Browsing by Author "Dr. Bibhuti Bhattacharyya, Committee Member"

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    Development of a Thermal Neutron Imaging Facility at the N.C. State University PULSTAR reactor
    (2005-10-11) Mishra, Kaushal Kishor; Dr. Man-Sung Yim, Committee Member; Dr. Bibhuti Bhattacharyya, Committee Member; Dr. Ayman I. Hawari, Committee Chair
    A Thermal Neutron Imaging facility is being set up at the PULSTAR reactor at North Carolina State University. The PULSTAR is an open pool type light water moderated research reactor with a full power of 1-MWth and fuel that is enriched to 4% in U-235. It is equipped with 6 Beam Tubes (BT) to extract the radiation out of the reactor core. BT #5 is being used for the neutron imaging facility. Neutron imaging has expanded rapidly as a means of Non-Destructive Testing of materials. It offers some very explicit advantages over the usual γ-ray (or x-ray) imaging. Neutron cross-sections, being almost independent of the atomic number (Z) of the material, result in neutron imaging being capable of discerning materials of similar Z and/or low Z materials even when they are present inside high Z surroundings. Also, hydrogen, which is a very important element in determining the properties of materials, can be imaged even if present in minute quantities due to its significant neutron scattering and absorption cross-sections. Neutrons also offer the advantage of being capable to differentiate between isotopes of an element. Furthermore, radioactive materials which cannot be imaged using photons due to fogging of the detector can be imaged with neutrons using the transfer technique. The facility at the PULSTAR is intended to have both radiographic and tomographic capabilities. The radiography capabilities include using conventional film, digital image plate systems, as well as a real-time radiography system. In the present work the design of the facility is being presented. The collimator constitutes the major part of the imaging facility. The collimator design and its performance were simulated using MCNP. The designed collimator has a poly-crystal bismuth filter that is 4-inches in length, and a single crystal sapphire filter that is 6-inches in length. To aid in the design process, the bismuth and sapphire thermal neutron scattering cross-sections were calculated and implemented as libraries that can be used in MCNP calculations. The L/D of the system ranges from 100 to 150. The filter length can be changed to vary the estimated neutron flux from 1.8x10⁶ to 7x10⁶ n/cm².sec at full power with a sub-cadmium neutron content >98% as estimated by the MCNP simulations. Using the designed collimator, the beam divergence angle is 2° which translates to a beam size of 35-cm at 6-m from the aperture. Radiography and tomography simulations were also performed using MCNP and the effect of scattering was observed in the image. In addition, the Point Spread Function (PSF) for different detection systems was simulated and the corresponding resolution defined by the FWHM for film, image plate and real time detection systems was obtained and found to be between 33 to 50-μm, 106 to 118-μm and 113 to 118-μm respectively. The results obtained were in good agreement with the measurement performed using a 25-μm thick gadolinium foil. The designed beam was evaluated using the standards of the American Society of Testing and Materials (ASTM) and it was found that the designed beam achieves quality I[superscript A] ranking. Initial radiographs using the facility have been taken and are presented. The real-time radiography and tomography system will be setup in the near future.
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    Generalized Mixed Integer Rounding Valid Inequalities for Mixed Integer Programming Problems
    (2007-05-17) Kianfar, Kiavash; Dr. Bibhuti Bhattacharyya, Committee Member; Dr. Yahya Fathi, Committee Chair; Dr. Shu-cherng Fang, Committee Member; Dr. Henry L. W. Nuttle, Committee Member
    Many decision-making problems in practice can be formulated as Mixed Integer Programming (MIP) problems, which are NP-hard in their general form. Over the past few decades, an enormous amount of research has been carried out to develop the theory and algorithms for solving MIP problems. Valid inequalities are a crucial part of these developments since they can be added to the MIP problem as cutting planes to tighten the feasible region of its linear programming relaxation toward the convex hull of its MIP solutions. Mixed Integer Rounding (MIR) is a fundamental approach to generating cutting planes for general MIP problems. Recently, MIR has received special attention from several researchers. MIR inequalities are obtained from facets of certain simple mixed integer sets (MIR facets). A significant contribution in this context has been the work by Dash and Gunluk (2006) who introduced the 2-step MIR inequalities. The work of Dash and Günlük is also one of the recent advancements in the area of valid inequalities related to Gomory's group problems. These problems are of special significance in the context of MIP because facets of their corresponding polyhedra are sources for generating valid inequalities for MIP problems. In this dissertation, we generalize the concept of MIR valid inequalities. Based on this generalization, we develop new families of MIR inequalities for general MIP problems and show that they define (new) facets for the finite and infinite group polyhedra, and hence are potentially strong cuts. More specifically, the contributions of this research are as follows: First, we show that MIR facets are not limited to 1-step or 2-step facets, but for any positive integer n, n facets of a certain (n+1)-dimensional mixed integer set can be obtained through a process which includes n consecutive applications of MIR. The last of these facets is of special importance and we call it the n-step MIR facet. As a result, we generate an infinite number of MIR facets (one for each n), which we then use to generate valid inequalities for MIP problems. Second, we develop a procedure which, for any n, uses the n-step MIR facet to generate a family of valid inequalities for the feasible set of a general MIP constraint. We refer to these as the n-step MIR inequalities. The well-known Gomory Mixed Integer Cut and the 2-step MIR inequality of Dash and Gunluk are simply the first two families corresponding to n=1,2, respectively. The n-step MIR inequalities are easily produced using closed-form periodic functions, which we call the n-step MIR functions. None of these functions dominates the other on its whole period. Third, we establish a significant connection between the n-step MIR functions and facets of Gomory's group polyhedra. We prove that for any n, the n-step MIR inequalities define new families of facets for the finite and the infinite group polyhedra, and hence are potentially strong cuts. Many of these facets are new facets that have not been introduced in the literature before.
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    Nonparametric and semiparametric inference about ROC curves
    (2008-07-06) Gu, Jiezhun; Dr. Daowen Zhang, Committee Member; Dr. Subhashis Ghosal, Committee Chair; Dr. Bibhuti Bhattacharyya, Committee Member; Dr. Montserrat Fuentes, Committee Member