较高阶非线性抽运-探测过程中的空间效应

在飞秒抽运一探测光谱技术中，空间分辨的探测光信号反映了在不同空间位置的材料的非线性效应。当抽运光强度增大时，探测光信号中会出现明显的高阶特别是五阶非线性效应。利用劈裂算子方法直接解决了一维非线性传播方程的问题。在数值模拟中，研究了在不同抽运强度和位置下的抽运一探测过程中的五阶非线性效应。在足够高的抽运场下，探测信号出现清晰的振荡，显示了三阶和五阶非线性效应之间的干涉。当空间位置离抽运场中心足够远时，五阶比三阶非线性效应的衰减快得多，对其物理机制和趋势进行了定性的讨论。

Simulation of shock-induced bubble collapse with application to vascular injury in shockwave lithotripsy

Shockwave lithotripsy is a noninvasive medical procedure wherein shockwaves are repeatedly focused at the location of kidney stones in order to pulverize them. Stone comminution is thought to be the product of two mechanisms: the propagation of stress waves within the stone and cavitation erosion. However, the latter mechanism has also been implicated in vascular injury. In the present work, shock-induced bubble collapse is studied in order to understand the role that it might play in inducing vascular injury. A high-order accurate, shock- and interface-capturing numerical scheme is developed to simulate the three-dimensional collapse of the bubble in both the free-field and inside a vessel phantom. The primary contributions of the numerical study are the characterization of the shock-bubble and shock-bubble-vessel interactions across a large parameter space that includes clinical shockwave lithotripsy pressure amplitudes, problem geometry and tissue viscoelasticity, and the subsequent correlation of these interactions to vascular injury. Specifically, measurements of the vessel wall pressures and displacements, as well as the finite strains in the fluid surrounding the bubble, are utilized with available experiments in tissue to evaluate damage potential. Estimates are made of the smallest injurious bubbles in the microvasculature during both the collapse and jetting phases of the bubble's life cycle. The present results suggest that bubbles larger than 1 μm in diameter could rupture blood vessels under clinical SWL conditions.

Imperfection Insensitive Thin Shells

The buckling of axially compressed cylindrical shells and externally pressurized spherical shells is extremely sensitive to even very small geometric imperfections. In practice this issue is addressed by either using overly conservative knockdown factors, while keeping perfect axial or spherical symmetry, or adding closely and equally spaced stiffeners on shell surface. The influence of imperfection-sensitivity is mitigated, but the shells designed from these approaches are either too heavy or very expensive and are still sensitive to imperfections. Despite their drawbacks, these approaches have been used for more than half a century.

This thesis proposes a novel method to design imperfection-insensitive cylindrical shells subject to axial compression. Instead of following the classical paths, focused on axially symmetric or high-order rotationally symmetric cross-sections, the method in this thesis adopts optimal symmetry-breaking wavy cross-sections (wavy shells). The avoidance of imperfection sensitivity is achieved by searching with an evolutionary algorithm for smooth cross-sectional shapes that maximize the minimum among the buckling loads of geometrically perfect and imperfect wavy shells. It is found that the shells designed through this approach can achieve higher critical stresses and knockdown factors than any previously known monocoque cylindrical shells. It is also found that these shells have superior mass efficiency to almost all previously reported stiffened shells.

Experimental studies on a design of composite wavy shell obtained through the proposed method are presented in this thesis. A method of making composite wavy shells and a photogrametry technique of measuring full-field geometric imperfections have been developed. Numerical predictions based on the measured geometric imperfections match remarkably well with the experiments. Experimental results confirm that the wavy shells are not sensitive to imperfections and can carry axial compression with superior mass efficiency.

An efficient computational method for the buckling analysis of corrugated and stiffened cylindrical shells subject to axial compression has been developed in this thesis. This method modifies the traditional Bloch wave method based on the stiffness matrix method of rotationally periodic structures. A highly efficient algorithm has been developed to implement the modified Bloch wave method. This method is applied in buckling analyses of a series of corrugated composite cylindrical shells and a large-scale orthogonally stiffened aluminum cylindrical shell. Numerical examples show that the modified Bloch wave method can achieve very high accuracy and require much less computational time than linear and nonlinear analyses of detailed full finite element models.

This thesis presents parametric studies on a series of externally pressurized pseudo-spherical shells, i.e., polyhedral shells, including icosahedron, geodesic shells, and triambic icosahedra. Several optimization methods have been developed to further improve the performance of pseudo-spherical shells under external pressure. It has been shown that the buckling pressures of the shell designs obtained from the optimizations are much higher than the spherical shells and not sensitive to imperfections.

高阶群速度色散引起的高斯超短脉冲宽度的展宽和形变

基于动量守恒和光参变过程中的三波耦合波方程, 和负单轴非线性光学晶体CsLiB6O10的色散方程, 研究了在光参变效应中超短激光脉冲由于群速度色散引起的展宽和形变。数值模拟显示, 在超短脉冲波形为双曲正割形和无啁啾调制时, 高阶群速度色散引起的超短脉冲为50 fs时, 晶体长度为10 mm, 紫外光213 nm作为基波入射时的脉冲展宽是波长为532 nm绿光在同等条件下的1.6倍。脉冲展宽程度与入射波长和晶体长度有关, 波长越短和晶体长度越长则脉冲展宽和波形变化越严重,高阶色散引起的超短高斯脉冲展宽, 将

Fast numerical methods for mixed, singular Helmholtz boundary value problems and Laplace eigenvalue problems - with applications to antenna design, sloshing, electromagnetic scattering and spectral geometry

This thesis presents a novel class of algorithms for the solution of scattering and eigenvalue problems on general two-dimensional domains under a variety of boundary conditions, including non-smooth domains and certain "Zaremba" boundary conditions - for which Dirichlet and Neumann conditions are specified on various portions of the domain boundary. The theoretical basis of the methods for the Zaremba problems on smooth domains concern detailed information, which is put forth for the first time in this thesis, about the singularity structure of solutions of the Laplace operator under boundary conditions of Zaremba type. The new methods, which are based on use of Green functions and integral equations, incorporate a number of algorithmic innovations, including a fast and robust eigenvalue-search algorithm, use of the Fourier Continuation method for regularization of all smooth-domain Zaremba singularities, and newly derived quadrature rules which give rise to high-order convergence even around singular points for the Zaremba problem. The resulting algorithms enjoy high-order convergence, and they can tackle a variety of elliptic problems under general boundary conditions, including, for example, eigenvalue problems, scattering problems, and, in particular, eigenfunction expansion for time-domain problems in non-separable physical domains with mixed boundary conditions.

The astrophysics of strongly interacting systems

This thesis presents investigations in four areas of theoretical astrophysics: the production of sterile neutrino dark matter in the early Universe, the evolution of small-scale baryon perturbations during the epoch of cosmological recombination, the effect of primordial magnetic fields on the redshifted 21-cm emission from the pre-reionization era, and the nonlinear stability of tidally deformed neutron stars.

In the first part of the thesis, we study the asymmetry-driven resonant production of 7 keV-scale sterile neutrino dark matter in the primordial Universe at temperatures T >~ 100 MeV. We report final DM phase space densities that are robust to uncertainties in the nature of the quark-hadron transition. We give transfer functions for cosmological density fluctuations that are useful for N-body simulations. We also provide a public code for the production calculation.

In the second part of the thesis, we study the instability of small-scale baryon pressure sound waves during cosmological recombination. We show that for relevant wavenumbers, inhomogenous recombination is driven by the transport of ionizing continuum and Lyman-alpha photons. We find a maximum growth factor less than ≈ 1.2 in 10⁷ random realizations of initial conditions. The low growth factors are due to the relatively short duration of the recombination epoch.

In the third part of the thesis, we propose a method of measuring weak magnetic fields, of order 10^-19 G (or 10^-21 G if scaled to the present day), with large coherence lengths in the inter galactic medium prior to and during the epoch of cosmic reionization. The method utilizes the Larmor precession of spin-polarized neutral hydrogen in the triplet state of the hyperfine transition. We perform detailed calculations of the microphysics behind this effect, and take into account all the processes that affect the hyperfine transition, including radiative decays, collisions, and optical pumping by Lyman-alpha photons.

In the final part of the thesis, we study the non-linear effects of tidal deformations of neutron stars (NS) in a compact binary. We compute the largest three- and four-mode couplings among the tidal mode and high-order p- and g-modes of similar radial wavenumber. We demonstrate the near-exact cancellation of their effects, and resolve the question of the stability of the tidally deformed NS to leading order. This result is significant for the extraction of binary parameters from gravitational wave observations.

XPM-induced pulse compression in birefringent dispersion decreasing fiber

The pulse compression induced by cross-phase modulation in birefringent dispersion decreasing fiber is discussed theoretically by solving the coupled Schrodinger equations which include the contribution of the high-order non-linear effects, and third-order dispersion. In particular, it is found that a high quality compressed signal pulse can be obtained by a pump pulse of low intense through the technique. The dependence of optimum compression on the non-linear factor N, time delay tau(d) and the dispersive ratio f is also discussed in detail. (c) 2005 Elsevier B.V. All rights reserved.

In situ surface topography measurement method of granite base in scanning wafer stage with laser interferometer

Topography of a granite surface has an effect on the vertical positioning of a wafer stage in a lithographic tool, when the wafer stage moves on the granite. The inaccurate measurement of the topography results in a bad leveling and focusing performance. In this paper, an in situ method to measure the topography of a granite surface with high accuracy is present. In this method, a high-order polynomial is set up to express the topography of the granite surface. Two double-frequency laser interferometers are used to measure the tilts of the wafer stage in the X- and Y-directions. From the sampling tilts information, the coefficients of the high-order polynomial can be obtained by a special algorithm. Experiment results shows that the measurement reproducibility of the method is better than 10 nm. (c) 2006 Elsevier GmbH. All rights reserved.

Distributed Optimal Control of Cyber-Physical Systems: Controller Synthesis, Architecture Design and System Identification

The centralized paradigm of a single controller and a single plant upon which modern control theory is built is no longer applicable to modern cyber-physical systems of interest, such as the power-grid, software defined networks or automated highways systems, as these are all large-scale and spatially distributed. Both the scale and the distributed nature of these systems has motivated the decentralization of control schemes into local sub-controllers that measure, exchange and act on locally available subsets of the globally available system information. This decentralization of control logic leads to different decision makers acting on asymmetric information sets, introduces the need for coordination between them, and perhaps not surprisingly makes the resulting optimal control problem much harder to solve. In fact, shortly after such questions were posed, it was realized that seemingly simple decentralized optimal control problems are computationally intractable to solve, with the Wistenhausen counterexample being a famous instance of this phenomenon. Spurred on by this perhaps discouraging result, a concerted 40 year effort to identify tractable classes of distributed optimal control problems culminated in the notion of quadratic invariance, which loosely states that if sub-controllers can exchange information with each other at least as quickly as the effect of their control actions propagates through the plant, then the resulting distributed optimal control problem admits a convex formulation.

The identification of quadratic invariance as an appropriate means of "convexifying" distributed optimal control problems led to a renewed enthusiasm in the controller synthesis community, resulting in a rich set of results over the past decade. The contributions of this thesis can be seen as being a part of this broader family of results, with a particular focus on closing the gap between theory and practice by relaxing or removing assumptions made in the traditional distributed optimal control framework. Our contributions are to the foundational theory of distributed optimal control, and fall under three broad categories, namely controller synthesis, architecture design and system identification.

We begin by providing two novel controller synthesis algorithms. The first is a solution to the distributed H-infinity optimal control problem subject to delay constraints, and provides the only known exact characterization of delay-constrained distributed controllers satisfying an H-infinity norm bound. The second is an explicit dynamic programming solution to a two player LQR state-feedback problem with varying delays. Accommodating varying delays represents an important first step in combining distributed optimal control theory with the area of Networked Control Systems that considers lossy channels in the feedback loop. Our next set of results are concerned with controller architecture design. When designing controllers for large-scale systems, the architectural aspects of the controller such as the placement of actuators, sensors, and the communication links between them can no longer be taken as given -- indeed the task of designing this architecture is now as important as the design of the control laws themselves. To address this task, we formulate the Regularization for Design (RFD) framework, which is a unifying computationally tractable approach, based on the model matching framework and atomic norm regularization, for the simultaneous co-design of a structured optimal controller and the architecture needed to implement it. Our final result is a contribution to distributed system identification. Traditional system identification techniques such as subspace identification are not computationally scalable, and destroy rather than leverage any a priori information about the system's interconnection structure. We argue that in the context of system identification, an essential building block of any scalable algorithm is the ability to estimate local dynamics within a large interconnected system. To that end we propose a promising heuristic for identifying the dynamics of a subsystem that is still connected to a large system. We exploit the fact that the transfer function of the local dynamics is low-order, but full-rank, while the transfer function of the global dynamics is high-order, but low-rank, to formulate this separation task as a nuclear norm minimization problem. Finally, we conclude with a brief discussion of future research directions, with a particular emphasis on how to incorporate the results of this thesis, and those of optimal control theory in general, into a broader theory of dynamics, control and optimization in layered architectures.

一种新的光学非球面度计算方法

提出了一种新的、能完全统一二次非球面与高次非球面的非球面度计算,且能直接得出最接近球的球心位置的计算方法面积长度法.该方法的计算内涵是两条相似曲线分别与某一固定点围成的面积应相等,且两条曲线的长度应非常接近.计算实例表明该方法计算结果准确,且易于编程,运算速度快.

基于正交频率变换的高功率蓝绿全固态激光器

对多横模全固态激光器使用正交频率变换进行了分析,计算了频率转换效率与激光发散角的关系。使用双KTP晶体正交倍频的方法,对Nd∶YAG激光器输出的含有高阶横模的激光进行倍频实验研究。在1064 nm Nd∶YAG激光基波功率密度为121 MW/cm2时,其谐波转换效率达到75.5%。研究表明,对于光束质量较差的基波激光,采用正交频率变换的方式,适当选择晶体参数,同样可以获得较高效率的二次谐波输出。

大模场面积多模光纤激光器的横模控制

缠绕技术通常被用于大模场面积多模光纤激光器的横模控制。将光纤弯曲成不同半径的圆环，多模光纤激光器的高阶横模逐个被抑制并在缠绕半径为20mm时，获得15.4W的单模激光输出。实验研究表明，缠绕半径减小时，由于激光器高阶模式被抑制，其光束质量变好，同时其斜率效率降低。实验测量了多模光纤激光器在不同缠绕半径下的输出性能，并理论计算了各阶模式在不同缠绕半径下的损耗特性。实验测量结果与理论计算结果符合得较好。

多模光纤激光器实现高功率低阶模输出

采用光纤缠绕的方法，来抑制大模场面积（LMA）双包层光纤激光器中的高阶模振荡。将光纤缠绕至两种不同半径，实验测量了相应条件下激光器的输出功率和光束质量因子M2。缠绕半径为165mm时，输出功率为217W，M2为2.96；缠绕半径为52mm时，输出功率为160W，M2为1.38。光纤激光器相应的斜率效率分别为60％和48％。光纤缠绕半径较小时，虽然激光器输出功率减小，但其亮度是大缠绕半径时对应值的3.4倍。