Given the recent popularity and clear evidence of wide applicability of wavelets, this thesis is devoted to several statistical applications of Wavelet transforms. Statistical multiscale modeling has, in the most recent decade, become a well-established area in both theoretical and applied statistics, with impact on developments in statistical methodology. Wavelet-based methods are important in statistics in areas such as regression, density and function estimation, factor analysis, modeling and forecasting in time series analysis, assessing self-similarity and fractality in data, and spatial statistics. In this thesis we show applicability of the wavelets by considering three problems: First, we consider a binary wavelet-based linear classifier. Both consistency results and implemental issues are addressed. We show that under mild assumptions wavelet-based classification rule is both weakly and strongly universally consistent. The proposed method is illustrated on synthetic data sets in which the truth is known and on applied classification problems from the industrial and bioengineering fields. Second, we develop wavelet shrinkage methodology based on testing multiple hypotheses in the wavelet domain. The shrinkage/thresholding approach by implicit or explicit simultaneous testing of many hypotheses had been considered by many researchers and goes back to the early 1990's. We propose two new approaches to wavelet shrinkage/thresholding based on local False Discovery Rate (FDR), Bayes factors and ordering of posterior probabilities. Finally, we propose a novel method for the analysis of straight-line alignment of features in the images based on Hough and Wavelet transforms. The new method is designed to work specifically with Transmission Electron Microscope (TEM) images taken at nanoscale to detect linear structure formed by the atomic lattice.

In this dissertation, we present the Slattery-Oh-Fu theory extending continuum mechanics to the nanoscale and its applications. We begin with an analysis of supercritical adsorption of argon, krypton, and methane on Graphon before we fully develop the theory. We compare our results both with existing experimental data and with prior molecular-based theories. Then, we present the general theory, which is based upon a long history of important developments beginning with Hamaker (1937). In the context of continuum mechanics, nanoscale problems always involve the immediate neighborhood of a phase interface or the immediate neighborhood of a three-phase line of contact or common line. We test this theory by using it to predict both the surface tensions of the n-alkanes and the static contact angles for the n-alkanes on PTFE and for several liquids on PDMS. For the contact angle predictions, the results are compatible with previously published experimental data. The results for the contact angle analysis also provide a successful test of a previously derived form of Young??s equation for the true, rather than apparent, common line. We also studied Mode I fracture at nanoscale. While we don??t have experimental data to compare, we get reasonable crack configuration and avoid stress singularity at the crack tip. Coalescence problems are revisited to explore the retardation effects in the computation of intermolecular forces. We get good agreement with experimental results. We conclude with a confidence that this theory can be used as a bridge between continuum mechanics and other molecular-based methods.

Nanocrystalline films are promising in various fields such as microelectronics. Low temperature deposition techniques are desirable since they would enable the use of new substrates that are temperature sensitive, leading to a wide range of new applications. This thesis explores nanocrystalline silver film deposition by impacting nanoparticles (NP) onto a substrate, a technique that enables low process temperatures. This work aims at better understanding the physical parameters governing the sticking probability of NP upon impaction. To achieve this, various substrate materials have been used (metallic and non metallic) and the influence of the impacted substrate temperature has been studied, among other experiments. These parameters showed a significant influence on the collection efficiency of NPs. These experimental results are analyzed in light of published computer simulations studies predicting the behavior of impacting NP to deposit nanostructured films. Secondly, a study of the mechanical properties of the deposited films has been attempted. Compression tests have been carried out varying the applied load, loading time and process temperature. The produced films are nanocrystalline and porous (~70% relative density). Densification has been observed even at room temperature, and the goal of this study is to understand which mechanisms cause the densification to occur. The experimental densification data are compared with a model describing the densification of microparticles compacts by hot pressing that has been adapted to nanocrystalline silver, and the mechanisms leading to densification are discussed. / text

In a sub-wavelength scale, even approaching to the atomic scale, nanoscale physics shows various novel phenomena. Since it has been named, nanoscience and nanotechnology has been employed to explore and exploit this small scale world. For example, with various functionalized features, nanowire (NW) has been making its leading position in the researches of physics, chemistry, biology, and engineering as a miniaturized building block. Its individual characteristic shows superior and unique features compared with its bulk counterpart. As one part of these research efforts and progresses, and with a part of the fulfillment of degree study, novel methodologies and device structures in nanoscale were devised and developed to show the abilities of high performing thermoelectrical, biological, and optical applications. A single β-SiC NW was characterized for its thermoelectric properties (thermal conductivity, Seebeck coefficient, and figure of merit) to compare with its bulk counterpart. The combined structure of Ag NW and ND was made to exhibit its ability of clear imaging of a fluorescent cell. And a plasmonic nanosture of silver (Ag) nanodot array and a β-SiC NW was fabricated to show a high efficient light harvesting device that allows us to make a better efficient solar cell. Novel nanomanipulation techniques were developed and employed in order to fabricate all of these measurement platforms. Additionally, one of these methodological approaches was used to successfully isolate a few layer graphene.

To study the effect of the substrate support on the nanoscale contact, three different regimes, i.e., graphene on rigid (ultra-crystalline diamond) and on elastic (Polydimethylsiloxane) supports and free-standing graphene, were considered. The contribution of the graphene support to the mechanical and electrical characteristics of the graphene/metal contact was studied using the conductive atomic force microscopy (AFM) technique.The results revealed that the electrical conductivity of the graphene/metal contact highly depends on the nature of the graphene support. The conductivity increased when transitioning from suspended to elastic and then to rigid substrates, which is attributed to the changes in the contact area being higher for the suspended graphene and lower for the rigid substrate. The experimental observations showed good agreement with theoretical results obtained from modeling of the studied material systems. Further, the results indicated that in addition to the substrate support, the nature of the contact, static or dynamic, results in large variations of the electrical conductivity of the graphene/metal contacts. In case of the static mode, the contact made with supported graphene was very stable for a wide range of applied normal loads. Transitioning to the dynamic mode led to instability of the graphene/metal contact as demonstrated by lowering in the electrical conductivity values. This transition was even more pronounced for free-standing graphene which is attributed to graphene sagging during rapid scanning of the tip over the graphene surface. This study creates a new knowledge on understanding of the nanoscale contacts forming with 2D materials thus enabling further advances in the applications of 2D materials in highly stable and reliable electronic devices.

Doctor of Philosophy / Department of Chemistry / Christer B. Aakeroy / The work presented in this thesis has demonstrated that supramolecular synthons can be used to make multicomponent crystals, and various synthons can be combined to make supermolecules. The synthons can also be used to construct nanoscale assemblies. Molecules containing single and multiple hydrogen-bond (HB) and halogen-bond (XB) acceptor sites have been synthesized in an effort to carry out supramolecular synthesis in order to establish a reliable hierarchy for intermolecular interactions. Pyrazole-based molecules have been made, combined with various carboxylic acids, and characterized using infrared (IR) spectroscopy to give a success rate of 55-70%. Reactions that gave a positive result were converted to solution experiments, and crystals were grown and characterized using single-crystal X-ray diffraction (XRD). The co-crystals display infinite 1-D chains with the intended stoichiometry and structural landscape on 6/6 occasions. The salts, on the other hand, display unpredictable stoichiometry and structural landscape on 5/5 occasions. Furthermore, the electrostatic charge on the primary hydrogen-bond acceptor, N(pyz), can be altered by adding a nitro, R-NO2, covalent handle to the backbone of the pyrazole molecule. Addition of a strongly electron withdrawing group significantly lowered the charge on the pyrazole nitrogen atom and, in turn, lowered the supramolecular yield to 10%. Ditopic molecules containing pyrazole and pyridine on the same molecular backbone were synthesized and characterized using 1H NMR. The molecules were co-crystallized with carboxylic acids, and the resulting solids were characterized using IR spectroscopy. The solids could then be classified as co-crystal or salt using specific markers in the IR spectrum. Single-crystal XRD was used to observe the intermolecular interactions in the co-crystals and salts, and the co-crystals were assigned to two groups: Group 1 (2) and Group 2 (2). The salts (4) show more unpredictability with stoichiometry and structural landscape. A library of ditopic molecules containing triazole and pyridine acceptor sites were synthesized and characterized using 1H and 13C NMR. The molecules were co-crystallized with carboxylic acids and the resulting solids were characterized using IR spectroscopy which demonstrated a 100% supramolecular yield whenever a pyridine moiety was present, consistent with results from Chapter 3. Single-crystal XRD was used to identify the intermolecular interactions in the co-crystals (2) and salt (1), and the results show that triazole can compete with pyridine for hydrogen bond donors. A library of ditopic molecules was also used for halogen-bonding (XB) studies with a series of activated iodine and bromine-based donors. The results show that iodine donors have a higher success rate range (12.5-75%) compared to bromine donors (16.7-50%) based on results obtained from IR spectra. Furthermore, the results from the XRD show that pyrazole nitrogen atoms can compete with pyridine for forming XB, and two groups of supramolecular synthons were observed. Finally, relatively weak non-covalent interactions, HB and XB, can influence the assembly of nanoparticles based on IR spectroscopy and TEM images. The assembly of the particles is influenced by specific capping ligands, which were synthesized and characterized using 1H, 13C and 19F NMR. The results demonstrate that relatively weak non-covalent interactions based on HB and XB interactions can influence nanoparticle assembly.

This thesis presents the controller design and implementation of a high-precision 6-degree-of-freedom (6-DOF) magnetically levitated (maglev) positioner. This high-precision positioning system consists of a novel concentrated-field magnet matrix and a triangular single-moving part that carries three 3-phase permanent-magnet linear-levitation-motor armatures. Since only a single levitated moving part, namely the platen, generates all required fine and coarse motions, this positioning system is reliable and low-cost. Three planar levitation motors based on the Lorentz-force law not only generate the vertical force to levitate the triangular platen but control the platen??s position and orientation in the horizontal plane. All 6-DOF motions are controlled by magnetic forces only. The platen is regarded a pure mass system, and the spring and damping coefficients are neglected except for the vertical directions. Single-input single-output (SISO) digital lead-lag controllers are designed and implemented on a digital signal processor (DSP). This 6-DOF fully magnetically levitated positioner has a total mass of 5.91 kg and currently exhibits a 120 mm ?? 120 mm travel range. This positioner is highly suitable for semiconductor-manufacturing applications such as wafer steppers. Several experimental motion profiles are presented to demonstrate the maglev stage??s capability of accurately tracking any planar and 3-D paths.

This thesis presents the controller design and implementation of a high-precision 6-degree-of-freedom (6-DOF) magnetically levitated (maglev) positioner. This high-precision positioning system consists of a novel concentrated-field magnet matrix and a triangular single-moving part that carries three 3-phase permanent-magnet linear-levitation-motor armatures. Since only a single levitated moving part, namely the platen, generates all required fine and coarse motions, this positioning system is reliable and low-cost. Three planar levitation motors based on the Lorentz-force law not only generate the vertical force to levitate the triangular platen but control the platen??s position and orientation in the horizontal plane. All 6-DOF motions are controlled by magnetic forces only. The platen is regarded a pure mass system, and the spring and damping coefficients are neglected except for the vertical directions. Single-input single-output (SISO) digital lead-lag controllers are designed and implemented on a digital signal processor (DSP). This 6-DOF fully magnetically levitated positioner has a total mass of 5.91 kg and currently exhibits a 120 mm ?? 120 mm travel range. This positioner is highly suitable for semiconductor-manufacturing applications such as wafer steppers. Several experimental motion profiles are presented to demonstrate the maglev stage??s capability of accurately tracking any planar and 3-D paths.

This thesis describes the development and applications of sub-micron current-perpendicular-to plane devices fabricated by three-dimensional etching with a focused ion beam microscope. This technique was applied to a range of materials, including the study of c-axis Josephson junctions in the high temperature superconductor Tl2Ba2CaCu2O8, the fabrication of superconducting quantum interference devices with sub-micron loop areas, and GaN light emitting diodes. The main body of research was carried out in the study of Nb based Josephson junctions working at a temperature of 4.2 K. Junctions with normal metal, insulating and ferromagnetic barriers were characterised, as well as the first metallic antiferromagnetic Josephson junctions using γ-Fe50Mn50 as the barrier. 'Pseudo-spin-valve' Josephson junctions were also created using aCo/Cu/Fe20Ni80 barrier. In this case the relative orientation of the magnetic moments of the Co and Fe20Ni80 could be changed with an applied magnetic field. The magnetoresistance and critical current of the device showed a strong correlation, implying a direct influence of the magnetic structure of the device on the critical current.

Embedded systems which are targeted towards portable applications are required to have low power consumption because such portable devices are typically powered by batteries. During the memory accesses of such battery operated portable systems, including laptops, cell phones and other devices, a significant amount of power or energy is consumed which significantly affects the battery life. Therefore, efficient and leakage power saving cache designs are needed for longer operation of battery powered applications. Design engineers have limited control over many design parameters of the circuit and hence face many chal-lenges due to inherent process technology variations, particularly on static random access memory (SRAM) circuit design. As CMOS process technologies scale down deeper into the nanometer regime, the push for high performance and reliable systems becomes even more challenging. As a result, developing low-power designs while maintaining better performance of the circuit becomes a very difficult task. Furthermore, a major need for accurate analysis and optimization of various forms of total power dissipation and performance in nanoscale CMOS technologies, particularly in SRAMs, is another critical issue to be considered. This dissertation proposes power-leakage and static noise margin (SNM) analysis and methodologies to achieve optimized static random access memories (SRAMs). Alternate topologies of SRAMs, mainly a 7-transistor SRAM, are taken as a case study throughout this dissertation. The optimized cache designs are process-voltage-temperature (PVT) tolerant and consider individual cells as well as memory arrays.