MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

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

Vývoj a aplikace molekulové dynamiky pro molekulovou spektroskopii

This Thesis deals with simulations of chiroptical spectra using a combination of molecular dynamics and quantum chemistry. Molecular dynamics was used to explore conformational behaviour of studied systems (proteins), quantum chemistry for calculation of spectral prop- erties. The Quantum chemical methods are limited to relatively small systems. We overcome this problem mostly by a fragmentation of studied systems, when smaller, computationally feasible, fragments are created and used for the quantum chemical calculations. Calculated properties were then transferred to the big molecule. Vibrational Optical Activity (VOA) spectra of poly-L-glutamic acid fibrils (PLGA), insulin prefibrillar form and native globular proteins were studied. The simulated spectra provided satisfactory agreement with the experiment and were used for its interpretation. Experimental Vibrational Circular Dichroism (VCD) spectra of poly-L-glutamic acid fibrils were only qualitatively reproduced by the simulation. We could reproduce the major amide I band and a smaller negative band associated with the side chain carboxyl group. Our simulation procedure was then extended to a set of globular proteins and their Raman Optical Activity (ROA) spectra. Here we achieved an exceptional precision. For example, we were able to reproduce...Katedra fyzikální a makromol. chemieDepartment of Physical and Macromolecular ChemistryFaculty of SciencePřírodovědecká fakult