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We explore the mathematics behind a solution to the 2 x 2 x 2 Rubik's cube. This includes a look at permutations involved in the solving of the puzzle. A method of cyclic notation is discussed that allows for the tracking of both the position and orientation of colors on the cube. The solution to the puzzle has been reduced to three steps and is aided by the mentioned notation allowing for a systematic approach to solving the cube.
Second Life© is a powerful tool for creating and interacting with those models. Some universities have created an entire campus within Second Life© in order to provide an additional learning environment for students. As one example, Ohio University has an entire campus on Second Life, much like the main campus, which allows students unique learning and collaboration opportunities. By creating a 3-dimensional model of a common Capital University classroom and scripting the equipment to work as expected, users can simulate the classroom environment and practice using the equipment in the room. Models can be created within Second Life© using combinations of basic shapes or imported from a more complicated program, such as 3D Studio MAX©. The models can be scripted so users can simulate interacting with the models. Through interactive models of campus buildings, rooms, and equipment, both students and faculty can be given the opportunity to learn and work together from anywhere in the world.
The uneven heating of tree stems in wild land surface fires is a pervasive phenomenon that leads to uneven charring and fire scars. It is caused by the interaction between flames, ambient wind, and the cylindrical stem. The Fire Dynamics Simulator developed by the National Institute of Standards and Technology has been used to numerically model the results of an experimental study on the charring of tree stems in a wind tunnel. The wind tunnel was modeled as a 42 x 42 x 200 cm rectangular chamber having a fire-brick base with a variable diameter stem section in the center. The ends were open, allowing a constant velocity wind flow through the chamber. The fire was modeled as a constant speed heading fire with a heat release rate of 260 kW/m2. The charring pattern was inferred from data on temperature and heat flux at the boundary on both the windward and leeward sides of the tree. Charring patterns were generated for tree diameters of 4, 6, and 8 cm with wind speeds of 1.0, 2.5, and 4.0 m/s with a constant rate of fire spread and compared with the experimental results of Inoue. The effect of varying the rate of the fire spread from 0.05 to 0.25 m/s was also investigated for a tree diameter of 6 cm and 1 m/s wind speed.
The Great Pacific Ocean Garbage Patch is one of the newly discovered environmental problems of today. Not only is the garbage patch aesthetically displeasing but it also harms marine life. The goal of this project is to compare possible solutions to the Garbage Patch, which include banning the use of polystyrene and direct partial cleanup of the garbage patch. These two solutions have varying costs and benefits; we create a model to weight the options and recommend the most cost-effective strategy. We create a differential equations model using the software STELLA® to model the growth in size of the Garbage Patch over a period of 50 years. We examine two scenarios, one in which there is a ban on polystyrene and one in which there is a partial clean up of the patch. The model shows that a partial clean up of the Garbage Patch is much more effective in reducing the growth of the patch. A combination of both also shows a significant reduction in the growth rate of the patch. We can conclude that a direct partial cleanup does not only show a greater reduction in the growth of the Garbage Patch but is also much more cost effective than a ban on polystyrene.
On June 11, 2009, the World Health Organization declared the outbreak of novel influenza A (H1N1) a pandemic. With limited supplies of vaccines and antivirals, countries and individuals are looking at ways to reduce the spread of H1N1, particularly options that are cost effective and relatively easy to implement. Recent experiences with the SARS and 2009 H1N1 epidemics show that people would wear facemasks to protect themselves against infection; however, little research has been done to quantify the impact of the use of facemasks in reducing the spread of disease. We construct and analyze a mathematical model in which a portion of the population wears a facemask during the pandemic. We look at two scenarios, one in which N95 respirators are worn and one in which surgical masks are worn. To estimate the parameter values used for the effectiveness of facemasks, we used available data from studies done on N95 respirators and surgical masks. If N95 respirators are 20% effective in reducing susceptibility and infectivity only 10% of the population would have to wear them to significantly reduce the number of novel H1N1 cases. We conclude from our model that, if worn properly, facemasks are an effective intervention strategy in reducing the spread of novel H1N1.
The future of electrical production is one of the most pressing issues facing society. Microbial fuel cells have the potential to offset some of this problem through their ability to use many different materials to generate electrical power. Nine microbial fuel cells were constructed using different cathode materials and carbon cloth anodes for voltage production from a pig manure substrate. The open circuit voltage (OCV) of each of these cells was collected continuously, and the internal resistance (Rint) was measured at periodic intervals. From this information, the current (I) could be estimated. The change in the bacterial load of the manure in colony forming units per mL (CFU/mL) was also determined. Data collection on six of the cells was discontinued due to low voltage production. The remaining three cells (copper, brass, and carbon cloth) continuously generated an OCV for over eighteen weeks. Compared to the discontinued cells, the copper and brass cathode cells produced consistently higher voltages (approximately 0.65 V and 0.55 V) and had currents in the range of 15 to 25 mA and 8 to 10 mA, respectively, for the majority of their life spans. The carbon cloth cathode cell produced high voltages, approximately 0.68 V, but displayed a current of less than 10 mA. These three cells displayed an average bacterial load reduction of 93.6%. This information can be applied towards the development of more efficient microbial fuel cells with higher OCV and current outputs, and cells with increasing efficacy at reducing the bacterial load.
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