The study of the propagation of multiple cracks is essential to modeling and predicting structural integrity. The interaction between two cracks depends on a number of factors such as the domain geometry, the relative crack sizes and the separation between the two crack tips. In this paper, we study the interaction between two dynamically propagating cracks. We use the phase field method to track the crack paths, since this method can handle complex crack behavior such as crack branching, without any ad hoc criteria for crack evolution. The results from our dynamic simulations indicate that, unlike crack inter- action under quasi-static or fatigue loading, the presence of another crack does not accelerate crack propagation when dynamic loads are applied. However, some similarities in the crack topologies are observed for both quasi-static and dynamic loading.
Several constitutive theories have been proposed in the literature to model the viscoelastic response of soft tissue, including widely used rheological constitutive models. These models are characterized by certain parameters (“time constants”) that define the time scales over which the tissue relaxes. These parameters are primarily obtained from stress relaxation experiments using curve-fitting techniques. However, the question of how best to estimate these time constants remains open.
As a step towards answering this question, we develop an optimal experimental design approach based on ideas from information geometry, namely Fisher information and Kullback-Leibler divergence. Tissue is modeled as a standard linear solid and described using a one- or two-term Prony series. Treating the time constants as unknowns, we develop expressions for the Fisher information and Kullback-Leibler divergence that allow us to maximize information gain from experimental data. Based on the results of this study, we propose that the largest time constant estimated from a stress relaxation experiment for a linear viscoelastic material should be at most one-fifth of the total time of the experiment in order to maximize information gain.
The purpose of this project is to consider and evaluate the economic attractiveness of a process producing 250,000 lb/h of acetic acid by the selective carbonylation of methanol via carbon monoxide with the use of an iridium tri-iodide catalyst. Initial cost estimates of this process will be completed prior to the completed rigorous design to ensure the process is economically viable and meets product specifications. A full cost analysis will then be made on the initial design to further verify the process will meet product specifications and is economically attractive to the business. A recommendation to continue investigating will be made based on the analysis of the investment cost and annual operating costs of this reaction/separation system.
An economic analysis was performed on the selected design. The total capital cost for this project is $145 million, with a yearly utility and incremental cost of $62 million and $90 million, respectively. The required ten-year return on investment was found to be 15%, when the Acetic Acid is sold at a price of $437 /ton. When the Acetic Acid is sold at $745/ton (achieves 15% 1-year ROI), an ROI of 547% is achieved for a 10-year period. In order to achieve a five-year ROI of 15%, the selling price of Acetic Acid is only increased to roughly $455/ton.
This project aimed at effectively implementing eye tracking MATLAB. The team created an eye tracking program that uses a webcam to locate where a person is looking on a computer screen. The program was tested with a simple experiment that presented the user with a set of colors and found which colors the user looked at most.