etd@IISc Community:http://hdl.handle.net/2005/62016-01-29T06:35:21Z2016-01-29T06:35:21ZElasticity And Structural Phase Transitions Of Nanoscale ObjectsMogurampelly, Santoshhttp://hdl.handle.net/2005/24982015-12-14T10:17:11Z2015-12-13T18:30:00ZTitle: Elasticity And Structural Phase Transitions Of Nanoscale Objects
Authors: Mogurampelly, Santosh
Abstract: Elastic properties of carbon nanotubes (CNT), boron nitride nanotubes (BNNT), double stranded DNA (dsDNA), paranemic-juxtapose crossover (PX-JX) DNA and dendrimer bound DNA are discussed in this thesis. Structural phase transitions of nucleic acids induced by external force, carbon nanotubes and graphene substrate are also studied extensively. Electrostatic interactions have a strong effect on the elastic properties of BNNTs due to large partial atomic charges on boron and nitrogen atoms. We have computed Young’s modulus (Y ) and shear modulus (G) of BNNT and CNT as a function of the nanotube radius and partial atomic charges on boron and nitrogen atoms using molecular mechanics calculation. Our calculation shows that Young’s modulus of BNNTs increases with increase in magnitude of the partial atomic charges on B and N atoms and can be larger than the Young’s modulus of CNTs of same radius. Shear modulus, on the other hand depends weakly on the magnitude of partial atomic charges and is always less than the shear modulus of the CNT. The values obtained for Young’s modulus and shear modulus are in excellent agreement with the available experimental results. We also study the elasticity of dsDNA using equilibrium fluctuation methods as well as nonequilibrium stretching simulations. The results obtained from both methods quantitatively agree with each other. The end-to-end length distribution P(ρ) and angle distribution P(θ) of the dsDNA has a Gaussian form which gives stretch modulus (γ1) to be 708 pN and persistence length (Lp) to be 42 nm, respectively. When dsDNA is stretched along its helix axis, it undergoes a large conformational change and elongates about 1.7 times its initial contour length at a critical force. Applying a force perpendicular to the DNA helix axis, dsDNA gets unzipped and separated into two single-stranded DNA (ssDNA). DNA unzipping is a fundamental process in DNA replication. As the force at one end of the DNA is increased the DNA starts melting above a critical force depending on the pulling direction. The critical force fm , at which dsDNA melts completely decreases as the temperature of the system is increased. The melting force in the case of unzipping is smaller compared to the melting force when the dsDNA is pulled along the helical axis. In the case of melting through unzipping, the double-strand separation has jumps which correspond to the different energy minima arising due to sequence of different base-pairs. Similar force-extension curve has also been observed when crossover DNA molecules are stretched along the helix axis. In the presence of mono-valent Na+ counterions, we find that the stretch modulus (γ1 ) of the paranemic crossover (PX) and its topoisomer juxtapose (JX) DNA structure is significantly higher (30 %) compared to normal B-DNA of the same sequence and length. When the DNA motif is surrounded by a solvent of divalent Mg2+ counterions, we find an enhanced rigidity compared to in Na+ environment due to the electrostatic screening effects arising from the divalent nature of Mg2+ counterions. This is the first direct determination of the mechanical strength of these crossover motifs which can be useful for the design of suitable DNA motifs for DNA based nanostructures and nanomechanical devices with improved structural rigidity. Negatively charged DNA can be compacted by positively charged dendrimer and the degree of compaction is a delicate balance between the strength of the electrostatic interaction and the elasticity of DNA. When the dsDNA is compacted by dendrimer, the stretch modulus, γ1 and persistence length, Lp decreases dramatically due to backbone charge neutralization of dsDNA by dendrimer. We also study the effect of CNT and graphene substrate on the elastic as well as adsorption properties of small interfering RNA (siRNA) and dsDNA. Our results show that siRNA strongly binds to CNT and graphene surface via unzipping its base-pairs and the propensity of unzipping increases with the increase in the diameter of the CNTs and is maximum on graphene. The unzipping and subsequent wrapping events are initiated and driven by van der Waals interactions between the aromatic rings of siRNA nucleobases and the CNT/graphene surface. However, dsDNA of the same sequence undergoes much less unzipping and wrapping on the CNT/graphene due to smaller interaction energy of thymidine of dsDNA with the CNT/graphene compared to that of uridine of siRNA. Unzipping probability distributions fitted to single exponential function give unzipping time (τ) of the order of few nanoseconds which decrease exponentially with temperature. From the temperature variation of unzipping time we estimate the free energy barrier to unzipping. We have also investigated the binding of siRNA to CNT by translocating siRNA inside CNT and find that siRNA spontaneously translocates inside CNT of various diameters and chiralities. Free en- ergy profiles show that siRNA gains free energy while translocating inside CNT and the barrier for siRNA exit from CNT ranges from 40 to 110 kcal/mol depending on CNT chirality and salt concentration. The translocation time τ decreases with the increase of CNT diameter having a critical diameter of 24 A for the translocation. After the optimal binding of siRNA to CNT/graphene, the complex is very stable which can serve as siRNA delivery agent for biomedical applications. Since siRNA has to undergo unwinding process in the presence of RNA-induced silencing complex, our proposed delivery mechanism by single wall CNT possesses potential advantages in achieving RNA interference (RNAi).2015-12-13T18:30:00ZRiesz Transforms Associated With Heisenberg Groups And Grushin OperatorsSanjay, P Khttp://hdl.handle.net/2005/24962015-12-08T10:07:31Z2015-12-07T18:30:00ZTitle: Riesz Transforms Associated With Heisenberg Groups And Grushin Operators
Authors: Sanjay, P K
Abstract: We characterise the higher order Riesz transforms on the Heisenberg group and also show that they satisfy dimension-free bounds under some assumptions on the multipliers. We also prove the boundedness of the higher order Riesz transforms associated to the Hermite operator. Using transference theorems, we deduce boundedness theorems for Riesz transforms on the reduced Heisenberg group and hence also for the Riesz transforms associated to special Hermite and Laguerre expansions.
Next we study the Riesz transforms associated to the Grushin operator G = - Δ - |x|2@t2 on Rn+1. We prove that both the first order and higher order Riesz transforms are bounded on Lp(Rn+1): We also prove that norms of the first order Riesz transforms are independent of the dimension n.2015-12-07T18:30:00ZStudies On Bayesian Approaches To Image Restoration And Super Resolution Image ReconstructionChandra Mohan, Shttp://hdl.handle.net/2005/24902015-11-24T07:20:14Z2015-11-23T18:30:00ZTitle: Studies On Bayesian Approaches To Image Restoration And Super Resolution Image Reconstruction
Authors: Chandra Mohan, S
Abstract: High quality image /video has become an integral part in our day-to-day life ranging from many areas of science, engineering and medical diagnosis. All these imaging applications call for high resolution, properly focused and crisp images. However, in real situations obtaining such a high quality image is expensive, and in some cases it is not practical. In imaging systems such as digital camera, blur and noise degrade the image quality. The recorded images look blurred, noisy and unable to resolve the finer details of the scene, which are clearly notable under zoomed conditions. The post processing techniques based on computational methods extract the hidden information and thereby improve the quality of the captured images.
The study in this thesis focuses on deconvolution and eventually blind de-convolution problem of a single frame captured at low light imaging conditions arising from digital photography/surveillance imaging applications. Our intention is to restore a sharp image from its blurred and noisy observation, when the blur is completely known/unknown and such inverse problems are ill-posed/twice ill-posed. This thesis consists of two major parts. The first part addresses deconvolution/blind deconvolution problem using Bayesian approach with fuzzy logic based gradient potential as a prior functional.
In comparison with analog cameras, artifacts are visible in digital cameras when the images are enlarged and there is a demand to enhance the resolution. The increased resolution can be in spatial, temporal or even in both the dimensions. Super resolution reconstruction methods reconstruct images/video containing spectral information beyond that is available in the captured low resolution images. The second part of the thesis addresses resolution enhancement of observed monochromatic/color images using multiple frames of the same scene. This reconstruction problem is formulated in Bayesian domain with an aspiration of reducing blur, noise, aliasing and increasing the spatial resolution. The image is modeled as Markov random field and a fuzzy logic filter based gradient potential is used to differentiate between edge and noisy pixels. Suitable priors are adaptively applied to obtain artifact free/reduced images.
In this work, all our approaches are experimentally validated using standard test images. The Matlab based programming tools are used for carrying out the validation. The performance of the approaches are qualitatively compared with results of recently proposed methods. Our results turn out to be visually pleasing and quantitatively competitive.2015-11-23T18:30:00ZStudies Of Electronic, Magnetic And Entanglement Properties Of Correlated Models In Low-Dimensional SystemsSahoo, Shaonhttp://hdl.handle.net/2005/24802015-09-04T09:41:54Z2015-09-03T18:30:00ZTitle: Studies Of Electronic, Magnetic And Entanglement Properties Of Correlated Models In Low-Dimensional Systems
Authors: Sahoo, Shaon
Abstract: This thesis consists of six chapters. The first chapter gives an introduction to the field of low-dimensional magnetic and electronic systems and relevant numerical techniques. The recent developments in molecular magnets are highlighted. The numerical techniques are reviewed along with their advantages and disadvantages from the present perspective. Study of entanglement of a system can give a great insight into the system. At the last part of this chapter a general overview is given regarding entanglement, its measures and its significance in studying many-body systems.
Chapter 2 deals with the technique that has been developed by us for the full symmetry adaptation of non-relativistic Hamiltonians. It is advantageous both computationally and physically/chemically to exploit both spin and spatial symmetries of a system. It has been a long-standing problem to target a state which has definite total spin and also belongs to a definite irreducible representation of a point group, particularly for non-Abelian point groups. A very general technique is discussed in this chapter which is a hybrid method based on valence-bond basis and the basis of the z-component of the total spin. This technique is not only applicable to a system with arbitrary site spins and belonging to any point group symmetry, it is also quite easy to implement computationally. To demonstrate the power of the method, it is applied to the molecular magnetic system, Cu6Fe8, with cubic symmetry.
In chapter 3, the extension of the previous hybrid technique to electronic systems is discussed. The power of the method is illustrated by applying it to a model icosahedral half-filled electronic system. This model spans a huge Hilbert space (dimension 1,778,966) and is in the largest non-Abelian point group. All the eigenstates of the model are obtained using our technique.
Chapter 4 deals with the thermodynamic properties of an important class of single-chain magnets (SCMs). This class of SCMs has alternate isotropic spin-1/2 units and anisotropic high spin units with the anisotropy axes being non-collinear. Here anisotropy is assumed to be large and negative, as a result, anisotropic units behave like canted spins at low temperatures; but even then simple Ising-type model does not capture the essential physics of the system due to quantum mechanical nature of the isotropic units. A transfer matrix (TM) method is developed to study statistical behavior of this class of SCMs. For the first time, it is also discussed in detail that how weak inter-chain interactions can be treated by a TM method. The finite size effect is also discussed which becomes important for low temperature dynamics. This technique is applied to a real helical chain magnet, which has been studied experimentally.
In the fifth chapter a bipartite entanglement entropy of finite systems is studied using exact diagonalization techniques to examine how the entanglement changes in the presence of long-range interactions. The PariserParrPople model with long-range interactions is used for this purpose and corresponding results are com-pared with those for the Hubbard and Heisenberg models with short-range interactions. This study helps understand why the density matrix renormalization group (DMRG) technique is so successful even in the presence of long-range interactions in the PPP model. It is also investigated if the symmetry properties of a state vector have any significance in relation to its entanglement. Finally, an interesting observation is made on the entanglement profiles of different states, across the full energy spectrum, in comparison with the corresponding profile of the density of states.
The entanglement can be localized between two noncomplementary parts of a many-body system by performing local measurements on the rest of the system. This localized entanglement (LE) depends on the chosen basis set of measurement (BSM). In this chapter six, an optimality condition for the LE is derived, which would be helpful in finding optimal values of the LE, besides, can also be of use in studying mixed states of a general bipartite system. A canonical way of localizing entanglement is further discussed, where the BSM is not chosen arbitrarily, rather, is fully determined by the properties of a system. The LE obtained in this way, called the localized entanglement by canonical measurement (LECM), is not only easy to calculate practically, it provides a nice way to define the entanglement length. For spin-1/2 systems, the LECM is shown to be optimal in some important cases. At the end of this chapter, some numerical results are presented for j1 −j2 spin model to demonstrate how the LECM behaves.2015-09-03T18:30:00Z