Browsing by Subject "Inverse Problems"
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Item Development of Technical Nuclear Forensics for Spent Research Reactor Fuel(2012-11-20) Sternat, Matthew Ryan 1982-Pre-detonation technical nuclear forensics techniques for research reactor spent fuel were developed in a collaborative project with Savannah River National Lab ratory. An inverse analysis method was employed to reconstruct reactor parameters from a spent fuel sample using results from a radiochemical analysis. In the inverse analysis, a reactor physics code is used as a forward model. Verification and validation of different reactor physics codes was performed for usage in the inverse analysis. The verification and validation process consisted of two parts. The first is a variance analysis of Monte Carlo reactor physics burnup simulation results. The codes used in this work are MONTEBURNS and MCNPX/CINDER. Both utilize Monte Carlo transport calculations for reaction rate and flux results. Neither code has a variance analysis that will propagate through depletion steps, so a method to quantify and understand the variance propagation through these depletion calculations was developed. The second verification and validation process consisted of comparing reactor physics code output isotopic compositions to radiochemical analysis results. A sample from an Oak Ridge Research Reactor spent fuel assembly was acquired through a drilling process. This sample was then dissolved in nitric acid and diluted in three different quantities, creating three separate samples. A radiochemical analysis was completed and the results were compared to simulation outputs at different levels ofdetail. After establishing a forward model, an inverse analysis was developed to re-construct the burnup, initial uranium isotopic compositions, and cooling time of a research reactor spent fuel sample. A convergence acceleration technique was used that consisted of an analytical calculation to predict burnup, initial 235U, and 236U enrichments. The analytic calculation results may also be used stand alone or in a database search algorithm. In this work, a reactor physics code is used as a for- ward model with the analytic results as initial conditions in a numerical optimization algorithm. In the numerical analysis, the burnup and initial uranium isotopic com- positions are reconstructed until the iterative spent fuel characteristics converge with the measured data. Upon convergence of the sample?s burnup and initial uranium isotopic composition, the cooling time can be reconstructed. To reconstruct cooling time, the standard decay equation is inverted and solved for time. Two methods were developed. One method uses the converged burnup and initial uranium isotopic compositions along in a reactor depletion simulation. The second method uses an isotopic signature that does not decay out of its mass bin and has a simple production chain. An example would be 137Cs which decays into the stable 137Ba. Similar results are achieved with both methods, but extended shutdown time or time away from power results in over prediction of the cooling time. The over prediction of cooling time and comparison of different burnup reconstruction isotope results are indicator signatures of extended shutdown or time away from power. Due to dynamic operation in time and function, detailed power history reconstruction for research reactors is very challenging. Frequent variations in power, repeated variable shutdown time length, and experimentation history affect the spectrum an individual assembly is burned with such that full reactor parameter reconstruction is difficult. The results from this technical nuclear forensic analysis may be used with law enforcement, intelligence data, macroscopic and microscopic sample characteristics in a process called attribution to suggest or exclude possible sources of origin for a sample.Item Quantitative Modeling and Estimation in Systems Biology using Fluorescent Reporter Systems(2013-12-10) Bansal, LoveleenaBuilding quantitative models of biological systems is a challenging task as these models can consist of a very large number of components with complex interactions between them and the experimental data available for model validation is often sparse and noisy. The focus in this work is on modeling and parameter estimation of biological systems that are monitored using fluorescent reporter systems. Fluorescent reporter systems are widely used for various applications such as monitoring gene expression, protein localization and protein-protein interactions. This dissertation presents various techniques to facilitate modeling of biological systems containing fluorescent reporters with special attention given to challenges arising due to limited experimental data, simultaneous monitoring of multiple events and variability in the observed response due to phenotypic differences. First, an inverse problem is formulated to estimate the dynamics of transcription factors, a crucial molecule that initiates the transcription process, using data of fluorescence intensity profiles obtained from a fluorescent reporter system. The resulting inverse problem is ill-conditioned and it is solved with the aid of regularization techniques. The main contribution is that, with the presented technique, any complex dynamics of transcription factors can be estimated using limited data of fluorescence measurements. The technique has been evaluated using simulated data as well as experimental data of a GFP reporter system of STAT3. Second, an experimental design formulation is developed to facilitate the use of multiple fluorescent reporters, with overlapping emission spectra, in the same experiment. This work develops a criterion to select the fluorescent proteins for simultaneous use such that the accuracy in the estimated contributions of individual proteins to the overall observed intensity is maximized. This technique has been validated using mixtures of different E. coli strains which express different fluorescent proteins. Finally, a population balance model of a cell population containing a fluorescence reporter system is developed to describe the variability in the observed fluorescence in cells. Factors such as rate of fluorescent protein formation as well as partitioning of the fluorescent protein on cell division have been taken into account to describe the dynamics of fluorescence intensity distributions in the cell populations. The model has been used to obtain preliminary hypotheses to explain the difference in response of HeLa cells containing the Tet-on expression system on stimulation by different levels doxycycline. Thus, this work describes techniques for building robust predictive models of biological systems such as regularization for solving ill-posed estimation problems, experimental design techniques as well as using population balance modeling to model complex multi-scale dynamics. Moreover, while the examples discussed here are motivated for fluorescent reporter systems, the developed techniques can be used for different kinds of linear or non-linear dynamic biological systems.Item Spherical radon transforms and mathematical problems of thermoacoustic tomography(2009-06-02) Ambartsoumian, GaikThe spherical Radon transform (SRT) integrates a function over the set of all spheres with a given set of centers. Such transforms play an important role in some newly developing types of tomography as well as in several areas of mathematics including approximation theory, integral geometry, inverse problems for PDEs, etc. In Chapter I we give a brief description of thermoacoustic tomography (TAT or TCT) and introduce the SRT. In Chapter II we consider the injectivity problem for SRT. A major breakthrough in the 2D case was made several years ago by M. Agranovsky and E. T. Quinto. Their techniques involved microlocal analysis and known geometric properties of zeros of harmonic polynomials in the plane. Since then there has been an active search for alternative methods, which would be less restrictive in more general situations. We provide some new results obtained by PDE techniques that essentially involve only the finite speed of propagation and domain dependence for the wave equation. In Chapter III we consider the transform that integrates a function supported in the unit disk on the plane over circles centered at the boundary of this disk. As is common for transforms of the Radon type, its range has an in finite co-dimension in standard function spaces. Range descriptions for such transforms are known to be very important for computed tomography, for instance when dealing with incomplete data, error correction, and other issues. A complete range description for the circular Radon transform is obtained. In Chapter IV we investigate implementation of the recently discovered exact backprojection type inversion formulas for the case of spherical acquisition in 3D and approximate inversion formulas in 2D. A numerical simulation of the data acquisition with subsequent reconstructions is made for the Defrise phantom as well as for some other phantoms. Both full and partial scan situations are considered.