Data management plan for the grant, "Collaborative Research: Conference: Texas-Oklahoma Representations and Automorphic forms (TORA)."

Data management plan for the research grant, "Collaborative Research: Using Uncertainty Quantification and Validated Computational Models to Analyze Pumping Performance of Valveless, Tubular Hearts." This project will develop a computational model of the essential features of the circulatory system: the electrical activity of the heart, muscle contractions of the tube walls, and the fluid-structure interactions of the heart walls and blood within. This computational framework aims to be faithful to that of a real, model animal (tunicate, or sea squirt). The model will then be analyzed with mathematical tools to determine the physical limits of the pumping system. Results of this project will improve the understanding of human heart development at the earliest stages. Also, it will point to how the large, multi-chambered hearts of vertebrates could have evolved from smaller structures.

Data management plan for the research grant, "Using uncertainty quantification and machine learning techniques to study the evolution of odor capture." This research proposes the application of uncertainty quantification (UQ) and machine learning (ML) to a CFD model of odor capture to understand the role of hair-array morphology, kinematics, and fluid environment in odor capture. The combination of CFD modeling and UQ&ML techniques can map out the performance space under which these chemosensory hair arrays operate and the relative sensitivity of each parameter of odor capture to construct a global, quantitative understanding of how parameters control odor-capture performance. Furthermore, this analysis can eliminate parameters that have no influence on odor capture, extracting the root principles of odor capture and providing a more efficient way to construct bioinspired devices for chemical detection. This work is of interest to the Army for extracting design principles that can be used for biomimetic and/or bioinspired devices for sensing hazardous chemicals in the environment (e.g. explosives).

Data management plan for the grant, "Southwest Local Algebra Meeting 2023." No data will be collected or reported for this grant.

Data management plan for the grant, "Approximation Theory and Complex Dynamics." This project involves the study of approximation theory in the setting of complex functions, with applications to complex dynamics. Approximation theory seeks to understand the extent to which the behavior of a general function can be effectively modeled by that of functions drawn from a more restricted class. Efficient approximation of functions is of relevance for numerical calculation. Since the only calculations that can be carried out numerically are the elementary operations of addition, subtraction, multiplication, and division, in practical terms it is of importance to understand when the values of general functions are well approximated by the values of either polynomial or rational functions. In many situations, the values of the approximant resemble those of the general function only for a sampling of input values. What can be said about values of the approximant for other choices of input? This is the main question studied in this project, with the following application in mind: when a general function is iterated to produce a dynamical system, to what extent does the dynamical behavior of an approximant resemble the dynamical behavior of the original function? The project will also contribute …

Data management plan for the grant, "Conference: Dynamical Systems and Fractal Geometry."