Essays on mixed-frequency data : forecasting and unit root testing

Doutoramento em Economia

Design and Applications of a Decade-Spanning Terahertz Frequency Comb Spectrometer: Doppler-limited Rotational Spectroscopy of Methanol and Methanol-OD

This thesis details the design and applications of a terahertz (THz) frequency comb spectrometer. The spectrometer employs two offset locked Ti:Sapphire femtosecond oscillators with repetition rates of approximately 80 MHz, offset locked at 100 Hz to continuously sample a time delay of 12.5 ns at a maximum time delay resolution of 15.6 fs. These oscillators emit continuous pulse trains, allowing the generation of a THz pulse train by the master, or pump, oscillator and the sampling of this THz pulse train by the slave, or probe, oscillator via the electro-optic effect. Collecting a train of 16 consecutive THz pulses and taking the Fourier transform of this pulse train produces a decade-spanning frequency comb, from 0.25 to 2.5 THz, with a comb tooth width of 5 MHz and a comb tooth spacing of ~80 MHz. This frequency comb is suitable for Doppler-limited rotational spectroscopy of small molecules. Here, the data from 68 individual scans at slightly different pump oscillator repetition rates were combined, producing an interleaved THz frequency comb spectrum, with a maximum interval between comb teeth of 1.4 MHz, enabling THz frequency comb spectroscopy.

The accuracy of the THz frequency comb spectrometer was tested, achieving a root mean square error of 92 kHz measuring selected absorption center frequencies of water vapor at 10 mTorr, and a root mean square error of 150 kHz in measurements of a K-stack of acetonitrile. This accuracy is sufficient for fitting of measured transitions to a model Hamiltonian to generate a predicted spectrum for molecules of interest in the fields of astronomy and physical chemistry. As such, the rotational spectra of methanol and methanol-OD were acquired by the spectrometer. Absorptions from 1.3 THz to 2.0 THz were compared to JPL catalog data for methanol and the spectrometer achieved an RMS error of 402 kHz, improving to 303 kHz when excluding low signal-to-noise absorptions. This level of accuracy compares favorably with the ~100 kHz accuracy achieved by JPL frequency multiplier submillimeter spectrometers. Additionally, the relative intensity performance of the THz frequency comb spectrometer is linear across the entire decade-spanning bandwidth, making it the preferred instrument for recovering lineshapes and taking absolute intensity measurements in the THz region. The data acquired by the Terahertz Frequency Comb Spectrometer for methanol-OD is of comparable accuracy to the methanol data and may be used to refine the fit parameters for the predicted spectrum of methanol-OD.

Design of an Experimental Rig to Characterize the Gust Response of Small Wind Turbines and Autorotating Seeds

This thesis investigates the rotational behavior of abstracted small-wind-turbine rotors exposed to a sudden increase in oncoming flow velocity, i.e. a gust. These rotors consisted of blades with aspect ratios characteristic of samara seeds, which are known for their ability to maintain autorotation in unsteady wind. The models were tested in a towing tank using a custom-built experimental rig. The setup was designed and constructed to allow for the measurement of instantaneous angular velocity of a rotor model towed at a prescribed kinematic profile along the tank. The conclusions presented in this thesis are based on the observed trends in effective angle-of-attack distribution, tip speed ratio, angular velocity, and time delay in the rotational response for each of rotors over prescribed gust cases. It was found that the blades with the higher aspect ratio had higher tip speed ratios and responded faster than the blades with a lower aspect ratio. The decrease in instantaneous tip speed ratio during the onset of a prescribed gust correlated with the time delay in each rotor model's rotational response. The time delays were found to increase nonlinearly with decreasing durations over which the simulated gusts occurred.

A principal component approach to space-based gravitational wave astronomy

The current approach to data analysis for the Laser Interferometry Space Antenna (LISA) depends on the time delay interferometry observables (TDI) which have to be generated before any weak signal detection can be performed. These are linear combinations of the raw data with appropriate time shifts that lead to the cancellation of the laser frequency noises. This is possible because of the multiple occurrences of the same noises in the different raw data. Originally, these observables were manually generated starting with LISA as a simple stationary array and then adjusted to incorporate the antenna's motions. However, none of the observables survived the flexing of the arms in that they did not lead to cancellation with the same structure. The principal component approach is another way of handling these noises that was presented by Romano and Woan which simplified the data analysis by removing the need to create them before the analysis. This method also depends on the multiple occurrences of the same noises but, instead of using them for cancellation, it takes advantage of the correlations that they produce between the different readings. These correlations can be expressed in a noise (data) covariance matrix which occurs in the Bayesian likelihood function when the noises are assumed be Gaussian. Romano and Woan showed that performing an eigendecomposition of this matrix produced two distinct sets of eigenvalues that can be distinguished by the absence of laser frequency noise from one set. The transformation of the raw data using the corresponding eigenvectors also produced data that was free from the laser frequency noises. This result led to the idea that the principal components may actually be time delay interferometry observables since they produced the same outcome, that is, data that are free from laser frequency noise. The aims here were (i) to investigate the connection between the principal components and these observables, (ii) to prove that the data analysis using them is equivalent to that using the traditional observables and (ii) to determine how this method adapts to real LISA especially the flexing of the antenna. For testing the connection between the principal components and the TDI observables a 10x 10 covariance matrix containing integer values was used in order to obtain an algebraic solution for the eigendecomposition. The matrix was generated using fixed unequal arm lengths and stationary noises with equal variances for each noise type. Results confirm that all four Sagnac observables can be generated from the eigenvectors of the principal components. The observables obtained from this method however, are tied to the length of the data and are not general expressions like the traditional observables, for example, the Sagnac observables for two different time stamps were generated from different sets of eigenvectors. It was also possible to generate the frequency domain optimal AET observables from the principal components obtained from the power spectral density matrix. These results indicate that this method is another way of producing the observables therefore analysis using principal components should give the same results as that using the traditional observables. This was proven by fact that the same relative likelihoods (within 0.3%) were obtained from the Bayesian estimates of the signal amplitude of a simple sinusoidal gravitational wave using the principal components and the optimal AET observables. This method fails if the eigenvalues that are free from laser frequency noises are not generated. These are obtained from the covariance matrix and the properties of LISA that are required for its computation are the phase-locking, arm lengths and noise variances. Preliminary results of the effects of these properties on the principal components indicate that only the absence of phase-locking prevented their production. The flexing of the antenna results in time varying arm lengths which will appear in the covariance matrix and, from our toy model investigations, this did not prevent the occurrence of the principal components. The difficulty with flexing, and also non-stationary noises, is that the Toeplitz structure of the matrix will be destroyed which will affect any computation methods that take advantage of this structure. In terms of separating the two sets of data for the analysis, this was not necessary because the laser frequency noises are very large compared to the photodetector noises which resulted in a significant reduction in the data containing them after the matrix inversion. In the frequency domain the power spectral density matrices were block diagonals which simplified the computation of the eigenvalues by allowing them to be done separately for each block. The results in general showed a lack of principal components in the absence of phase-locking except for the zero bin. The major difference with the power spectral density matrix is that the time varying arm lengths and non-stationarity do not show up because of the summation in the Fourier transform.

Modelling and PI Control of an Irrigation Canal

The main goal of this paper is to expose and validate a methodology to design efficient automatic controllers for irrigation canals, based on the Saint-Venant model. This model-based methodology enables to design controllers at the design stage (when the canal is not already built). The methodology is applied on an experimental canal located in Portugal. First the full nonlinear PDE model is calibrated, using a single steady-state experiment. The model is then linearized around a functioning point, in order to design linear PI controllers. Two classical control strategies are tested (local upstream control and distant downstream control) and compared on the canal. The experimental results show the effectiveness of the model.

Delay time of a vacuum gap triggered by an exploding wire

The experimental results of delay time of a vacuum gap triggered by an exploding wire plasma have been reported. It consists of explosion delay time and propagation delay time. The explosion delay time has been found to be dependent on the parameters of the exploding wire and the exploding wire circuit and is independent of vacuum gap configuration. The propagation delay time depends on the properties of the exploding wire plasma and vacuum gap parameters such as the number of injection slots, gap spacing, gap polarity, etc. In the absence of prebreakdown current in the vacuum gap, the breakdown can be initiated only after the plasma completely bridges the gap spacing. Under this specific condition, it has been shown that the delay time data can be used to calculate the plasma velocity.

Delay optimal scheduling of a discrete-time batch service queue for point-to-point channel code rate selection

We consider the problem of characterizing the minimum average delay, or equivalently the minimum average queue length, of message symbols randomly arriving to the transmitter queue of a point-to-point link which dynamically selects a (n, k) block code from a given collection. The system is modeled by a discrete time queue with an IID batch arrival process and batch service. We obtain a lower bound on the minimum average queue length, which is the optimal value for a linear program, using only the mean (λ) and variance (σ2) of the batch arrivals. For a finite collection of (n, k) codes the minimum achievable average queue length is shown to be Θ(1/ε) as ε ↓ 0 where ε is the difference between the maximum code rate and λ. We obtain a sufficient condition for code rate selection policies to achieve this optimal growth rate. A simple family of policies that use only one block code each as well as two other heuristic policies are shown to be weakly optimal in the sense of achieving the 1/ε growth rate. An appropriate selection from the family of policies that use only one block code each is also shown to achieve the optimal coefficient σ2/2 of the 1/ε growth rate. We compare the performance of the heuristic policies with the minimum achievable average queue length and the lower bound numerically. For a countable collection of (n, k) codes, the optimal average queue length is shown to be Ω(1/ε). We illustrate the selectivity among policies of the growth rate optimality criterion for both finite and countable collections of (n, k) block codes.

Shock tube study of JP-10 ignition delay time

JP-10 (exo-tetrahydrodicyclopentadiene, C10H16) ignition delay times were measured in a preheated shock tube. The vapor pressures of the JP-10 were measured directly by using a high-precision vacuum gauge, to remedy the difficulty in determining the gaseous concentrations of heavy hydrocarbon fuel arising from the adsorption on the wall in shock tube experiments. The whole variation of pressure and emission of the OH or CH radicals were observed in the ignition process by a pressure transducer and a photomultiplier with a monochromator. The emission of the OH or CH radicals was used to identify the time to ignition. Experiments were performed over the pressure range of 151-556 kPa, temperature range of 1000-2100 K, fuel concentrations of 0.1%-0.55% mole fraction, and stoichiometric ratios of 0.25, 0.5, 1.0 and 2.0. The experimental results show that for the lower and higher temperature ranges, there are different dependency relationships of the ignition time on the temperature and the concentrations of JP-10 and oxygen.

Determining of the delay time for a heating ventilating and air-conditioning plant using two weighted neural network approach

This paper presents an two weighted neural network approach to determine the delay time for a heating, ventilating and air-conditioning (HVAC) plan to respond to control actions. The two weighted neural network is a fully connected four-layer network. An acceleration technique was used to improve the General Delta Rule for the learning process. Experimental data for heating and cooling modes were used with both the two weighted neural network and a traditional mathematical method to determine the delay time. The results show that two weighted neural networks can be used effectively determining the delay time for AVAC systems.

Determining of the delay time for a heating ventilating and air-conditioning plant using multi-weights neurons approach

This paper presents an multi weights neurons approach to determine the delay time for a Heating ventilating and air-conditioning (HVAC) plan to respond to control actions. The multi weights neurons is a fully connected four-layer network. An acceleration technique was used to improve the general delta rule for the learning process. Experimental data for heating and cooling modes were used with both the multi weights neurons and a traditional mathematical method to determine the delay time. The results show that multi weights neurons can be used effectively determining the delay time for HVAC systems.

MEASUREMENT AND SIMULATION OF THE TURN-ON DELAY TIME JITTER IN GAIN-SWITCHED SEMICONDUCTOR-LASERS

The turn-on delay time jitter of four different unbiased gain-switched laser types is determined by measuring the temporal probability distribution of the leading edge of the emitted optical pulse. One single-mode 1.5-mu-m distributed feed-back laser and three multimode Fabry-Perot lasers emitting at 750 nm and 1.3-mu-m are investigated. The jitter is found to decrease for all lasers with increasing injection current. For multimode lasers it decreases from 8 ps excited slightly above threshold down to below 2 ps at three times the threshold current. The jitter of the distributed feedback (DFB) laser is a factor of 3-5 larger than the jitter of the three multimode lasers. A new model to predict the turn-on delay time jitter is presented and explains the experiments quantitatively.

Typical delay determines waiting time on periodic-food schedules: Static and dynamic tests.

Pigeons and other animals soon learn to wait (pause) after food delivery on periodic-food schedules before resuming the food-rewarded response. Under most conditions the steady-state duration of the average waiting time, t, is a linear function of the typical interfood interval. We describe three experiments designed to explore the limits of this process. In all experiments, t was associated with one key color and the subsequent food delay, T, with another. In the first experiment, we compared the relation between t (waiting time) and T (food delay) under two conditions: when T was held constant, and when T was an inverse function of t. The pigeons could maximize the rate of food delivery under the first condition by setting t to a consistently short value; optimal behavior under the second condition required a linear relation with unit slope between t and T. Despite this difference in optimal policy, the pigeons in both cases showed the same linear relation, with slope less than one, between t and T. This result was confirmed in a second parametric experiment that added a third condition, in which T + t was held constant. Linear waiting appears to be an obligatory rule for pigeons. In a third experiment we arranged for a multiplicative relation between t and T (positive feedback), and produced either very short or very long waiting times as predicted by a quasi-dynamic model in which waiting time is strongly determined by the just-preceding food delay.

Enhanced target detection in clutter using dispersive delay lines and time reversal

On the basis of the technique of time reversal (TR), a new method for low dielectric contrast target detection in clutter by adding dispersive delay lines (DDLs) to each element of the TR mirror (TRM) is proposed. When compared with a conventional TR system, the proposed method improves refocusing to a target by reducing the impact of other scatterers in the environment. The proposed method makes it unnecessary to estimate the position of the target and removes the need for subsequent subtraction as traditionally required. Theoretical and numerical simulated results demonstrate the proposed method.