Dartmouth Institute for Health Policy and Clinical Practice
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Action This Day: The Mathematics and Machinations that Bested the German Enigma
This thesis presents a comprehensive and chronological overview of cryptographic techniques designed to break Enigma, beginning in 1932 and culminating in the creation of the Turing-Welchman Bombe. We discuss the mathematical theory and electromechanical implements used to decode one of history\u27s greatest ciphers.
Reexamining the Bombe through the lens of modern group theory, we critique Alan Turing\u27s estimation of the number of stops that the Bombe produces for various plaintext-ciphertext pairing structures. To address its limitations, we introduce a new framework for estimating the number of stops by extending John Dixon\u27s theorem concerning the probability that uniformly distributed elements of Sn generate a transitive subgroup. Our formulation generalizes this result to compute the probability of transitivity when permutations are sampled from arbitrary distributions over conjugacy classes.
All results are supported by extensive simulation, and a full suite of implementations of various cryptographic techniques are made available via an open source repository to provide researchers with new tools to study the methods discussed herein
Barefooting the Northeast 111: A Hiker Discovers the Intensity of Pinpricks, Grit, and Mud
Climbing without shoes in the Catskills, then the Adirondacks, the White Mountains of New Hampshire, and Maine, he learned to focus on the here-and-now
Rigorous Care: The Early Warning Syllabus 2.0
This document includes a set of policies that are designed to provide efficient ways for instructors to implement pedagogies of care. The principle of “rigorous care” is informed by research on learning, accessibility, and mental health. The idea of “early warnings” is meant to help students identify their needs and seek support before problems become unmanageable. Both ideas respect the fact that both students and instructors work under enormous pressure.
Each policy statement is preceded by a brief framing justification and followed by a selected bibliography of the research and testimonials that have informed the policy
Wear of High Entropy Alloys: Understanding Effects of Cryogenic Temperatures and Surface Nitriding on Wear Behavior
Cryogenic tribological applications have become increasingly important with the development and innovation of advanced equipment in aerospace, polar regions, superconductivity, and more. Traditional lubrication methods are not viable under these harsh environments, so metallic materials must be able to maintain excellent mechanical properties and withstand the constant impact and wear alone. High entropy alloys (HEAs) have emerged as potential candidates for these applications because of their wide variety of excellent room temperature properties and apparent improvement of mechanical properties of some HEAs at extremely low temperatures. Despite their promising nature, very limited work has been done on understanding the wear behavior of these HEAs under cryogenic sliding conditions and even less work has focused on offering comparisons to other HEAs or traditionally-used materials.
This thesis investigates the tribological properties and specific wear mechanisms experienced by two single-phase face-centered cubic (f.c.c) HEAs, an equiatomic CoCrMnNiFe (Cantor HEA) and 1.1 at% C-doped Fe40.4Ni11.3Mn34.8Al7.5Cr6 (CHEA), as well as a two-phase HEA, Fe28.2Ni18.8Mn32.9Al14.1Cr6 (two-phase HEA), under cryogenic temperatures and room temperature. Overall, it was found that the two-phase HEA outperformed the 316 SS by up to 5x and the single-phase HEAs by up to 10x under the same sliding conditions at 77 K. It was observed that the better wear performance of the two-phase HEA was directly related to its sub-surface microstructural gradient and more even strain distribution. Amongst the single-phase HEAs, the CHEA showed the best wear resistance at cryogenic temperature due to the formation of stable and adherent oxides and the exclusive appearance of twins and secondary phases.
An additional chapter also explored the potential of utilizing a gas nitriding treatment to improve the wear resistance of the two-phase HEA. It was found that the nitrided pins only performed better than their as-cast counterparts under low sliding speed. This was due to the thickness, continuity, and chemistry of the mechanically mixed layer formed on each wear pin surface as well as changes in hardness
Voices of Rebellion: A Lesson on Feminism, Identity, and Popular Music
This lesson focuses on the rise of the feminist punk rock movement Riot Grrrl, and the political, social, and cultural conversations brought about by the band that created the genre, Bikini Kill. Students will explore the history of the genre and how its emergence had a great influence on political movements, female empowerment, the 3rd-wave of feminism, as well as the punk rock scene as a whole. Through engaging discussions, lyrical and performance analysis, and scholarly research on popular music, the lesson will highlight the ways in which artists have represented, subverted, and critiqued societal norms and politics surrounding gender across musical genres and time periods.
Students will begin by understanding the historical impact of Riot Grrrl, before engaging in full class discussions that stimulate an understanding of how the lyrics, performances, and image of artists create meaning and may evoke greater societal change. They will then listen to two different examples of music made by artists who are at the center of feminist critique, Bikini Kill and Sabrina Carpenter. By the end of the lesson, students will be able to identify how feminist messaging, and the political and societal implications of it change over time, as well as develop a deeper appreciation and awareness of the ways their favorite music artists develop meaning in their music
Audience Attention: A Lesson in Confident Public Speaking
We’ve all sat through a speech that lost our attention. This lesson helps students ensure their own isn’t one of them. This lesson serves as an introduction or a supplementary lesson in the art of public speaking. Many people have nerves about public speaking, so this lesson will provide students with tools to grow more confident in public speaking, specifically in keeping their audience engaged. Through discussions, a mini-lecture, and interactive speeches, students explore how rhetorical appeals (ethos, pathos, and logos) and the concept of identification help build a stronger connection with their audience. The lesson begins with a discussion on Steve Jobs’ Stanford Commencement Address, followed by a mini lecture on specific tips and tricks of public speaking, then moves into a hands-on practice activity where students deliver and revise short speeches, and closes with a reflection on confidence and connection. By the end, students leave with greater awareness of how to hold attention, build trust, and speak with purpose
Exploring Path Complex Networks: Implications for Drug Development
This project explores an approach called Path Complex Networks part of a general technique called Graph Neural Network (GNN). In a recent paper by Professor Truong and Professor Chin, a PCN was developed that performed better than the Weisfeiler-Lehman Test. PCN prevents obscurity: PCN can distinguish between 2 molecules that might look similar that a typical GNN might not be able to distinguish. PCN can distinguish molecules that were previously imperceptible.https://digitalcommons.dartmouth.edu/wetterhahn_2025/1016/thumbnail.jp
Two-Phase Heat Exchanger Design for a Cryocooler
Recuperators are valuable components in refrigeration-cycle devices as they move heat between separate stages within the cycle, lessening the work done by compressors and improving the overall efficiency of the device. For Creare, a Hanover-based engineering firm and our sponsor, a recuperator must be designed to accommodate a mixed-gas flow at cryogenic temperatures. However, upon condensation, mixed-gas becomes a two-phase stream giving rise to heat exchange inefficiencies as the two phases separate and behave thermally distinctly. One way to address this is by incorporating a large surface area porous metal into the recuperator body to remix the two phases into one homogeneous stream and increase thermal contact with the other stream. In this project, we explored this solution by designing, fabricating, and testing a heat exchanger with porous aluminum interstitial section. A two-phase flow of water/air was used to examine stream remixing while water/steam was employed to test heat transfer. Our initial prototype was constructed pragmatically and achieved a lower NTU efficiency than a brazed-plate recuperator used as control, but we observed a notably high interface heat transfer coefficient ultimately indicating a feasible prototype. Research on other materials for use as the porous interstitial was also conducted and the benefits of sintered over un-sintered metals were considered. Finally, we gave recommendations to Creare on future design and implementation cases for their device. This work, which is focused on furthering cooling technology, could have potential use in the aerospace, healthcare, and energy sectors