Integrability, Recursion Operators and Soliton Interactions

This volume contains selected papers based on the talks,presented at the Conference "Integrability, Recursion Operators and Soliton Interactions", held in Sofia, Bulgaria (29 - 31 August 2012) at the Institute for Nuclear Research and Nuclear Energy of the Bulgarian Academy of Sciences. Included are also invited papers presenting new research developments in the thematic area. The Conference was dedicated to the 65-th birthday of our esteemed colleague and friend Vladimir Gerdjikov. The event brought together more than 30 scientists, from 6 European countries to celebrate Vladimir's scientific achievements. All participants enjoyed a variety of excellent talks in a friendly and stimulating atmosphere. The main topics of the conference were those where Vladimir has contributed enormously during his career: integrable nonlinear partial differential equations, underlying algebraic and geometric structures of the integrable systems, soliton solutions, soliton interactions, quantum integrable systems, discrete integrable systems and applications of the nonlinear models. The papers, included in this volume will be useful to researchers with interests in these areas

The development of a heterodyne receiver at 10.7 THz for the observation of molecular hydrogen

The focus of this thesis is the development of a superconducting hot electron bolometer(HEB) mixer intended for the operation as a heterodyne receiver for the observation of the electric quadrupole transition of molecular hydrogen in space at 10.7 THz. The developed detector is based on a quasi-optical receiver concept using a lens to couple the RF-signal to an antenna. The mixing element is a phonon-cooled niobium nitride microbridge that is integrated in the center of the antenna. The detector consists of a copper tellurium detector block containing the IF-board and IF-connector and the HEB-device glued to the flat backside of the silicon lens. The HEB-device is a circular RF-chip based on a 9 μm thick silicon carrier membrane with the RF-circuit structures and integrated HEB-element on its upper side. For the development of the RF-circuits the dielectric properties of the carrier substrate that consists of high resistivity float zone silicon (HRFZ Si) have been determined since the data available is insufficient for this high frequency range at cryogenic temperatures. The dielectric properties were investigated by means of transmission measurements of different plane parallel silicon samples with two Fourier Transform Spectrometers (FTS) within a frequency range from 4 THz to 18 THz for temperatures between 5 K to 300 K. The measured refractive index increases less than 0.002 with frequency within a frequency interval of 12 THz. From 300 K to 5 K it is reduced by 0.83 % in average. The absorption coefficient of HRFZ Si roughly decreases by 35 % from 300 K to 5 K. The determined permittivity of the carrier substrate at cryogenic operating temperatures of the receiver is 11.4(±0.1). In total 20 different designs of RF-circuits have been developed and fabricated on one wafer by E-beam and UV-lithography technology in the in-house microfabrication facility. The RF-circuits are based on three different broadband antennas and variations of a narrow-band antenna. One narrow-band and one broadband RF-circuit address an operating frequency around 4.7 THz instead of 10.7 THz to enable a comparison with the UpGreat receiver which has been developed in our research group. The broadband antennas are a self-complementary logarithmic, a logarithmic and an Archimedean spiral antenna. The narrow-band antenna is a double-slot antenna of a full effective wavelength in length that is attached to an RF-filter. To investigate the influence of the lens on the antenna beam of the 10.7 THz double-slot antennas a software has been developed and evaluated that is based on a spectral ray tracing technique because the available commercial CST software is not suitable for that task within the present resources and time constraints. According to numerical calculations the double-slot antenna out of the investigated antennas reaches the highest overall coupling efficiency. The predicted Gaussian coupling efficiency without considering losses within the gold layers is 49 % for the designed 4.7 THz double-slot antenna when being mounted at the backside of the silicon lens without an anti-reflection coating. From all broadband antennas the Archimedean spiral antenna that typically is used for distinct lower frequencies below 1 THz, is predicted to obtain the highest overall power coupling to a Gaussian beam of about 39.4 %. Applying an anti-reflection layer on the lens these Gaussian coupling efficiencies are expected to increase to about 64% and 57% for the double-slot antenna and for the Archimedean spiral antenna,respectively. In total five different RF-circuits have successfully been assembled in the detector block and used as an external power detector of an FTS to determine their spectral response within an interval from 3 THz to 12 THz. They are based on three narrow-band designs for 10.7 THz, one narrow-band design for 4.7 THz and a broadband circuit based on the Archimedean spiral antenna. The detectors with the double-slot antennas exhibit a distinct polarization-dependent sensitivity that is maximal at the dedicated polarization direction of the DS-antenna and vanishes for the polarization direction perpendicular to it. All assembled 10.7 THz narrow-band detectors show a response peak slightly below the intended operating frequency with deviations of the center frequencies less than 4 % to 8 %. The measured curves of the RF-response around the operating frequency agree well with the predicted curves of the coupling efficiency between the HEB-element and the antenna. The detector with the Archimedean spiral antenna shows a significant direct response over the entire frequency range from 3 THz to 12 THz. To our knowledge the Archimedean spiral antenna as well as the double-slot antenna till now so far are the only antennas designed for 10.7 THz that have been realized and verified as direct HEB power detectors. The measurement results confirm that these HEB-devices are suitable candidates for future heterodyne measurements. The local oscillator (LO) source that is needed to operate the detectors in heterodyne mode is a Quantum Cascade Laser developed by the Quantum Optoelectronics Group of the IQE, ETH Zurich, and has not yet been completed at the end of this work

Electromagnetic Wave Propagation for Industry and Biomedical Applications

This book highlights original research and high-quality technical briefs on electromagnetic wave propagation, radiation, and scattering, and their applications in industry and biomedical engineering. It also presents recent research achievements in the theoretical, computational, and experimental aspects of electromagnetic wave propagation, radiation, and scattering. The book is divided into three sections. Section 1 consists of chapters with general mathematical methods and approaches to the forward and inverse problems of wave propagation. Section 2 presents the problems of wave propagation in superconducting materials and porous media. Finally, Section 3 discusses various industry and biomedical applications of electromagnetic wave propagation, radiation, and scattering

The employment and wages policies in a socialist economy : The Egyptian economy since 1945.

The aim of this study is to solve numerically an infinite horizon optimum growth path and investigate the qualities of such a path. To do this, I surveyed the macroeconomic behaviour of the Egyptian economy over a limited period of time (1945-1965). Statistics on population, employment, wages, investment and production for the two main sectors in Egypt were analyzed with the view to establishing the production and consumption patterns in each sector. In both sectors, neo-classical production functions provided the framework for the available time series data on agricultural and industrial production. Under the assumptions of a constant exponential rate of growth of the population and constant rates of depreciation of the capital stocks in the sectors, the dynamic behaviour of the population and the capital stocks was determined. The rate of change of the proportion of labour in the urban sector was assumed to depend on the real wage differential between the two sectors and the size of the urban sector. This behavioural relationship turned out to be quite crucial in the determination of the optimum path. The index of performance chosen was that of a constant elasticity of utility functional. Although the utility function is convex in its main argument (consumption), the convexity of the utility functional subject to the dynamic constraints was difficult to establish through either analytic or numerical methods. Consequently any computed optimum path was provisionally assumed to be a local one. The final optimum path was obtained by repeated computations. The methods used for the main computations are fully explained in a technical chapter and the Appendix. The importance of computation errors and the problem of numerical stability of the solutions are fully explored. The Optimum path was surprising in many aspects: 1. Initial high rates of savings in the agricultural and the urban sectors. 2. The agricultural sector was virtually depleted of all its labour force within the first fourteen years. During this period urban capital reached its peak and agricultural capital its apogee. 3. A reversal of the early trend occured 30 years after the start of the program. This meant that agricultural capital was rebuilt, and labour flowed back into agriculture. 4. The effect of increasing the gross rate of discount was to render the optimization inoperative after 40 years. In the short run, increasing the discount rate reduced slightly the rates of savings in both sectors. The basic model was extended to cover two possible aspects of Government expenditure policies on education and their effects on the rate of unemployment in the urban sector. Labour in agriculture was assumed to be fixed. The net result was to shift the savings burden on to the urban sector where the initial rate was up to 80% of urban output. Part of the urban savings was used to build up agricultural capital. Finally an attempt was made to compare the optimum path with the actual path for the first 20 years of the program. The actual path was found to be closer to the optimum path of the second model than the first