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Numerical Solution for Multi-parameter Singularly Perturbed Initial and Boundary Value Problems
Get PDFThe main objective of this thesis is to provide some efficient numerical techniques for solving various class of singularly perturbed ordinary and partial differential equations. Generally, in singular perturbation problems(SPPs), a small parameter " known as “singular perturbation parameter” is involved as the coefficient of the highest order derivatives. When the parameter " goes to zero, the perturbations are operative over a thin region, where the dependent variable undergoes very rapid change on the domain of interest. These thin regions are frequently referred as boundary layers. Due to the layer behavior, classical numerical methods are unfit for solving such problems on uniform meshes unless the mesh size is too small in comparison with the ". Also, these approaches on a uniform mesh fails to decrease the maximum pointwise error until the size of mesh and the parameter " have the same order of magnitude. In this context, sufficient mesh points are placed inside the layers to produce a satisfactory numerical approximation. These drawbacks motivate to develop parameter uniform numerical methods, where the maximum pointwise error on discrete maximum norm are independent of the parameter. The theme of this thesis is, therefore, to analyze, improve and optimize some parameter-uniform numerical methods for singularly perturbed initial and boundary value problems. This is accomplished by constructing special type of layer adapted meshes resolving the boundary layers. At first, a hybrid numerical scheme is proposed for singularly perturbed initial value problems on layer adapted meshes like standard Shishkin mesh (S-mesh), Bakhvalov-Shishkin mesh (B-S mesh) and Vulanovic mesh (V-mesh). The finite difference scheme combines the second order central difference scheme on the fine mesh with a modified midpoint upwind scheme on the coarse mesh which provides a second order optimal accuracy for both numerical solution and scaled numerical derivatives. Then, a new spline based hybrid finite difference technique is introduced which combines the cubic spline difference scheme on the fine mesh with a modified midpoint upwind scheme on the coarse mesh. It is observed, that the newly proposed hybrid scheme on the B-S mesh is optimal and more accurate than the one obtained on the S-mesh. Thereafter, two parameter SPP is considered which contains a delay term. Till date no result exists so far for two parameter SPP containing a delay term. To obtain "-uniform convergence for such model, an upwind scheme is used followed by a hybrid scheme on S-mesh. Then, such idea is extended for a singularly perturbed parabolic reaction-diffusion problem with time delay. In this context, an upwind scheme is used for the space direction on S-mesh and B-S mesh and the implicit Euler scheme for the time variable is used on an uniform mesh to approximate the solution. It is shown that the proposed scheme is of first order rate of convergence which is optimal on B-S mesh. To increase the rate of convergence, a hybrid scheme which consists the upwind scheme, midpoint upwind scheme and the second order central difference scheme for the spatial derivatives and the backward Euler scheme on a uniform mesh in the time derivative is developed, which provides a second second order accuracy. Finally, a singularly perturbed parabolic PDE containing both positive and negative shift arguments (small) in the space variable as well as delay in the time variable is approximated by using the upwind finite difference scheme for space on Shishkin type meshes and the backward Euler scheme for time derivative on uniform mesh. It is observed that the proposed method is " uniform convergent and first order with respect to both space and time. Extensive numerical results are shown in shape of tables and figures which confirm the theoretical findings
Analytical and Numerical Solutions for Stochastic Integral and Differential Equations in Mathematical Modelling
No full textThe theory of deterministic chaos has enjoyed during the last three decades a rapidly increasing audience of mathematicians, physicists, engineers, biologists, economists, etc. However, this type of "chaos" can be understood only as quasi-chaos in which all states of a system can be predicted and reproduced by experiments. Meanwhile, many experiments in natural sciences have brought about hard evidence of stochastic effects. The best known example is perhaps the Brownian motion where pollen submerged in a fluid experience collisions with the molecules of the fluid and thus exhibit random motions. The study of stochasticity was initiated in the early years of the 1900's. Einstein, Smoluchowsky and Langevin wrote pioneering investigations. This work was later resumed and extended by Ornstein and Uhlenbeck. This research monograph concerns analysis of discrete-time approximations for stochastic differential equations (SDEs) driven by Wiener processes. The first chapter of the book provides a theoretical basis for working with SDEs and stochastic processes. In the present dissertation, various analytical methods like Kudryashov method, Improved sub equation method, Jacobi elliptic function (JEF) expansion method, Extended auxiliary equation method have been utilized for getting analytical solutions for stochastic differential equations viz. as Wick-type stochastic Zakharov-Kuznetsov (ZK) equation, Wick-type stochastic Kudryashov-Sinelshchikov equation, Wick-type stochastic modified Boussinesq equations, Wick-type stochastic Kersten-Krasil’shchik coupled KdV-mKdV equations and Wick-type stochastic nonlinear Schrödinger equation equations have been presented by using various analytical methods. Wavelet methodologies such as Hybrid-Legendre block pulse functions, Second kind Chebyshev wavelets, Bernstein polynomials and two dimensional second kind Chebyshev wavelets have been used to solve the stochastic integral equations. Furthermore, by applying wavelet methods, the approximate solutions of the stochastic Volterra-Fredholm integral equation, stochastic mixed Volterra-Fredholm integral equation, multi-dimensional stochastic integral equations, fractional stochastic Itô-Volterra integral equation, non-linear fractional stochastic Itô-Volterra integral equation and have been discussed in the present work. Also semi-implicit Euler-Maruyama scheme and Chebyshev spectral collocation have been applied to solve stochastic Fisher Equation and stochastic Fitzhungh Nagumo equation. These equations have lot of applications in physical phenomenon. The Fisher equation is one of the reaction-diffusion equations and is widely used in the study of biological invasion and the FitzHugh –Nagumo model is one of the classical standard models in neuroscience. Also, numerical methods viz., Euler-Maruyama method, order 1.5 strong Taylor method, Split-step forward Euler-Maruyama method, derivative free Milstein method and higher order approximation scheme have been successfully employed to fractional differential stochastic point kinetics equation for obtaining mean neutron population
Fabrication of Titanium Dioxide Thin Films by Dip Coating Process for Resistive Switching Applications
No full textResistive switching devices have recently drawn enormous attention for the fabrication of next generation memory devices. Metal oxide thin films have drawn great deal of interest for memristor devices due to their CMOS compatibility. Titanium oxide (TiO2) is an excellent material for resistive switching applications because it is an insulating material, which consists of oxygen vacancies and has good thermal stability with high dielectric constant as well. TiO2 based resistive random-access memory (RRAM) devices have boosted up due to their higher writing speed and low operation power. In this research, TiO2 thin films are prepared by the sol-gel dip coating process with the optimized annealed temperature of 500 ºC. The morphological, structural characterizations of TiO2 thin films have been carried out by the Field Emission scanning electron microscope (FESEM, Nova Nano SEM 450), X-ray diffraction (XRD, Rigaku Ultima IV) and Raman spectroscopy techniques, respectively. The oxide and interface charge density of TiO2 thin films are estimated by capacitance-voltage measurements using Al/TiO2/Si metal oxide semiconductor (MOS) structures. The resistive switching behavior of TiO2 thin films are carried out using Al/TiO2/p++ Si metal insulator metal (MIM) structure. The switching operation has taken place by the formation and rupture of conductive filament, which is investigated further by estimating the current On/Off ratio. The films, coated with a withdrawal speed of 1 cm/min, have shown better resistive switching properties. The effects of different rapid thermal annealing process parameters on the resistive switching studies of TiO2 films are investigated. The resistive switching behavior is found to be varied with rapid thermal annealing (RTA) temperature, duration and ambient. For the improvement of resistive switching studies, structural modifications such as porous, thin film-nanorods hybrid structures, multilayer TiO2 films are synthesized. Porous TiO2 are synthesized using Pluronic F-127, thiourea additives with appropriate molar ratio. The film deposition for 8 % of thiourea has shown Set current with On/Off ratio of 1.4 × 105. The phase of the TiO2 film is found to be changed from anatase to rutile phase for high temperature annealing. The thin film-nanorods hybrid structures of TiO2 are fabricated with various nanorod growth parameters such as temperature and time and followed by dip coating at 1 cm/min to coat thin film layer on nanorods. The samples, grown at 180 ºC for 60 min, have shown improved resistive switching behavior. Thereafter, TiO2-ZnO multilayer films are synthesized in order to investigate the resistive switching behavior of ix the stack layers. The stack layers, synthesized with TiO2/ZnO/TiO2/TiO2 geometry, have shown Set current On/Off ratio of 1.45 × 104. The significant improvement in the current On/Off ratio has depicted the use of dip coated TiO2 films for futuristic low cost, high performance memory devices
Outlier Detection using Unsupervised Learning Techniques
No full textOutlier Detection is a technique to detect anomalous events or outliers during analysis of the data in various domains such as computer network intrusion detection, fraud detection, medical and public health, sensor network, text analysis etc. Analysis of outliers leads to get some interesting information. Many outlier detection techniques have been proposed over decades. Those are broadly classified into three classes such as supervised technique, semi-supervised technique and unsupervised technique. Supervised and semi-supervised techniques have a dependency on the labeled dataset to train the model. Hence, unsupervised techniques are popular due to its independency upon labeled training dataset. Many parametric and non-parametric outlier detection approaches have been proposed over the last couple of decades. The existing neighborhood-based non-parametric unsupervised approaches like LOF, symmetric neighborhood, LDOF are proven to be effective when outliers are in a region of variable density. However, these techniques wrongly treat an outlier point as inlier in certain scenarios (outlier located between a dense cluster and close to a sparse cluster)
Performance Analysis and Optimization of Interference Limited Multiantenna Bidirectional Relay System
No full textOver the past decade, cooperative communication has emerged as an attractive technique for overcoming the shortcomings of point-to-point wireless communication systems. Cooperative relaying improves the performance of wireless networks by creating an array of multiple independent virtual sources transmitting the same information as the source node. Also, when relays are deployed near the edge of the cellular network, they can provide additional coverage in network blind spots. But due to dense-frequency reuse, they are typically exposed to co-channel interference (CCI). Therefore, CCI often dominates AWGN in high frequency and degrades the performance of wireless systems. Moreover, in wireless sensor networks, the interferers transmit power level similar to the source and therefore limit the signal-to-interference-plus-noise ratio (SINR). This thesis investigates the impact of co-channel interference on multi-antenna cooperative two-way relay networks and underlay relaying systems.
First, we study the performance analysis of multi-antenna amplify-and-forward (AF) two-way relay network (TWRN) in the presence of CCI. To fully exploit multiple antenna diversity by avoiding high feedback overhead, we employ transmit and receive antenna selection at the user nodes. Specifically, we formulate the exact expression of the generalized signal-to-interference-plus-noise ratio (SINR). Based on the derived SINR, we further derived the upper-bounded cumulative distribution function. Subsequently, we evaluate the expression of the symbol error rate and outage probability (OP). We determined the overall outage probability (OOP) and the overall symbol error rate to assess the overall performance of the system. With the aim to gain more insights, high SNR analysis of OP and OOP are analyzed, which provides the information about coding gain and diversity order of the system. Based on Jensen’s inequality, we derive upper bounds on the achievable rate. Furthermore, we formulate three optimization problems to minimize outage viz., optimization of relay location, optimization of power allocation and joint optimization of relay location and power allocation.
Next, we extend the analysis of a multi-antenna based two-way relay system with CCI under Nakagami-m fading. Herein, we employ maximum-ratio-transmission (MRT)/maximum-ratio-combining (a.k.a. beamforming) at user nodes in the presence of CCI at all the terminals. With such a complicated but practical set-up, we first deduce the instantaneous end-to-end SINRs after performing partial and self-interference cancellation. Vii Based on SINRs, we obtained the CDF and probability density function (PDF). We further derive a tight lower bound on OP that has a simple and compact closed-form representation. To acquire the overall performance, we obtained an upper bound expression of sum symbol error rate (SSER). Furthermore, to render insights into the performance degradation due to the effect of interference, asymptotic expression of OP and SSER are obtained, which easily enables us to evaluate diversity order and coding gain. We further investigate the joint optimization problem of relay location and power allocation to minimize the OP and SSER.
We further extend to present the comparative analysis of beamforming and antenna selection in the presence of interferers with different powers. Herein, a single-antenna relay terminal helps the users with an arbitrary number of antenna to exchange information bi-directionally. Under such a scenario, we evaluate and compare the performance of multi-antenna transmission strategies viz., antenna selection and beamforming. We derive the generalized tight upper bound expressions of OP for both the strategies over Rayleigh fading channel. To gain more insights, we determine the achievable diversity order of the considered system through asymptotic analysis. We further analyze the power optimization problem to minimize the OP for both scenarios.
The last part of the thesis focuses on the investigation of a practical scenario of interference-limited spectrum sharing systems. It consists of multi-antenna primary user (PU) network and multi-antenna multiple secondary user (SU) network with a single antenna relay. The distinct fading parameters, as well as unequal average fading powers between the interference and relaying links, are assumed under Nakagami-m fading. Using the underlay cognitive approach with the cooperation process among the SU nodes, an approximate closed-form expression for the OOP of the secondary network is derived. In this analysis, an opportunistic scheduling and antenna selection algorithm in the secondary network has been employed. Considering the interference constraints due to the presence of PU receiver, power allocation of the secondary user is done. We examined the effects of PU & SU transmit antenna, number of SUs, fading severity parameter and secondary network relay placement on the system performance. We further investigate the relay location optimization to minimize the secondary network OOP.
The tightness of our analysis is attested through Monte Carlo simulation and highlights the impact of interference under various antenna configuration on the overall system performance
Development of Iontophoresis-Responsive Oleogels for Facile Delivery of Upconversion Nanoparticle and Drug across the Skin
No full textAccording to the World Health Organization, one out of every three cancers detected these days is skin cancer, which grows and spreads within epidermis and dermis. Photon induced therapy through the generation of reactive oxygen species (ROS); although shows a promising potential toward the treatment of skin cancers, the practical application of such therapeutic modality has been extremely limited due to the difficulty in localizing the photo-therapeutic agents to the inner skin structure via transdermal route. Near infra-red (NIR) activated upconversion nanoparticle (UCNP), in spite of exhibiting a well-established photo-theranostic effect against many different types of cancers in vivo; could not be explored in the therapeutic context of skin cancers. The major reason of this limitation lies in the fact that the stratum corneum (SC) layer of human skin is practically impermeable and it is a major challenge to deliver and localize any therapeutic nanoparticles including UCNP to the inner layers of the skin i.e. epidermis and dermis via transdermal route. The prime content of this Ph.D. thesis is thus focussed on developing a method to localize UCNP, capable of generating NIR-induced ROS to the inner skin structure; overcoming the SC barrier by non-invasive skin permeation. The context and the significance of this dissertation has been presented in the first chapter as Introduction.
There exist two major non-invasive pathways to overcome the SC barrier. One, is the use of skin permeation-enhancing agents and the other is the use of external electrical current-induced iontophoresis. Soybean oil-based oleogel was selected as the host matrix of delivering UCNP across the skin. The stearic acid present as the gelator in the soybean oil-based oleogels and other unsaturated fatty acids found in the soybean oil have been reported to act as skin permeation enhancer. It is hypothesized that incurring iontophoretic property within such oleogels would exert the dual effects of both type of skin permeation enhancement strategy and thus expected to the development of a facile transdermal delivery system (TDS) for UCNP. 2
The first aim is to develop an iontophoresis-responsive oleogel, which is capable of showing drug delivery triggered by incorporating alternating electric field-induced iontophoresis. For this purpose, magnetic nanoparticle (MNP) incorporated soybean oil-based oleogels were developed. The details are included in the second chapter of this thesis (Colloids Surf. B, 157 (2017) 118-129).
Next, in the third chapter, the skin permeation capability of UCNP incorporated oleogels was explored. This system was designed to deliver UCNP across the full thickness of an animal skin model by overcoming the impermeable barrier of stratum corneum based on the skin-permeation enhancing effect of the components of the oleogel (Chem Eng J., 379 (2020) 122272). In an attempt to develop a faster and controlled delivery of UCNP and drug, the iontophoretic property was introduced within UCNP containing oleogel, by incorporating MNP within the same to magnify the skin-permeation enhancement effect. The details have been presented in the fourth chapter (Nano Express, 1 (2020) 010012).
Further, an effort was made to demonstrate the transdermal delivery of photosensitizer-linked UCNP across the skin for the generation of singlet oxygen (1O2) based ROS upon activation by NIR radiation. The ability of localizing ROS generating UCNP to the inner skin tissue was expected to enable such TDS suitable for its potential application in skin cancer. This work has been presented as the fifth chapter (Colloids Surf. B, 190 (2020) 110945). Finally, by incorporating gold nanoparticles within UCNP-oleogel, an attempt was also made to design a superior iontophoresis-responsive, controlled drug and UCNP delivery system, which was able to deliver therapeutic UCNP across the skin in the fastest possible manner among all the TDS described in this thesis as described in the sixth chapter. These results are expected to pave the way for the potential anti-skin cancer application of UCNP in future
Nonasymptotic Analysis of Massive MIMO under Different Wireless Scenarios
No full textThe data rate demand is increasing as per Moore's law over the past two decades. This surge in data demand is a key source of motivation for the researchers to build robust wireless network and smarter wireless devices like smartphones, tabs, PCs, laptops, etc. From 2G to 4G, throughput maximization was the main driving force for the researchers of information and communication technology (ICT) industry. On the other side, energy efficiency (EE) is an essential figure of merit for the next generation (5G) wireless technology. 5G technology also improvises data rates, latency, massive connectivity, and network reliability significantly. Massive multiple-input-multiple-output (MIMO) emerges as one of the vital technologies for next-generation wireless communication. 5G technology, a base station (BS) can have hundreds or even more antenna that can improvise the spectrum efficiency (SE) and energy efficiency (EE), significantly. It can achieve all merits of conventional MIMO to a much larger scale. Despite the advantage of massive MIMO, challenges like hardware mismatch (HM), antenna correlation, pilot contamination, improper resource allocation, etc., undermine the benefits.
The first part of this thesis considers a massive multi-user MIMO network, which utilizes time-division duplexing (TDD) scheme. HM is a severe concern in massive MIMO, which limits the potential of time-division multiplexing (TDD) scheme. A novel hardware calibration technique, which helps for generating the downlink (DL) channel matrix using the estimated uplink (UL) channel at a minimal computational cost, is proposed. HM causes amplitude and phase impairment in the received signal and makes the wireless channel non-reciprocal. Considering complex Gaussian hardware response at each antenna terminal of the base station (BS) or user terminal (UT) side, we derive the probability density function (PDF) of amplitude and phase mismatch are derived individually. The joint PDF of amplitude mismatch (AM) between each terminal of BS to the UT and vice-versa is also derived at a constant phase response. This joint PDF reduces the computational cost of the UT by processing signal at the BS end. The DL system performances are evaluated with the proposed algorithm under three different linear precoder like matched filter (MF), regularized zero-forcing (RZF), and zero-forcing (ZF).
In the second part of this thesis considered three different antenna correlation environments based on the placement of antennas. It also considers a very large but finite number of BS antenna, and spacing between adjacent antenna elements is half of the wavelength. Using three linear detectors (maximum ratio combiner (MRC), ZF, and minimum mean square error (MMSE)), UL data rate and power efficiency in antenna correlation regime is obtained and compared to the independent and identically distributed (IID) wireless channel. Considering the impact of adjacent antenna element misalignment, for different range of degree of misalignment is also validated through the numerical simulation.
In the third part of this thesis, a relay assisted cooperative network, where the base station (BS) and relay station (RS) have a very large but finite number of the antenna, is considered. An analytical expression for the UL rate in different channel conditions (perfect/imperfect) is derived, and the impact of a large number of BS and RS antenna over the UL rate is verified. Different cooperation protocol for improvising the ease of cooperative selection diversity have also been incorporated. On the other side, suitable linear precoder and decoder improvise the end-to-end SNR and end-user capacity in a dual-hop wireless network. When MIMO size increases asymptotically; the random matrix theory (RMT) helps to obtain the closed-form solution. In such a network, when statistics of the channel matrix and precoding matrix are known then, the SNR and achievable rate is easily obtained through the RMT
Dynamic Analysis and Active Control of Functionally Graded Rotor Shaft System
No full textFunctionally graded (FG) shaft finds applications in gas turbines and aircraft jet engine rotors to withstand the thermal and mechanical loads. The present work deals with the finite element modelling, and dynamic analysis and active control of different kinds of FG rotating shaft systems considering temperature-independent (TID) and temperature-dependent (TD) material properties. Aluminum oxide (Al2O3), stainless steel (SUS304), and titanium alloy (Ti-6Al-4V) are considered as the FG shaft materials. One dimensional (1D) and two dimensional (2D) distributions of material properties of the FG shafts have been obtained. Material properties of the FG shafts are determined based on the power-law distribution. A time-dependent two-dimensional (2D) temperature distribution problem is assumed for the FG shafts; it has been solved using the finite difference method (FDM). Based on the Timoshenko beam theory (TBT), a three noded beam element has been developed for the finite element (FE) modelling and dynamic analysis of the FG spinning shaft systems. The present FE modelling is based on the first-order shear deformation theory considering rotary inertia and gyroscopic effects. The governing equation of motion is derived using the Hamilton principle.
In this present work, electromagnetic actuator (EMA) has also been used to provide the non-contact control force for actuation, which significantly can reduce the rotor vibration due to unbalance forces by enhancing the stability limit speed of the rotor-shaft system which can lead the safe operations at higher speeds. The mathematical model of the EMA has been carried out for the determination of input current and generated force. It has been found from the obtained results that eigenfrequencies, stability limit speed (SLS), maximum real parts, and frequency and time-domain responses have significantly been influenced by temperature variation, power-law index, and internal viscous and hysteretic damping. Proportional-derivative (PD) control scheme has also been implemented to control the above responses by varying the number of coil turns (N) and pole face area (Ap) of the EMA
Evaporation and Magnetic Field Induced Organization of Nanoparticles for Wetting and Catalytic Applications
No full textIn recent years, most of the electronic and several other devices are getting smaller day by day because of technological advancements; essentially, these devices required small chips, electronic circuits, microprocessors, sensors, etc. As the dimension of these devices decreases to micro or nano-level, it is almost impossible to fabricate those parts with the help of any precise machine. However, the fabrication of these devices at small-scale has been more accessible and inexpensive by the use of a relatively novel technique such as “self-assembly” of nanoparticles (NPs). Self-assembly (SA) refers to a bottom-up process by which any kind of colloidal or nanoparticles, macromolecules are organized into a specific arrangement driven by some favorable intermolecular (capillary forces, van der Waals interaction, hydrogen bond) or externally induced forces (evaporative flux, electrical, and magnetic forces). Among all available techniques of self-assembly; drying-mediated or evaporation-induced assembly (EISA) of nanoparticles is the simplest method of assembling particles on surfaces. Similarly, NPs can also be organized in the bulk phase/ solution phase to get various types of 1D, 2D, or 3D nanostructures (such as nanowire, nanochains, nanoplates, nanocubes). In this case, molecules or particles form a nucleus first and then grow into a larger organized structure because of the favorable interaction with the neighboring building blocks. These types of assemblies are assisted by different interactions, external electrical, or magnetic fields. In recent years, assembled nanostructures are preferred for numerous applications such as wetting, catalysis, sensing, biological and electronic fields over the unorganized one because of unique and enhanced collective properties.
In this thesis, two types of patterns, fractal, and chain-like patterns were developed using evaporation induced and magnetic field-assisted bulk phase assembly, respectively. In the first part of the work (Chapter-3), fractal patterns formation of sodium carboxymethyl cellulose (CMCNa) on various surfaces were investigated during the evaporation of sessile drop in the presence of oxalic acid. These patterns are branched type and typically referred as ‘‘Fractal trees’’. The produced sodium oxalate salt from the reaction of CMCNa and oxalic acid is mainly responsible for the pattern formation due to the dendritic crystallization. These patterns formed under the influence of inner coffee ring deposits and different intermolecular forces. The mechanism of fractal pattern formation, the effects of various parameters, such as the effect of salt, temperature, and reaction components were discussed in this work. Later in continuation, these patterns were used as a removable template for the organization of other NPs (SiO2, TiO2, and PTFE) into fractal patterns on glass and metallic surfaces (Chapter-4). First of all, metallic oxides SiO2 and TiO2 were organized into fractal patterns on the glass surface. The pure NPs suspension showed “coffee ring effect” and did not form an organized pattern on the glass surface after drying. Later these NPs were organized into fractal patterns using an easily removable template consist of CMCNa and oxalic acid mixture in the presence of a cationic surfactant (CTAB). The obtained fractal patterns of SiO2 and TiO2 coated glass surfaces showed superhydrophilic nature with the average water contact angle of ~ 6 and ~8 respectively after calcination, whereas, coating of only NPs without pattern could not achieve such low average contact angle. These coated surfaces showed the antifogging property. Similarly, polytetrafluoroethylene (PTFE) NPs were organized on flat surfaces (glass and steel) and stainless steel mesh using CMCNa template, which in turn leads to the superhydrophobic surface after sintering at 250 ºC (Chapter-5). These PTFE coated surfaces showed the average water contact angle ~152º for glass and flat stainless steel surfaces and 154º for stainless steel mesh with excellent self-cleaning property. The superhydrophobic mesh also showed good efficiency for oil-water separation. In the next part of the thesis, Palladium NPs were synthesized using clove and acacia extract and organized into flower-like fractal morphology on glass and silicon surfaces via evaporation induced assembly (Chapter-6). These organized patterns surface showed enhanced catalytic activity for the reduction of 4 nitrophenol (4- NPh) to 4-Aminophenol (4-APh) and also suitable anode material for direct borohydride fuel cell than the unorganized NPs. The last part of work is related to the organization of Ni NPs in the bulk phase (Chapter-7). Herein, Ni NPs were organized into nanochains in the presence of an external magnetic field in bulk media. The length of as-synthesized chains was 10±2 µm, and 85 nm diameter. These chains showed good magnetic properties and the application of these nanochains showed excellent catalytic activity for the reduction 4 NPh to 4-APh in comparison with only NPs with easy recovery with the help of a magnet. These nanochains also showed very good electro-catalytic activity for ethanol oxidation. The Ni nanochains showed 5.4 times higher current density compared to NPs due to low charge transfer resistance and surface area. The current decay was also less over a period for Ni nanochains, indicating the higher stability of chains than NPs. The thesis provides some important insights, such as cheap and robust strategies for the assembly of particles flat surfaces for several practical applications with improved wetting, catalytic, and electrochemical properties
Gait Analysis of the Lower Limbs: A Systematic Approach for Design and Analysis of an Orthotic
No full textThe application of three-dimensional (3D) motion analysis to study the intricacies of biomechanics associated with the human locomotion has enabled researchers to approach and study the various issues pertaining to gait with much better precision. The present study makes use of a 3D motion analysis system along with statistical and numerical tools to classify human gait and predict the mechanical behaviour of an assistive device that may be used for rehabilitative purposes. The data from motion analysis have been analysed to quantify the extent of significant correlation between subject anthropometric data and the gait parameters. A novel outlook has also been proposed in Chapter 3, wherein various regression models may be used to identify the underlying independent variables responsible for the asymmetry in gait. These models have clinical significance for the identification of the essential causes of asymmetry in the gait of subjects with pathology arising out of similar type of causative events. The motion analysis data has also been used to train an artificial neural network and implemented to identify the gender of individuals utilising the characteristic peaks of the ground reaction forces with an accuracy of more than 99.99 %. Chapter 4 focuses on the design of an orthotic device intended to alleviate the conditions associated with the gait pathologies responsible for lack of heel-strike in individuals. The experimental data were used to define the transient loading conditions of the orthotic, and proper boundary conditions were applied for the finite element analysis (FEA) of the orthotic. The results from this study demonstrate that this orthotic model can withstand the gait loading conditions in the static and transient modes without failing. The reconstruction of a foot bone and tissue model and its assembly has been presented and discussed in Chapter 5. The foot model has been assembled with and without the orthotic model in two separate configurations that are placed upon the ground and shoe sole geometries. The FEA results indicate that the use of the orthotic device reduces the maximum plantar pressure on the foot and has multiple benefits. Chapter 6 deals with the design, fabrication and motion analysis of the spring orthotic device comprising two leaflets to test its effectiveness in transforming kinetic energy to deformation energy and vice-versa in the early and late stance phases of gait. The gait trials for this study have been conducted under the barefoot, shod and orthotic modes wherein the significant differences in the resulting gait patterns between the barefoot-orthotic and the shod-orthotic trials were obtained. The trials with orthotic present a longer stance phase and a smaller mean radii of curvature for the rollover shapes. The orthotic demonstrates power absorption and drop of peak forces and moments in major characteristic peaks of the gait cycle, the reduced radii of curvature of the rollover shape suggest a decrease in stability during the early stance. Thus the proposed orthotic device presents satisfactory results and indicates potential application in rehabilitation healthcare