Rose–Hulman Institute of Technology
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ReSurge: Reusable Electrosurgical Handheld Devices Business Plan for Hospitals in East Africa
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Are All Weakly Convex and Decomposable Polyhedral Surfaces Infinitesimally Rigid?
Full text linkIt is conjectured that all decomposable (that is, interior can be triangulated without adding new vertices) polyhedra with vertices in convex position are infinitesimally rigid and only recently has it been shown that this is indeed true under an additional assumption of codecomposability (that is, the interior of the difference between the convex hull and the polyhedron itself can be triangulated without adding new vertices). One major set of tools for studying infinitesimal rigidity happens to be the (negative) Hessian MT of the discrete Hilbert-Einstein functional. Besides its theoretical importance, it provides the necessary machinery to tackle the problem experimentally. To search for potential counterexamples to the conjecture, one constructs an explicit family of so-called T-polyhedra, all of which are weakly convex and decomposable, while being non-codecomposable. Since infinitesimal rigidity is equivalent to a non-degenerate MT, one can let Mathematica search for the eigenvalues of MT and gather experimental evidence that such a flexible, weakly convex and decomposable T-polyhedron may not exist
Modeling the Effect of Human Behavior on Disease Transmission
Full text linkMany infectious disease models build upon the classic Susceptible-Infected-Recovered (SIR) model, a compartmental system that is used to simulate disease transmission in a population. The SIR model focuses on the transmission of disease but rarely includes behavioral or informational components that explore how disease perception influences transmission. In this paper, we propose a six-compartment behavioral SIR model that further segments the classic SIR system based on knowledge of information about the disease, and we explore how sharing information affects disease transmission. We designate two states as aware and unaware based on whether the relevant information is known by the population. Additionally, we include two types of information: good information that reduces transmission rates and bad information that increases transmission rates. We find that while compliance with good information is useful in decreasing community transmission, compliance with bad information has a greater magnitude of effect in terms of total cases. These results reaffirm that knowledge and human behavior are influential factors in disease transmission and should be included in future human disease models for more accurate transmission representation
On the Singular Pebbling Number of a Graph
Full text linkIn this paper, we define a new parameter of a connected graph as a spin-off of the pebbling number (which is the smallest t such that every supply of t pebbles can satisfy every demand of one pebble). This new parameter is the singular pebbling number, the smallest t such that a player can be given any configuration of at least t pebbles and any target vertex and can successfully move pebbles so that exactly one pebble ends on the target vertex. We also prove that the singular pebbling number of any graph on 3 or more vertices is equal to its pebbling number, that the singular pebbling number of the disconnected graph on two vertices is equal to its pebbling number, and we find the singular pebbling numbers of the two remaining graphs, K1 and K2, which are not equal to their pebbling numbers
Storage and Interaction Diagrams: Extending the Diagrammatic Framework of Kinetic and Free-Body Diagrams to other Conservation and Accounting Principles
Full text linkAfter defining a system for analysis, a rigorous process is taught to students in their Statics and Dynamics courses on how to draw proper kinetic, free-body, and impulse-momentum diagrams. While numerous techniques and mnemonics have been mentioned in literature, any experienced instructor can tell a correct free-body diagram apart from an incorrect one. Unfortunately, this is not the case when considering scalar properties such as mass, energy, exergy, and entropy. Different fluid mechanics and thermodynamics texts have treated the diagrammatic representation of these properties either very poorly, or in the case of the latter two, not at all. In this paper, the concept of the storage and interaction diagrams is introduced as a graphical tool to represent the aforementioned scalar properties. The storage and interaction diagrams combine the conservation and accounting of extensive properties with a template similar to the kinetic, free-body, and impulse-momentum diagrams. Three examples are provided to show the application of this general diagrammatic approach to different types of problems that involve the change in multiple properties. The impact of incorporating storage and interaction diagrams when introducing conservation and accounting principles involving scalar properties is assessed through the evaluation of student performance on exams and student feedback. A comparison of two cohorts of students suggests that emphasizing drawing storage and interaction diagrams may help reduce the ramp-up time that most students need to get acclimated to the conservation and accounting principles problem-solving framework
