Fluid phenomena dominated by viscous effects can, in many cases, be modeled by the Stokes equations. The boundary integral form of the Stokes equations reduces the number of degrees of freedom in a numerical discretization by reformulating the three-dimensional problem to two-dimensional integral equations to be discretized over the boundaries of the domain. Hence for the study of objects immersed in a fluid, such as drops or elastic/solid particles, integral equations are to be discretized over the surfaces of these objects only. As outer boundaries or confinements are added these must also be included in the formulation. An inherent difficulty in the numerical treatment of boundary integrals for Stokes flow is the integration of the singular fundamental solution of the Stokes equations, e.g. the so called Stokeslet. To alleviate this problem we developed a set of high-order quadrature rules for the numerical integration of the Stokeslet over a flat surface. Such a quadrature rule was first designed for singularities of the type <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?1/%7C%5Cmathbf%7Bx%7D%7C" />. To assess the convergence properties of this quadrature rule a theoretical analysis has been performed. The slightly more complicated singularity of the Stokeslet required certain modifications of the integration rule developed for <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?1/%7C%5Cmathbf%7Bx%7D%7C" />. An extension of this type of quadrature rule to a cylindrical surface is also developed. These quadrature rules are tested also on physical problems that have an analytic solution in the literature. Another difficulty associated with boundary integral problems is introduced by periodic boundary conditions. For a set of particles in a periodic domain periodicity is imposed by requiring that the motion of each particle has an added contribution from all periodic images of all particles all the way up to infinity. This leads to an infinite sum which is not absolutely convergent, and an additional physical constraint which removes the divergence needs to be imposed. The sum is decomposed into two fast converging sums, one that handles the short range interactions in real space and the other that sums up the long range interactions in Fourier space. Such decompositions are already available in the literature for kernels that are commonly used in boundary integral formulations. Here a decomposition in faster decaying sums than the ones present in the literature is derived for the periodic kernel of the stress tensor. However the computational complexity of the sums, regardless of the decomposition they stem from, is <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Cmathcal%7BO%7D(N%5E%7B2%7D)" />. This complexity can be lowered using a fast summation method as we introduced here for simulating a sedimenting fiber suspension. The fast summation method was initially designed for point particles, which could be used for fibers discretized numerically almost without any changes. However, when two fibers are very close to each other, analytical integration is used to eliminate numerical inaccuracies due to the nearly singular behavior of the kernel and the real space part in the fast summation method was modified to allow for this analytical treatment. The method we have developed for sedimenting fiber suspensions allows for simulations in large periodic domains and we have performed a set of such simulations at a larger scale (larger domain/more fibers) than previously feasible. / <p>QC 20121122</p>

The approaches for discretizing the direction variable in particle transport calculations are the discrete-ordinates method and function-expansion methods. Both approaches are limited if the transport solution is not smooth. Angular discretization errors in the discrete-ordinates method arise from the inability of a given quadrature set to accurately perform the needed integrals over the direction ("angular") domain. We propose that an adaptive discrete-ordinate algorithm will be useful in many problems of practical interest. We start with a "base quadrature set" and add quadrature points as needed in order to resolve the angular flux function. We compare an interpolated angular-flux value against a calculated value. If the values are within a user specified tolerance, the point is not added; otherwise it is. Upon the addition of a point we must recalculate weights. Our interpolatory functions map angular-flux values at the quadrature directions to a continuous function that can be evaluated at any direction. We force our quadrature weights to be consistent with these functions in the sense that the quadrature integral of the angular flux is the exact integral of the interpolatory function (a finite-element methodology that determines coefficients by collocation instead of the usual weightedresidual procedure). We demonstrate our approach in two-dimensional Cartesian geometry, focusing on the azimuthal direction The interpolative methods we test are simple linear, linear in sine and cosine, an Abu-Shumays “base” quadrature with a simple linear adaptive and an Abu-Shumays “base” quadrature with a linear in sine and cosine adaptive. In the latter two methods the local refinement does not reduce the ability of the base set to integrate high-order spherical harmonics (important in problems with highly anisotropic scattering). We utilize a variety of one-group test problems to demonstrate that in all cases, angular discretization errors (including "ray effects") can be eliminated to whatever tolerance the user requests. We further demonstrate through detailed quantitative analysis that local refinement does indeed produce a more efficient placement of unknowns. We conclude that this work introduces a very promising approach to a long-standing problem in deterministic transport, and we believe it will lead to fruitful avenues of further investigation.

Quadrature LO signal is a key element in many of the RF transceivers which tend to dominate today’s wireless communication technology. The design of a quadrature LC VCO with better phase noise and lower power consumption forms the core of this work. This thesis investigates a coupling mechanism to implement a quadrature voltage controlled oscillator using indirect injection method. The coupling network in this QVCO couples the two LC cores with their super-harmonic and it recycles its bias current back into the LC tank such that the power consumed by the coupling network is insignificant. This recycled current enables the oscillator to achieve higher amplitude of oscillation for the same power consumption compared to conventional design, hence assuring better phase noise. Mathematical analysis has been done to study the mechanism of quadrature operation and mismatch effects of devices on the quadrature phase error of the proposed QVCO. The proposed quadrature LC VCO is designed in TSMC 0.18 μm technology. It is tunable from 2.61 GHz - 2.85 GHz with sensitivity of 240 MHz/V. Its worst case phase noise is -120 dBc/Hz at 1 MHz offset. The total layout area is 1.41 mm^2 and the QVCO core totally draws 3 mA current from 1.8 V supply.

This research aims to design and implement GaAs HBT MMICs for the two crucial components in W-CDMA transmitters, quadrature modulator and upconverter, with thorough evaluation of the package and PCB effects. To construct a strong theoretical foundation, the small-signal modeling of HBTs and the EM-characterization of package and PCB interconnects are intensively studied. In this dissertation, a novel extrinsic-inductance independent approach is developed for direct extraction of the intrinsic elements in a hybrid-pi equivalent circuit of HBTs. The interconnects of leadless RFIC packages and test PCBs are investigated using the 3-D EM simulation tools and transformed into the equivalent circuits for co-analysis with the designed HBT MMICs. The first HBT MMIC design is a W-CDMA direct-conversion quadrature modulator incorporating a new 90 degrees phase shifter. Although the proposed 90 degrees phase shifter has a remarkable advantage over the others in implementation loss, it is rather susceptible to the package and PCB effects, resulting in a moderate degradation of EVM. The second HBT MMIC design is a W-CDMA upconverter incorporating a popular micromixer. Although the micromixer-based upconverter consumes much less current at low output powers to achieve the same high linearity when compared to a Gilbert mixer-based design, it is quite susceptible to the package and PCB effects, causing a significant degradation in ACPR. Comparison between theory and measurement shows good agreement in evaluating the influences of package and PCB interconnects on both HBT MMICs.

The approaches for discretizing the direction variable in particle transport calculations are the discrete-ordinates method and function-expansion methods. Both approaches are limited if the transport solution is not smooth. Angular discretization errors in the discrete-ordinates method arise from the inability of a given quadrature set to accurately perform the needed integrals over the direction ("angular") domain. We propose that an adaptive discrete-ordinate algorithm will be useful in many problems of practical interest. We start with a "base quadrature set" and add quadrature points as needed in order to resolve the angular flux function. We compare an interpolated angular-flux value against a calculated value. If the values are within a user specified tolerance, the point is not added; otherwise it is. Upon the addition of a point we must recalculate weights. Our interpolatory functions map angular-flux values at the quadrature directions to a continuous function that can be evaluated at any direction. We force our quadrature weights to be consistent with these functions in the sense that the quadrature integral of the angular flux is the exact integral of the interpolatory function (a finite-element methodology that determines coefficients by collocation instead of the usual weightedresidual procedure). We demonstrate our approach in two-dimensional Cartesian geometry, focusing on the azimuthal direction The interpolative methods we test are simple linear, linear in sine and cosine, an Abu-Shumays â baseâ quadrature with a simple linear adaptive and an Abu-Shumays â baseâ quadrature with a linear in sine and cosine adaptive. In the latter two methods the local refinement does not reduce the ability of the base set to integrate high-order spherical harmonics (important in problems with highly anisotropic scattering). We utilize a variety of one-group test problems to demonstrate that in all cases, angular discretization errors (including "ray effects") can be eliminated to whatever tolerance the user requests. We further demonstrate through detailed quantitative analysis that local refinement does indeed produce a more efficient placement of unknowns. We conclude that this work introduces a very promising approach to a long-standing problem in deterministic transport, and we believe it will lead to fruitful avenues of further investigation.

This paper presents numerical solutions to integration problems with bivariate integrands. Using equally spaced nodes in Adaptive Simpson's Rule as a base case, two ways of sampling the domain over which the integration will take place are examined. Drawing from Ouellette and Fiume, Voronoi sampling is used along both axes of integration and the corresponding points are used as nodes in an unequally spaced degree two Newton-Cotes method. Then the domain of integration is triangulated and used in the Triangular Prism Rules discussed by Limaye. Finally, both of these techniques are tested by running simulations over heavily oscillatory and monomial (up to degree five) functions over polygonal regions.

Ανασκόπηση του κανόνα ολοκλήρωσης του gauss. Αναπαραστάσεις και εκτιμήσεις του υπολοίπου του. Τέλος περί της σύγκλισης του κανόνα ολοκλήρωσης. / A survey on gaussian quqdrature rules. Representation and estimates of its remainder. And about its convergence.

The rapid growth of the market for short-range wireless devices, with standards such as Bluetooth and Wireless LAN (IEEE 802.11) being the most important, has created a need for highly integrated transceivers that target drastic power and area reduction while providing a high level of integration. The radio section of the devices designed to establish communications using these standards is the limiting factor for the power reduction efforts. A key building block in a transceiver is the frequency synthesizer, since it operates at the highest frequency of the system and consumes a very large portion of the total power in the radio. This dissertation presents the basic theory and a design methodology of frequency synthesizers targeted for short-range wireless applications. Three different examples of synthesizers are presented. First a frequency synthesizer integrated in a Bluetooth receiver fabricated in 0.35μm CMOS technology. The receiver uses a low-IF architecture to downconvert the incoming Bluetooth signal to 2MHz. The second synthesizer is integrated within a dual-mode receiver capable of processing signals of the Bluetooth and Wireless LAN (IEEE 802.11b) standards. It is implemented in BiCMOS technology and operates the voltage controlled oscillator at twice the required frequency to generate quadrature signals through a divide-by-two circuit. A phase switching prescaler is featured in the synthesizer. A large capacitance is integrated on-chip using a capacitance multiplier circuit that provides a drastic area reduction while adding a negligible phase noise contribution. The third synthesizer is an extension of the second example. The operation range of the VCO is extended to cover a frequency band from 4.8GHz to 5.85GHz. By doing this, the synthesizer is capable of generating LO signals for Bluetooth and IEEE 802.11a, b and g standards. The quadrature output of the 5 - 6 GHz signal is generated through a first order RC - CR network with an automatic calibration loop. The loop uses a high frequency phase detector to measure the deviation from the 90° separation between the I and Q branches and implements an algorithm to minimize the phase errors between the I and Q branches and their differential counterparts.

Optical Coherence Tomography (OCT) is a subsurface imaging technique with many biomedical and industrial applications. In this thesis, we describe our design and implementation of a time domain OCT system. We used this system to obtain OCT images of objects that are important in different applications. We also used an existing quadrature OCT system to obtain both real and imaginary parts of an OCT image. We introduced a new interpretation of OCT images as the 2nd derivative of the scattering potential of an object. To obtain this scattering potential from its 2nd derivative, we implemented a method of definite integration in the spectral-domain. The obtained scattering potential was used to separate the scattering profile from the absorption profile of an object. We applied this new spectroscopic imaging method to quadrature OCT images of different objects.

Abstract Subsampling can be used in a radio receiver to perform signal downconversion and sample-and-hold operations in order to relieve the operation frequency and bandwidth requirements of the subsequent discrete-time circuitry. However, due to the inherent aliasing behaviour of wideband noise and interference in subsampling, and the difficulty of implementing appropriate bandpass anti-aliasing filtering at high frequencies, straightforward use of a low subsampling rate can result in significant degradation of the receiver dynamic range. The aim of this thesis is to investigate and implement methods for integrating filtering into high-frequency signal sampling and downconversion by subsampling to alleviate the requirements for additional front-end filters and to mitigate the effects of noise and out-of-band signal aliasing, thereby facilitating use in integrated high-quality radio receivers. The charge-domain sampling technique studied here allows simple integration of both continuous-and discrete-time filtering functions into high-frequency signal sampling. Gated current integration results in a lowpass sin(x)/x(sinc(x)) response capable of performing built-in anti-aliasing filtering in baseband signal sampling. Weighted integration of several successive current samples can be further used to obtain an embedded discrete-time finite-impulse-response (FIR) filtering response, which can be used for internal anti-aliasing and image-rejection filtering in the downconversion of bandpass signals by subsampling. The detailed analysis of elementary charge-domain sampling circuits presented here shows that the use of integrated FIR filtering with subsampling allows acceptable noise figures to be achieved and can provide effective internal anti-aliasing rejection. The new methods for increasing the selectivity of elementary charge-domain sampling circuits presented here enable the integration of advanced, digitally programmable FIR filtering functions into high-frequency signal sampling, thereby markedly relieving the requirements for additional anti-aliasing, image rejection and possibly even channel selection filters in a radio receiver. BiCMOS and CMOS IF sampler implementations are presented in order to demonstrate the feasibility of the charge-domain sampling technique for integrated anti-aliasing and image-rejection filtering in IF signal quadrature downconversion by subsampling. Circuit measurements show that this sampling technique for built-in filtering results in an accurate frequency response and allows the use of high subsampling ratios while still achieving a competitive dynamic range.