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Throughput and complexity tradeoffs in the multi-antenna downlink

Swannack, Charles (Charles Henry)
Fonte: Massachusetts Institute of Technology Publicador: Massachusetts Institute of Technology
Tipo: Tese de Doutorado Formato: 77 p.; 3346386 bytes; 3349522 bytes; application/pdf; application/pdf
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This thesis considers the joint design of the multiplexing and scheduling of independent data streams for the Gaussian multiple-input multiple-output (MIMO) broadcast channel. It is well known that the use of multiple transmit antennas can greatly increase the capacity of the broadcast channel. However, the complexity of a capacity-achieving strategy is dominated by the underlying search for the best user subset to multiplex across the transmitter array, which can be prohibitively high if the number of users is much greater than the transmit dimension. To reduce this complexity, one can limit the search to a smaller set of users while ensuring that this restricted pool contains a set that is close to optimal with high probability. To this end, we define sets with guaranteed signal to interference ratio (SIR) and signal to noise ratio (SNR) values. We provide bounds on the probability that such a set exists. These bounds are derived through an interpretation of the multi-user multi-antenna channel as a random packing of the unit sphere. As such, we provide refined estimates on the content of spherical caps so that they can be applied as a model for interference. We then employ recent developments in the area of random geometric graph theory to characterize the probability of existence.; (cont.) We further show there is a phase transition phenomenon in channel geometry that can be used in the design of efficient algorithms for scheduling in the MIMO broadcast channel. Further...

Distributed computing with imperfect randomness

Vaikuntanathan, Vinod
Fonte: Massachusetts Institute of Technology Publicador: Massachusetts Institute of Technology
Tipo: Tese de Doutorado Formato: 43 p.; 1925681 bytes; 1925680 bytes; application/pdf; application/pdf
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Randomness is a critical resource in many computational scenarios, enabling solutions where deterministic ones are elusive or even provably impossible. However, the randomized solutions to these tasks assume access to a pure source of unbiased, independent coins. Physical sources of randomness, on the other hand, are rarely unbiased and independent although they do seem to exhibit somewhat imperfect randomness. This gap in modeling questions the relevance of current randomized solutions to computational tasks. Indeed, there has been substantial investigation of this issue in complexity theory in the context of the applications to efficient algorithms and cryptography. This work seeks to determine whether imperfect randomness, modeled appropriately, is "good enough" for distributed algorithms. Namely, can we do with imperfect randomness all that we can do with perfect randomness, and with comparable efficiency ? We answer this question in the affirmative, for the problem of Byzantine agreement. We construct protocols for Byzantine agreement in a variety of scenarios (synchronous or asynchronous networks, with or without private channels), in which the players have imperfect randomness. Our solutions are essentially as efficient as the best known randomized Byzantine agreement protocols...

Development of an immersion maskless lithography system

Chao, David, Ph. D. Massachusetts Institute of Technology
Fonte: Massachusetts Institute of Technology Publicador: Massachusetts Institute of Technology
Tipo: Tese de Doutorado Formato: 87 p.; 4995090 bytes; 4999207 bytes; application/pdf; application/pdf
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As lithography quickly approaches its limits with current technologies, a host of new ideas is being proposed in hopes of pushing lithography to new levels of performance. The work presented in this thesis explores the use of an immersion scheme to improve the performance of a maskless lithographic technique known as Zone-Plate-Array Lithography (ZPAL). This is believed to be the first implementation of an immersion scheme in a maskless lithography system. This thesis provides a complete description of the Immersion Zone-Plate-Array Lithography (iZPAL) system. Since the zone plate component of the system is largely responsible for its lithographic performance, a thorough analysis of zone plate theory, design, and fabrication is also presented. The focusing performance of an immersion zone plate is then characterized through the experimental reconstruction of its point spread function. Finally, lithography results obtained with the iZPAL system are compared to those obtained with the non-immersion ZPAL system, demonstrating the improvement in resolution, exposure latitude, and depth-of-focus achieved with the immersion scheme.; by David Chao.; Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science...

A quantitative design and analysis of magnetic nanoparticle heating systems

Khushrushahi, Shahriar Rohinton
Fonte: Massachusetts Institute of Technology Publicador: Massachusetts Institute of Technology
Tipo: Tese de Doutorado Formato: 89 leaves; 4096919 bytes; 4298707 bytes; application/pdf; application/pdf
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Magnetic particles under the influence of an alternating magnetic field act as localized heating sources due to various loss mechanisms. This effect has been extensively investigated in hypothermia studies over the past decades and has recently been applied at the molecular level to control the dehybridization of DNA molecules. As a result, it has the potential of controlling and studying biological systems. To ensure that the nanoparticles are the only source of heat requires a very efficient system that minimizes heat transfer from sources other than the magnetic field. A quantitative analysis of the requirements and the design of such a system was investigated and tested experimentally. Although the results were affected by transmission line effects, the theory supporting the approach is sound and explains the crucial parameters that are necessary for optimizing localized ferromagnetic nanoparticle heating.; by Shahriar Rohinton Khushrushahi.; Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, February 2006.; Includes bibliographical references (leaves 81-89).

Acoustic signal estimation using multiple blind observations

Lee, Joonsung
Fonte: Massachusetts Institute of Technology Publicador: Massachusetts Institute of Technology
Tipo: Tese de Doutorado Formato: 111 p.; 3670858 bytes; 3951085 bytes; application/pdf; application/pdf
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This thesis proposes two algorithms for recovering an acoustic signal from multiple blind measurements made by sensors (microphones) over an acoustic channel. Unlike other algorithms that use a posteriori probabilistic models to fuse the data in this problem, the proposed algorithms use results obtained in the context of data communication theory. This constitutes a new approach to this sensor fusion problem. The proposed algorithms determine inverse channel filters with a predestined support (number of taps). The Coordinated Recovery of Signals From Sensors (CROSS) algorithm is an indirect method, which uses an estimate of the acoustic channel. Using the estimated channel coefficients from a Least-Squares (LS) channel estimation method, we propose an initialization process (zero-forcing estimate) and an iteration process (MMSE estimate) to produce optimal inverse filters accounting for the room characteristics, additive noise and errors in the estimation of the parameters of the room characteristics.; (cont.) Using a measured room channel, we analyze the performance of the algorithm through simulations and compare its performance with the theoretical performance. Also, in this thesis, the notion of channel diversity is generalized and the Averaging Row Space Intersection (ARSI) algorithm is proposed. The ARSI algorithm is a direct method...

New foundations for efficient authentication, commutative cryptography, and private disjointness testing

Weis, Stephen August, 1978-
Fonte: Massachusetts Institute of Technology Publicador: Massachusetts Institute of Technology
Tipo: Tese de Doutorado Formato: 115 p.
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This dissertation presents new constructions and security definitions related to three areas: authentication, cascadable and commutative crytpography, and private set operations. Existing works relevant to each of these areas fall into one of two categories: efficient solutions lacking formal proofs of security or provably-secure, but highly inefficient solutions. This work will bridge this gap by presenting new constructions and definitions that are both practical and provably-secure. The first contribution in the area of efficient authentication is a provably-secure authentication protocol named HB+. The HB+ protocol is efficient enough to be implemented on extremely low-cost devices, or even by a patient human with a coin to flip. The security of HB+ is based on the hardness of a long-standing learning problem that is closely related to coding theory. HB+ is the first authentication protocol that is both practical for low-cost devices, like radio frequency identification (RFID) tags, and provably secure against active adversaries. The second contribution of this work is a new framework for defining and proving the security of cascadable cryptosystems, specifically commutative cryptosystems.; (cont.) This new framework addresses a gap in existing security definitions that fail to handle cryptosystems where ciphertexts produced by cascadable encryption and decryption perations may contain some message-independent history. Several cryptosystems...

Robust stability and contraction analysis of nonlinear systems via semidefinite optimization

Aylward, Erin M
Fonte: Massachusetts Institute of Technology Publicador: Massachusetts Institute of Technology
Tipo: Tese de Doutorado Formato: 110 p.
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A wide variety of stability and performance problems for linear and certain classes of nonlinear dynamical systems can be formulated as convex optimization problems involving linear matrix inequalities (LMIs). These formulations can be solved numerically with computationally-effcient interior-point methods. Many of the first LMI-based stability formulations applied to linear systems and the class of nonlinear systems representable as an interconnection of a linear system with bounded uncertainty blocks. Recently, stability and performance analyses of more general nonlinear deterministic systems, namely those with polynomial or rational dynamics, have been converted into an LMI framework using sum of squares (SOS) programming. SOS programming combines elements of computational algebra and convex optimization to provide e±cient convex relaxations for various computationally-hard problems. In this thesis we extend the class of systems that can be analyzed with LMI-based methods.; (cont.) We show how to analyze the robust stability properties of uncertain non-linear systems with polynomial or rational dynamics, as well as a class of systems with external inputs, via contraction analysis and SOS programming. Specifically, we show how contraction analysis...

Characterization of nanofilter arrays for small molecule separation

Bow, Hansen Chang
Fonte: Massachusetts Institute of Technology Publicador: Massachusetts Institute of Technology
Tipo: Tese de Doutorado Formato: 60 p.
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Experimental studies were performed to evaluate methods of improving separation resolution and speed in microfabricated nanofilter arrays. Experiment parameters investigated include electric field strength, nanofilter geometry, and buffer concentration. DNA polymers of size 25-1000 base pairs were the subject of our study. We concluded that increasing electric field strength resulted in inferior separation for larger DNA polymers (400-1000 bp). Additionally, we quantified the improvement in resolution of smaller nanofilter pores and lower buffer concentration. A theoretical model based on Macrotransport Theory was developed to estimate average species velocity and peak dispersion.; by Hansen Chang Bow.; Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.; Includes bibliographical references (p. 59-60).

Algorithms for data mining

Wang, Grant J. (Grant Jenhorn), 1979-
Fonte: Massachusetts Institute of Technology Publicador: Massachusetts Institute of Technology
Tipo: Tese de Doutorado Formato: 89 p.
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Data of massive size are now available in a wide variety of fields and come with great promise. In theory, these massive data sets allow data mining and exploration on a scale previously unimaginable. However, in practice, it can be difficult to apply classic data mining techniques to such massive data sets due to their sheer size. In this thesis, we study three algorithmic problems in data mining with consideration to the analysis of massive data sets. Our work is both theoretical and experimental - we design algorithms and prove guarantees for their performance and also give experimental results on real data sets. The three problems we study are: 1) finding a matrix of low rank that approximates a given matrix, 2) clustering high-dimensional points into subsets whose points lie in the same subspace, and 3) clustering objects by pairwise similarities/distances.; by Grant J. Wang.; Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.; Includes bibliographical references (p. 81-89).

Characterization and computation of equilibria in infinite games

Stein, Noah D. (Noah Daniel)
Fonte: Massachusetts Institute of Technology Publicador: Massachusetts Institute of Technology
Tipo: Tese de Doutorado Formato: 82 p.
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Broadly, we study continuous games (those with continuous strategy spaces and utility functions) with a view towards computation of equilibria. We cover all of the game-theoretic background needed to understand these results in detail. Then we present new work, which can be divided into three parts. First, it is known that arbitrary continuous games may have arbitrarily complicated equilibria, so we investigate some properties of games with polynomial utility functions and a class of games with polynomial-like utility functions called separable games. We prove new bounds on the complexity of equilibria of separable games in terms of the complexity of the utility functions. In order to measure this complexity we propose a new definition for the rank of a continuous game; when applied to the case of finite games this improves on the results known in that setting. Furthermore, we prove a characterization theorem showing that several conditions which are necessary for a game to possess a finite-dimensional representation each define the class of separable games precisely, providing evidence that separable games are the natural class of continuous games in which to study computation. The characterization theorem also provides a natural connection between separability and the notion of the rank of a game. Second...

A low-power cochlear implant system

Baker, Michael W. (Michael Warren), 1977-
Fonte: Massachusetts Institute of Technology Publicador: Massachusetts Institute of Technology
Tipo: Tese de Doutorado Formato: 179 p.
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Cochlear implants, or bionic ears, restore hearing to the profoundly deaf by bypassing missing inner-ear hair cells in the cochlea and electrically stimulating the auditory nerve. For miniaturized cochlear implants, including behind-the-ear (BTE) models, power consumption is the chief factor in determining cost and patient convenience. This thesis reports on the design of a low-power bionic ear system by addressing three critical signal and power processing subsystems in low-cost CMOS ICs. First, the design of a low-power current-mode front-end for subminiature microphones demonstrates 78dB dynamic range performance with attention to RF noise and supply immunity. Second, hearing-impaired patients need strategies that decide intelligently between listening conditions in speech or noise. This work describes an automatic gain control (AGC) design which uses programmable hybrid analog-digital current-mode feedback to implement a dual-loop strategy, a well-known algorithm for speech in noisy environments. The AGC exhibits level-invariant. stability, programmable time constants and consumes less than 36pW. Third, a feedback-loop technique is explored for analyzing and designing RF power links for transcutaneous bionic ear systems.; (cont.) Using feedback tools to minimize algebraic manipulations...

Development of terahertz quantum-cascade lasers; Development of THz QCLs

Kumar, Sushil, Ph. D. Massachusetts Institute of Technology
Fonte: Massachusetts Institute of Technology Publicador: Massachusetts Institute of Technology
Tipo: Tese de Doutorado Formato: 340 p.
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The terahertz or the far-infrared frequency range of the electromagnetic spectrum ( ... ) has historically been technologically underdeveloped despite having many potential applications, primarily due to lack of suitable sources of coherent radiation. Following on the remarkable development of mid-infrared ( ... ) quantum-cascade lasers (QCLs) in the past decade, this thesis describes the development of electrically-pumped terahertz quantum-cascade lasers in GaAs/AlsGal_.As heterostructures that span a spectral range of 1.59 - 5.0 THz ( ... ). A quantum-cascade laser (QCL) emits photons due to electronic intersubband transitions in the quantum-wells of a semiconductor heterostructure. The operation of terahertz QCLs at frequencies below the Reststrahlen band in the semiconductor ( ... ), is significantly more challenging as compared to that of the mid-infrared QCLs. Firstly, due to small energy separation between the laser levels various intersubband scattering mechanisms are activated, which make it difficult to selectively depopulate the lower laser level. Additionally, as electrons gain enough kinetic energy in the upper laser level thermally activated longitudinal-optical (LO) phonon scattering reduces the level lifetime and makes it difficult to sustain population inversion at higher temperatures.; (cont.) Secondly...

Fabrication of a luminescent solar concentrator that minimizes self-absorption losses using inter-chromophore energy transfer

Currie, Michael James
Fonte: Massachusetts Institute of Technology Publicador: Massachusetts Institute of Technology
Tipo: Tese de Doutorado Formato: 59 p.
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The projected need for carbon-free power during this century is immense. Solar power offers the largest resource base to supply this need, but in light of recent silicon shortages, it is an open question whether silicon photovoltaics can keep pace with demand. The development of economical concentrators could relieve this resource pressure. The luminescent solar concentrator (LSC) is an architecture that collects and concentrates light using the luminescent properties of chromophores embedded in a waveguide. This method of concentration alleviates the need for expensive tracking equipment necessary for optical concentration. Combined with the low cost and flexible fabrication of organic materials, this technology is inherently scalable. A major limitation to LSC efficiency is self-absorption between different chromophores within the waveguide. Finding inspiration from the architecture of phycobilisome antenna complexes, a system of chromophores is developed that minimizes self-absorption through Firster energy transfer. Precise control of intermolecular spacing is achieved through thermal evaporation of small molecule organics. A LSC with a geometric gain of 25 is fabricated that employs this optimized system. External quantum efficiencies of 32% are achieved across nearly half the visible spectrum...

On the synthesis of switched output feedback controllers for linear, time-invariant systems

Santarelli, Keith R. (Keith Robert), 1977-
Fonte: Massachusetts Institute of Technology Publicador: Massachusetts Institute of Technology
Tipo: Tese de Doutorado Formato: 193 p.
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The theory of switching systems has seen many advances in the past decade. Its beginnings were founded primarily due to the physical limitations in devices to implement control such as relays, but today there exists a strong interest in the development of switching systems where switching is introduced as a means of increasing performance. With the newer set of problems that arise from this viewpoint comes the need for many new tools for analysis and design. Analysis tools which include, for instance, the celebrated work on multiple Lyapunov functions are extensive. Tools for the design of switched systems also exist, but, in many cases, the method of designing stabilizing switching laws is often a separate process from the method which is used to determine the set of vector fields between which switching takes place. For instance, one typical method of designing switching controllers for linear, time-invariant (LTI) systems is to first design a set of stabilizing LTI controllers using standard LTI methods, and then design a switching law to increase performance. While such design algorithms can lead to increases in performance, they often impose restrictions that do not allow the designer to take full advantage of the switching architecture being considered.; (cont.) For instance...

A verification framework for hybrid systems

Mitra, Sayan
Fonte: Massachusetts Institute of Technology Publicador: Massachusetts Institute of Technology
Tipo: Tese de Doutorado Formato: 205 p.
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Combining; discrete state transitions with differential equations, Hybrid system models provide an expressive formalism for describing software systems that interact with a physical environment. Automatically checking properties, such as invariance and stability, is extremely hard for general hybrid models, and therefore current research focuses on models with restricted expressive power. In this thesis we take a complementary approach by developing proof techniques that are not necessarily automatic, but are applicable to a general class of hybrid systems. Three components of this thesis, namely, (i) semantics for ordinary and probabilistic hybrid models, (ii) methods for proving invariance, stability, and abstraction, and (iii) software tools supporting (i) and (ii), are integrated within a common mathematical framework. (i) For specifying nonprobabilistic hybrid models, we present Structured Hybrid I/O Automata (SHIOAs) which adds control theory-inspired structures, namely state models, to the existing Hybrid I/O Automata, thereby facilitating description of continuous behavior. We introduce a generalization of SHIOAs which allows both nondeterministic and stochastic transitions and develop the trace-based semantics for this framework. (ii) We present two techniques for establishing lower-bounds on average dwell time (ADT) for SHIOA models. This provides a sufficient condition of establishing stability for SHIOAs with stable state models. A new simulation-based technique which is sound for proving ADT-equivalence of SHIOAs is proposed. We develop notions of approximate implementation and corresponding proof techniques for Probabilistic I/O Automata. Specifically...

Scheduling algorithms for throughput maximization in data networks

Brzezinski, Andrew
Fonte: Massachusetts Institute of Technology Publicador: Massachusetts Institute of Technology
Tipo: Tese de Doutorado Formato: 226 p.
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This thesis considers the performance implications of throughput optimal scheduling in physically and computationally constrained data networks. We study optical networks, packet switches, and wireless networks, each of which has an assortment of features and constraints that challenge the design decisions of network architects. In this work, each of these network settings are subsumed under a canonical model and scheduling framework. Tools of queueing analysis are used to evaluate network throughput properties, and demonstrate throughput optimality of scheduling and routing algorithms under stochastic traffic. Techniques of graph theory are used to study network topologies having desirable throughput properties. Combinatorial algorithms are proposed for efficient resource allocation. In the optical network setting, the key enabling technology is wavelength division multiplexing (WDM), which allows each optical fiber link to simultaneously carry a large number of independent data streams at high rate. To take advantage of this high data processing potential, engineers and physicists have developed numerous technologies, including wavelength converters, optical switches, and tunable transceivers.; (cont.) While the functionality provided by these devices is of great importance in capitalizing upon the WDM resources...

Multiple-antenna systems in ad-hoc wireless networks

Govindasamy, Siddhartan, 1975-
Fonte: Massachusetts Institute of Technology Publicador: Massachusetts Institute of Technology
Tipo: Tese de Doutorado Formato: 229 leaves
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The increasing demand for wireless communication services has resulted in crowding of the electromagnetic spectrum. The "spectral-commons" model, where a portion of the electromagnetic spectrum is public and used on an ad-hoc basis, has been proposed to free up spectrum that has been allocated but underutilized. Ad-hoc wireless networks (networks with no central control) are also interesting in their own right as they do not require costly infrastructure, are robust to single-node failures, and can be deployed in environments where it is difficult to deploy infrastructure. The main contributions of this thesis are expressions for the mean and in some cases the variance of the spectral efficiency (bits/second/Hz) of single-hop links in random wireless networks as a function of the number of antennas per node, link-length, interferer density, and path-loss-exponent (an environmental parameter that determines signal decay with distance), under assumptions chosen for realistic implementability in the near future. These results improve our understanding of such systems as they indicate the data rates achievable as a function of tangible parameters like user density and environmental characteristics, and are useful for designers of wireless networks to trade-off hardware costs...

Stabilizing the dual inverted pendulum : a practical approach

Barton, Taylor Wallis
Fonte: Massachusetts Institute of Technology Publicador: Massachusetts Institute of Technology
Tipo: Tese de Doutorado Formato: 99 p.
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A dual inverted pendulum system, consisting of two individual pendulums of different lengths on a single cart, was fully designed and implemented as a demonstration of classical control theory. This document contains an analysis of the complete control system for both a single and dual inverted pendulum system, as well as the results of the implementation. Also presented are the all-analog systems which were used along with an industrial permanent magnet linear synchronous motor to control and drive the pendulum cart, including a voltage-controlled oscillator, three-phase switching power amplifier, and acceleration feedback controller.; by Taylor Wallis Barton.; Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008.; This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.; Includes bibliographical references (p. 99).

Ferrofluid surface and volume flows in uniform rotating magnetic fields

Elborai, Shihab M. (Shihab Mahmoud), 1977-
Fonte: Massachusetts Institute of Technology Publicador: Massachusetts Institute of Technology
Tipo: Tese de Doutorado Formato: 260 p.
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Ferrofluid surface and volume effects in uniform dc and rotating magnetic fields are studied. Theory and corroborating measurements are presented for meniscus shapes and resulting surface driven flows, spin-up flows, and Hele-Shaw cell flows and instabilities. To characterize the water-based and oil-based ferrofluids used in experiments, measurements were made of the magnetization curve, surface tension, viscosity, density, and the speed of sound. Extensive measurements of the height and shape of ferrofluid menisci in applied uniform dc magnetic fields show that the height of the meniscus increases for vertical applied magnetic fields, whereas horizontal magnetic fields decrease meniscus height. An approximate energy minimization analysis agrees with the observed trends in ferrofluid meniscus height. The effects of ferrofluid meniscus curvature on spin-up flow were modeled under simplified assumptions. Analytical solutions were derived for two dimensional low Reynolds number flows and extended results were obtained numerically using COMSOL's Multiphysics finite element software package (FEMLAB) to solve for three dimensional recirculating flows at higher Reynolds numbers.; (cont.) Familiar magnetostatic energy expressions in linear magnetic media were extended to non-linear magnetization relations. These energy expressions were applied to study the effects of linear and non-linear magnetization on flows and instabilities in Hele-Shaw cells with simultaneously applied in-plane rotating and dc axial magnetic fields. Ultrasound velocimetry of the spin-up flow in the bulk region of water-based ferrofluids conclusively demonstrates the co-rotation of the bulk of the ferrofluid with the applied rotating magnetic field with and without a free surface. Careful ultrasound investigation of flow profiles at different heights in uncovered ferrofluid cylinders showed flow direction reversal between the counter-rotating top free surface and the co-rotating bulk region of the ferrofluid. A framework for a numerical solution of the coupled governing equations of conservation of linear and angular momentum in magnetic spin-up flows that considers all the terms in the first Shliomis magnetization relaxation equation was formulated and solved. Previous solutions in the literature which decouple the magnetic and fluid mechanical dynamics by neglecting the linear and spin velocities in the magnetization relaxation equations result in no spin-up flow in uniform magnetic fields in the absence of spin diffusion effects.; (cont.) Contrary to the commonly held view in the literature...

Efficient numerical algorithms for surface formulations of mathematical models for biomolecule analysis and design

Bardhan, Jaydeep Porter, 1978-
Fonte: Massachusetts Institute of Technology Publicador: Massachusetts Institute of Technology
Tipo: Tese de Doutorado Formato: 193 p.
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This thesis presents a set of numerical techniques that extend and improve computational modeling approaches for biomolecule analysis and design. The presented research focuses on surface formulations of modeling problems related to the estimation of the energetic cost to transfer a biomolecule from the gas phase to aqueous solution. The thesis discusses four contributions to modeling biomolecular interactions. First, the thesis presents an approach to allow accurate discretization of the most prevalent mathematical definitions of the biomolecule-solvent interface; also presented are a number of accurate techniques for numerically integrating possibly singular functions over the discretized surfaces. Such techniques are essential for solving surface formulations numerically. The second part of the thesis presents a fast multiscale numerical algorithm, FFTSVD, that efficiently solves large boundary-element method problems in biomolecule electrostatics. The algorithm synthesizes elements of other popular fast algorithms to achieve excellent efficiency and flexibility. The third thesis component describes an integral-equation formulation and boundary-element method implementation for biomolecule electrostatic analysis.; (cont.) The formulation and implementation allow the solution of complicated molecular topologies and physical models. Furthermore...