etd@IISc Community:http://hdl.handle.net/2005/62016-07-05T07:50:46Z2016-07-05T07:50:46ZFiber Bragg Grating Sensors : An Exploration Of Applications In Diverse FieldsGuru Prasad, A Shttp://hdl.handle.net/2005/25072016-03-01T06:04:50Z2016-02-29T18:30:00ZTitle: Fiber Bragg Grating Sensors : An Exploration Of Applications In Diverse Fields
Authors: Guru Prasad, A S
Abstract: Sensors have become essential elements in human life for safe and comfortable existence in the ever demanding world. Various technologies over decades have contributed in their own way fulfilling innumerable sensing requirements. The discovery of optical sensor technologies has revolutionized the sensing field due to their inherent advantages. Among the large number of fiber optic sensor technologies, FBG based sensors have become widely known and popular within and outside the photonics community and has seen a prominent rise in their utilization.
This thesis explores the use of FBG sensors for a wide range of applications scanning across a variety of engineering and medical applications, in the areas of civil engineering, biomechanical engineering, aerospace engineering, geoengineering, etc. It also deals with newer methods of packaging FBG sensors for the measurement of specific engineering parameters like strain, temperature, pressure, displacement and vibration.
In the field of civil engineering, FBG sensors are employed for strain sensing on a prism and furthermore tested on a full size brick wallet. During this study, emphasis is made on substituting traditional sensors by specially packaged FBG sensors with the intent of either enhancing the sensing system’s performance or in merging/uniting the inherent advantages of FBG sensors.
In the area of biomechanics, a novel sensor methodology using FBG sensors, for measuring surface strains generated on the skin of the calf muscle during various leg exercises is proposed. This methodology is used to address one of the most critical and life threatening issues in long distance air travel, namely the Deep Vein Thrombosis. Further, a FBG sensor based plantar sensing plate, is designed and developed, to measure plantar strain distribution in foot and also to analyze the postural stability.
In the field of aerospace engineering, FBG sensors are used for addressing two of the most vital issues; Structural Health Monitoring (SHM) and direct measurement of pressure and temperature on the surface of an aircraft under hypersonic wind flow. Carbon Fiber Composite coupon level testing is carried out to obtain a generic strain calibration factor for the FBG sensor. Further, FBG sensors are exploited for the direct measurement of absolute temperature and pressure on the leeward surface of blunt cone at hypersonic wind speeds.
In the domain of geoengineering, the feasibility studies have been undertaken to use a FBG as a seismic sensor and as a bore-well characterizing sensor. A novel FBG seismic sensor package is developed using a single FBG sensor to pick up the seismic waves propagating through the ground generated from earthquakes and ground tremors. Further, FBG sensors are used for measurement of temperature profiles in a bore-well to delineate and characterize the behavior of fractures during seasonal climatic changes. To summarize, the present thesis demonstrates a comprehensive experimental study which bring out the utility of FBG sensors in a variety of challenging applications.2016-02-29T18:30:00ZGrothendieck InequalityRay, Samya Kumarhttp://hdl.handle.net/2005/25402016-06-20T07:01:17Z2016-06-19T18:30:00ZTitle: Grothendieck Inequality
Authors: Ray, Samya Kumar
Abstract: Grothendieck published an extraordinary paper entitled ”Resume de la theorie metrique des pro¬duits tensoriels topologiques” in 1953. The main result of this paper is the inequality which is commonly known as Grothendieck Inequality.
Following Kirivine, in this article, we give the proof of Grothendieck Inequality. We refor¬mulate it in different forms. We also investigate the famous Grothendieck constant KG. The Grothendieck constant was achieved by taking supremum over a special class of matrices. But our attempt will be to investigate it, considering a smaller class of matrices, namely only the positive definite matrices in this class. Actually we want to use it to get a counterexample of Matsaev’s conjecture, which was proved to be right by Von Neumann in some specific cases.
In chapter 1, we shall state and prove the Grothendieck Inequality. In chapter 2, we shall introduce tensor product of vector spaces and different tensor norms. In chapter 3, we shall formulate Grothendieck Inequality in different forms and use the notion of tensor norms for its equivalent formation .In the last chapteri.ein chapter4we shall investigate on the Grothendieck constant.2016-06-19T18:30:00ZProlate Shaped Dark Matter Halo And The Galactic WarpRahul Nath, Rhttp://hdl.handle.net/2005/25222016-04-26T09:57:49Z2016-04-25T18:30:00ZTitle: Prolate Shaped Dark Matter Halo And The Galactic Warp
Authors: Rahul Nath, R
Abstract: The physical explanation for the existence of the galactic warp is one of the major research areas in Astronomy. People have proposed various theories but nobody has yet given a convincing explanation. Most of the spiral galaxies are observed to be warped which reveals that the galactic warp is a stable characteristic. In the theory of kinematic bending wave, warp is considered as a wave that is propagated through the galactic disk with a speed called pattern speed.
If the pattern initially had straight line of nodes, according to bending wave theory, the warp would tend to wind up rapidly in the gravitational field of galactic disk. But still we observe warped galaxies in the sky. In the literature, it has been claimed that the winding problem of galactic warp may be solved by incorporating the effect of gravitational field of the dark matter halo in which the galactic disk is embedded. Recently some works on the dynamics of galactic disk claim that the shape of the dark matter halo is pro late spheroid. In this thesis, the effect of the gravitational field of a prolate spheroidal dark matter halo with varying eccentricity to the galactic warp is calculated and discussed.
Chapter1 gives the general introduction of the topics discussed in the following chapters. The structure of the spiral galaxy, their classifications, and the disk dynamics are discussed in the first few sections. One of the revolutionary concepts that emerged in the previous century was the existence of the dark matter. Presently tracing the mass distribution and the constituent particles of dark matter is one of the major research areas in theoretical and experimental physics. In this thesis, the effect of a particular type of mass distribution in dark matter halo on the warp is discussed in detail.
In the next few sections, the following topics are discussed namely; how the concept of dark matter came into astrophysics, how to measure the total mass inside a given radius and what are the different distributions used for various purposes. A new theory called Modified Newtonian Mechanism was also proposed in the previous century as an alternative to the dark matter concept which is also discussed briefly. Kinematic bending wave theory and the winding problem of the galactic warp is also discussed in detail. In the last section a relation between the pattern speed of the warp and the shape of the dark matter halo is obtained.
The calculation of the potential of a prolate spheroidal mass distribution with varying eccentricity is not done in any literature as we know. The calculation of the potential and the patten speed of prolate spheroidal mass distributions and of the galactic disk are described in chapter 2. The calculations of oblate spheroidal mass distribution are also discussed in this chapter but that is out of main theme.
In chapter 3 we apply the equations obtained in the Chapter 2 to one simple toy model and to the Galaxy. The rotation curve and the pattern speed of a warp in the gravitational ﬁeld of prolate spheroidal mass distribution of varying eccentricity are described. Usually the Milky Way disk is treated as an in infinitesimally thin disk but for our calculations the three dimensional but thin disk is used. The usually people use some approximation to calculate the potential due to galactic infinitesimal thin disk. The difference of the work from earlier works done by different people(with the approximation mentioned in above line) is also discussed in this Chapter. Chapter 4 discusses the summary of the entire work.2016-04-25T18:30:00ZCurvature Calculations Of The Operators In Cowen-Douglas ClassDeb, Prahlladhttp://hdl.handle.net/2005/22842014-03-03T09:38:06Z2014-03-02T18:30:00ZTitle: Curvature Calculations Of The Operators In Cowen-Douglas Class
Authors: Deb, Prahllad
Abstract: In a foundational paper “Operators Possesing an Open Set of Eigenvalues” written several decades ago, Cowen and Douglas showed that an operator T on a Hilbert space ‘H possessing an open set Ω C of eigenvalues determines a holomorphic Hermitian vector bundle ET . One of the basic theorems they prove states that the unitary equivalence class of the operator T and the equivalence class of the holomorphic Hermitian vector bundle ET are in one to one correspondence. This correspondence appears somewhat mysterious until one detects the invariants for the vector bundle ET in the operator T and vice-versa. Fortunately, this is possible in some cases. Thus they point out that if the operator T possesses the additional property that the dimension of the eigenspace at ω is 1 for all ω Ω then the map ω ker(T - ω) admits a non-zero holomorphic section, say γ, and therefore defines a line bundle on Ω. As is well known, the curvature defined by the formula is a complete invariant for the line bundle . On the other hand, define
and note that NT (ω)2 = 0. It follows that if T is unitarily equivalent to T˜, then the corresponding operators NT (ω) and NT˜(ω) are unitarily equivalent for all ω Ω. However, Cowen and Douglas prove the non-trivial converse, namely that if NT (ω) and NT˜(ω) are unitarily equivalent for all ω Ω then T and T˜ are unitarily equivalent. What does this have to do with the line bundles and .To answer this question, we must ask what is a complete invariant for the unitary equivalence class of the operator NT (ω). To find such a complete invariant we represent NT (ω) with respect to the orthonormal basis obtained from the two linearly independent vectors γ(ω),∂γ(ω) by Gram-Schmidt orthonormalization process. Then an easy computation shows that It then follows that is a complete invariant for NT (ω), ω Ω. This explains the relationship between the line bundle and the operator T in an explicit manner.
Subsequently, in the paper ”Operators Possesing an Open Set of Eigenvalues”, Cowen and Douglas define a class of commuting operators possessing an open set of eigenvalues and attempt to provide similar computations as above. However, they give the details only for a pair of commuting operators. While the results of that paper remain true in the case of an arbitrary n tuple of commuting operators, it requires additional effort which we explain in this thesis.2014-03-02T18:30:00Z