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Using the One Dimensional Wave Equation to Represent Electromagnetic Waves in a Vacuum

The differential wave equation can be used to describe electromagnetic waves in a vacuum. In the one dimensional case, this takes the form $\frac{\partial^2\phi}{\partial x^2}-\frac{1}{c^2}\frac{\partial^2\phi}{\partial t^2} = 0$. A general function $f(x,t) = x \pm ct$ will propagate with speed c. To represent the properties of electromagnetic waves, however, the function $\phi(x,t) = \phi _0 sin(kx-\omega t)$ must be used. This gives the Electric and Magnetic field equations to be $E (z,t) = \hat{x} E _0 sin(kz-\omega t)$ and $B (z,t) = \hat{y} B _0 sin(kz-\omega t)$. Using this solution as well as Maxwell's equations the relation $\frac{E_0}{B_0} = c$ can be derived. In addition, the average rate of energy transfer can be found to be $\bar{S} = \frac{E_0 ^2}{2 c \mu _0} \hat{z}$ using the poynting vector of the fields.

Eric Minor

What is the maximum altitude reached by a Superpressure balloon?Can we control the balloons altitude with an air pump?

A detailed report of findings on the altitudes which can be reached by super pressure balloons and how various factors and considerations affect this. Superpressure balloons are deployed and researched by various organisations including NASA, to solve technical limitations such as cell tower coverage as well as advancing fields of research. Balloons are used in planetary exploration, and weather prediction to teaching primary school physics. The versatile yet simple aerostat has been a valuable tool in many areas of engineering and their altitude ceiling is of great scientific interest. To solve the problem without the ability to physically reproduce the scenario, required mathematical models to be created as a means of simulating the effects of real world physics. A degree great enough to output an accurate and hence useful result without becoming too complex to be computable is the fine balance attempted to be created by this paper.

Charles Poppy

Sommarmatte

Just some summer math courses.

Alexander Nielsen

Economía de la felicidad

En el siguiente ensayo, usted podrá encontrar encuestas que le brindaran información disponible en la pagina web del DANE, que le mostraran los diferentes estratos socioeconómicos en la ciudad de Medellín. El propósito de este ensayo es mostrar una relación entre los ingresos de los individuos y su felicidad. Dado a que la mayoría de la población de Medellín consta con bajos recursos y sufren necesidades por la falta de ciertas modalidades indispensables para sobrevivir, ellos son felices y están plenos con su estilo de vida.

Maicol Rojas

Indoor Air Quality Assessment of Campus Spaces with Carbon Dioxide as a Measure of Adverse Health Effects

Indoor air quality (IAQ) is referred to as “the air quality within and around buildings and structures, especially as it relates to the health and comfort of building occupants” (US EPA, 2015). Indoor pollutant levels further determine the quality of indoor air, and one of the indicators used to measure IAQ is carbon dioxide (CO2). Drawing on data collected from a classroom, auditorium, and gym setting in the Mount Royal University campus, the aim of this report is to determine if CO2 levels present are within established margins substantial to result in adverse health effects. Environmental factors that are considered in this report include: room size, supply air, and occupant load in the specified spaces on the campus. The results of this study suggest that there are a myriad of factors that may affect IAQ and that CO2 is merely an indicator of poor air quality. Overall, peak indoor CO2 levels can further be used to determine appropriate ventilation rates in an indoor space.

Graham Brown, Isabella Luu

Using Timing Attacks Against Cryptographic Algorithms

Computer algorithms that are written with the intent to keep data private are used in every day cryptography. These algorithms may exhibit execution time behaviour which is dependant on secret information that is not known to an outsider. When carefully analysed, this dependency may leak information that can be used to gain unintended access to private data, effectively nullifying the use of such algorithms. This threat poses a vital risk to the field of computer cryptography, and analysis should be done in attempt to eradicate this potential threat from any algorithms in modern day use.
In this paper, attacks are orchestrated against several algorithms that have previously been used in cryptography, resulting in the successful retrieval of secret data within a manageable time-scale.

Harry Budd