Performance of Gabion Faced Reinforced Earth Retaining Walls

Gabion faced re.taining walls are essentially semi rigid structures that can generally accommodate large lateral and vertical movements without excessive structural distress. Because of this inherent feature, they offer technical and economical advantage over the conventional concrete gravity retaining walls. Although they can be constructed either as gravity type or reinforced soil type, this work mainly deals with gabion faced reinforced earth walls as they are more suitable to larger heights. The main focus of the present investigation was the development of a viable plane strain two dimensional non linear finite element analysis code which can predict the stress - strain behaviour of gabion faced retaining walls - both gravity type and reinforced soil type. The gabion facing, backfill soil, In - situ soil and foundation soil were modelled using 20 four noded isoparametric quadrilateral elements. The confinement provided by the gabion boxes was converted into an induced apparent cohesion as per the membrane correction theory proposed by Henkel and Gilbert (1952). The mesh reinforcement was modelled using 20 two noded linear truss elements. The interactions between the soil and the mesh reinforcement as well as the facing and backfill were modelled using 20 four noded zero thickness line interface elements (Desai et al., 1974) by incorporating the nonlinear hyperbolic formulation for the tangential shear stiffness. The well known hyperbolic formulation by Ouncan and Chang (1970) was used for modelling the non - linearity of the soil matrix. The failure of soil matrix, gabion facing and the interfaces were modelled using Mohr - Coulomb failure criterion. The construction stages were also modelled.Experimental investigations were conducted on small scale model walls (both in field as well as in laboratory) to suggest an alternative fill material for the gabion faced retaining walls. The same were also used to validate the finite element programme developed as a part of the study. The studies were conducted using different types of gabion fill materials. The variation was achieved by placing coarse aggregate and quarry dust in different proportions as layers one above the other or they were mixed together in the required proportions. The deformation of the wall face was measured and the behaviour of the walls with the variation of fill materials was analysed. It was seen that 25% of the fill material in gabions can be replaced by a soft material (any locally available material) without affecting the deformation behaviour to large extents. In circumstances where deformation can be allowed to some extents, even up to 50% replacement with soft material can be possible.The developed finite element code was validated using experimental test results and other published results. Encouraged by the close comparison between the theory and experiments, an extensive and systematic parametric study was conducted, in order to gain a closer understanding of the behaviour of the system. Geometric parameters as well as material parameters were varied to understand their effect on the behaviour of the walls. The final phase of the study consisted of developing a simplified method for the design of gabion faced retaining walls. The design was based on the limit state method considering both the stability and deformation criteria. The design parameters were selected for the system and converted to dimensionless parameters. Thus the procedure for fixing the dimensions of the wall was simplified by eliminating the conventional trial and error procedure. Handy design charts were developed which would prove as a hands - on - tool to the design engineers at site. Economic studies were also conducted to prove the cost effectiveness of the structures with respect to the conventional RCC gravity walls and cost prediction models and cost breakdown ratios were proposed. The studies as a whole are expected to contribute substantially to understand the actual behaviour of gabion faced retaining wall systems with particular reference to the lateral deformations.

Systematic trends in self-consistent calculations of linear quantum wires

Systematic trends in the properties of a linear split-gate heterojunction are studied by solving iteratively the Poisson and Schrödinger equations for different gate potentials and temperatures. A two-dimensional approximation is presented that is much simpler in the numerical implementation and that accurately reproduces all significant trends. In deriving this approximation, we provide a rigorous and quantitative basis for the formulation of models that assumes a two-dimensional character for the electron gas at the junction.

Linear Low Density Polyethylene-Biodegradability Using Bacteria from Marine Benthic Environment and Photodegradability Using Ultraviolet Light

Various compositions of linear low density polyethylene(LLDPE) containing bio-filler(either starch or dextrin)of various particle sizes were prepared.The mechanical,thermal,FTIR,morphological(SEM),water absorption and melt flow(MFI) studies were carried out.Biodegradability of the compositions were determined using a shake culture flask containing amylase producing bacteria(vibrios),which were isolated from marine benthic environment and by soil burial test. The effect of low quantities of metal oxides and metal stearate as pro-oxidants in LLDPE and in the LLDPE-biofiller compositions was established by exposing the samples to ultraviolet light.The combination of bio-filler and a pro-oxidant improves the degradation of linear low density polyethylene.The maleation of LLDPE improves the compatibility of the c blend components and thepro-oxidants enhance the photodegradability of the compatibilised blends.The responsibility studies on the partially biodegradable LLDPE containing bio-fillers and pro-oxidants suggest that the blends could be repeatedly reprocessed without deterioration in mechanical properties.

Spectral Analysis of Bounded Self-adjoint operators - A Linear Algebraic Approach

This thesis Entitled Spectral theory of bounded self-adjoint operators -A linear algebraic approach.The main results of the thesis can be classified as three different approaches to the spectral approximation problems. The truncation method and its perturbed versions are part of the classical linear algebraic approach to the subject. The usage of block Toeplitz-Laurent operators and the matrix valued symbols is considered as a particular example where the linear algebraic techniques are effective in simplifying problems in inverse spectral theory. The abstract approach to the spectral approximation problems via pre-conditioners and Korovkin-type theorems is an attempt to make the computations involved, well conditioned. However, in all these approaches, linear algebra comes as the central object. The objective of this study is to discuss the linear algebraic techniques in the spectral theory of bounded self-adjoint operators on a separable Hilbert space. The usage of truncation method in approximating the bounds of essential spectrum and the discrete spectral values outside these bounds is well known. The spectral gap prediction and related results was proved in the second chapter. The discrete versions of Borg-type theorems, proved in the third chapter, partly overlap with some known results in operator theory. The pure linear algebraic approach is the main novelty of the results proved here.

Modification of Linear Low Density Polyethylene for Improved Photo and Biodegradation

LLDPE was blended with poly (vinyl alcohol) and mechanical, thermal, spectroscopic properties and biodegradability were investigated. The biodegradability of LLDPE/PVA blends has been studied in two environments, viz. (1) a culture medium containing Vibrio sp. and (2) a soil environment over a period of 15 weeks. Nanoanatase having photo catalytic activity was synthesized by hydrothermal method using titanium-iso-propoxide. The synthesized TiO2 was characterized by X-Ray diffraction (XRD), BET studies, FTIR studies and scanning electron microscopy (SEM). The crystallite size of titania was calculated to be ≈ 6nm from the XRD results and the surface area was found to be about 310m2/g by BET method. SEM shows that nanoanatase particles prepared by this method are spherical in shape. Linear low density polyethylene films containing polyvinyl alcohol and a pro-oxidant (TiO2 or cobalt stearate with or without vegetable oil) were prepared. The films were then subjected to natural weathering and UV exposure followed by biodegradation in culture medium as well as in soil environment. The degradation was monitored by mechanical property measurements, thermal studies, rate of weight loss, FTIR and SEM studies. Higher weight loss, texture change and greater increments in carbonyl index values were observed in samples containing cobalt stearate and vegetable oil. The present study demonstrates that the combination of LLDPE/PVA blends with (I) nanoanatase/vegetable oil and (ii) cobalt stearate/vegetable oil leads to extensive photodegradation. These samples show substantial degradation when subsequent exposure to Vibrio sp. is made. Thus a combined photodegradation and biodegradation process is a promising step towards obtaining a biodegradable grade of LLDPE.

Some non- linear problems in theoretical physics

An immense variety of problems in theoretical physics are of the non-linear type. Non~linear partial differential equations (NPDE) have almost become the rule rather than an exception in diverse branches of physics such as fluid mechanics, field theory, particle physics, statistical physics and optics, and the construction of exact solutions of these equations constitutes one of the most vigorous activities in theoretical physics today. The thesis entitled ‘Some Non-linear Problems in Theoretical Physics’ addresses various aspects of this problem at the classical level. For obtaining exact solutions we have used mathematical tools like the bilinear operator method, base equation technique and similarity method with emphasis on its group theoretical aspects. The thesis deals with certain methods of finding exact solutions of a number of non-linear partial differential equations of importance to theoretical physics. Some of these new solutions are of relevance from the applications point of view in diverse branches such as elementary particle physics, field theory, solid state physics and non-linear optics and give some insight into the stable or unstable behavior of dynamical Systems The thesis consists of six chapters.

Fluid mechanics-non-linear waves studies on korteweg-de vries equations

In this thesis the author has presented qualitative studies of certain Kdv equations with variable coefficients. The well-known KdV equation is a model for waves propagating on the surface of shallow water of constant depth. This model is considered as fitting into waves reaching the shore. Renewed attempts have led to the derivation of KdV type equations in which the coefficients are not constants. Johnson's equation is one such equation. The researcher has used this model to study the interaction of waves. It has been found that three-wave interaction is possible, there is transfer of energy between the waves and the energy is not conserved during interaction.

Importance of the embedding environment on the strain within small rings in siliceous materials

The effect of the local environment on the energetic strain within small (SiO)N rings (with N=2,3) in silica materials is investigated via periodic model systems employing density functional calculations. Through comparison of the energies of various nonterminated systems containing small rings in strained and relatively unstrained environments, with alpha quartz, we demonstrate how small ring strain is affected by the nature of the embedding environment. We compare our findings with numerous previously reported calculations, often predicting significantly different small-ring strain energies, leading to a critical assessment of methods of calculating accurate localized ring energies. The results have relevance for estimates of the strain-induced response (e.g., chemical, photo, and radio) of small silica rings, and the propensity for them to form in bulk glasses, thin films, and nanoclusters.

Feature Extraction Methods Based on Linear Predictive Coding and Wavelet Packet Decomposition for Recognizing Spoken Words in Malayalam

Speech signals are one of the most important means of communication among the human beings. In this paper, a comparative study of two feature extraction techniques are carried out for recognizing speaker independent spoken isolated words. First one is a hybrid approach with Linear Predictive Coding (LPC) and Artificial Neural Networks (ANN) and the second method uses a combination of Wavelet Packet Decomposition (WPD) and Artificial Neural Networks. Voice signals are sampled directly from the microphone and then they are processed using these two techniques for extracting the features. Words from Malayalam, one of the four major Dravidian languages of southern India are chosen for recognition. Training, testing and pattern recognition are performed using Artificial Neural Networks. Back propagation method is used to train the ANN. The proposed method is implemented for 50 speakers uttering 20 isolated words each. Both the methods produce good recognition accuracy. But Wavelet Packet Decomposition is found to be more suitable for recognizing speech because of its multi-resolution characteristics and efficient time frequency localizations

Ultrasound Image Despeckling using Local Binary Pattern Weighted Linear Filtering

Speckle noise formed as a result of the coherent nature of ultrasound imaging affects the lesion detectability. We have proposed a new weighted linear filtering approach using Local Binary Patterns (LBP) for reducing the speckle noise in ultrasound images. The new filter achieves good results in reducing the noise without affecting the image content. The performance of the proposed filter has been compared with some of the commonly used denoising filters. The proposed filter outperforms the existing filters in terms of quantitative analysis and in edge preservation. The experimental analysis is done using various ultrasound images

Characterization of Linear Low-Density Polyethylene/ Poly(vinyl alcohol) Blends and Their Biodegradability by Vibrio sp. Isolated from Marine Benthic Environment

Increasing amounts of plastic waste in the environment have become a problem of gigantic proportions. The case of linear low-density polyethylene (LLDPE) is especially significant as it is widely used for packaging and other applications. This synthetic polymer is normally not biodegradable until it is degraded into low molecular mass fragments that can be assimilated by microorganisms. Blends of nonbiodegradable polymers and biodegradable commercial polymers such as poly (vinyl alcohol) (PVA) can facilitate a reduction in the volume of plastic waste when they undergo partial degradation. Further, the remaining fragments stand a greater chance of undergoing biodegradation in a much shorter span of time. In this investigation, LLDPE was blended with different proportions of PVA (5–30%) in a torque rheometer. Mechanical, thermal, and biodegradation studies were carried out on the blends. The biodegradability of LLDPE/PVA blends has been studied in two environments: (1) in a culture medium containing Vibrio sp. and (2) soil environment, both over a period of 15 weeks. Blends exposed to culture medium degraded more than that exposed to soil environment. Changes in various properties of LLDPE/PVA blends before and after degradation were monitored using Fourier transform infrared spectroscopy, a differential scanning calorimeter (DSC) for crystallinity, and scanning electron microscope (SEM) for surface morphology among other things. Percentage crystallinity decreased as the PVA content increased and biodegradation resulted in an increase of crystallinity in LLDPE/PVA blends. The results prove that partial biodegradation of the blends has occurred holding promise for an eventual biodegradable product

Design and Synthesis of Donor-Acceptor Low Band Gap Copolymers for Photoconductive and Non-linear Optical Applications

The main focus of the present study was to develop ideal low band gap D-A copolymers for photoconducting and non-linear optical applications. This chapter summarizes the overall research work done. Designed copolymers were synthesized via direct arylation or Suzuki coupling reactions. Copolymers were characterized by theoretical and experimental methods. The suitability of these copolymers in photoconducting and optical limiting devices has been investigated.The results suggest that the copolymers investigated in the present study have a good non-linear optical response and are comparable to or even better than the D-A copolymers reported in the literature and hence could be chosen as ideal candidates with potential applications for non-linear optics. The results also show that the structures of the polymers have great impact on NLO properties. Copolymers studied here exhibits good optical limiting property at 532 nm wavelength due to two-photon absorption (TPA) process. The results revealed that the two copolymers, (P(EDOT-BTSe) and P(PH-TZ)) exhibited strong two-photon absorption and superior optical power limiting properties, which are much better than that of others.

Computation of locally free class groups

We show that the locally free class group of an order in a semisimple algebra over a number field is isomorphic to a certain ray class group. This description is then used to present an algorithm that computes the locally free class group. The algorithm is implemented in MAGMA for the case where the algebra is a group ring over the rational numbers.

On Vessiot's Theory of Partial Differential Equations

The object of research presented here is Vessiot's theory of partial differential equations: for a given differential equation one constructs a distribution both tangential to the differential equation and contained within the contact distribution of the jet bundle. Then within it, one seeks n-dimensional subdistributions which are transversal to the base manifold, the integral distributions. These consist of integral elements, and these again shall be adapted so that they make a subdistribution which closes under the Lie-bracket. This then is called a flat Vessiot connection. Solutions to the differential equation may be regarded as integral manifolds of these distributions. In the first part of the thesis, I give a survey of the present state of the formal theory of partial differential equations: one regards differential equations as fibred submanifolds in a suitable jet bundle and considers formal integrability and the stronger notion of involutivity of differential equations for analyzing their solvability. An arbitrary system may (locally) be represented in reduced Cartan normal form. This leads to a natural description of its geometric symbol. The Vessiot distribution now can be split into the direct sum of the symbol and a horizontal complement (which is not unique). The n-dimensional subdistributions which close under the Lie bracket and are transversal to the base manifold are the sought tangential approximations for the solutions of the differential equation. It is now possible to show their existence by analyzing the structure equations. Vessiot's theory is now based on a rigorous foundation. Furthermore, the relation between Vessiot's approach and the crucial notions of the formal theory (like formal integrability and involutivity of differential equations) is clarified. The possible obstructions to involution of a differential equation are deduced explicitly. In the second part of the thesis it is shown that Vessiot's approach for the construction of the wanted distributions step by step succeeds if, and only if, the given system is involutive. Firstly, an existence theorem for integral distributions is proven. Then an existence theorem for flat Vessiot connections is shown. The differential-geometric structure of the basic systems is analyzed and simplified, as compared to those of other approaches, in particular the structure equations which are considered for the proofs of the existence theorems: here, they are a set of linear equations and an involutive system of differential equations. The definition of integral elements given here links Vessiot theory and the dual Cartan-Kähler theory of exterior systems. The analysis of the structure equations not only yields theoretical insight but also produces an algorithm which can be used to derive the coefficients of the vector fields, which span the integral distributions, explicitly. Therefore implementing the algorithm in the computer algebra system MuPAD now is possible.