This volume highlights the mathematical research presented at the 2019 Association for Women in Mathematics (AWM) Research Symposium held at Rice University, April 6-7, 2019. The symposium showcased research from women across the mathematical sciences working in academia, government, and industry, as well as featured women across the career spectrum: undergraduates, graduate students, postdocs, and professionals. The book is divided into eight parts, opening with a plenary talk and followed by a combination of research paper contributions and survey papers in the different areas of mathematics represented at the symposium: algebraic combinatorics and graph theory algebraic biology commutative algebra analysis, probability, and PDEs topology applied mathematics mathematics education

This volume highlights the mathematical research presented at the 2019 Association for Women in Mathematics (AWM) Research Symposium held at Rice University, April 6-7, 2019. The symposium showcased research from women across the mathematical sciences working in academia, government, and industry, as well as featured women across the career spectrum: undergraduates, graduate students, postdocs, and professionals. The book is divided into eight parts, opening with a plenary talk and followed by a combination of research paper contributions and survey papers in the different areas of mathematics represented at the symposium: algebraic combinatorics and graph theory algebraic biology commutative algebra analysis, probability, and PDEs topology applied mathematics mathematics education

Despite the improved design of biological and Mechanical Heart Valves (MHV), thrombus formation remains a challenge in clinical practice. Abnormal blood flow through the foreign valve components is recognized as the greatest limitation. An important aspect of MHV selection and design lies in the understanding of the fundamental principles that govern the complex dynamical interactions between blood and valve. Therefore, a novel approach has been adopted to predict the valve movement by utilizing the fluid-structure interaction model which is innovative and fundamentally distinct from the prevailing methods of simulation that assume valve movement a priori. Based on a fictitious domain method and an operator splitting scheme, a mathematical formulation has been outlined for a fluid-structure model. Numerical simulations are performed for non-moving and moving rigid bodies to visualize the flow field. Simulations have also extended to rigid rectangular flaps following a rotational movement about fixed points in an unsteady flow as an initial attempt to model a 2D MHV. The study should be helpful to educators and professionals in the field of industrial and biological applications.