MATH Theses and Dissertations

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    Modeling the melt pool during powder bed fusion additive manufacturing
    (Wichita State University, 2023-12) Murray, Ann Marie; Lu, Tianshi
    In powder bed fusion additive manufacturing properties of the melt pool are of deep interest to ensure the structure of the nal product is as desired. Speci cally of concern in this work is estimating the melt pool with regards to width and depth considering also maximum temperature. Because analytic estimation formulas require simpli ed assumptions, OpenFOAM is used to numerically simulate the melt pool as well. The approximation formulas are compared to the numerical simulations and experiment data to validate.
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    Computation of plane potential flow in multiple connected domains using series methods and conformal mapping
    (Wichita State University, 2023-12) Mears, Justin Laurence; DeLillo, Thomas K.
    This paper presents a method for calculating potential flow in the exterior of multiplyconnected circle domains in the complex plane. The method employs a Laurent series expansion of the potential function on the circular boundaries, which can be easily written into a linear system for finding the Laurent coefficients. This system exhibits the form of “identity plus a low-rank matrix”, enabling efficient utilization of conjugate-gradient-like methods. Through the use of conformal mapping, the method is extended to calculate the potential flow in multiply-connected domains exterior to any closed curves. This is achieved by computing the potential flow over an appropriate circle domain and mapping this result to the desired physical domain using an approximation of the Laurent series for the conformal map. Circulations around each boundary can be specified or calculated, with a specific focus on multi-element airfoils where the circulations are determined to satisfy the Kutta condition at trailing edges. Comparisons with alternatives methods for computing flow in circle domains, namely reflection and least-squares methods, are included to demonstrate the accuracy and efficiency of the new method. Finally, there are many examples of flow calculations over multiplyconnected regions with smooth boundaries and multi-element airfoils.
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    Closed form expressions for the sums of infinite series
    (Wichita State University, 1958-06) Durbin, John R.; Buschman, R.G.
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    A general legendre transformation
    (Wichita State University, 1958-06) Damaskos, Nickander J.
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    Bernoulli polynomials of the first kind
    (Wichita State University, 1958-06) Bargen, Ralph K.; Buschman, R.G.
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