Simulating the Spread of the Common Cold

This modeling scenario guides students to simulate and investigate the spread of the common cold in a residence hall. An example floor plan is given, but the reader is encouraged to use a more relevant example. In groups, students run repeated simulations, collect data, derive a differential equation model, solve that equation, estimate parameter values by hand and through regression, visually evaluate the consistency of the model with their data, and present their results to the class

Lost at Sea: Introduction to Numerical Methods through Navigation

Excerpt: The ship, El Perdido, was damaged during a storm which knocked out its main and backup power generators. Before the backup generator failed, Captain Miguel Gomez sent a distress call and the crew have been able to keep El Perdido a oat, but the ship is adrift in the Pacific Ocean off the coast of California. Thankfully, a US Coast Guard rescue operation is underway after receiving the distress call. The Coast Guard has El Perdido\u27s last known position and has mapped out the surface water velocities in this area as slope fields for longitude (x) and latitude (y), which they have updated using historical data and estimated predictions. Since the search grid is small enough, this curved region on the surface of the earth is relatively at

Logistics of Mathematical Modeling-Focused Projects

This article addresses the logistics of implementing projects in an undergraduate mathematics class and is intended both for new instructors and for instructors who have had negative experiences implementing projects in the past. Project implementation is given for both lower and upper division mathematics courses with an emphasis on mathematical modeling and data collection. Projects provide tangible connections to course content which can motivate students to learn at a deeper level. Logistical pitfalls and insights are highlighted as well as descriptions of several key implementation resources. Effective assessment tools, which allowed me to smoothly adjust to student feedback, are demonstrated for a sample class. As I smoothed the transition into each project and guided students through the use of the technology, their negative feedback on projects decreased and more students noted how the projects had enhanced their understanding of the course topics. Best practices learned over the years are given along with project summaries and sample topics. These projects were implemented at a small liberal arts university, but advice is given to extend them to larger classes for broader use.Comment: 27 pages, no figures, 1 tabl

NTP comparison process

The systems engineering process for the concept definition phase of the program involves requirements definition, system definition, and consistent concept definition. The requirements definition process involves obtaining a complete understanding of the system requirements based on customer needs, mission scenarios, and nuclear thermal propulsion (NTP) operating characteristics. A system functional analysis is performed to provide a comprehensive traceability and verification of top-level requirements down to detailed system specifications and provides significant insight into the measures of system effectiveness to be utilized in system evaluation. The second key element in the process is the definition of system concepts to meet the requirements. This part of the process involves engine system and reactor contractor teams to develop alternative NTP system concepts that can be evaluated against specific attributes, as well as a reference configuration against which to compare system benefits and merits. Quality function deployment (QFD), as an excellent tool within Total Quality Management (TQM) techniques, can provide the required structure and provide a link to the voice of the customer in establishing critical system qualities and their relationships. The third element of the process is the consistent performance comparison. The comparison process involves validating developed concept data and quantifying system merits through analysis, computer modeling, simulation, and rapid prototyping of the proposed high risk NTP subsystems. The maximum amount possible of quantitative data will be developed and/or validated to be utilized in the QFD evaluation matrix. If upon evaluation of a new concept or its associated subsystems determine to have substantial merit, those features will be incorporated into the reference configuration for subsequent system definition and comparison efforts

Systems overview

Charts and accompanying text are presented that provide a brief synopsis of the contracted efforts for FY-92 in assessing nuclear thermal propulsion requirements, concepts, and associated issues. The objective of the effort is to provide NASA LeRC with assistance in space nuclear propulsion system requirements management and public acceptance planning

Expendable launch vehicle transportation for the space station

Logistics transportation will be a critical element in determining the Space Station Freedom's level of productivity and possible evolutionary options. The current program utilizes the Space Shuttle as the only logistics support vehicle. Augmentation of the total transportation capability by expendable launch vehicles (ELVs) may be required to meet demanding requirements and provide for enhanced manifest flexibility. The total operational concept from ground operations to final return of support hardware or its disposal is required to determine the ELV's benefits and impacts to the Space Station Freedom program. The characteristics of potential medium and large class ELVs planned to be available in the mid-1990's (both U.S. and international partners' vehicles) indicate a significant range of possible transportation systems with varying degrees of operational support capabilities. The options available for development of a support infrastructure in terms of launch vehicles, logistics carriers, transfer vehicles, and return systems is discussed

An Elementary Proof of Dodgson's Condensation Method for Calculating Determinants

In 1866, Charles Ludwidge Dodgson published a paper concerning a method for evaluating determinants called the condensation method. His paper documented a new method to calculate determinants that was based on Jacobi's Theorem. The condensation method is presented and proven here, and is demonstrated by a series of examples. The condensation method can be applied to a number of situations, including calculating eigenvalues, solving a system of linear equations, and even determining the different energy levels of a molecular system. The method is much more efficient than cofactor expansions, particularly for large matrices; for a 5 x 5 matrix, the condensation method requires about half as many calculations. Zeros appearing in the interior of a matrix can cause problems, but a way around the issue can usually be found. Overall, Dodgson's condensation method is an interesting and simple way to find determinants. This paper presents an elementary proof of Dodgson's method.Comment: 7 pages, no figure

Smart-Contract Enabled Blockchains for the Control of Supply Chain Order Variance

Conflicts between supply chain members emerge because individually strategic actions may not be jointly optimal. Efforts to forecast consumer demand represent a source of conflict. Coordination of forecasts require a powerful incentive alignment approach. This work proposes a smart-contract equipped consortium blockchain system that creates an incentive structure which makes coordination with respect to forecasts economically appealing to a retailer and supplier. Distortions of demand due to uncoordinated forecasting is captured by a bullwhip measure which factors both forecast error and variance. Cooperation under the system is shown to help minimize this bullwhip measure. New outcomes to supply chain participants that allow for a higher reward is provided by the system. Under a fixed payout structure, the system achieves credibility of continued cooperation thus promoting an optimal coordinated equilibrium between retailer and supplier. Blockchain technology represents a consensus formation mechanism which can intermediate the behavior of supply chain network

Algae Population Self-Replenishment

This modeling scenario investigates the massive algal blooms that struck Lake Chapala, Mexico, in 1994. After reading a summary of news articles on the incident, students create an ODE system model from a verbal description of the factors, visualize this system using an executable Java applet (PPLANE) to predict overall behavior, and then analyze the nonlinear system using the Jacobian matrix, eigenvalues, phase plane, and feasibility conditions on parameters to fully describe the system behavior. Students are expected to be familiar with systems of differential equations, equilibria, jacobian matrices, and eigenvalues. Students will learn modeling from qualitative descriptions, nondimensionalization, applying feasibility conditions to parameters, and how to use technology to interactively analyze a system of differential equations

Graphene Oxide Nanomaterials for Active Biosensing

From the Washington University Office of Undergraduate Research Digest (WUURD), Vol. 12, 05-01-2017. Published by the Office of Undergraduate Research. Joy Zalis Kiefer, Director of Undergraduate Research and Associate Dean in the College of Arts & Sciences; Lindsey Paunovich, Editor; Helen Human, Programs Manager and Assistant Dean in the College of Arts and Sciences. Mentor: Pratim Biswa