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We demonstrate hyperspectral imaging using two time-delayed, coherent extreme ultraviolet (XUV) sources. The approach combines broadband XUV high-harmonic generation, holographic imaging, and Fourier transform spectroscopy. The two harmonics sources are spatially separated at generation,and overlap in the far field resulting in a double slit diffraction pattern. We record the two-dimensional intensity modulation as a function of relative time delay; the Fourier transform determines the spatially dependent spectrum. To reduce the delay jitter and improve the spectral resolution, we demonstrate a novel experimental setup that records the relative delay of the two pulses through optical interference. Moreover, we have demonstrated that this broadband approach can be extended to Fourier transform holographic imaging, which avoids extensive phase retrieval computations. Applications include imaging of biological materials near the carbon K-edge.

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As the rapid evolution in semiconductor technology, transistors’ feature size has reached to 22nm and below, which brings great impact to analog and mixed-signal circuits. As the significant bridge connecting the analog world and digital system, data converter suffers from nonlinearity resulting from mismatch among its unit components. The smaller transistors are, the larger relative mismatch among them becomes. However, using larger transistors leads to more area cost and power consumption. Therefore, researchers have been working hard on how to alleviate the mismatch issue. In recent years, Dynamic Element Matching (DEM) becomes a popular approach that can significantly improve linearity, especially Spurious-free Dynamic Range (SFDR), of a data converter system. The basic idea of DEM is to shuffle the usage pattern of unit elements so that the mismatch error is no longer correlated to the input signal. Thus, DAC’s linearity will be improved. Generally, DEM Nyquist-rate DAC does mismatch scrambling, which smooths distortions resulting from mismatch into white noise. DEM Delta-Sigma DAC does mismatch shaping, which pushes distortions away from the signal band, typically lower frequencies. In this thesis, we focused on mismatch-shaping Delta-Sigma DACs. Two of those various algorithms are implemented logically and physically. With placement and routing information, we got more accurate result on the speed and power dissipation. The comparison shows the tradeoff among number of quantization levels, mismatch-shaping order, and hardware complexity. / text

We present a method for anisotropic mesh refinement to high-order numerical solutions. We accomplish this by assigning metrics to vertices that approximate the error in that region. To choose values for each metric, we first reconstruct an error equation from the leading order terms of the Taylor expansion. Then, we use a Fourier approximation to choose the metric associated with that vertex. After assigning a metric to each vertex, we refine the mesh anisotropically using three mesh operations. The three mesh operations we use are swapping to maximize quality, inserting at approximate circumcenters to decrease cell size, and vertex removal to eliminate small edges. Because there are no guarantees on the results of these modification tools, we use them iteratively to produce a quasi-optimal mesh. We present examples demonstrating that our anisotropic refinement algorithm improves solution accuracy for both second and third order solutions compared with uniform refinement and isotropic refinement. We also analyze the effect of using second derivatives for refining third order solutions.

a b s t r a c t In this paper, a hybrid method using active control and a High Order Differentiator (HOD) methodology is proposed to synchronize chaotic systems. Compared to some traditional active control methods, this new method can synchronize chaotic systems where only output states of the master system are available, i.e. the system is considered a black box. The HOD is used to estimate the derivative information of the master system followed by an active control methodology relying on HOD information. The Qi hyperchaotic system is used to verify the performance of this hybrid method. The proposed method is also compared to some traditional methods. Experimental results show that the proposed method has high synchronization precision and speed and is robust against uncertainties in the master system. The circus implements of the proposed synchronizing scheme are included in this paper. The simulation results show the feasibility of the proposed scheme.

We present a method for anisotropic mesh refinement to high-order numerical solutions. We accomplish this by assigning metrics to vertices that approximate the error in that region. To choose values for each metric, we first reconstruct an error equation from the leading order terms of the Taylor expansion. Then, we use a Fourier approximation to choose the metric associated with that vertex. After assigning a metric to each vertex, we refine the mesh anisotropically using three mesh operations. The three mesh operations we use are swapping to maximize quality, inserting at approximate circumcenters to decrease cell size, and vertex removal to eliminate small edges. Because there are no guarantees on the results of these modification tools, we use them iteratively to produce a quasi-optimal mesh. We present examples demonstrating that our anisotropic refinement algorithm improves solution accuracy for both second and third order solutions compared with uniform refinement and isotropic refinement. We also analyze the effect of using second derivatives for refining third order solutions.

We present a method for anisotropic mesh refinement to high-order numerical solutions. We accomplish this by assigning metrics to vertices that approximate the error in that region. To choose values for each metric, we first reconstruct an error equation from the leading order terms of the Taylor expansion. Then, we use a Fourier approximation to choose the metric associated with that vertex. After assigning a metric to each vertex, we refine the mesh anisotropically using three mesh operations. The three mesh operations we use are swapping to maximize quality, inserting at approximate circumcenters to decrease cell size, and vertex removal to eliminate small edges. Because there are no guarantees on the results of these modification tools, we use them iteratively to produce a quasi-optimal mesh. We present examples demonstrating that our anisotropic refinement algorithm improves solution accuracy for both second and third order solutions compared with uniform refinement and isotropic refinement. We also analyze the effect of using second derivatives for refining third order solutions. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

This thesis develops a study for the frequency warping introduced by time-domain methods. The work in this study focuses first on the time-domain methods used in the classical SPICE engine, that is the Backward Euler, the Trapezoidal Rule and the Gear's methods. Next, the thesis considers the newly developed high-order method based on the Obreshkov formula. This latter method was proved to have the A-stability and L-stability properties, and is therefore robust in circuit simulation. However, to the best of the author's knowledge, a mathematical study for the frequency warping introduced by this method has not been developed yet. The thesis therefore develops the mathematical derivation for the frequency warping of the Obreshkov-based method. The derivations produced reveal that those methods introduce much smaller warping errors than the traditional methods used by SPICE. In order to take advantage of the small warping error, the thesis develops a shooting method framework based on the Obreshkov-based method to compute the steady-state response of nonlinear circuits excited by periodical sources. The new method demonstrates that the steady-state response can be constructed with much smaller number of time points than what is typically required by the classical methods.

The research on transition in supersonic and hypersonic boundary layers has been reinvigorated in the last decades because of the increased interest in high-speed flight. The receptivity to environmental disturbances of high-speed boundary layers developing over flat plates or curved surfaces is a very important problem because the transition process is directly impacted by it. The main objective of the research is to determine the effect of small steps on laminar high-speed boundary-layers that are excited by freestream disturbances in the form of vorticity and acoustic waves. Both supesonic and hypersonic regimes are analyzed using a high-order compressible Navier-Stokes numerical algorithm. It is found that both the backward and the forward steps are capable of stabilizing the disturbances that propagate inside the boundary layer. This will potentially delay the formation of three-dimensional disturbances that are precursors to transition into turbulence.