Matching Items (54)
Description
Solution methods for certain linear and nonlinear evolution equations are presented in this dissertation. Emphasis is placed mainly on the analytical treatment of nonautonomous differential equations, which are challenging to solve despite the existent numerical and symbolic computational software programs available. Ideas from the transformation theory are adopted allowing one to solve the problems under consideration from a non-traditional perspective. First, the Cauchy initial value problem is considered for a class of nonautonomous and inhomogeneous linear diffusion-type equation on the entire real line. Explicit transformations are used to reduce the equations under study to their corresponding standard forms emphasizing on natural relations with certain Riccati(and/or Ermakov)-type systems. These relations give solvability results for the Cauchy problem of the parabolic equation considered. The superposition principle allows to solve formally this problem from an unconventional point of view. An eigenfunction expansion approach is also considered for this general evolution equation. Examples considered to corroborate the efficacy of the proposed solution methods include the Fokker-Planck equation, the Black-Scholes model and the one-factor Gaussian Hull-White model. The results obtained in the first part are used to solve the Cauchy initial value problem for certain inhomogeneous Burgers-type equation. The connection between linear (the Diffusion-type) and nonlinear (Burgers-type) parabolic equations is stress in order to establish a strong commutative relation. Traveling wave solutions of a nonautonomous Burgers equation are also investigated. Finally, it is constructed explicitly the minimum-uncertainty squeezed states for quantum harmonic oscillators. They are derived by the action of corresponding maximal kinematical invariance group on the standard ground state solution. It is shown that the product of the variances attains the required minimum value only at the instances that one variance is a minimum and the other is a maximum, when the squeezing of one of the variances occurs. Such explicit construction is possible due to the relation between the diffusion-type equation studied in the first part and the time-dependent Schrodinger equation. A modication of the radiation field operators for squeezed photons in a perfect cavity is also suggested with the help of a nonstandard solution of Heisenberg's equation of motion.
ContributorsVega-Guzmán, José Manuel, 1982- (Author) / Sulov, Sergei K (Thesis advisor) / Castillo-Chavez, Carlos (Thesis advisor) / Platte, Rodrigo (Committee member) / Chowell-Puente, Gerardo (Committee member) / Arizona State University (Publisher)
Created2013
Description
Vector Fitting (VF) is a recent macromodeling method that has been popularized by its use in many commercial software for extracting equivalent circuit's of simulated networks. Specifically for material measurement applications, VF is shown to estimate either the permittivity or permeability of a multi-Debye material accurately, even when measured in the presence of noise and interferences caused by test setup imperfections. A brief history and survey of methods utilizing VF for material measurement will be introduced in this work. It is shown how VF is useful for macromodeling dielectric materials after being measured with standard transmission line and free-space methods. The sources of error in both an admittance tunnel test device and stripline resonant cavity test device are identified and VF is employed for correcting these errors. Full-wave simulations are performed to model the test setup imperfections and the sources of interference they cause are further verified in actual hardware measurements. An accurate macromodel is attained as long as the signal-to-interference-ratio (SIR) in the measurement is sufficiently high such that the Debye relaxations are observable in the data. Finally, VF is applied for macromodeling the time history of the total fields scattering from a perfectly conducting wedge. This effort is an initial test to see if a time domain theory of diffraction exists, and if the diffraction coefficients may be exactly modeled with VF. This section concludes how VF is not only useful for applications in material measurement, but for the solution of modeling fields and interactions in general.
ContributorsRichards, Evan (Author) / Diaz, Rodolfo E (Thesis advisor) / Tsakalis, Konstantinos (Committee member) / Platte, Rodrigo (Committee member) / Arizona State University (Publisher)
Created2013
Description
The properties of materials depend heavily on the spatial distribution and connectivity of their constituent parts. This applies equally to materials such as diamond and glasses as it does to biomolecules that are the product of billions of years of evolution. In science, insight is often gained through simple models with characteristics that are the result of the few features that have purposely been retained. Common to all research within in this thesis is the use of network-based models to describe the properties of materials. This work begins with the description of a technique for decoupling boundary effects from intrinsic properties of nanomaterials that maps the atomic distribution of nanomaterials of diverse shape and size but common atomic geometry onto a universal curve. This is followed by an investigation of correlated density fluctuations in the large length scale limit in amorphous materials through the analysis of large continuous random network models. The difficulty of estimating this limit from finite models is overcome by the development of a technique that uses the variance in the number of atoms in finite subregions to perform the extrapolation to large length scales. The technique is applied to models of amorphous silicon and vitreous silica and compared with results from recent experiments. The latter part this work applies network-based models to biological systems. The first application models force-induced protein unfolding as crack propagation on a constraint network consisting of interactions such as hydrogen bonds that cross-link and stabilize a folded polypeptide chain. Unfolding pathways generated by the model are compared with molecular dynamics simulation and experiment for a diverse set of proteins, demonstrating that the model is able to capture not only native state behavior but also partially unfolded intermediates far from the native state. This study concludes with the extension of the latter model in the development of an efficient algorithm for predicting protein structure through the flexible fitting of atomic models to low-resolution cryo-electron microscopy data. By optimizing the fit to synthetic data through directed sampling and context-dependent constraint removal, predictions are made with accuracies within the expected variability of the native state.
ContributorsDe Graff, Adam (Author) / Thorpe, Michael F. (Thesis advisor) / Ghirlanda, Giovanna (Committee member) / Matyushov, Dmitry (Committee member) / Ozkan, Sefika B. (Committee member) / Treacy, Michael M. J. (Committee member) / Arizona State University (Publisher)
Created2011
Description
This thesis describes an approach to system identification based on compressive sensing and demonstrates its efficacy on a challenging classical benchmark single-input, multiple output (SIMO) mechanical system consisting of an inverted pendulum on a cart. Due to its inherent non-linearity and unstable behavior, very few techniques currently exist that are capable of identifying this system. The challenge in identification also lies in the coupled behavior of the system and in the difficulty of obtaining the full-range dynamics. The differential equations describing the system dynamics are determined from measurements of the system's input-output behavior. These equations are assumed to consist of the superposition, with unknown weights, of a small number of terms drawn from a large library of nonlinear terms. Under this assumption, compressed sensing allows the constituent library elements and their corresponding weights to be identified by decomposing a time-series signal of the system's outputs into a sparse superposition of corresponding time-series signals produced by the library components. The most popular techniques for non-linear system identification entail the use of ANN's (Artificial Neural Networks), which require a large number of measurements of the input and output data at high sampling frequencies. The method developed in this project requires very few samples and the accuracy of reconstruction is extremely high. Furthermore, this method yields the Ordinary Differential Equation (ODE) of the system explicitly. This is in contrast to some ANN approaches that produce only a trained network which might lose fidelity with change of initial conditions or if facing an input that wasn't used during its training. This technique is expected to be of value in system identification of complex dynamic systems encountered in diverse fields such as Biology, Computation, Statistics, Mechanics and Electrical Engineering.
ContributorsNaik, Manjish Arvind (Author) / Cochran, Douglas (Thesis advisor) / Kovvali, Narayan (Committee member) / Kawski, Matthias (Committee member) / Platte, Rodrigo (Committee member) / Arizona State University (Publisher)
Created2011
Description
Conformational changes in biomolecules often take place on longer timescales than are easily accessible with unbiased molecular dynamics simulations, necessitating the use of enhanced sampling techniques, such as adaptive umbrella sampling. In this technique, the conformational free energy is calculated in terms of a designated set of reaction coordinates. At the same time, estimates of this free energy are subtracted from the potential energy in order to remove free energy barriers and cause conformational changes to take place more rapidly. This dissertation presents applications of adaptive umbrella sampling to a variety of biomolecular systems. The first study investigated the effects of glycosylation in GalNAc2-MM1, an analog of glycosylated macrophage activating factor. It was found that glycosylation destabilizes the protein by increasing the solvent exposure of hydrophobic residues. The second study examined the role of bound calcium ions in promoting the isomerization of a cis peptide bond in the collagen-binding domain of Clostridium histolyticum collagenase. This study determined that the bound calcium ions reduced the barrier to the isomerization of this peptide bond as well as stabilizing the cis conformation thermodynamically, and identified some of the reasons for this. The third study represents the application of GAMUS (Gaussian mixture adaptive umbrella sampling) to on the conformational dynamics of the fluorescent dye Cy3 attached to the 5' end of DNA, and made predictions concerning the affinity of Cy3 for different base pairs, which were subsequently verified experimentally. Finally, the adaptive umbrella sampling method is extended to make use of the roll angle between adjacent base pairs as a reaction coordinate in order to examine the bending both of free DNA and of DNA bound to the archaeal protein Sac7d. It is found that when DNA bends significantly, cations from the surrounding solution congregate on the concave side, which increases the flexibility of the DNA by screening the repulsion between phosphate backbones. The flexibility of DNA on short length scales is compared to the worm-like chain model, and the contribution of cooperativity in DNA bending to protein-DNA binding is assessed.
ContributorsSpiriti, Justin Matthew (Author) / van der Vaart, Arjan (Thesis advisor) / Chizmeshya, Andrew (Thesis advisor) / Matyushov, Dmitry (Committee member) / Fromme, Petra (Committee member) / Arizona State University (Publisher)
Created2011
Description
Molecular dynamics (MD) simulations provide a particularly useful approach to understanding conformational change in biomolecular systems. MD simulations provide an atomistic, physics-based description of the motions accessible to biomolecular systems on the pico- to micro-second timescale, yielding important insight into the free energy of the system, the dynamical stability of contacts and the role of correlated motions in directing the motions of the system. In this thesis, I use molecular dynamics simulations to provide molecular mechanisms that rationalize structural, thermodynamic, and mutation data on the interactions between the lac repressor headpiece and its O1 operator DNA as well as the ERK2 protein kinase. I performed molecular dynamics simulations of the lac repressor headpiece - O1 operator complex at the natural angle as well as at under- and overbent angles to assess the factors that determine the natural DNA bending angle. I find both energetic and entropic factors contribute to recognition of the natural angle. At the natural angle the energy of the system is minimized by optimization of protein-DNA contacts and the entropy of the system is maximized by release of water from the protein-DNA interface and decorrelation of protein motions. To identify the mechanism by which mutations lead to auto-activation of ERK2, I performed a series of molecular dynamics simulations of ERK1/2 in various stages of activation as well as the constitutively active Q103A, I84A, L73P and R65S ERK2 mutants. My simulations indicate the importance of domain closure for auto-activation and activity regulation. My results enable me to predict two loss-of-function mutants of ERK2, G83A and Q64C, that have been confirmed in experiments by collaborators. One of the powerful capabilities of MD simulations in biochemistry is the ability to find low free energy pathways that connect and explain disparate structural data on biomolecular systems. An extention of the targeted molecular dynamics technique using constraints on internal coordinates will be presented and evaluated. The method gives good results for the alanine dipeptide, but breaks down when applied to study conformational changes in GroEL and adenylate kinase.
ContributorsBarr, Daniel Alan (Author) / van der Vaart, Arjan (Thesis advisor) / Matyushov, Dmitry (Committee member) / Wolf, George (Committee member) / Shumway, John (Committee member) / Arizona State University (Publisher)
Created2011
Description
This thesis considers the application of basis pursuit to several problems in system identification. After reviewing some key results in the theory of basis pursuit and compressed sensing, numerical experiments are presented that explore the application of basis pursuit to the black-box identification of linear time-invariant (LTI) systems with both finite (FIR) and infinite (IIR) impulse responses, temporal systems modeled by ordinary differential equations (ODE), and spatio-temporal systems modeled by partial differential equations (PDE). For LTI systems, the experimental results illustrate existing theory for identification of LTI FIR systems. It is seen that basis pursuit does not identify sparse LTI IIR systems, but it does identify alternate systems with nearly identical magnitude response characteristics when there are small numbers of non-zero coefficients. For ODE systems, the experimental results are consistent with earlier research for differential equations that are polynomials in the system variables, illustrating feasibility of the approach for small numbers of non-zero terms. For PDE systems, it is demonstrated that basis pursuit can be applied to system identification, along with a comparison in performance with another existing method. In all cases the impact of measurement noise on identification performance is considered, and it is empirically observed that high signal-to-noise ratio is required for successful application of basis pursuit to system identification problems.
ContributorsThompson, Robert C. (Author) / Platte, Rodrigo (Thesis advisor) / Gelb, Anne (Committee member) / Cochran, Douglas (Committee member) / Arizona State University (Publisher)
Created2012
Description
The Quantum Harmonic Oscillator is one of the most important models in Quantum Mechanics. Analogous to the classical mass vibrating back and forth on a spring, the quantum oscillator system has attracted substantial attention over the years because of its importance in many advanced and difficult quantum problems. This dissertation deals with solving generalized models of the time-dependent Schrodinger equation which are called generalized quantum harmonic oscillators, and these are characterized by an arbitrary quadratic Hamiltonian of linear momentum and position operators. The primary challenge in this work is that most quantum models with timedependence are not solvable explicitly, yet this challenge became the driving motivation for this work. In this dissertation, the methods used to solve the time-dependent Schrodinger equation are the fundamental singularity (or Green's function) and the Fourier (eigenfunction expansion) methods. Certain Riccati- and Ermakov-type systems arise, and these systems are highlighted and investigated. The overall aims of this dissertation are to show that quadratic Hamiltonian systems are completely integrable systems, and to provide explicit approaches to solving the time-dependent Schr¨odinger equation governed by an arbitrary quadratic Hamiltonian operator. The methods and results established in the dissertation are not yet well recognized in the literature, yet hold for high promise for further future research. Finally, the most recent results in the dissertation correspond to the harmonic oscillator group and its symmetries. A simple derivation of the maximum kinematical invariance groups of the free particle and quantum harmonic oscillator is constructed from the view point of the Riccati- and Ermakov-type systems, which shows an alternative to the traditional Lie Algebra approach. To conclude, a missing class of solutions of the time-dependent Schr¨odinger equation for the simple harmonic oscillator in one dimension is constructed. Probability distributions of the particle linear position and momentum, are emphasized with Mathematica animations. The eigenfunctions qualitatively differ from the traditional standing waves of the one-dimensional Schrodinger equation. The physical relevance of these dynamic states is still questionable, and in order to investigate their physical meaning, animations could also be created for the squeezed coherent states. This will be addressed in future work.
ContributorsLopez, Raquel (Author) / Suslov, Sergei K (Thesis advisor) / Radunskaya, Ami (Committee member) / Castillo-Chavez, Carlos (Committee member) / Platte, Rodrigo (Committee member) / Arizona State University (Publisher)
Created2012
Description
Modern measurement schemes for linear dynamical systems are typically designed so that different sensors can be scheduled to be used at each time step. To determine which sensors to use, various metrics have been suggested. One possible such metric is the observability of the system. Observability is a binary condition determining whether a finite number of measurements suffice to recover the initial state. However to employ observability for sensor scheduling, the binary definition needs to be expanded so that one can measure how observable a system is with a particular measurement scheme, i.e. one needs a metric of observability. Most methods utilizing an observability metric are about sensor selection and not for sensor scheduling. In this dissertation we present a new approach to utilize the observability for sensor scheduling by employing the condition number of the observability matrix as the metric and using column subset selection to create an algorithm to choose which sensors to use at each time step. To this end we use a rank revealing QR factorization algorithm to select sensors. Several numerical experiments are used to demonstrate the performance of the proposed scheme.
ContributorsIlkturk, Utku (Author) / Gelb, Anne (Thesis advisor) / Platte, Rodrigo (Thesis advisor) / Cochran, Douglas (Committee member) / Renaut, Rosemary (Committee member) / Armbruster, Dieter (Committee member) / Arizona State University (Publisher)
Created2015
Description
Factory production is stochastic in nature with time varying input and output processes that are non-stationary stochastic processes. Hence, the principle quantities of interest are random variables. Typical modeling of such behavior involves numerical simulation and statistical analysis. A deterministic closure model leading to a second order model for the product density and product speed has previously been proposed. The resulting partial differential equations (PDE) are compared to discrete event simulations (DES) that simulate factory production as a time dependent M/M/1 queuing system. Three fundamental scenarios for the time dependent influx are studied: An instant step up/down of the mean arrival rate; an exponential step up/down of the mean arrival rate; and periodic variation of the mean arrival rate. It is shown that the second order model, in general, yields significant improvement over current first order models. Specifically, the agreement between the DES and the PDE for the step up and for periodic forcing that is not too rapid is very good. Adding diffusion to the PDE further improves the agreement. The analysis also points to fundamental open issues regarding the deterministic modeling of low signal-to-noise ratio for some stochastic processes and the possibility of resonance in deterministic models that is not present in the original stochastic process.
ContributorsWienke, Matthew (Author) / Armbruster, Dieter (Thesis advisor) / Jones, Donald (Committee member) / Platte, Rodrigo (Committee member) / Gardner, Carl (Committee member) / Ringhofer, Christian (Committee member) / Arizona State University (Publisher)
Created2015