N=1 SUSY Conformal Block Recursive Relations

We present explicit recursive relations for the four-point superconformal block functions that are essentially particular contributions of the given conformal class to the four-point correlation function. The approach is based on the analytic properties of the superconformal blocks as functions of the conformal dimensions and the central charge of the superconformal algebra. The results are compared with the explicit analytic expressions obtained for special parameter values corresponding to the truncated operator product expansion. These recursive relations are an efficient tool for numerically studying the four-point correlation function in Super Conformal Field Theory in the framework of the bootstrap approach, similar to that in the case of the purely conformal symmetry.Comment: 12 pages, typos corrected, reference adde

Structure Constants and Conformal Bootstrap in Liouville Field Theory

An analytic expression is proposed for the three-point function of the exponential fields in the Liouville field theory on a sphere. In the classical limit it coincides with what the classical Liouville theory predicts. Using this function as the structure constant of the operator algebra we construct the four-point function of the exponential fields and verify numerically that it satisfies the conformal bootstrap equations, i.e., that the operator algebra thus defined is associative. We consider also the Liouville reflection amplitude which follows explicitly from the structure constants.Comment: 31 pages, 2 Postscript figures. Important note about existing (but unfortunately previously unknown to us) paper which has significant overlap with this work is adde

Detection of water leakage in buried pipes using infrared technology; a comparative study of using high and low resolution infrared cameras for evaluating distant remote detection

Water is one of the most precious commodities around the world. However, significant amount of water is lost daily in many countries through broken and leaking pipes. This paper investigates the use of low and high resolution infrared systems to detect water leakage in relatively dry countries. The overall aim is to develop a non-contact and high speed system that could be used to detect leakage in pipes remotely via the effect of the change in humidity on the temperature of the ground due to evaporation. A small scale experimental test rig has been constructed to simulate water leakage in The Great Man- Made River Project in Libya, taking into consideration the dryness level of the desert sand and the scaled dimensions of the system. The results show that the infrared technology is an effective technology in detecting water leakage in pipes. The low resolution system has been found as valuable as the high resolution system in detecting water leakage. The results indicate the possibility of distant remote detection of leakage in water systems using infrared technologies which could be mobilised using drones, helium balloons, aeroplanes or other similar technologies

The design and development of an innovative simulator for an open loop system for extracting energy from flooded coal mines

Water source heat pumps, in comparison to air-to-air heat pumps, have significant advantage for heating or cooling applications due to the relatively regulated temperature of most water resources. In the UK, similar to many other countries, disused coal mines have untapped potential for low cost green energy due to the flooding of coal mines with water at reasonable warm temperature due to the availability of geothermal energy at different depths. This allows to use water source heat pumps in locations away from rivers and seas for heating and cooling applications. Extracting energy from flooded coal mines using water heat pumps with open loop systems is still relatively a new concept, but can provide much heating capacity due to eliminating the time needed for heat transfer between the external environment and the heating loop in case of closed loop systems. The use of real systems to conduct research could be an expensive task or impractical to users of the application such as the residents of the served building. On the other hand, computer simulation includes significant assumptions that might not be accurate in many real situations. In this paper, the authors have developed a small scale simulator to help in understanding such energy systems and to conduct research in this field for the benefit of researchers, educators and students within the applied and renewable energy field. The paper describes the detailed design, the complete prototype and initial assessment of the system using infrared thermography and temperature monitoring. The results show that the system has been found successful in conveying the concept of extracting energy from coal mines and to characterize the general performance

An innovative design and evaluation of a stratified hot water storage system - the Water Snake

The increase in energy prices and the demand to reduce carbon emission is attracting the attention to the implementation of diverse heating technologies such as heat pumps, solar energy, gas boilers, CHP and electric heaters. Heating applications for integrated technologies include district heating, domestic small scale applications and commercial large scale buildings. Thermal storage is likely to become key to energy efficient heating. A stratified hot water tank will play an important role in the integration of several heating technologies that operate efficiently at different level of temperatures with reduced implementation cost. This paper describes the concept and the assessment of the ‘Water Snake’, a novel low cost concept of a stratified hot water tank. The results show that the new concept could provide efficient stratification at a very low cost using this invention

Differential equation for four-point correlation function in Liouville field theory and elliptic four-point conformal blocks

Liouville field theory on a sphere is considered. We explicitly derive a differential equation for four-point correlation functions with one degenerate field $V_{-\frac{mb}{2}}$. We introduce and study also a class of four-point conformal blocks which can be calculated exactly and represented by finite dimensional integrals of elliptic theta-functions for arbitrary intermediate dimension. We study also the bootstrap equations for these conformal blocks and derive integral representations for corresponding four-point correlation functions. A relation between the one-point correlation function of a primary field on a torus and a special four-point correlation function on a sphere is proposed