Rose–Hulman Institute of Technology
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An Investigation of Engineering Students\u27 Information Sorting Approaches Using an Open-Ended Design Scenario
No full textBoard 398: Sustaining and Scaling the Impact of the MIDFIELD Project at the American Society for Engineering Education (Year 2)
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Counting the Classes of Projectively-Equivalent Pentagons on Finite Projective Planes of Prime Order
Full text linkIn this paper, we examine the number of equivalence classes of pentagons on finite projective planes of prime order under projective transformations. We are interested in those pentagons in general position, meaning that no three vertices are collinear. We consider those planes which can be constructed from finite fields of prime order, and use algebraic techniques to characterize them by their symmetries. We are able to construct a unique representative for each pentagon class with nontrivial symmetries. We can then leverage this fact to count classes of pentagons in general. We discover that there are (1/10)((p+3)(p-3)+4rp) such classes, where p is the order of the plane and rp is the number of roots of x2-x-1 on the finite field of order p, a generalization of the golden ratio, ϕ
Graphene-Infused Hybrid Biobattery–Supercapacitor Powered by Wastewater for Sustainable Energy Innovation
No full textWang Tilings in Arbitrary Dimensions
Full text linkThis paper makes a new observation about arbitrary dimensional Wang Tilings,demonstrating that any d -dimensional tile set that can tile periodically along d − 1 axes must be able to tile periodically along all axes.This work also summarizes work on Wang Tiles up to the present day, includingdefinitions for various aspects of Wang Tilings such as periodicity and the validity of a tiling. Additionally, we extend the familiar 2D definitions for Wang Tiles and associated properties into arbitrary dimensional spaces. While there has been previous discussion of arbitrary dimensional Wang Tiles in other works, it has been largely informal. This work formalizes and proves several key assertions that previous work has referenced as folklore, including the fact that periodicity of a tiling is captured by a lattice
Engineering Silicon Metalenses in Wide Field Revers-Telephoto Optical Systems for Long-Wave Infrared Thermal Imaging
Full text linkA novel optical system designed to image light emitted from a CO 2 laser (10.6 μm) is presented here. This system utilizes a positive conventional lens and a negative all silicon metalens. Demonstrated here is the ability of metalenses to replace a combination of optical elements to produce more compact and light-weight optical systems. It also shows how metalenses can replace comparatively expensive custom-manufactured lenses. Several systems that utilize meta-surfaces are explored, including positive and negative metalenses, a meta-corrector, a metalens doublet imaging system that corrects for 0 th -order images overlapping 1 st -order images, and several telephoto optical systems. To further this, several meta-atom geometries, heights, and unit cell sizes are explored and compared to determine which design fulfills the requirements of this system best. The optical system, as designed, is based on the telephoto system but the negative metalens placed in front of a positive lens which is integral to the system creating a reverse-telephoto lens system. The final design uses a –20mm focal metalens with a diameter of 6.4 mm in the reverse telephoto. Electron lithography has been used to fabricate the metalens
