrasonic is a good tool to investigate the elastic properties of crystals. It enables one to determine all the elastic constants, Poisson’s ratios, volume compressibility and bulk modulus of crystals from velocity measurements. It also enables one to demonstrate the anisotropy of elastic properties by plotting sections of the surfaces of phase velocity, slowness, group velocity, Young’s modulus and linear compressibility along the a-b, b-c and a-c planes. They also help one to understand more about phonon amplification and help to interpret various phenomena associated with ultrasonic wave propagation, thermal conductivity, phonon transport etc. Study of nonlinear optical crystals is very important from an application point of view. Hundreds of new NLO materials are synthesized to meet the requirements for various applications. Inorganic, organic and organometallic or semiorganic classes of compounds have been studied for several reasons. Semiorganic compounds have some advantages over their inorganic and inorganic counterparts with regard to their mechanical properties. High damage resistance, high melting point, good transparency and non-hygroscopy are some of the basic requirements for a material to be suitable for device fabrication. New NLO materials are being synthesized and investigation of the mechanical and elastic properties of these crystals is very important to test the suitability of these materials for technological applications

Multipole Theory Analysis of Cutoff Wavenumbers of Waveguides Partially Filled with Dielectric

A new approach, the multipole theory (MT) method, is presented for the computation of cutoff wavenumbers of waveguides partially filled with dielectric. The MT formulation of the eigenvalue problem of an inhomogeneous waveguide is derived. Representative computational examples, including dielectric-rod-loaded rectangular and double-ridged waveguides, are given to validate the theory, and to demonstrate the degree of its efficiency