BAO Extractor: bias and redshift space effects

We study a new procedure to measure the sound horizon scale via Baryonic Acoustic Oscillations (BAO). Instead of fitting the measured power spectrum (PS) to a theoretical model containing the cosmological informations and all the nonlinear effects, we define a procedure to project out (or to "extract") the oscillating component from a given nonlinear PS. We show that the BAO scale extracted in this way is extremely robust and, moreover, can be reproduced by simple theoretical models at any redshift. By using N-body simulations, we discuss the effect of the nonlinear evolution of the matter field, of redshift space distortions and of scale-dependent halo bias, showing that all these effects can be reproduced with sub-percent accuracy. We give a one-parameter theoretical model based on a simple (IR) modification of 1-loop perturbation theory, which reproduces the BAO scale from measurements of halo clustering in redshift space at better than $0.1\%$ level and does not need any external UV input, such as coefficients measured from N-body simulations.Comment: Published version. 32 pages, 15 figure

Non-linear conductivity of charge-density-wave systems

We consider the problem of sliding motion of a charge-density-wave subject to static disorder within an elastic medium model. Starting with a field-theoretical formulation, which allows exact disorder averaging, we propose a self-consistent approximation scheme to obtain results beyond the standard large-velocity expansion. Explicit calculations are carried out in three spatial dimensions. For the conductivity, we find a strong-coupling regime at electrical fields just above the pinning threshold. Phase and velocity correlation functions scale differently from the high-field regime, and static phase correlations converge to the pinned-phase behaviour. The sliding charge-density-wave is accompanied by narrow-band noise.Comment: 16 pages, 6 figure

Hawking Radiation on an Ion Ring in the Quantum Regime

This paper discusses a recent proposal for the simulation of acoustic black holes with ions. The ions are rotating on a ring with an inhomogeneous, but stationary velocity profile. Phonons cannot leave a region, in which the ion velocity exceeds the group velocity of the phonons, as light cannot escape from a black hole. The system is described by a discrete field theory with a nonlinear dispersion relation. Hawking radiation is emitted by this acoustic black hole, generating entanglement between the inside and the outside of the black hole. We study schemes to detect the Hawking effect in this setup.Comment: 42 pages (one column), 17 figures, published revised versio

Continuous-time self-tuning algorithms

This thesis proposes some new self-tuning algorithms. In contrast to the conventional discrete-time approach to self-tuning control, the continuous-time approach is used here, that is continuous-time design but digital implementation is used. The proposed underlying control methods are combined with a continuous-time version of the well-known discrete recursive least squares algorithms. The continuous-time estimation scheme is chosen to maintain the continuous-time nature of the algorithms. The first new algorithm proposed is emulator-based relay control (which has already been described in a paper by the author). The algorithm is based on the idea of constructing the switching surface by emulators; that is, unrealisable output derivatives are replaced by their emulated values. In particular, the relay is forced to operate in the sliding mode. In this case, it is shown that emulator-based control and its proposed relay version become equivalent in the sense that both give the same control law. The second new algorithm proposed is a continuous-time version of the discrete-time generalized predictive control (GPC) of Clarke et al (which has already been described in a paper by the author). The algorithm, continuous-time generalized predictive control (CGPC), is based on similar ideas to the GPC, however the formulation is very different. For example, the output prediction is accomplished by using the Taylor series expansion of the output and emulating the output derivatives involved. A detailed closed-loop analysis of this algorithm is also given. It is shown that the CGPC control law only changes the closed-loop pole locations leaving the open-loop zeros untouched (except one special case). It is also shown that LQ control can be considered in the CGPC framework. Further, the CGPC is extended to include some design polynomials so that the model-following and pole-placement control can be considered in the same framework. A third new algorithm, a relay version of the CGPC, is described. The method is based on the ideas of the emulator-based relay control and again it is shown that the CGPC and its relay version become equivalent when the relay operates in the sliding mode. Finally, the CGPC ideas are extended to the multivariable systems and the resulting closed-loop system is analysed in some detail. It is shown that some special choice of design parameters result in a decoupled closed-loop system for certain systems. In addition, it is shown that if the system is decouplable, it is possible to obtain model-following control. It is also shown that LQ control, as in the scalar case, can be considered in the same framework. An illustrative simulation study is also provided for all of the above methods throughout the thesis

Experimental investigations of the Mach-effect for breakthrough space propulsion

This research was conducted within the framework of the SpaceDrive project funded by the German Aerospace Center to develop propellantless propulsion for interstellar travel. The experiments attempted to measure mass fluctuations predicted by the Mach-effect theory derived from General Relativity and observed through torsion balance measurements by Woodward (2012). The combination of such mass fluctuations with synchronized actuation promises propellantless thrust with a significantly better thrust-to-power ratio than photon sails. Thus, experiments using different electromechanical devices including the piezoelectric Mach-effect thruster as tested by Woodward et al. (2012) were pursued on sensitive thrust balances. The tests were automated, performed in vacuum and included proper electromagnetic shielding, calibrations, and different dummy tests. To obtain appropriate driving conditions for maximum thrust, characterization of the experimental devices involved spectrometry, vibrometry, finite element analysis, and circuit modeling. Driving modes consisted of sweeps, resonance tracking, fixed frequency, and mixed signals. The driving voltage, frequency, stack pre-tension, mounting, and thruster orientation were also varied. Lastly, different amplifier electronics were tested as well, including Woodward’s original equipment. Experiments on the double-pendulum and torsion balances with a resolution of under 10 nN and an accuracy of 88.1 % revealed the presence of force peaks with a maximum amplitude of 100 nN and a drift of up to 500 nN. The forces mainly consisted of switching transients whose signs depended on the device’s orientation. These force transients were also observed in the zero-thrust configurations. No additional thrust was observed above the balance drift, regardless of the driving conditions or devices tested. In addition, finite element and vibrometry analysis revealed that the vibration from the actuator was transmitted to the balance beam. Moreover, simulations using a simple spring-mass model showed that the slower transient effects observed can be reproduced using small amplitude, high-frequency vibrations. Hence, the forces observed can be explained by vibrational artifacts rather than the predicted Mach-effect thrust. Then, centrifugal balance experiments measured the mass of a device subjected to rotation and energy fluctuations, with a precision of up to 10 µg and a high time resolution. The measurements relied on piezoelectric- and strain gauges. Their calibration methods presented limitations in the frequency range of interest, resulting in discrepancies of up to 500 %. However, the tests conducted with capacitive and inductive test devices yielded experimental artifacts about three orders of magnitude below the mass fluctuations of several milligrams predicted by the Mach-effect theory. Although the piezoelectric devices presented more artifacts due to nonlinearity and electromagnetic interaction, all rotation experiments did not show the expected dependence on the rotation frequency. In summary, the search for low thrust and small mass fluctuations consisted of challenging experiments that led to the development of innovative and sensitive instruments, while requiring a careful consideration of experimental artifacts. The results analysis led to the rejection of mass fluctuations and thrusts claimed by Woodward’s Mach-effect theory and experiments. The quest for breakthrough space propulsion must thus continue a different theoretical or experimental path.:List of Figures List of Tables List of Abbreviations List of Variables and Symbols 1. Introduction 1.1 Research Motivation 1.2 Objectives 1.3 Content Overview 1.4 Team Work 2. Literature Review 2.1 Fundamentals of Space Propulsion 2.2 Mach’s Principle 2.3 Woodward’s Mach-effect Theory 2.3.1 Derivation of the Mass Fluctuation Equation 2.3.2 Design of a Mass Fluctuation Thruster 2.4 Woodward-type Experiments 2.5 Force and Transient Mass Measurements 3. Electromechanical Characterization 3.1 Piezoelectric Actuators 3.1.1 Basic Properties 3.1.2 Actuator Design 3.1.3 Mach-effect Thruster Devices 3.1.4 Magnetostrictive Actuator 3.1.5 Numerical Analysis of MET Behavior 3.1.6 Vibrometry Analysis 3.1.7 Impedance Spectroscopy 3.1.8 Circuit Modeling 3.1.9 Predictions 3.2 Electronics 3.2.1 Description 3.2.2 Characterization 3.3 Torsion Balances 3.3.1 Description 3.3.2 Characterization 3.3.3 Simulation 3.4 Double-pendulum Balance 3.4.1 Description 3.4.2 Characterization 3.5 Laboratory Setup 3.5.1 Vacuum Chambers 3.5.2 Software and Test Setup 4. Thrust Balance Experiments 4.1 Torsion Balance I Test Results 4.1.1 Dummy Tests 4.1.2 CU18A 4.1.3 MET03 4.1.4 MET04 4.1.5 Discussion 4.2 Torsion Balance II Test Results 4.2.1 Dummy Tests 4.2.2 MET05 4.2.3 Beam Vibration 4.2.4 Discussion 4.3 Double-pendulum Balance Test Results 4.3.1 Dummy Tests 4.3.2 MET03 4.3.3 Discussion 5. Centrifugal Balance Experiments 5.1 Centrifugal Balance 5.1.1 Description 5.1.2 Centrifugal Devices 5.1.3 Predictions 5.2 Transducer Calibration 5.2.1 Quasi-Static Calibration I 5.2.2 Quasi-Static Calibration II 5.2.3 Dynamic Calibration 5.3 Centrifugal Balance Test Results 5.3.1 Characterization 5.3.2 CD01 5.3.3 CD02 5.3.4 CD03 5.3.5 CD04 5.3.6 CD05 5.4 Discussion & Error Analysis 6 Conclusions 6.1 Research Summary 6.2 Further Research Appendix A Appendix B Bibliograph