We present a theoretical analysis of surface-plasmon-mediated mode-coupling in a planar thin film metal/insulator stack. The spatial overlap of a surface plasmon polariton (SPP) and a waveguide mode results in a Fano interference analog. Tuning of the material parameters effects the modes and output fields of the system. Lastly, the intensity and phase sensitivity of the system are compared to a standard surface plasmon resonance (SPR). We begin with background information on Fano interference, an interference effect between two indistinguishable pathways. Originally described for autoionization, we discuss the analogs in other systems. We discuss the features of Fano interference in the mode diagrams, and the Fano resonance observed in the output field. The idea of a geometric Fano resonance (GFR) occurring in the angular domain is presented. Background information on surface plasmon polaritons is covered next. The dielectric properties of metals and how they relate to surface plasmons is first reviewed. The theoretical background of SPPs on an infinite planar surface is covered. The modes of a two planar interface metal/insulator stack are reviewed and the leaky properties of the waveguide are shown in the reflectance. We solve for modes of a three interface metal/insulator stack and shows an avoided crossing in the modes indicative of Fano interference. We observe the asymmetric Fano resonance in the angular domain in the reflectance. The tunability of the material parameters tunes the GFR of the system. The GFR tuning is explored and different Fano lineshapes are observed. We also observe a reversal of the asymmetry Fano lineshape, attributed to the relate phase interactions of the non-interacting modes. The phase of the GFR is calculated and discussed for the variations of the parameters. The reflected field is explored as the insulator permittivities are varied. As the waveguide permittivity is varied, we show there is little response from the system. As the exterior permittivity is varied, the reflectance exhibits the geometric Fano resonance and the tunability of the lineshape is explored. Finally, we calculate the sensitivities of our metal/insulator stack to changes in the permittivity and compare them to the sensitivities of SPRs.

自從 Onnes 于1911 年發現超導現象以來，超導就一直是凝聚態領域非常熱門的一個課題。隨之而來的一個問題是超導在量子尺寸效應的影響下將如何變化。在1959 年，Anderson 提出了一個超導受尺寸影響而消失的判據：當超導體的尺寸足够小以至於超導體費米面附近電子的平均能隙大於超導能隙或與其相當時，超導便被尺寸效應破壞。基於這個判據，超導和費米面附近的電子態密度密切相關。Si(111)表面上生長的鉛島在調製費米面附近的態密度上是一個很好的系統，因為它既可以在垂直方向上通過量子阱態調節，也可以通過水平方向的尺寸限制來調節。另外，相對於其他系綜或者粉末超導體，在Si(111)表面上生長的單個鉛島系統上研究超導排除了諸如尺寸分佈，顆粒間相互耦合以及相位漲落等因素對於超導的影響。 / 在這篇論文的緒論中，我首先簡單介紹了基本的超導知識，如 BCS 理論，Eliashberg 理論以及超導在超導體-絶緣體-正常金屬形成的隧道結上的表現形式。跟著，我重點回顧了之前在系綜超導體以及金屬納米結構中進行的超導尺寸效應研究。對於目前廣泛研究的鉛島系統，我將重點談及最近發現的贗能隙，這對研究鉛島的超導至關重要。 / 在第二章，我簡單介紹了樣品的生長和掃描隧道譜的相關知識。爲了分析鉛島的超導譜，我們用了兩種方法去分析他們。一種是零電壓下電導的方法，另一種是超導譜分析方法。在這章的最後，我詳細介紹了Dynes 方程及去捲積的方法。 / 在第三章，我將介紹我博士學習期間一個非常重要的工作，提高儀器的能量分辨率。通過改造儀器結構，合理的接地，屏蔽射頻噪聲，以及清除電壓源的噪聲，我成功地將能量分辨率從0.9 meV 提高到0.2 meV。在最後我會將儀器改進后的結果與之前的結果儀器與其他組的結果進行比較。 / 在儀器改進之前，我們發現那時的測量結果非常差，由此得出的結論也是不正確的。爲了比較儀器改造的重要性，在第四章，我將簡單介紹儀器改進前的結果。在當時差的條件下，我們探測出對於9ML 厚的鉛島，3.2 K 以上不超導的鉛島尺寸，大約為30 nm²。並且鉛島經歷了一個從強電子聲子耦合到弱電子聲子耦合的轉變。 / 在儀器改進之後，我們不僅糾正了之前在九層鉛島上進行超導研究時的一些結論。此外，也觀察到了由於尺寸變化或者費米面上態密度變化導致超導的細微區別。由於尺寸效應，我們發現在一些小的鉛島上存在一個過渡區。另外，由於八層鉛島費米面上的態密度比九層的高，超導轉變溫度也因此有一個系統性的提高。對於這兩個層數的鉛島，他們的超導轉變溫度都隨尺寸減小受到一個緩慢的抑制。對於非常小的鉛島，我們發現其仍然超導。這和Anderson 判據的預期以及其他實驗結果不一致，激發我們進一步探索是否非晶化的潤濕層參與了這種非常小的鉛島的超導。 / 這些工作，對於全面理解超導的尺寸效應以及態密度影響是非常基本和關鍵的，這也將進一步激發人們在這個領域進行更多的探索。 / Superconductivity has always been a hot topic in the field of condensed matter physics since its discovery by Onnes in 1911. How the superconductivity was affected by size attracted much attention especially after P. W. Anderson proposed a criterion of the breakdown of superconductivity in 1959, where the superconductors will lose their superconductivity when the energy level spacing at Fermi level (E[subscript F]) is comparable to or larger than the superconducting energy gap. As stated in the criterion, the superconductivity correlates greatly with the density of states (DOS) at E[subscript F] within the superconducting gap. The system of individual Pb islands grown on Si(111) provides an ideal platform to modulate the DOS at EF through both the quantum size confinement and the quantum well states (QWS) effects. Moreover, this system excludes the problems of size distribution, couplings among particles and phase fluctuation of the previously studied ensembles of particles. / In my thesis, I first introduce briefly the basic knowledge of superconductivity, such as BCS theory and Eliashberg theory, as well as its behaviors in a normal metal-insulator-superconductor tunneling junction. Then the study of superconductivity by quantum size effect on ensemble superconductors and metallic nanostructures is reviewed. For the widely studied system of Pb islands, I discuss in more detail the recently discovered pseudogap which was important and critical for analyzing the superconductivity. / In chapter 2, the knowledge of sample growth is given and a simple introduction to scanning tunneling spectroscopy is presented. To study the superconductivity spectra of Pb islands, we use two methods to analyze them, one the zero bias conductance (ZBC) method and the other the superconductivity spectrum analysis. In the end of this chapter, Dynes function and deconvolution procedure are introduced in detail. / In chapter 3, I introduce one of my important works in my Phd study, to improve the instrumental energy resolution. By reconstructing the instrumental structure, grounding properly, shielding RF noise, and cleaning the voltage gap source, the instrumental energy resolution has been improved greatly from ~0.9 meV to ~0.2 meV. I compare our current results both with previous results and results from other groups. / Before the instrumental improvement, we find that the measurements were very poor and the conclusion thus obtained were incorrect. To show the importance of the instrumental improvement, I introduce briefly the previous work in chapter 4. Under the poor instrumental condition, we found that the limiting size of superconductivity above 3.2 K was determined to be ~30 nm² for 9 ML thick Pb islands and that Pb island superconductors undergo a change from strong to weak electron-phonon coupling. / After the instrumental improvement, we not only correct some conclusions of the previous studies on superconductivity of 9 ML Pb islands, but also observed the more non-trivial variation of superconductivity from the change of island size or density of state (DOS) at Fermi level (E[subscript F]) by the quantum well states (QWS). A critical regime is observed for small Pb islands. As the DOS of 8 ML Pb islands at E[subscript F] is larger than that of 9 ML Pb islands, the transition temperatures (T[subscript C]) of 8 ML Pb islands hold a systematic difference larger than those of 9 ML Pb islands. The T[subscript C] results for both 8 ML and 9 ML Pb islands follow the same gradual suppression and the ratio 2△(0)/k[subscript B]T[subscript C] remains unchanged by the size effect. Further study indicates that for very small 8 ML and 9 ML Pb islands they are still superconducting, inconsistent with the Anderson criteria and other experimental results. This observation suggests a possible role of wetting layer on superconductivity of these small Pb islands. / This work, I believe, is fundamentally interesting and beneficial to understand deeply the phenomena of superconductivity modulated by size effect and DOS change at E[subscript F] and will inspire more future studies in this field. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Liu, Jiepeng = 掃描隧道譜研究Si(111)表面上單個鉛島的超導尺寸效應及態密度影響 / 羅杰鵬. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 136-144). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese. / Liu, Jiepeng = Sao miao sui dao pu yan jiu Si(111) biao mian shang dan ge qian dao de chao dao chi cun xiao ying ji tai mi du ying xiang / Luo Jiepeng. / Chapter 1 --- Superconductivity affected by quantum size effect --- p.2 / Chapter 1.1 --- Overview --- p.3 / Chapter 1.2 --- Basic theories to superconductivity --- p.4 / Chapter 1.2.1 --- BeS theory --- p.5 / Chapter 1.2.2 --- Eliashberg equation --- p.8 / Chapter 1.2.3 --- Superconductivity of S-I-N tunneling junction --- p.10 / Chapter 1.3 --- Size effect of superconductivity for ensemble or powder superconductors --- p.12 / Chapter 1.3.1 --- Anderson criteria --- p.13 / Chapter 1.3.2 --- Size-dependent T[subscript C] for different superconductors --- p.13 / Chapter 1.4 --- Size effect of superconductivity for metallic nanostructures --- p.17 / Chapter 1.4.1 --- Metallic nanostructures --- p.17 / Chapter 1.4.2 --- Quantum well states of metallic nanostructures --- p.18 / Chapter 1.4.3 --- Pb nanostructures on Si(111)-7 x 7 --- p.20 / Chapter 1.5 --- summary --- p.25 / Chapter 2 --- Experimental introductions and data analysis methods --- p.26 / Chapter 2.1 --- Experimental introduction --- p.27 / Chapter 2.1.1 --- Growth of Pb islands --- p.28 / Chapter 2.1.2 --- Substrates effects --- p.32 / Chapter 2.2 --- STS studies of Pb islands --- p.36 / Chapter 2.2.1 --- Basic knowledge of STS --- p.36 / Chapter 2.2.2 --- STS results of Pb islands --- p.40 / Chapter 2.3 --- Data analysis methods --- p.41 / Chapter 2.3.1 --- Zero bias conductance analysis --- p.41 / Chapter 2.3.2 --- Superconductivity spectrum analysis --- p.43 / Chapter 2.4 --- Dynes function fitting --- p.44 / Chapter 2.4.1 --- Dynes function --- p.44 / Chapter 2.4.2 --- Deconvolution --- p.47 / Chapter 2.4.3 --- BCS-like analysis --- p.49 / Chapter 2.5 --- Summary --- p.50 / Chapter 3 --- Instrument improvements --- p.51 / Chapter 3.1 --- Previously existed problems --- p.52 / Chapter 3.2 --- Problem analysis and solutions --- p.54 / Chapter 3.2.1 --- Structure and Preamplifier --- p.54 / Chapter 3.2.2 --- Grounding --- p.56 / Chapter 3.2.3 --- Bias voltage source cleaning --- p.57 / Chapter 3.2.4 --- RF noise shielding --- p.60 / Chapter 3.3 --- Tip drift in perpendicular direction when taking STS --- p.65 / Chapter 3.4 --- Improved results --- p.68 / Chapter 3.4.1 --- Comparisons with previous results --- p.68 / Chapter 3.4.2 --- Comparisons with other groups --- p.69 / Chapter 3.5 --- Summary --- p.72 / Chapter 4 --- Superconductivity of 9 ML thick Pb islands with poor energy resolution --- p.75 / Chapter 4.1 --- STS results --- p.76 / Chapter 4.1.1 --- STS results at large energy scale --- p.76 / Chapter 4.1.2 --- STS results at small energy scale Zero bias conductance analysis --- p.79 / Chapter 4.2.1 --- ZBC results --- p.79 / Chapter 4.2.2 --- Comparisons with theoretical calculations --- p.83 / Chapter 4.3 --- Superconductivity spectrum analysis --- p.85 / Chapter 4.3.1 --- Method to obtain superconductivity spectra --- p.86 / Chapter 4.3.2 --- BCS-like analysis --- p.93 / Chapter 4.4 --- Explanation and possible mechanism --- p.97 / Chapter 4.5 --- Summary --- p.99 / Chapter 5 --- DOS modulated superconductivity with improved energy resolution --- p.101 / Chapter 5.1 --- Introduction --- p.102 / Chapter 5.2 --- Experiments --- p.103 / Chapter 5.3 --- Behaviors of zero bias conductance results --- p.104 / Chapter 5.3.1 --- Power law behavior --- p.104 / Chapter 5.3.2 --- Critical regime and To determination --- p.106 / Chapter 5.4 --- Recheck previous results --- p.112 / Chapter 5.4.1 --- Pseudogap --- p.112 / Chapter 5.4.2 --- Transition temperature --- p.115 / Chapter 5.5 --- DOS modulated superconductivity --- p.121 / Chapter 5.5.1 --- Quantum well states of 8 ML and 9 ML Pb islands --- p.121 / Chapter 5.5.2 --- T[subscript C] behavior on a 8 ML and 9 ML Pb island --- p.123 / Chapter 5.5.3 --- Superconductivity behaviors for a set of 8 ML and 9 ML Pb islands --- p.124 / Chapter 5.5.4 --- Superconductivity of very small Pb islands --- p.129 / Chapter 5.6 --- Summary --- p.130 / Chapter 6 --- Conclusions and outlook --- p.132 / Chapter 6.1 --- Conclusions --- p.133 / Chapter 6.2 --- Outlook --- p.134 / Bibliography --- p.136

Consider the graph induced by Z^d, equipped with uniformly elliptic random conductances on the edges. At time 0, place a Poisson point process of particles on Z^d and let them perform independent simple random walks with jump probabilities proportional to the conductances. It is well known that without conductances (i.e., all conductances equal to 1), an infection started from the origin and transmitted between particles that share a site spreads in all directions with positive speed. We show that a local mixing result holds for random conductance graphs and prove the existence of a special percolation structure called the Lipschitz surface. Using this structure, we show that in the setup of particles on a uniformly elliptic graph, an infection also spreads with positive speed in any direction. We prove the robustness of the framework by extending the result to infection with recovery, where we show positive speed and that the infection survives indefinitely with positive probability.

Ultrasonic descalers are used in dentistry to remove calculus and other contaminants from teeth. One mechanism which may assist in the cleaning is cavitation generated in cooling water around the descaler. The spatial distribution of cavitation around three designs of descaler tips and under three load conditions has been observed using sonochemiluminescence from a luminol solution and compared with the vibratory motion of the tips in a water bath, characterised by scanning laser vibrometry. The type of cavitation was confirmed by acoustic emission analysed by a ‘Cavimeter’ supplied by NPL. Surface profilometry and SEM of eroded hydroxyapatite pellets was performed to quantitatively study the erosion caused by a descaler tip in both contact and non-contact modes. Densitometry was used to study the erosion of black ink from a glass microscope slide, and determined that under the majority of conditions, no erosion was demonstrated via cavitation, by descalers operating in non-contact mode, although significant erosion was demonstrated with the tip in contact with the slide.

The annual cost of corrosion in the United States Navy and Coast Guard is in excess of $2.7 billion dollars. The salt water environment provides a ripe surrounding for rapid corrosion and deterioration of ship decking, which requires frequent and expensive maintenance. Decks of ships are susceptible to corrosion and wear, but must also maintain a non-slip surface in a constantly wet environment. Few options for non-skid deck materials are currently approved for use by the Navy and require frequent and expensive maintenance or replacement. A new material known as Laser Deposited Non-Skid, currently used in industrial flooring applications, shows potential for serving as a more durable non-skid material with extended service life and greater resistance to corrosion. The purpose of this research is to investigate the feasibility of Laser Deposited Non-Skid in decks of ships and to compare the corrosion, wear and cost data with existing deck materials. Sample plates of A36 and A572 steel and 5086 and 5456 marine grade aluminum alloy were coated with selected non-skid materials and subjected to laboratory salt fog testing and corrosion in environmental conditions in the Caribbean Sea. Wear behavior among non-skid materials was evaluated through wear cycles, measurement of coefficient of friction, and surface characterization. Salt fog testing was more corrosive than the actual operational environment in all cases and the Laser Deposited Non-Skid samples had the best resistance to wear and corrosion. The Peel and Stick Non-Skid demonstrated corrosion by undercutting while the Traditional Non-Skid corroded through the material. The relative area did not correlate well with friction or wear mass loss. Aluminum Laser Deposited Non-Skid appears suitable for use as a deck material on small boats. More research is needed to evaluate maintenance issues and possible stress cracking associated with the Laser Deposited Non-Skid on steel decks.

EEG has been used to explore the electrical activity of the brain for manydecades. During that time, different components of the EEG signal have been iso-lated, characterized, and associated with a variety of brain activities. However, nowidely accepted model characterizing the spatio-temporal structure of the full-brainEEG signal exists to date.Modeling the spatio-temporal nature of the EEG signal is a daunting task. Thespatial component of EEG is defined by the locations of recording electrodes (rang-ing between 2 to 256 in number) placed on the scalp, while its temporal componentis defined by the electrical potentials the electrodes detect. The EEG signal is gen-erated by the composite electrical activity of large neuron assemblies in the brain.These neuronal units often perform independent tasks, giving the EEG signal ahighly dynamic and non-linear character. These characteristics make the raw EEGsignal challenging to work with. Thus, most research focuses on extracting andisolating targeted spatial and temporal components of interest. While componentisolation strategies like independent component analysis are useful, their effective-ness is limited by noise contamination and poor reproducibility. These drawbacks tofeature extraction could be improved significantly if they were informed by a globalspatio-temporal model of EEG data.The aim of this thesis is to introduce a novel data-surface reconstruction (DSR)technique for EEG which can model the integrated spatio-temporal structure of EEGdata. To produce physically intuitive results, we utilize a hyper-coordinate transfor-mation which integrates both spatial and temporal information of the EEG signalinto a unified coordinate system. We then apply a non-uniform rational B spline(NURBS) fitting technique which minimizes the point distance from the computedsurface to each element of the transformed data. To validate the effectiveness of thisproposed method, we conduct an evaluation using a 5-state classification problem;with 1 baseline and 4 meditation states comparing the classification accuracy usingthe raw EEG data versus the surface reconstructed data in the broadband rangeand the alpha, beta, delta, gamma and higher gamma frequencies. Results demon-strate that the fitted data consistently outperforms the raw data in the broadbandspectrum and all frequency spectrums.

We quantify the chemical species present at and reactivity of the tetragonal (100) face of single-crystal methylammonium lead iodide, MAPbI3(100). MAPbI3 is an ABX3 perovskite, experiments utilized the orthogonal reactivity of the A+-site cation, the B2+-site cation, and the X–-site halide anion. Ambient-pressure exposure to BF3 solutions probe the reactivity of interfacial halides. Reactions with p-trifluoromethylanilinium chloride probe the exchange reactivity of the A+-site cation. The ligand 4,4’-bis(trifluoromethyl)-2,2’-bipyridine probe for interfacial B2+-site cations. Fluorine features in x-ray photoelectron spectroscopy (XPS) quantify reaction extents with each solution-phase species. XP spectra reveals adsorption of BF3 indicating surface-available halide anions on tetragonal MAPbI3(100) and preliminary examinations on the (112), (110), and thin-film surfaces. Temperature-programmed desorption (TPD) established a ~200 kJ mol–1 desorption activation energy from tetragonal MAPbI3(100). Adsorption of the fluorinated anilinium cation includes no concomitant adsorption of chlorine as revealed by the absence of Cl 2p features within the limits of XPS detection on the tetragonal (100) and (112) faces with no discernable exchange in preliminary experiments on tetragonal (110). Within detection limits, bipyridine ligand demonstrate no adsorption to tetragonal MAPbI3(100) or (112), while it does demonstrate significant adsorption on the (110) in preliminary experiments. We discuss the present results in the context of interfacial stability, passivation, and reactivity for perovskite-based energy conversion materials and some preliminary investigations into bilayer graphene-based dye sensitized photovoltaic materials.

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Surface plasmon resonance (SPR) biosensors have attracted great attention in scientific research in the past three decades. Extensive studies on the immobilisation of biorecognition elements have been conducted in pursuit of higher sensitivity, but trialled formats have focussed on a thin layer modification next to the plasmon film, which usually requires in situ derivatization. This thesis investigates an 'off-chip' immobilisation strategy for SPR biosensing using silica particles and considers the implications of a particle-modified evanescent field on the signal amplitude and kinetics, for an exemplar affinity binding between immobilised IgG and its anti-IgG complement. Submicron silica particles were synthesized as carriers for the bio-recognition elements. They were then immobilised to form a sub-monolayer on the gold film of an SPR biosensor using two methods: thiolsilane coupling and physical adsorption aided by mechanical pressure. The bio-sensitivity towards an antigen/antibody interaction was lower than an SPR biosensor with an alkanethiolate SAM due to the difference in ligand capacity and position in the evanescent field. The binding kinetics of antigen/antibody pair was found to follow the Langmuir model closely in a continuous flow configuration but was heavily limited by the mass transport from the bulk to the sensor surface in a stop-flow configuration. A packed channel configuration was designed with larger gel particles as ligand carriers, packed on top of a gold film to create a column-modified SPR biosensor. This sensor has comparable bio-sensitivity to the previous sub-monolayer particle-modified systems, but the binding and dissociation of the analyte was heavily dependent on mass transport and binding equilibria across the column. A bi-directional diffusion mechanism was proposed based on a two-compartment mass transport model and the expanded model fitted well with the experimental data. The column-modified sensor was also studied by SPR imaging and analyte band formation was observed and analysed. Using the lateral resolution, a multiplexing particle column configuration was explored, and its potential in distinguishing a multicomponent analyte.

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