Towards the higher point holographic momentum space amplitudes

In this paper, we calculate higher point tree level vector amplitudes propagating in AdS$_4$. We use bulk perturbation theory to compute tree level Witten diagrams. We show that when these amplitudes are written in momentum space, they reduce to relatively simple expressions. We explicitly compute four and five point correlators and also sketch a general strategy to compute the full six-point correlators.Comment: 20 pages, 6 figures, minor typos corrected, journal versio

Studies on the foraging behaviour of damselfly larvae (Odonata; Zygoptera)

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Synthesis, Structural and Magnetic Properties of Copper Doped Cerium Oxide Nanoparticles

In this thesis, synthesis, structural and magnetic properties of the undoped and copper doped cerium oxide nanoparticles have been investigated. The nanoparticles were prepared by sol-gel preparation method. Undoped samples were prepared with different particles sizes by annealing the as-prepared sample at different temperatures Ta = 200°C, 400°C, 550°C, 700°C, 800°C. The particle size varied from 3 nm to 42 nm with increasing annealing temperatures. Copper was doped into CeO2 by annealing the samples at 400°C in ultra high pure nitrogen. The nominal percentages of copper in doped cerium oxide were 2.5%, 5%, 7.5% and 10%.;Structural characterization of the nanoparticles was done using transmission electron microscope (TEM) and x-ray diffraction (XRD). Inductive coupled plasma optical emission spectroscopy was done to detect the impurity concentrations of Iron (Fe) which was found to be present in ppm levels. The nano-particles were found to be nearly spherical in shape in both undoped and doped samples. The particle sizes in undoped samples were found to be increasing with increase in annealing temperatures. As all the copper doped samples were annealed at same temperatures, they were all in the 5 nm size range. The particle size values from XRD and TEM were comparable. Lattice constant and the strain in undoped CeO2 nanoparticles was found to decrease with increase in particle size. In Cu-doped CeO2, lattice constant was increasing with increase in doping concentration levels.;Magnetic properties of these nanoparticles were measured using a superconducting quantum interface device (SQUID) magnetometer. Susceptibility and hysteresis loops plots were plotted using magnetization data from SQUID. Increasing paramagnetism was found with decreasing particle size in the undoped samples which is attributed to increase in Ce3+ concentration. The small amount of ferromagnetism found in the undoped samples is suggested to originate from the Fe present in ppm levels. In Cu-doped CeO2 nanoparticles, the paramagnetic and ferromagnetic parts were found to be increasing with increase in doping concentration of Cu in CeO2. The observed room temperature ferromagnetism in Cu-doped CeO2 is suggested to result from the effects of copper doping

SCATTERING AMPLITUDES IN FLAT SPACE AND ANTI-DE SITTER SPACE

We calculate gauge theory one-loop amplitudes with the aid of the complex shift used in the Britto- Cachazo-Feng-Witten (BCFW) recursion relations of tree amplitudes. We apply the shift to the integrand and show that the contribution from the limit of infinite shift vanishes after integrating over the loop momentum, with a judicious choice of basis for polarization vectors. This enables us to write the one-loop amplitude in terms of on-shell tree and lower-point one-loop amplitudes. Some of the tree amplitudes are forward amplitudes. We show that their potential singularities do not contribute and the BCFW recursion relations can be applied in such a way as to avoid these singularities altogether. We calculate in detail n-point one-loop amplitudes for n = 2, 3, 4, and outline the generalization of our method to n \u3e 4. In addition to scattering amplitudes in flat space, we studied amplitudes in Antide Sitter (AdS) space, which is equivalent to conformal correlators in the boundary of the Anti-de Sitter space. We discuss the use of the embedding formalism and Mellin transform in the calculation of tree-level correlators of scalar and vector fields in AdS/CFT. We present an iterative procedure that builds amplitudes by sewing together lower-point off-shell diagrams. Both scalar and vector correlators are shown to be given in terms of Mellin amplitudes. We apply the procedure to the explicit calculation of three-, four- and five-point correlators

Fabrication of Nanoelectrode Arrays for Dopamine Detection

Recent advancements in the semiconductor fabrication technologies have greatly helped in advancing the understanding of electrochemistry at nano scale (10-9 m). Electrodes are being produced at micro (10-6 m) and nano scale with varied materials, designs and for diverse applications. Better electrochemical sensing and detecting capabilities are achieved with nanoelectrodes in comparison with regular macroelectrodes. Lot of theoretical studies of electrochemistry at these nanoelectrodes have been proposed and developed. Despite the theoretical advancements, little has been done in experimental studies of nanoelectrodes. The progress is majorly impeded by lack of reliable fabrication procedures to produce such nanoelectrodes and test them experimentally.;The main goal of this thesis is to develop a new procedure to fabricate nanoelectrode arrays (NEA) for enhanced electrochemical detection. A large area gold NEA is fabricated using nanosphere lithography. The electrochemical advantages of the nanoelectrodes over macro electrodes such as better mass transport of analytes, independent diffusional domains, and faster chemical reaction rates are studied. The dimensions of the electrode are optimized to get the best possible electrochemical sensing capabilities. The optimized NEA is used as a biological sensor for detecting dopamine, a neurotransmitter, in presence of biological levels of ascorbic acid.;The optimized NEA geometry has shown an excellent ability to differentiate and detect the dopamine in presence of high levels of ascorbic acid. This is attributed to the enhanced mass transport of analytes and faster chemical reaction rates at the surface of the nanoelectrodes. Bare gold macroelectrode of similar exposed area has failed to differentiate the dopamine and ascorbic acid signals

Development of novel therapeutic approaches: (I) Targeting allergic responses to peanuts and (II) Inhibition of DPP-IV enzyme involved in diabetes

There is an increase in prevalence of peanut allergy, especially in the western world. The only current treatment for peanut allergy is avoidance of peanut from diet and contact. Additionally, there is currently no specific vaccine that can be taken to decrease peanut allergies. The method of desensitizing a person allergic to peanut allergy is deemed unsafe as the smallest amount of peanut can trigger an anaphylaxis reaction. Thus, various allergoids were created by modifying major peanut protein allergen Ara h2 using various cross-linkers and modification agents in order to disrupt the binding surface epitopes of the antigen to antibody. Diabetes is also a growing problem that affects millions of people globally. Having diabetes is known to lead to various morbidity as well which can be detrimental to the patient and a burden to the economy. Various drugs are available as monotherapy for diabetes; however, we aimed to develop dual acting compounds that would not only control type 2 diabetes but also commonly associated diagnosis of hypertension as well. Thus, we have successfully synthesized and tested compounds in vitro as effective dipeptidyl peptidase-IV (DPP-IV) inhibitors and potentially effective in treating hypertension (future study) associated with diabetes by utilizing cyanopyrrolidines and Beta-amino alcohols scaffolds in the structure, respectively