Why and How to Implement Worked Examples in Upper Division Theoretical Physics

Studying worked examples has been shown by extensive research to be an effective method for learning to solve well-structured problems in physics and mathematics. The effectiveness of learning with worked examples has been demonstrated and documented in many research projects. In this work, we propose a new four-step approach for teaching with worked examples that includes writing explanations and finding and correcting errors. This teaching method can even be implemented in courses in which homework performance constitutes part of the grading system. This four-step approach is illustrated in the context of Lagrangian mechanics, which is ideal for the application of worked examples due to its universal approach to solve problems

Cryogenic Q-factor measurement of optical substrates for optimization of gravitational wave detectors

Future generations of gravitational wave interferometers are likely to be operated at cryogenic temperatures because one of the sensitivity limiting factors of the present generation is the thermal noise of end mirrors and beam splitters that occurs in the optical substrates as well as in the dielectric coatings. A possible method for minimizing thermal noise is cooling to cryogenic temperatures, maximizing the mechanical quality factor Q, and maximizing the eigenfrequencies of the substrate. We present experimental details of a new cryogenic apparatus that is suitable for the measurement of the temperature-dependent Q-factor of reflective, transmissive as well as nano-structured grating optics down to 5 K. In particular, the SQUID-based and the optical interferometric approaches to the measurement of the amplitude of vibrating test bodies are compared and the method of ring-down recording is described

Energy as a source of pre-service teachers' conceptions about radioactivity

Although researchers have extensively studied student conceptions of radioactivity, the conceptions held by pre-service teachers on this subject are largely absent from the literature. We conducted a qualitative content analysis of problem-centered interviews with pre-service teachers N = 13 to establish which conceptions are held by pre-service teachers and to examine these conceptions' structure in coordination classes. As has already been observed in students, some pre-service teachers inadequately differentiate between radioactive matter and ionizing radiation and between fission and decay. We also observed that pre-service teachers tend to describe the activation of materials due to ionizing radiation despite having previously denied an activation, thus showing that the conception of activation of materials can reemerge in particular framings. Within the interviews conducted, the concept of energy emerged as a central coordination class regarding radioactivity. This coordination class appeared across contexts and proved fruitful in explaining pre-service teachers' conceptions about radioactivity. We will use the results from this study to develop a teaching-learning laboratory for pre-service teachers in which they can actively study high school students' conceptions while reflecting on their own. In this way, these findings will contribute to improving the structure of nuclear physics courses at the university.Comment: accepted by Physical Review Physics Education Research (PRPER

Kryogene Gütemessung an optischen Substratmaterialien für zukünftige Gravitationswellendetektoren

Die vorliegende Arbeit befasst sich mit der Reduktion des thermischen Rauschens optischer Komponenenten für Gravitationswellendetektoren. Thermisches Rauschen stellt den Prozess dar, der aktuellen Detektoren in ihrer Empfindlichkeit limitiert. Durch den Einsatz tiefer Temperaturen und Materialien mit einer hohen mechanischen Güte, lässt sich das thermische Rauschen reduzieren. Kernpunkt der Arbeit ist der Aufbau eines neuartigen Messsystems für die experimentelle Untersuchung der Temperaturabhängigkeit der mechanischen Güte

Birefringence Measurements on Crystalline Silicon

Crystalline silicon has been proposed as a new test mass material in third generation gravitational wave detectors such as the Einstein Telescope (ET). Birefringence can reduce the interferometric contrast and can produce dynamical disturbances in interferometers. In this work we use the method of polarisation-dependent resonance frequency analysis of Fabry-Perot-cavities containing silicon as a birefringent medium. Our measurements show a birefringence of silicon along the (111) axis of the order of $\Delta\, n \approx 10^{-7}$ at a laser wavelength of 1550nm and room temperature. A model is presented that explains the results of different settings of our measurements as a superposition of elastic strains caused by external stresses in the sample and plastic strains possibly generated during the production process. An application of our theory on the proposed ET test mass geometry suggests no critical effect on birefringence due to elastic strains.Comment: 19 pages, 6 figures, 2 table

Mechanical losses in low loss materials studied by Cryogenic Resonant Acoustic spectroscopy of bulk materials (CRA spectroscopy)

Mechanical losses of crystalline silicon and calcium fluoride have been analyzed in the temperature range from 5 to 300 K by our novel mechanical spectroscopy method, cryogenic resonant acoustic spectroscopy of bulk materials (CRA spectrocopy). The focus lies on the interpretation of the measured data according to phonon-phonon interactions and defect induced losses in consideration of the excited mode shape.Comment: 4 pages, 4 figures, proceedings of the PHONONS 2007, submitted to Journal of Physics: Conference Serie

Mechanical loss of a hydroxide catalysis bond between sapphire substrates and its effect on the sensitivity of future gravitational wave detectors

Hydroxide catalysis bonds are low mechanical loss joints which are used in the fused silica mirror suspensions of current room temperature interferometric gravitational wave detectors, one of the techniques which was essential to allow the recent detection of gravitational radiation by LIGO. More sensitive detectors may require cryogenic techniques with sapphire as a candidate mirror and suspension material, and thus hydroxide catalysis bonds are under consideration for jointing sapphire. This paper presents the first measurements of the mechanical loss of such a bond created between sapphire substrates and measured down to cryogenic temperatures. The mechanical loss is found to be 0.03±0.01 at room temperature, decreasing to (3±1)×10−4 at 20 K. The resulting thermal noise of the bonds on several possible mirror suspensions is presented

Potential mechanical loss mechanisms in bulk materials for future gravitational wave detectors

Low mechanical loss materials are needed to further decrease thermal noise in upcoming gravitational wave detectors. We present an analysis of the contribution of Akhieser and thermoelastic damping on the experimental results of resonant mechanical loss measurements. The combination of both processes allows the fit of the experimental data of quartz in the low temperature region (10 K to 25 K). A fully anisotropic numerical calculation over a wide temperature range (10 K to 300 K) reveals, that thermoelastic damping is not a dominant noise source in bulk silicon samples. The anisotropic numerical calculation is sucessfully applied to the estimate of thermoelastic noise of an advanced LIGO sized silicon test mass.Comment: 7 pages, 3 figures, submitted to Journal of Physics: Conference Series (AMALDI8