Article expanding the Intrinsic Diophantine approximation on fractals first proposed by K. Mahler (1984). This article describes and develops the theory of infinite de Bruijn sequences and answers questions related to Hausdorff dimension, Diophantine approximation, Dirichlet function, and height function.

Article proves the existence of an infinite number of radial solutions to ∆u+K(r)f(u) = 0 on ℝᶰ such that limᵣ →∞ u(r) = 0 with prescribed number of zeros on the exterior of the ball of radius R > 0 where f is odd with f < 0 on (0, β), f > 0 on (β, ∞) with f superlinear for large u, and K(r) ∼ r ⁻ᵅ with α > 2(N − 1).

Article

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, "Conference: Dynamical Systems and Fractal Geometry."