Photonic bandgap materials are periodic structures that exclude electromagnetic field propagation over frequency intervals known as bandgaps. These materials exhibit remarkable wave dispersion and have found use in many applications that require control over dynamic electromagnetic fields, as their properties can be tailored by design. The two principal objectives of this thesis are the development of a liquid crystal-based microwave photonic bandgap device whose bandgap could be tuned during operation and the design and implementation of a spectral transmission-line modeling method for band structure calculations. The description of computational methods comprises an overview of the implemented numerical routines, a derivation of the spectral properties of the transmission-line modeling method in periodic domains, and the development of an efficient sparse matrix eigenvalue algorithm that formed the basis of the spectral transmission-line modeling method. The discussion of experimental methods considers the use of liquid crystals in microwave applications and details the design and fabrication of several devices. These include a series of modified twisted nematic cells that were used to evaluate liquid crystal alignment and switching, a patch resonator that was used to measure liquid crystal permittivity, and the liquid crystal photonic bandgap device itself. Numerical experiments showed that the spectral transmission-line modeling method is accurate and substantially faster and less memory intensive than the reference plane wave method for problems of high dielectric contrast or rapidly varying spatial detail. Physical experiments successfully realized a microwave photonic bandgap structure whose bandgap could be continuously tuned with a bias voltage. The very good agreement between simulated and measured results validate the computational and experimental methods used, particularly the resonance-based technique for permittivity measurement. This work's results may be applied to many applications, including microwave filters, negative group velocity/negative refraction materials, and microwave permittivity measurement of liquid crystals.

Darbe nagrinėjama periodinės dzeta funkcijos antrojo momento liekamojo nario išreikštinis pavidalas ir šios funkcijos asimptotinio elgesio charakterizacija ribinių teoremų silpnojo tikimybinių matų konvergavimo prasmė įvairiose erdvėse pagalba. Darbo uždaviniai yra šie: 1. Įrodyti Atkinsono formulę periodinai dzeta funkcijai kritinėje tiesėje. 2. Įrodyti Atkinsono formulę periodinai dzeta funkcijai kritinėje juostoje. 3. Įrodyti ribinę teoremą su ribinio mato išreikštiniu pavidalu kompleksinėje plokštumoje periodinei dzeta funkcijai. 4. Įrodyti ribinę teoremą su ribinio mato išreikštiniu pavidalu analizinių funkcijų erdvėje periodinei dzeta funkcijai. Atkinsono formulė duoda momentų asimptotinės formulės liekamojų narių išreikštinį pavidalą. Tai ne tik įdomus, bet ir turintis rimtų pritaikymų, pavyzdžiui, tiriant aukštesniuosius momentus, rezultatas. Tikimybinės ribinės teoremos charakterizuoja dzeta funkcijų asimptotinio elgesio reguliarumą. Be to, buvo pastebėta, kad tokios teoremos yra svarbiausia dzeta funkcijų universalumo įrodymo grandis. Periodinė dzeta funkcija nėra klasikinė, ji yra Rymano (Riemann) dzeta funkcijos apibendrinimas, tačiau ji pasirodo įvairiuose analizinės skaičių teorijos uždaviniuose. Pavyzdžiui, ji įeina į Hurvico (Hurvitz) ir Lercho (Lerch) dzeta funkcijų antrojo momento parametro atžvilgiu asimptotinę formulę. Iš kitos pusės, darbų, skirtų periodinei dzeta funkcijai, yra nedaug, aukščiau minėti autoriai daugiausia dėmesio skyrė... [toliau žr. visą tekstą] / In the thesis, the Atkinson formula for the periodic zeta-function on the critical line and the critical strip, and limit theorems in the sense of weak convergence of probability measures in various spaces are considered. The aim of the thesis is to solve the following problems: 1. To obtain the Atkinson formula on the critical line for the periodic zeta-function. 2. To obtain the Atkinson formula in the critical strip for the periodic zeta-function. 3. To prove limit theorems on the complex plane in the sense of weak convergence for the periodic zeta-function. 4. To prove limit theorems in the space of analytic functions for the periodic zeta-function. To solve them analytical and probabilistic methods are applied. For the proof of Atkinson formula, we use properties of the error term in the Dirichlet divisor problem and classical Voronoi formula. For the proof of limit theorems, the theory of weak convergence of probability measures, in particular, the Prokhorov's theory is applied. All results obtained in the thesis are new. The Atkinson formula for periodic zeta-function was not known. The same is true for limit theorems for periodic zeta-function. The Atkinson formula gives the explicit formula for the error term in the asymptotic formula for the first moment. This result is not only interesting itself but also has a series of applications, for example, in the investigation of higher moments. Probabilistic limit theorems are used for the characterization of... [to full text]

In the thesis, the Atkinson formula for the periodic zeta-function on the critical line and the critical strip, and limit theorems in the sense of weak convergence of probability measures in various spaces are considered. The aim of the thesis is to solve the following problems: 1. To obtain the Atkinson formula on the critical line for the periodic zeta-function. 2. To obtain the Atkinson formula in the critical strip for the periodic zeta-function. 3. To prove limit theorems on the complex plane in the sense of weak convergence for the periodic zeta-function. 4. To prove limit theorems in the space of analytic functions for the periodic zeta-function. To solve them analytical and probabilistic methods are applied. For the proof of Atkinson formula, we use properties of the error term in the Dirichlet divisor problem and classical Voronoi formula. For the proof of limit theorems, the theory of weak convergence of probability measures, in particular, the Prokhorov's theory is applied. All results obtained in the thesis are new. The Atkinson formula for periodic zeta-function was not known. The same is true for limit theorems for periodic zeta-function. The Atkinson formula gives the explicit formula for the error term in the asymptotic formula for the first moment. This result is not only interesting itself but also has a series of applications, for example, in the investigation of higher moments. Probabilistic limit theorems are used for the characterization of... [to full text] / Darbe nagrinėjama periodinės dzeta funkcijos antrojo momento liekamojo nario išreikštinis pavidalas ir šios funkcijos asimptotinio elgesio charakterizacija ribinių teoremų silpnojo tikimybinių matų konvergavimo prasmė įvairiose erdvėse pagalba. Darbo uždaviniai yra šie: 1. Įrodyti Atkinsono formulę periodinai dzeta funkcijai kritinėje tiesėje. 2. Įrodyti Atkinsono formulę periodinai dzeta funkcijai kritinėje juostoje. 3. Įrodyti ribinę teoremą su ribinio mato išreikštiniu pavidalu kompleksinėje plokštumoje periodinei dzeta funkcijai. 4. Įrodyti ribinę teoremą su ribinio mato išreikštiniu pavidalu analizinių funkcijų erdvėje periodinei dzeta funkcijai. Atkinsono formulė duoda momentų asimptotinės formulės liekamojų narių išreikštinį pavidalą. Tai ne tik įdomus, bet ir turintis rimtų pritaikymų, pavyzdžiui, tiriant aukštesniuosius momentus, rezultatas. Tikimybinės ribinės teoremos charakterizuoja dzeta funkcijų asimptotinio elgesio reguliarumą. Be to, buvo pastebėta, kad tokios teoremos yra svarbiausia dzeta funkcijų universalumo įrodymo grandis. Periodinė dzeta funkcija nėra klasikinė, ji yra Rymano (Riemann) dzeta funkcijos apibendrinimas, tačiau ji pasirodo įvairiuose analizinės skaičių teorijos uždaviniuose. Pavyzdžiui, ji įeina į Hurvico (Hurvitz) ir Lercho (Lerch) dzeta funkcijų antrojo momento parametro atžvilgiu asimptotinę formulę. Iš kitos pusės, darbų, skirtų periodinei dzeta funkcijai, yra nedaug, aukščiau minėti autoriai daugiausia dėmesio skyrė... [toliau žr. visą tekstą]

Two broad surveys of community- level water consumption and pricing behavior are used to answer questions about water demand in a more flexible and dynamic context than is provided in the literature. Central themes of price representation, aggregation, and dynamic adjustment tie together three econometric demand analyses. The centerpiece of each analysis is an exogenous weighted price representation. A model in first-differences is estimated by ordinary least squares using data from a personally-conducted survey of Texas urban water suppliers. Annual price elasticity is found to vary with weather and income, with a value of -0.127 at the data mean. The dynamic model becomes a periodic error correction model when the residuals of 12 static monthly models are inserted into the difference model. Distinct residential, commercial, and industrial variables and historical climatic conditions are added to the integrated model, using new national data. Quantity demanded is found to be periodically integrated with a common stochastic root. Because of this, the structural monthly models must be cointegrated to be consistent, which they appear to be. The error correction coefficient is estimated at -0.187. Demand is found to be seasonal and slow to adjust to shocks, with little or no adjustment in a single year and 90% adjustment taking a decade or more. Residential and commercial demand parameters are found to be indistinguishable. The sources of price endogeneity and historical fixes are reviewed. Ideal properties of a weighted price index are identified. For schedules containing exactly two rates, weighting is equivalent to a distribution function in consumption. This property is exploited to derive empirical weights from the national data, using values from a nonparametric generalization of the structural demand model and a nonparametric cumulative density function. The result is a generalization of the price difference metric to a weighted level-price index. The validity of a uniform weighting is not rejected. The weighted price index is data intensive, but the payoff is increased depth and precision for the economist and accessibility for the practitioner.

This thesis presents both theoretical and experimental investigations of the performance and capabilities of frequency selective surfaces (FSS) applied at THz frequencies. The aim is to explore and extend the use of FSS, traditionally limited to microwave frequencies, towards the THz regime of the spectrum, where interesting applications such as imaging, sensing and communications exist. The contribution of this work lies in three main areas within the scope of THz FSS, namely, performance, prototyping and applications. Unlike microwave FSS where extensive research has been performed to evaluate the performance of different FSS designs, particular problems arise at THz frequencies, significantly, the ohmic losses. While a few notable studies can be found on the issue of ohmic losses, part of this thesis investigates, for the first time, the power dissipation due to the presence of both ohmic and dielectric losses, in relation to the power stored in the vicinity of the FSS, the currents induced in the elements of the array and the array’s terminal impedance. By doing so, a better understanding of the performance of THz FSS has been given in terms of their quality factor, allowing for design guidelines previously unavailable. In order to demonstrate multiband operation experimentally, a novel fabrication process has been designed and developed to manufacture capacitive or dipole-based THz FSS on a dielectric layer. Dry deep-reactive ion etching has been employed in order to avoid the use of wet etching to provide better control of etch characteristics. Various FSS operating around 15THz have been demonstrated experimentally. In addition, THz FSS have been investigated theoretically in the realm of three different applications, namely, multiband operation, sensing capability and reconfigurability. Multiband characteristics using single-screen FSS have been achieved by perturbed dipole FSS exhibiting up to four resonances due to the excitation of even and odd current modes. After studying the near-fields in perturbed FSS, it has been found that this type of FSS represent a very attractive candidate for sensing applications due to the revealed near-field enhancement phenomena related to the excitation of the odd mode, where currents flow in opposite directions. Finally, a novel tunability approach to reach frequency reconfigurability by varying the near-field coupling between two closely spaced layers in a dual-layer configuration has been proposed. A MEMS movable four-arm membrane has been suggested to vary the distance between the two layers mechanically, leading to the frequency tuning effect. This approach has been shown to be particularly suitable for THz frequencies, and has been applied to demonstrate theoretically tunable FSS and other periodic structures, such as artificial magnetic conductors and dielectric gratings.

Photonic bandgap materials are periodic structures that exclude electromagnetic field propagation over frequency intervals known as bandgaps. These materials exhibit remarkable wave dispersion and have found use in many applications that require control over dynamic electromagnetic fields, as their properties can be tailored by design. The two principal objectives of this thesis are the development of a liquid crystal-based microwave photonic bandgap device whose bandgap could be tuned during operation and the design and implementation of a spectral transmission-line modeling method for band structure calculations. The description of computational methods comprises an overview of the implemented numerical routines, a derivation of the spectral properties of the transmission-line modeling method in periodic domains, and the development of an efficient sparse matrix eigenvalue algorithm that formed the basis of the spectral transmission-line modeling method. The discussion of experimental methods considers the use of liquid crystals in microwave applications and details the design and fabrication of several devices. These include a series of modified twisted nematic cells that were used to evaluate liquid crystal alignment and switching, a patch resonator that was used to measure liquid crystal permittivity, and the liquid crystal photonic bandgap device itself. Numerical experiments showed that the spectral transmission-line modeling method is accurate and substantially faster and less memory intensive than the reference plane wave method for problems of high dielectric contrast or rapidly varying spatial detail. Physical experiments successfully realized a microwave photonic bandgap structure whose bandgap could be continuously tuned with a bias voltage. The very good agreement between simulated and measured results validate the computational and experimental methods used, particularly the resonance-based technique for permittivity measurement. This work's results may be applied to many applications, including microwave filters, negative group velocity/negative refraction materials, and microwave permittivity measurement of liquid crystals.

The maintenance of equipment has been an important issue for companies for many years. For systems with hidden or unrevealed failures (i.e., failures are not self-announcing), a common practice is to regularly inspect the system looking for such failures. Examples of these systems include protective devices, emergency devices, standby units, underwater devices etc. If no periodical inspection is scheduled, and a hidden failure has already occurred, severe consequences may result. Research on periodical inspection seeks to establish the optimal inspection interval (Failure Finding Interval) of systems to maximize availability and/or minimize expected cost. Research also focuses on important system parameters such as unavailability. Most research in this area considers non-negligible downtime due to repair/replacement but ignores the downtime caused by inspections. In many situations, however, inspection time is non-negligible. We address this gap by proposing an optimal failure finding interval (FFI) considering both non-negligible inspection time and repair/replacement time. A novel feature of this work is the development of models for both age-based and calendar-based inspection policies with random/constant inspection time and random/constant repair/replacement time. More specifically, we first study instantaneous availability for constant inspection and repair/replacement times. We start with the assumption of renewal of the system at each inspection. We then consider models with the assumption of renewal only after failure. We also develop limiting average availability models for random inspection and repair/replacement times, considering both age-based and calendar-based inspection policies. We optimize these availability models to obtain an optimal FFI in order to maximize the system’s availability. Finally, we develop several cost models for both age-based and calendar-based inspection policies with random inspection time and repair/replacement time. We formulate the model for constant inspection time and repair/replacement time as a special case. We investigate the optimization of cost models for each case to obtain optimal FFI in order to minimize the expected cost. The numerical examples and case study presented in the dissertation demonstrate the importance of considering non-negligible downtime due to inspection.

The maintenance of equipment has been an important issue for companies for many years. For systems with hidden or unrevealed failures (i.e., failures are not self-announcing), a common practice is to regularly inspect the system looking for such failures. Examples of these systems include protective devices, emergency devices, standby units, underwater devices etc. If no periodical inspection is scheduled, and a hidden failure has already occurred, severe consequences may result. Research on periodical inspection seeks to establish the optimal inspection interval (Failure Finding Interval) of systems to maximize availability and/or minimize expected cost. Research also focuses on important system parameters such as unavailability. Most research in this area considers non-negligible downtime due to repair/replacement but ignores the downtime caused by inspections. In many situations, however, inspection time is non-negligible. We address this gap by proposing an optimal failure finding interval (FFI) considering both non-negligible inspection time and repair/replacement time. A novel feature of this work is the development of models for both age-based and calendar-based inspection policies with random/constant inspection time and random/constant repair/replacement time. More specifically, we first study instantaneous availability for constant inspection and repair/replacement times. We start with the assumption of renewal of the system at each inspection. We then consider models with the assumption of renewal only after failure. We also develop limiting average availability models for random inspection and repair/replacement times, considering both age-based and calendar-based inspection policies. We optimize these availability models to obtain an optimal FFI in order to maximize the system’s availability. Finally, we develop several cost models for both age-based and calendar-based inspection policies with random inspection time and repair/replacement time. We formulate the model for constant inspection time and repair/replacement time as a special case. We investigate the optimization of cost models for each case to obtain optimal FFI in order to minimize the expected cost. The numerical examples and case study presented in the dissertation demonstrate the importance of considering non-negligible downtime due to inspection.

A set of tools are proposed for the efficient modeling of several classes of problems related to periodic structures in microwave and optical regimes with Finite-Difference Time-Domain method. The first category of problems under study is the interaction of non-periodic sources and printed elements with infinitely periodic structures. Such problems would typically require a time-consuming simulation of a finite number of unit cells of the periodic structures, chosen to be large enough to achieve convergence. To alleviate computational cost, the sine-cosine method for the Finite-Difference Time-Domain based dispersion analysis of periodic structures is extended to incorporate the presence of non-periodic, wideband sources, enabling the fast modeling of driven periodic structures via a small number of low cost simulations. The proposed method is then modified for the accelerated simulation of microwave circuit geometries printed on periodic substrates. The scheme employs periodic boundary conditions applied at the substrate, to dramatically reduce the computational domain and hence, the cost of such simulations. Emphasis is also given on radiation pattern calculation, and the consequences of the truncated computational domain of the proposed method on the computation of the electric and magnetic surface currents invoked in the near-to-far-field transformation. It has been further demonstrated that from the mesh truncation point of view, the scheme, which has a unified form regardless dispersion and conductivity, serves as a much simpler but equally effective alternative to the Perfectly Matched Layer provided that the simulated domain is periodic in the direction of termination. The second category of problems focuses on the efficient characterization of nonlinear periodic structures. In Finite-Difference Time-Domain, the simulation of these problems is typically hindered by the fine spatial and time gridding. Originally proposed for linear structures, the Alternating-Direction Implicit Finite-Difference Time-Domain method, as well as a novel spatial filtering method, are extended to incorporate nonlinear media. Both methods are able to use time-step sizes beyond the conventional stability limit, offering significant savings in simulation time.

This doctoral thesis deals with designs and developments of multi(wide)-band multifunctional antennas based on folded dipoles. In the beginning, the concept of Orthogonal Folded Dipoles (OFD) are put forward. Orthogonal folded dipoles are formed by two identical two-port folded dipoles orthogonally joining with each other at the center, and can be fed through different combinations of feed nodes to offer dual- and wide-band modes, respectively. The impedances of the 2 modes are studied both by analytical models and by commercial electromagnetic simulation tools. The properties of the linearly polarized radiation patterns in the two modes vary quite little, except for ±45◦  rotation of two principal planes. In this way, orthogonal folded dipoles can possibly provide pattern reconfigurability in a context of switchable types and orientations of polarizations. Next, the concept of Log-Periodic Folded Dipole Array (LPFDA) is proposed. It stems from the traditional log-periodic dipole array, whereas folded dipoles instead of straight dipoles are applied as the elements of the array. Two configurations, i.e. partly-scaled LPFDA and fully-scaled LPFDA, are studied through simulations and optimizations. The comparison shows that the latter outperforms the former in terms of higher directivity, reduced front-to-back ratio and lower crosspolar level. The key parts of this thesis focus on exploiting Eleven antennas, based on the LPFDAs, in a variety of applications. First, the 4-port L-band lab model for use in satellite terminals demonstrates that the radiation patterns for monopulse tracking can be achieved through different excitation combinations of the multiport Eleven antenna. Second, a decade bandwidth, an unchanged phase center and nearly constant directivities over the whole band can be regarded as the major figure-of-merit of the Eleven antenna, which makes it suitable as feed for prime-fed reflector antennas. Through endeavors of using Genetic Algorithms, the wideband Eleven antennas have been gradually optimized in term of matching as well as efficiencies. Besides, the rotationally symmetric circular Eleven feed is a very promising solution for improving the BOR1 efficiency and therefore the aperture efficiency by a fraction of dB. Last but not least, the two multiport L-band lab models measured in a reverberation chamber demonstrate that the Eleven antenna with MIMO diversity ports can possibly overcome narrowband multipath fading in a real radio link and improve the link quality in terms of a significant diversity gain and high maximum available capacity.