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  1. The Electrical capacitance tomography (ECT) method has recently been adapted to obtain tomographic images of the cross section of a diesel particulate filter (DPF). However, a soot mass estimation algorithm is still needed to translate the ECT image pixel data to obtain soot load in the DPF. In this paper, we propose an estimation method to quantify the soot load in a DPF through an inverse algorithm that uses the ECT images commonly generated by a back-projection algorithm. The grayscale pixel data generated from ECT is used in a matrix equation to estimate the permittivity distribution of the cross section of the DPF. Since these permittivity data has direct correlation with the soot mass present inside the DPF, a permittivity to soot mass distribution relationship is established first. A numerical estimation algorithm is then developed to compute the soot mass accounting for the mass distribution across the cross-section of the DPF as well as the dimension of the DPF along the exhaust flow direction. Experimental data has been used to validate the proposed soot estimation algorithm which compared the estimated values with the actual measured soot mass. The estimated soot mass for various soot load amounts were found to correlate reasonably well with the measured soot masses in those cases. 
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  2. This work presents innovative origami optimization methods for the design of unit cells for complex origami tessellations that can be utilized for the design of deployable structures. The design method used to create origami tiles utilizes the principles of discrete topology optimization for ground structures applied to origami crease patterns. The initial design space shows all possible creases and is given the desired input and output forces. Taking into account foldability constraints derived from Maekawa's and Kawasaki's theorems, the algorithm designates creases as active or passive. Geometric constraints are defined from the target 3D object. The periodic reproduction of this unit cell allows us to create tessellations that are used in the creation of deployable shelters. Design requirements for structurally sound tessellations are discussed and used to evaluate the effectiveness of our results. Future work includes the applications of unit cells and tessellation design for origami inspired mechanisms. Special focus will be given to self-deployable structures, including shelters for natural disasters. 
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  3. Topology optimization is broadly recognized as a design approach to generate high-performance conceptual designs suitable for freeform fabrication, e.g., additive manufacturing. When other fabrication methods are considered, topology optimization must integrate manufacturing constraints. The integration of constraints for extrusion and casting has been addressed in the past by a few researcher groups. In this work, extrusion and casting constraints are revisited and extended to include plastic injection. The proposed method relies on the use of intersection planes and the definition of a parting line within the planes. The resulting topologies can be injected in a two-plate mold without the use of inserts. The implementation and results of the proposed approach are demonstrated in classic three-dimensional problems that include a cantilevered beam with different load conditions. 
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