Poles in the SS-Matrix of Relativistic Chern-Simons Matter theories from Quantum Mechanics

An all orders formula for the $S$-matrix for 2 $\rightarrow$ 2 scattering in large N Chern-Simons theory coupled to a fundamental scalar has recently been conjectured. We find a scaling limit of the theory in which the pole in this $S$-matrix is near threshold. We argue that the theory must be well described by non-relativistic quantum mechanics in this limit, and determine the relevant Schroedinger equation. We demonstrate that the $S$-matrix obtained from this Schroedinger equation agrees perfectly with this scaling limit of the relativistic $S$-matrix; in particular the pole structures match exactly. We view this matching as a nontrivial consistency check of the conjectured field theory $S$-matrix.Comment: 12 pages, minor correction

Moisture Aided Degradation of Oil Impregnated Paper Insulation in Power Transformers

Transformers are the most expensive and critical asset in any electrical power network. Their failure results in long interruption of power supply with consequent loss of reliability and revenue. Understanding and detection of the failure mechanism helps in avoiding catastrophic failures, unplanned outages and improving the power system reliability. Oil impregnated paper (OIP) and pressboards form the main soild insulation in a transformer. Life of the transformer is governed mostly by the life of OIP insulation. Until recently, it was thought that ageing of the OIP insulation in power transformer and its eventual failure, is mainly a function of temperature and electrical stresses. However, it has now been realized that the moisture causes rapid degradation of OIP and needs a special attention. Considering its practical relevance, this research program was formulated with goals: (i) to study the ageing of OIP insulation under temperature and moisture stresses, (ii) to seek correlation between diagnostic ageing indices and end-of-life (EOL) and (iii) to develop a life model for OIP considering moisture along with the thermal stress. Observing that working with actual transformers or even the prototypes are rather inordinately expensive, experiments were conducted with paper strips immersed in oil in test tubes with paper to oil ratio kept same as that in power transformers. In order to cater for the statistical nature of the phenomena, adequate numbers of test specimens were employed (25 numbers for each experiment). Experiments were conducted for two years at temperatures 90°C, 110°C & 120°C and moisture 1%, 2% & 3%. Following the literature, the degree of polymerization (DP) was chosen as the primary index for ageing. As measurement of DP is not only destructive, but also impractical on most of the working transformers, with an aim to develop suitable diagnostic indices for ageing, 2-furfural (2-FAL) and oxides of carbon (CO and CO2) were also measured. Empirical relation between ageing and amount of stresses and time have been deduced for the relevant range. Limiting value of these indices to prescribe the end-of-life, as well as, their correlation with DP have been worked out and reported. In order to bring the role of moisture explicitly, based on earlier work on multi-stress ageing, a multiplicative power law supplementing the Arrhenius factor is envisaged. Accordingly, a phenomenological combined stress model involving the time to failure, temperature, and moisture content is deduced. Based on the experimental results, this model is statistically validated and the values of parameters appearing in the model is obtained. Thus the combined stress model enables one to estimate the life of OIP insulation at any temperature and moisture under synergy. In summary, this work through experimental and analytical approach has contributed to the evaluation of the aging of OIP insulation used in power transformers under the combined action of moisture and temperature

પ્રાથમિક શિક્ષણ પર જિલ્લા શિક્ષણ અને તાલીમ ભવનોની અસરકારક્તા

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Unitarity, Crossing Symmetry and Duality of the S-matrix in large N Chern-Simons theories with fundamental matter

We present explicit computations and conjectures for $2 \to 2$ scattering matrices in large $N$ {\it $U(N)$} Chern-Simons theories coupled to fundamental bosonic or fermionic matter to all orders in the 't Hooft coupling expansion. The bosonic and fermionic S-matrices map to each other under the recently conjectured Bose-Fermi duality after a level-rank transposition. The S-matrices presented in this paper may be regarded as relativistic generalization of Aharonov-Bohm scattering. They have unusual structural features: they include a non analytic piece localized on forward scattering, and obey modified crossing symmetry rules. We conjecture that these unusual features are properties of S-matrices in all Chern-Simons matter theories. The S-matrix in one of the exchange channels in our paper has an anyonic character; the parameter map of the conjectured Bose-Fermi duality may be derived by equating the anyonic phase in the bosonic and fermionic theories.Comment: 66 pages+ 45 pages appendices, 20 figures, Few typos corrected and few references adde

Currents and Radiation from the large DD Black Hole Membrane

It has recently been demonstrated that black hole dynamics in a large number of dimensions $D$ reduces to the dynamics of a codimension one membrane propagating in flat space. In this paper we define a stress tensor and charge current on this membrane and explicitly determine these currents at low orders in the expansion in $\frac{1}{D}$. We demonstrate that dynamical membrane equations of motion derived in earlier work are simply conservation equations for our stress tensor and charge current. Through the paper we focus on solutions of the membrane equations which vary on a time scale of order unity. Even though the charge current and stress tensor are not parametrically small in such solutions, we show that the radiation sourced by the corresponding membrane currents is generically of order $\frac{1}{D^D}$. In this regime it follows that the `near horizon' membrane degrees of freedom are decoupled from asymptotic flat space at every perturbative order in the $\frac{1}{D}$ expansion. We also define an entropy current on the membrane and use the Hawking area theorem to demonstrate that the divergence of the entropy current is point wise non negative. We view this result as a local form of the second law of thermodynamics for membrane motion.Comment: 104 pages plus 69 pages appendix, 1 figure, Minor correction