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An incomplete Latin square is a v x v array with an empty n x n subarray with every row and every column containing each symbol at most once and no row or column with an empty cell containing one of the last n symbols. A set of t incomplete mutually orthogonal Latin squares of order v and hole size n is a set of t incomplete Latin squares (containing the same empty subarray on the same set of symbols) with a natural extension to the condition of orthogonality. The existence of such sets have been previously explored only for small values of t. We determine an asymptotic result for the existence of t incomplete mutually orthogonal Latin squares for general t requiring large holes, which we develop from our results on incomplete pairwise balanced designs and incomplete group divisible designs. / Graduate

本研究希望在市面上常見的潔淨操作檯做迅速、有效的診斷及改進措施。為了實際了解氣流速率大小及分佈情況對塵粒數的影響，需作風速、塵粒數及壓力量測。將潔淨操作檯有效的工作空間分成三層，每層細分15個點位，共計45個量測點。在一般條件下運轉潔淨檯，量測45點位之風速值；之後僅抽換不同形狀之孔洞底板，原底板之孔洞為長條型，實驗加入之形狀為六角形及圓形，並一一重新量測前述各值。考慮到潔淨操作檯後方的流線並不圓滑，遂於其直角轉折處崁加金屬圓滑鈑，加強後方氣流流線之圓滑度，再一一重新量測前述各值重新量測。試驗結果顯示將底板孔洞形狀替換成圓形，潔淨操作檯最常使用的A層穩定度提升了4％，落塵量降低了89%。 / A popular clean bench used in Taiwan will be investigated and improved in a simple and economic way. The working space of the clean bench will be cut in three layers horizontally. There are nine points in a layer uniformly, in other words, there are 45 points in a working space to be measured for airflow speed. Then, to modulate the different airflow streams, different hole shapes and distributions on the bottom plate will be run in a series experiments. The route of the air flow back in the clean bench is existed a right angle, therefore, two smoothing metal plates will also be considered. Test result shows that circular hole is the best one of these experienced hole shapes, and it will increase the stability 4%, decrease the particle 89% in the layer A. / 摘 要 ii ABSTRACT iii 致 謝 iv 目 錄 v 表目錄 ix 圖目錄 xi 第一章 緒 論 1 1.1 研究動機 1 1.2 研究目的 2 1.3 研究方法 2 1.4 文獻回顧 3 1.5 章節內容 4 第二章 潔淨室的原理 5 2.1 潔淨室的起源 5 2.2 潔淨室的需求 6 2.3 潔淨室與氣流關係 7 2.4 無塵分類的規範 7 2.5 潔淨室標準的基礎 8 2.6 國際標準ISO 14644-1規定 9 第三章 實驗設置與研究方法 12 3.1垂直單向流潔淨操作台 12 3.1.1使用過程 13 3.2量測儀器 13 3.3多功能量測儀 14 3.3.1多功能量測儀按鍵 15 3.3.2多功能量測儀功能 16 3.3.3使用說明 17 3.4風速感應器 20 3.4.1風速感應器功能 20 3.4.2使用方法 21 3.4.3風速感應器圖片參考 21 3.5 落塵計 21 3.5.1 落塵計功能 22 3.5.2 落塵計過濾原理 23 3.5.3 落塵計特點 23 3.5.4 落塵計優點 24 3.5.5 落塵計按鍵 25 3.5.6 使用方法 26 3.6 實驗方法 26 3.6.1 儀器設備 26 3.6.2 量測內容 27 3.6.3 量測步驟 27 3.6.4 執行成果 29 3.6.5 孔洞率 30 3.6.6 改善孔洞率 30 第四章 實驗結果與分析討論 32 4.1內部氣流轉彎處未加圓滑金屬片的實驗數據 32 4.1.1長條狀金屬底板 32 4.1.2六角狀金屬底板 34 4.1.3圓孔狀金屬底板 36 4.2內部氣流轉彎處加圓滑金屬片的實驗數據 39 4.2.1長條狀金屬底板 39 4.2.2六角狀金屬底板 40 4.2.3圓孔狀金屬底板 42 4.3改進前綜合討論 45 4.4新圓型孔洞底板對風速及落塵之影響 50 4.5潔淨操作檯各層各點位各種試驗條件之紊流強度 54 4.5.1A層各點位各種試驗條件之紊流強度 54 4.5.2B層各點位各種試驗條件之紊流強度 55 4.5.3C層各點位各種試驗條件之紊流強度 56 4.6各條件之特性分析與討論 57 4.6.1潔淨操作檯試驗段8條件下各層平均風速 57 4.6.2潔淨操作檯8種試驗條件下三層之平均紊流強度 57 4.6.3潔淨操作檯8種試驗條件下三層之均勻度 58 4.6.4八種試驗條件下各層之穩定度及均勻度之平均值 59 4.7潔淨操作檯各層各點位各種試驗條件之穩定度及均勻度 60 4.7.1穩定度和均勻度對A層面的影響 60 4.7.2穩定度和均勻度對B層面的影響 62 4.7.3穩定度和均勻度對C層面的影響 64 4.7.4 綜合討論 65 第五章結論與建議 70 5.1 結 論 70 5.2 建 議 72 參考文獻 74

This thesis addresses the open questions of providing a cosmological model describing an accelerated expanding Universe without violating the energy conditions or a model that contributes to the physical interpretation of the dark energy. The former case is analyzed considering a closed model based on a regular lattice of black holes using the Einstein equation in vacuum. In the latter case I will connect the dark energy to the Shan-Chen equation of state. A comparison between these two proposals is then discussed. As a complementary topic I will discuss the motion of test particles in a general relativistic spacetime undergoing friction effects. This is modeled following the formalism of Poynting-Robertson whose link with the Stokes’ formula is presented. The cases of geodesic and non-geodesic motion are compared and contrasted for Schwarzschild, Tolman, Pant-Sah and Friedman metrics respectively.

Thesis (M.A.) -- University of Montana, 2008. / Title from author supplied metadata. Description based on contents viewed on June 22, 2009. ETD number: etd-12182008-103630. Includes bibliographical references.

Thesis (Ph. D.)--Montana State University--Bozeman, 2003. / Typescript. Chairperson, Graduate Committee: Aleksander Rebane. Includes bibliographical references (p. 178-199).

The rate of tidal disruption events (TDEs), R-TDE, is predicted to depend on stellar conditions near the super-massive black hole (SMBH), which are on difficult-to-measure sub-parsec scales. We test whether R-TDE depends on kpc-scale global galaxy properties, which are observable. We concentrate on stellar surface mass density, Sigma M-*, and velocity dispersion, sigma(nu), which correlate with the stellar density and velocity dispersion of the stars around the SMBH. We consider 35 TDE candidates, with and without known X-ray emission. The hosts range from star-forming to quiescent to quiescent with strong Balmer absorption lines. The last (often with post-starburst spectra) are overrepresented in our sample by a factor of 35(-17)(+21) or 18(-7)(+8), depending on the strength of the H delta absorption line. For a subsample of hosts with homogeneous measurements, Sigma M-* = 10(9)-10(10) M-circle dot/kpc(2), higher on average than for a volume-weighted control sample of Sloan Digital Sky Survey galaxies with similar redshifts and stellar masses. This is because (1) most of the TDE hosts here are quiescent galaxies, which tend to have higher Sigma M-* than the star-forming galaxies that dominate the control, and (2) the star-forming hosts have higher average Sigma M-* than the star-forming control. There is also a weak suggestion that TDE hosts have lower sigma(nu) than for the quiescent control. Assuming that R-TDE infinity Sigma M-*(alpha) x sigma(beta)(nu), and applying a statistical model to the TDE hosts and control sample, we estimate (alpha) over cap = 0.9 +/- 0.2 and (beta) over cap = -1.0 +/- 0.6. This is broadly consistent with RTDE being tied to the dynamical relaxation of stars surrounding the SMBH.

In this thesis we study near-horizon geometries of extreme black holes. We first consider stationary extreme black hole solutions to the Einstein-Yang-Mills theory with a compact semi-simple gauge group in four dimensions, allowing for a negative cosmological constant. We prove that any axisymmetric black hole of this kind possesses a near-horizon AdS2 symmetry and deduce its near-horizon geometry must be that of the abelian embedded extreme Kerr-Newman (AdS) black hole. We show that the near-horizon geometry of any static black hole is a direct product of AdS2 and a constant curvature space. We then consider near-horizon geometry in Einstein gravity coupled to a Maxwell field and a massive complex scalar field, with a cosmological constant. We prove that assuming non-zero coupling between the Maxwell and the scalar fields, there exists no solution with a compact horizon in any dimensions where the massive scalar is non-trivial. This result generalises to any scalar potential which is a monotonically increasing function of the modulus of the complex scalar. Next we determine the most general three-dimensional vacuum spacetime with a negative cosmological constant containing a non-singular Killing horizon. We show that the general solution with a spatially compact horizon possesses a second commuting Killing field and deduce that it must be related to the BTZ black hole (or its near-horizon geometry) by a diffeomorphism. We show there is a general class of asymptotically AdS3 extreme black holes with arbitrary charges with respect to one of the asymptotic-symmetry Virasoro algebras and vanishing charges with respect to the other. We interpret these as descendants of the extreme BTZ black hole. However descendants of the non-extreme BTZ black hole are absent from our general solution with a non-degenerate horizon. We then show that the first order deformation along transverse null geodesics about any near-horizon geometry with compact cross-sections always admits a finite-parameter family of solutions as the most general solution. As an application, we consider the first order expansion from the near-horizon geometry of the extreme Kerr black hole. We uncover a local uniqueness theorem by demonstrating that the only possible black hole solutions which admit a U(1) symmetry are gauge equivalent to the first order expansion of the extreme Kerr solution itself. We then investigate the first order expansion from the near-horizon geometry of the extreme self-dual Myers-Perry black hole in 5D. The only solutions which inherit the enhanced SU(2) X U(1) symmetry and are compatible with black holes correspond to the first order expansion of the extreme self-dual Myers-Perry black hole itself and the extreme J = 0 Kaluza-Klein black hole. These are the only known black holes to possess this near-horizon geometry. If only U(1) X U(1) symmetry is assumed in first order, we find that the most general solution is a three-parameter family which is more general than the two known black hole solutions. This hints the possibility of the existence of new black holes.

When intense laser pulses interact with an atomic or solid target, high order harmonics of the fundamental laser frequency are generated. In the case of atoms, this highly nonlinear optical process is initiated by ionization and terminated by the energetic recollision and recombination of the ionized electron with its correlated ion. In this thesis I demonstrate, both theoretically and experimentally, that high harmonics from bulk crystals can originate from the recollision of electrons with their associated holes, similarly to the atomic case, but where ionization is replaced by excitation of electron-hole pairs that accelerate within the material. This model is first derived from a quantum-mechanical theory of the solid-laser interaction, and then confirmed experimentally in ZnO and Si crystals. Despite the link I establish between high harmonic generation in solids and gases, there are notable dissimilarities. These include: a generalized motion of electrons and holes in their respective bands and its consequences, a more prominent role of dephasing and enhanced sensitivity to perturbing fields. These aspects are investigated throughout this thesis. Finally, I develop a method that exploits the recollision mechanism to reconstruct the momentum-dependent band structure of solids.

In his theory of General Relativity, Einstein describes gravity as a geometric property of spacetime, which deforms in the presence of mass and energy. The accelerated motion of masses produces deformations, which propagate outward from their source at the speed of light. We refer to these radiated deformations as gravitational waves. Over the past several decades, the goal of the Laser Interferometer Gravitational-wave Observatory (LIGO) has been the search for direct evidence of gravitational waves from astrophysical sources, using ground based laser interferometers. As LIGO moves into its Advanced era (aLIGO), the direct detection of gravitational waves is inevitable. With the technology at hand, it is imperative that we have the tools to analyze the detector signal and examine the interesting astrophysical properties of the source. Some of the main targets of this search are coalescing compact binaries. In this thesis, I describe and evaluate bhextractor, a data analysis algorithm that uses Principal Component Analysis (PCA) to identify the main features of a set of gravitational waveforms produced by the coalescence of two black holes. Binary Black Hole (BBH) systems are expected to be among the most common sources of gravitational waves in the sensitivity band of aLIGO. However, the gravitational waveforms emitted by BBH systems are not well modeled and require computationally expensive Numerical Relativity (NR) simulations. bhextractor uses PCA to decompose a catalog of available NR waveforms into a set of orthogonal Principal Components (PCs), which efficiently select the major common features of the waveforms in the catalog and represent a portion of the BBH parameter space. From these PCs, we can reconstruct any waveform in the catalog, and construct new waveforms with similar properties. Using Bayesian analysis and Nested Sampling, one can use bhextractor to classify an arbitrary BBH waveform into one of the available catalogs and estimate the parameters of the gravitational wave source.