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The project is an activity based, interdisciplinary curriculum for a simulated outdoor camp that occurs primarily within the elementary classroom. The purpose of the camp is to increase the students' level of awareness of and appreciation for the outdoors.

随着全球金融市场的日益创新和不断加剧的竞争，金融产品也变得越来越结构复杂。这些复杂的金融产品，从定价，对冲到风险管理，都对相应的数学技术提出越来越高的要求。在目前运用的技术中，蒙特卡洛模拟方法由于其广泛的适用性而备受欢迎。本篇论文对于在金融工程和工业界都受到广泛关注的两个问题进行研究：局部化以及对于受布朗运动驱动的随机微分方程的精确抽样；布朗河曲，重要性抽样已经对于扩散过程极值的无偏估计。 / 第一篇文章考虑了使用蒙特卡洛模拟方法产生随机微分方程的样本路径。离散化方法是此前普遍使用的近似产生路径的方法：这种方法很容易实施，但是会产生抽样偏差。本篇文章提出一种模拟方法，可用于随机微分方程路径的精确抽样。一个至关重要的发现是：随机微分方程的概率分布可以被分解为两部分的乘积，一部分是标准布朗运动的概率分布，另外一部分是双重随机的泊松过程。基于这样的分解和局部化技术，本篇文章提出一种接受-拒绝算法。数值试验可以验证，这种方法的均方误差-计算时间的收敛速度可以达到O(t⁻¹[superscript /]²)，优于传统的离散化方法。更进一步的优点是：这种方法可以对带边界的随机微分方程进行精确抽样，而带边界的微分方程正是传统离散方法经常遇到困难的情形。 / 第二篇文章研究了如何计算基于扩散过程极值的泛函。传统的离散化方法收率速度很慢。本篇文章提出了一种基于维纳测度分解的无偏蒙特卡洛估计。运用重要性抽样技术和对于布朗运动路径的威廉分解，本篇文章将对于一般性扩散过程的极值的抽样化简为对于两个布朗河曲的抽样。数值试验部分也验证了本篇文章所提方法的准确性和计算上的高效率。 / With increased innovation and competition in the current financial market, financial product has become more and more complicated, which requires advanced techniques in pricing, hedging and risk management. Monte Carlo simulation is among the most popular ones due to its great °exibility. This dissertation contains two problems recently arises and receives much attention from both the financial engineering and simulation communities: Localization and Exact Simulation of Brownian Motion Driven Stochastic Differential Equations; And Brownian Meanders, Importance Sampling and Un-biased Simulation of Diffusion Extremes. / The first essay considers generating sample paths of stochastic differential equations (SDE) using the Monte Carlo method. Discretization is a popular approximate approach to generating those paths: it is easy to implement but prone to simulation bias. This essay presents a new simulation scheme to exactly generate samples for SDEs. The key observation is that the law of a general SDE can be decomposed into a product of the law of standard Brownian motion and the law of a doubly stochastic Poisson process. An acceptance-rejection algorithm is devised based on the combination of this decomposition and a localization technique. The numerical results corroborates that the mean-square error of the proposed method is in the order of O(t⁻¹[superscript /]²), which is superior to the conventional discretization schemes. Furthermore, the proposed method also can generate exact samples for SDE with boundaries which the discretization schemes usually find difficulty in dealing with. / The second essay considers computing expected values of functions involving extreme values of diffusion processes. The conventional discretization Monte Carlo simulation schemes often converge very slowly. In this paper, we propose a Wiener measure decomposition-based approach to construct unbiased Monte Carlo estimators. Combined with the importance sampling technique and the celebrated Williams' path decomposition of Brownian motion, this approach transforms the task of simulating extreme values of a general diffusion process to the simulation of two Brownian meanders. The numerical experiments show the accuracy and efficiency of our Poisson-kernel unbiased estimators. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Huang, Zhengyu. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 107-115). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese. / Abstract --- p.i / Acknowledgement --- p.iv / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Background --- p.1 / Chapter 1.2 --- SDEs and Discretization Methods --- p.4 / Chapter 1.3 --- The Beskos-Roberts Exact Simulation --- p.15 / Chapter 1.4 --- Major Contributions --- p.19 / Chapter 1.5 --- Organization --- p.26 / Chapter 2 --- Localization and Exact Simulation of SDEs --- p.27 / Chapter 2.1 --- Main Result: A Localization Technique --- p.27 / Chapter 2.1.1 --- Sampling of ζ --- p.33 / Chapter 2.1.2 --- Sampling of Wζ^(T-t) --- p.35 / Chapter 2.1.3 --- Sampling of the Bernoulli I --- p.38 / Chapter 2.1.4 --- Comparison Involving Infinite Sums --- p.40 / Chapter 2.2 --- Discussions --- p.43 / Chapter 2.2.1 --- One Extension: SDEs with Boundaries --- p.43 / Chapter 2.2.2 --- Simulation Efficiency --- p.45 / Chapter 2.2.3 --- Extension to Multi-dimensional SDE --- p.48 / Chapter 2.3 --- Numerical Examples --- p.52 / Chapter 2.3.1 --- Ornstein-Uhlenbeck Mean-Reverting Process --- p.52 / Chapter 2.3.2 --- A Double-Well Potential Model --- p.56 / Chapter 2.3.3 --- Cox-Ingersoll-Ross Square-Root Process --- p.56 / Chapter 2.3.4 --- Linear-Drift CEV-Type-Diffusion Model --- p.62 / Chapter 2.4 --- Appendix --- p.62 / Chapter 2.4.1 --- Simulation of Brownian Bridges --- p.62 / Chapter 2.4.2 --- Proofs of Main Results --- p.64 / Chapter 2.4.3 --- The Oscillating Property of the Series --- p.71 / Chapter 3 --- Unbiased Simulation of Diffusion Extremes --- p.79 / Chapter 3.1 --- A Wiener Measure Decomposition --- p.79 / Chapter 3.2 --- Brownian Meanders and Importance Sampler of Diffusion Extremes --- p.81 / Chapter 3.2.1 --- Exact Simulation of (θT, KT, WT) --- p.83 / Chapter 3.2.2 --- Simulating Importance Sampling Weight --- p.84 / Chapter 3.3 --- Some Extensions --- p.88 / Chapter 3.3.1 --- Variance Reduction --- p.88 / Chapter 3.3.2 --- Double Barrier Options --- p.90 / Chapter 3.4 --- Numerical Examples --- p.94 / Chapter 3.5 --- Appendix --- p.98 / Chapter 3.5.1 --- Brownian Bridges and Meanders --- p.98 / Chapter 3.5.2 --- Proofs of Main Results --- p.101 / Bibliography --- p.107

Silicon photonics has witnessed rapid development in recent years for its fabrication compatibility with the cost-effective CMOS technology. The advancement of relevant simulation tools, however, is at a relatively slow pace. The high index contrast of the usual silicon waveguide that has imposed new challenges to the convergence and accuracy of the solution technique, the growing intricacy in solitary component design, and the increased complexity of their integration, are the impelling factors that motivate us to improve the computer-aided design, modeling, simulation, and optimization methods. The theme of the thesis is on the frequency domain simulation methods supported by the complex mode theory. The complex mode theory is introduced to the simulation domain truncated by the perfectly matching layers (PMLs) enclosed in the perfectly reflected boundaries (PRBs), wherein the discrete complex modes as eigen solutions can represent the continuous radiation fields, thus yields a unified approach for handling both guided (discrete) and radiation (continuous) waves. In this thesis, theoretical investigations have been conducted along a few different lines aiming at improving the efficiency and accuracy in complex mode expansion. Properties of high-order complex Berenger modes are firstly addressed through asymptotic solutions, and it is found that as the mode order increases, the symmetry of the cladding and substrate in the simulation domain, instead of the guiding schemes, plays a more and more decisive role regarding mode classification and modal field distribution. A weighed optical path method is then proposed to unify the high-order Berenger modes, and to enhance the symmetry of high order modes’ field distributions in the asymmetric structures, leading to the improvement in convergence speed and stability in the mode expansion. Next, an improved mode-matching method (MMM) is proposed based on an error-minimizing method instead of the conventional approach relying on the unreliable modal orthogonal property. The newly proposed method is significantly more robust as numerical errors usually jeopardize the modal orthogonality. This claim is exemplified by simulation results on silicon channel waveguide facet, bending waveguide, and silicon-germanium photo-detector waveguide. As a direct application of the improved complex mode theory, a hybrid plasmonic-photonic nano-ribbon waveguide is proposed, standing as a combination of the silicon slot and surface plasmon polariton (SPP) waveguides, is proposed and analyzed. We have found that the fundamental mode is featured at low loss as in optical waveguide as well as high confinement as in plasmonic structure. Simulations have shown that millimeter range propagation can be sustained with strong confinement. We have further studied such waveguide with an extra layer of phase changing material incorporated, attempting to realize the efficient electro-optical phase and/or loss modulation. Finally, an optical switch design is proposed by taking the full advantage of the aforementioned structure. / Thesis / Doctor of Philosophy (PhD)

The animated vehicle turning path simulation system on Internet/Intranet web browser presented in this project is intended to provide civil engineers with an easy-to-use, all functional simulation system that could help them with highway and street design.

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abstract: High Voltage Direct Current (HVDC) technology is being considered for several long distance point-to-point overhead transmission lines, because of their lower losses and higher transmission capability, when compared to AC systems. Insulators are used to support and isolate the conductors mechanically and electrically. Composite insulators are gaining popularity for both AC and DC lines, for the reasons of light weight and good performance under contaminated conditions. This research illustrates the electric potential and field computation on HVDC composite insulators by using the charge simulation method. The electric field is calculated under both dry and wet conditions. Under dry conditions, the field distributions along the insulators whose voltage levels range from 500 kV to 1200 kV are calculated and compared. The results indicate that the HVDC insulator produces higher electric field, when compared to AC insulator. Under wet conditions, a 500 kV insulator is modeled with discrete water droplets on the surface. In this case, the field distribution is affected by surface resistivity and separations between droplets. The corona effects on insulators are analyzed for both dry and wet conditions. Corona discharge is created, when electric field strength exceeds the threshold value. Corona and grading rings are placed near the end-fittings of the insulators to reduce occurrence of corona. The dimensions of these rings, specifically their radius, tube thickness and projection from end fittings are optimized. This will help the utilities design proper corona and grading rings to reduce the corona phenomena. / Dissertation/Thesis / M.S. Electrical Engineering 2013

<div>Life cycle cost analysis (LCCA) has been defined as a method to assess the total cost of a project. It is a simple tool to use when a single project has different alternatives that fulfill the original requirements. Different alternatives could differ in initial investment, operational and maintenance costs among other long term costs. The cost involved in building a bridge depends upon many different factors. Moreover, long-term cost needs to be considered to estimate the true overall cost of the project and determine its life-cycle cost. Without watchful consideration of the long-term costs and full life cycle costing, current investment decisions that look attractive could result in a waste of economic resources in the future. This research is focused on short and medium span bridges (between 30-ft and 130-ft) which represents 65\% of the NBI INDIANA bridge inventory. </div><div><br></div><div>Bridges are categorized in three different groups of span ranges. Different superstructure types are considered for both concrete and steel options. Types considered include: bulb tees, AASHTO prestressed beams, slab bridges, prestressed concrete box beams, steel beams, steel girders, folded plate girders and simply supported steel beams for dead load and continuous for live load (SDCL). A design plan composed of simply supported bridges and continuous spans arrangements was carried out. Analysis for short and medium span bridges in Indiana based on LCCA is presented for different span ranges and span configurations. </div><div><br></div><div>Deterministic and stochastic analysis were done for all the span ranges considered. Monte Carlo Simulations (MCS) were used and the categorization of the different superstructure alternatives was done based on stochastic dominance. First, second, almost first and almost second stochastic dominance rules were used to determined the efficient set for each span length and all span configurations. Cost-effective life cycle cost profiles for each superstructure type were proposed. Additionally, the top three cost-effective alternatives for superstructure types depending on the span length are presented as well as the optimum superstructure types set for both simply supported and continuous beams. Results will help designers to consider the most cost-effective bridge solution for new projects, resulting in cost savings for agencies involved.</div>

Philosophiae Doctor - PhD / In this thesis we study a range of related commercial banking problems in discrete and continuous time settings. The first problem is about a capital allocation strategy that optimizes the expected future value of a commercial bank’s total non-risk-weighted assets (TNRWAs) in terms of terminal time utility maximization. This entails finding optimal amounts of Total capital for investment in different bank assets. Based on the optimal capital allocation strategy derived for the first problem, we derive stochastic models for respectively the bank’s capital adequacy and liquidity ratios in the second and third problems. The Basel Committee on Banking Supervision (BCBS) introduced these ratios in an attempt to improve the regulation of the international banking industry in terms of capital adequacy and liquidity management. As a fourth problem we derive a multi-period deposit insurance pricing model which incorporates the optimal capital allocation strategy, the BCBS’ latest capital standard, capital forbearance and moral hazard. In the fifth and final problem we show how the values of LIBOR-in-arrears and vanilla interest rate swaps, typically used by commercial banks and other financial institutions to reduce risk, can be derived under a specialized version of the affine interest rate model originally considered by the bank in question. More specifically, in the first problem we assume that the bank invests its Total capital in a stochastic interest rate financial market consisting of three assets, viz., a treasury security, a marketable security and a loan. We assume that the interest rate in the market is described by an affine model, and that the value of the loan follows a jump-diffusion process. We wish to find the optimal capital allocation strategy that maximizes an expected logarithmic utility of the bank’s TNRWAs at a future date. Generally, analytical solutions to stochastic optimal control problems in the jump setting are very difficult to obtain. We propose an approximation method that exploits a similarity between the forms of the control problems of the jump-diffusion model and the diffusion model obtained by removing the jump. With the jump assumed sufficiently small, the analytical solution of the diffusion model then serves as a proxy to the solution of the control problem with the jump. In the second problem we construct models for the bank’s capital adequacy ratios in terms of the proxy. We present numerical simulations to characterize the behaviour of the capital adequacy ratios. Furthermore, in this chapter, we consider the approximate optimal capital allocation strategy subject to a constant Leverage Ratio, which is a specific non-risk-based capital adequacy ratio, at the minimum prescribed level. We derive a formula for the bank’s TNRWAs at constant (minimum) Leverage Ratio value and present numerical simulations based on the modified TNRWAs formula. In the third problem we model the bank’s liquidity ratios and we monitor the levels of the liquidity ratios under the proxy numerically. In the fourth problem we derive a multi-period deposit insurance pricing model, the latest capital standard a la Basel III, capital forbearance and moral hazard behaviour. The deposit insurance pricing method utilizes an asset value reset rule comparable to the typical practice of insolvency resolution by insuring agencies. We perform numerical computations with our model to study its implications. In the final problem, we specialize the affine interest rate model considered previously to the Cox-Ingersoll-Ross (CIR) interest rate dynamic. We consider fixed-for-floating interest rate swaps under the CIR model. We show how analytical expressions for the values of both a LIBOR-in-arrears swap and a vanilla swap can be derived using a Green’s function approach. We employ Monte Carlo simulation methods to compute the values of the swaps for different scenarios. We wish to make explicit the contributions of this project to the literature. A research article titled “An Optimal Portfolio and Capital Management Strategy for Basel III Compliant Commercial Banks” by Grant E. Muller and Peter J. Witbooi [1] has been published in an accredited scientific journal. In the aforementioned paper we solve an optimal capital allocation problem for diffusion banking models. We propose using the solution of the Brownian motions control problem of [1] as the proxy in problems two to four of this thesis. Furthermore, we wish to note that the methodology employed on the final problem of this study is actually from the paper [2] of Mallier and Alobaidi. In the paper [2] the authors did not present simulation studies to characterize their pricing models. We contribute a simulation study in which the values of the swaps are computed via Monte Carlo simulation methods.

With the emergence of Fifth Generation (5G) mobile networks, the employment ofhigher frequencies in the millimeter-wave (mmWave) range and the realization of agreat number of beams in 5G radio base stations (RBS) make the electromagnetic (EM)simulation of RBS products very costly in terms of hardware and time requirements.In order to compute the electromagnetic field (EMF) exposure in close proximity of theRBS, more efficient simulation methods are required.The move to mmWave frequencies enables the use of the so-called high frequencymethods for EM simulation with RBS antennas. In this thesis, conventional fullwavesimulation solvers and different implementations of hybridization of highfrequency methods with conventional methods are used with different commercial EMsimulation tools, and their performance is evaluated for the purpose of EMF exposureassessment in close proximity of 5G mmWave RBS.Among all the investigated methods, the hybrid scheme with Finite IntegrationTechnique (FIT) and Shooting and Bouncing Rays (SBR) methods, e.g., thatimplemented in CST Studio Suite 2020, outperforms in terms of hardwarerequirements and time costs, although the accuracy is compromised on the side andbehind the mmWave RBS. The Multilevel Fast Multipole Method (MLFMM), e.g.,that implemented in Altair FEKO 2019, though not a hybrid method, also has goodperformance but requires very large Random Access Memory (RAM), and it cannothandle very exquisite details of RBS. The Finite Difference Time Domain (FDTD)method implemented in EMPIRE XPU can also handle the investigated problemseffciently, but for extremely large problems, its requirements on RAM may become thebottleneck. In the thesis, many other hybrid implementations are also investigated,but it is found that they are not suitable for the EMF exposure assessment in closeproximity of the mmWave RBS with evaluation on a planar area of 0.42 m × 1 m at 28 GHz due to various reasons. / För den femte generationens (5G) mobilnät kommer användningen av millimetervågoroch det stora antalet lober som en radiobasstation (RBS) kan hantera att betydaett kraftigt ökat behov av hårdvara och större tidsåtgång för att göra beräkningarav exponeringen för elektromagnetiska fält nära utrustningen. Därför behövs mereffektiva simuleringsmetoder.Eftersom systemen opererar på millimetervåg-frekvenser kan högfrekvensmetoderanvändas i simuleringen av simuleringen av en RBS. I den här avhandlingenutvärderas konventionella metoder, samt olika hybridmetoder för beräkningenav EMF-exponeringen av millimetervågor i närheten av en RBS. De utvärderadehybridmetoderna är implementerade i olika mjukvaror och blandar användandet avhögfrekvensmetoder och konventionella metoder.Av alla utvärderade metoder fungerar hybridmetoden implementerad med finitaintegralmetoden (FIT) och ”Shooting and Bouncing Rays”-metoden (SBR) i CST bästi termer av vilken hårdvara som behövs för beräkningarna och för tidsåtgången.Dock är noggrannheten i beräkningarna på sidan av och bakom RBSen mindrebra. Multilevel Fast Multipole Method (MLFMM)”-lösaren i Feko i FEKO använderingen hybridmetod men presterar bra, men den kräver mycket RAM-minne och kaninte ta hänsyn till små detaljer i RBSen. Finita differensmetoden i tidsdomänen(FDTD) i EMPIRE kan också användas men dess RAM-krav blir en flaskhals förstora simuleringar. Ytterligare hybridmetoder är undersökta i avhandlingen men medslutsatsen att de inte är användbara (av olika anledningar) för beräkningen av EMFexponeringenfrån en RBS opererandes på frekvensen 28 GHz och över en yta som är0.42 x 1 m.