Vibrational modes of circular free plates under tension

The vibrational frequencies of a plate under tension are given by the eigenvalues $\omega$ of the equation $\Delta^2u-\tau\Delta u=\omega u$. This paper determines the eigenfunctions and eigenvalues of this bi-Laplace problem on the ball under natural (free) boundary conditions. In particular, the fundamental modes --- the eigenfunctions of the lowest nonzero eigenvalue --- are identified and found to have simple angular dependence.Comment: 17 pages. To be submitted for publication shortly

Analysis of the Brinkman-Forchheimer equations with slip boundary conditions

In this work, we study the Brinkman-Forchheimer equations driven under slip boundary conditions of friction type. We prove the existence and uniqueness of weak solutions by means of regularization combined with the Faedo-Galerkin approach. Next we discuss the continuity of the solution with respect to Brinkman's and Forchheimer's coefficients. Finally, we show that the weak solution of the corresponding stationary problem is stable

Variation du sex-ration chez les jeunes kangourous gris de l'est (Macropus giganteus) en fonction de caractéristiques maternelles

Pour une étude de population un sex-ratio à la naissance déviant de la parité peut avoir un impact important dans un contexte de conservation. En effet, un plus grand nombre d’individus d’un sexe peu affecter les dynamiques de population chez une espèce donnée. Plus d’une dizaine d’hypothèses tentent d’expliquer la variation du sex-ratio à la naissance chez les mammifères. La plupart de celles-ci sont construites sur l’idée qu’un investissement parental différentiel selon le sexe du jeune devrait affecter la valeur adaptative du ou des parents (Clutton-Brock and Iason, 1986; Frank, 1990; Clutton-Brock, 1991; West, 2009). Ce mémoire vise à étudier la variation du sex-ratio chez le kangourou gris de l’Est (Macropus giganteus) principalement selon des caractéristiques liées à la mère, au jeune et à l’environnement. L’hypothèse de Trivers et Willard (1973) sera aussi testée dans le cadre de ma maîtrise. Cette hypothèse stipule que pour un mammifère polygyne ayant un dimorphisme sexuel, les mères ayant la capacité de fournir un niveau élevé de soins maternels devraient produire plus de fils. Pour ce faire, un suivi longitudinal de deux populations a été effectué, de 2008 à 2013 au Wilsons Promontory National Park (Prom) et de 2007 à 2013 au Anglesea Golf Club, tous deux dans l’état du Victoria, en Australie. Au total, au sein de la population du Prom, 324 jeunes sont de sexe connu et les analyses ont été effectuées sur 166 paires de mères-jeunes. Un effet important de la masse ainsi que de la longueur de la jambe de la mère sur le sexe de son jeune a été trouvé. Les femelles plus lourdes ou ayant une plus longue jambe ont plus de chance de donner naissance à des fils. Pour un individu, une augmentation de 2 kg par rapport à la moyenne populationnelle en masse (27,5 kg) équivaut à une augmentation de 11 % en probabilité de produire un fils alors qu’une augmentation de 10 mm par rapport à la moyenne populationnelle en longueur de jambe (520 mm) correspond à 8 % d’augmentation en probabilité d’avoir un fils. Ces effets ne sont pas retrouvés chez les primipares, qui pourtant sont en moyennes plus petites et plus légères. Je ne suis pas en mesure d’expliquer ce résultat inattendu chez les femelles primipares. Contrairement à la masse, la condition corporelle de la mère, définie comme étant un reflet des réserves énergétiques d’une femelle et mesurée par un indice de condition relative, n’a aucun effet sur le sexe de son jeune. À ce sujet, je soulève un questionnement quant au choix d’un indice de condition corporelle pour une espèce ayant une croissance indéterminée comme le kangourou. En effet, les indices de condition corporelle lient la masse d’un individu à une longueur corporelle. Toutefois, lorsque ces deux variables varient annuellement, les changements d’indice ne sont donc pas clairement attribuables à l’une ou à l’autre de ces variables. Aucun des résultats obtenus pour la population du Prom n’est présent dans celle d’Anglesea. En fait, aucune des variables testées n’avaient d’effet sur le sexe de la progéniture. Ce projet ne supporte donc pas l’hypothèse de Trivers et Willard au sens strict puisque nous n’avons pas trouvé d’effet de la condition sur le sex-ratio. Nous suggérons plutôt que pour la population du Prom, la taille structurelle ainsi que la masse d’une femelle sont liées à son potentiel reproducteur. Donc, cette maîtrise supporte l’idée générale de cette hypothèse puisque les femelles ayant un plus grand potentiel reproducteur ont des fils. Ce projet souligne également l’importance des conditions environnementales au sein d’une population et à la fois pour deux populations retrouvées dans des conditions environnementales différentes qui présentait des résultats distincts. En effet, les résultats sur la variation du sex-ratio au Wilsons Promontory sont différents de ceux du Anglesea Golf Club, où il n’y a pas de lien entre masse ou taille maternelle et sex-ratio. Ce mémoire présente un portrait complexe du sex-ratio chez le kangourou gris de l’Est variant avec des effets très forts affectant celui-ci. De plus, de nouvelles réflexions émergent du projet notamment concernant le choix d’un indice de condition corporelle pour cette espèce, l’identification des variables environnementales affectant le sex-ratio et l’explication d’un résultat surprenant pour les primipares par rapport au sex-ratio. En conclusion, il sera intéressant de vérifier si les effets de la taille et la masse des femelles sur la progéniture étudiés dans ce projet de maîtrise persistent ou non à travers les années

Location Aided Energy Balancing Strategy in Green Cellular Networks

Most cellular network communication strategies are focused on data traffic scenarios rather than energy balance and efficient utilization. Thus mobile users in hot cells may suffer from low throughput due to energy loading imbalance problem. In state of art cellular network technologies, relay stations extend cell coverage and enhance signal strength for mobile users. However, busy traffic makes the relay stations in hot area run out of energy quickly. In this paper, we propose an energy balancing strategy in which the mobile nodes are able to dynamically select and hand over to the relay station with the highest potential energy capacity to resume communication. Key to the strategy is that each relay station merely maintains two parameters that contains the trend of its previous energy consumption and then predicts its future quantity of energy, which is defined as the relay station potential energy capacity. Then each mobile node can select the relay station with the highest potential energy capacity. Simulations demonstrate that our approach significantly increase the aggregate throughput and the average life time of relay stations in cellular network environment.Comment: 6 pages, 5 figures. arXiv admin note: text overlap with arXiv:1108.5493 by other author

Removal of Fluoride from Mine Water via Adsorption for Land-Applied Soil Amendment

The team researched, designed, and economically analyzed a full-scale adsorption column system to be applied in mining processes that leave high amounts of fluoride in their effluent. This system was designed to remove fluoride from water saturated with calcium sulfate, as calcium sulfate is present in high amounts in certain mining processes. Currently, high density sludge (HDS) is commonly employed to reduce fluoride concentrations, but due to solubility limits the sludge treatment cannot lower fluoride below 10 mg/L (ppm). The current enforceable EPA standard for discharged water is at 4 mg/L (ppm), although mining companies anticipate that this standard will soon be lowered to 2 ppm. The team was tasked with designing a process to lower 10 ppm fluoride down to 2 ppm. The team investigated various methods such as precipitation, ion exchange, and reverse osmosis to remove fluoride from the system. These methods were not cost-effective and did not produce environmentally friendly byproducts. The team ultimately presented the solution of bone char as an adsorbent, with a byproduct that can be safely applied as a soil amendment. A full-scale facility with two adsorption columns was designed to treat 1000 gpm of water

Removal of Fluoride from Mine Water via Adsorption for Land-Applied Soil Amendment

The Moo Pig Sooie’s researched, designed, and economically analyzed a full-scale adsorption column system to be applied in mining processes that leave high amounts of fluoride in their effluent. This system was designed to remove fluoride from water saturated with calcium sulfate, as calcium sulfate is present in high amounts in certain mining processes. Currently, high density sludge (HDS) is commonly employed to reduce fluoride concentrations, but due to solubility limits the sludge treatment cannot lower fluoride below 10 mg/L (ppm). The current enforceable EPA standard for discharged water is at 4 mg/L (ppm), although mining companies anticipate that this standard will soon be lowered to 2 ppm. The Moo Pig Sooie’s were tasked with designing a process to lower 10 ppm fluoride down to 2 ppm. Moo Pig Sooie investigated various methods such as precipitation, ion exchange, and reverse osmosis to remove fluoride from the system. These methods were not cost-effective and did not produce environmentally friendly byproducts. The team ultimately presented the solution of bone char as an adsorbent, with a byproduct that can be safely applied as a soil amendment. A full-scale facility with two adsorption columns was designed to treat 1000 gpm of water

Removal of Fluoride from Mine Water via Adsorption for Land-Applied Soil Amendment

The process of mining minerals and elements from ores and rocks creates acid rock drainage (ARD). This drainage is water that contains heavy metals and minerals that can be dangerous for human consumption or damaging to the environment. The mining industry has employed various water treatment methods to prevent these metals and minerals from being discharged into water sources such as ponds, lakes, and streams. Currently, the most used treatment process in the mining industry is a cost-effective highdensity sludge (HDS) process. This method reduces the concentration of metals and elements with the use of lime/limestone. However, the concentration of fluoride is not reduced to Environmental Protection Agency (EPA) standards, and so it is necessary to design a fluoride removal system. Reverse osmosis (RO) was considered as well as precipitation, ion exchange, and adsorption by media such as biochars, bone char, and activated alumina. Although RO is perhaps the most obvious solution to reducing fluoride concentrations, this method was eliminated due to expensive overhead and maintenance costs. Many metals and compounds present in the mine water will lead to severe scaling and precipitates collecting in the membrane, requiring constant upkeep and high maintenance costs. Precipitation was eliminated because it produced a byproduct only suitable for landfilling, and ion exchange was eliminated due to its high cost and complications with competitive ions. Adsorption was chosen as a viable option for fluoride removal because of its low cost and environmentally friendly byproduct generation. The adsorption media was chosen based on a ranking system designed by our team. This system provided a way for our team to compare the adsorption capacity, rate of adsorption, byproduct application, and price per ton for each adsorbent. From this ranking system, Moo Pig Sooie is presenting a solution of cow bone char as a fluoride adsorbent. This type of biochar can be bought pre-charred and can be land applied as a fertilizer once the char is spent. A full-scale facility was designed to treat 1000 gallons per minute (GPM) of mine water 24 hours a day, seven days a week, for eight months out of the year. To achieve this flowrate and timeline, two packed beds with volumes of 8,900 ft3 each were designed to run in parallel to ensure loading does not occur until the 168-hour mark, the end of the work week. Once the bone char is loaded, the spent bone char will be hauled offsite to be land applied in soil that is naturally slightly acidic. Our experimental results indicate that minimal amounts of fluoride are stripped from bone char in acidic environments. Applying spent bone char to soil presented a desirable environmentally friendly solution for our byproduct. The overall capital cost of a full-scale facility is approximately $750,894 with a yearly operating cost of$4,778,840. Although this is high, the proposed solution will reduce the concentration of fluoride to EPA standards of 2ppm and the process will generate a land-applicable byproduct. Since consuming fluoride in excessive amounts can lead to health issues, public awareness is a necessary aspect of this solution. Citizens affected by the application of fluoride to their soil and water sources should be regularly involved in and aware of the fluoride levels in their environment. From our analysis of bone char adsorption, Moo Pig Sooie believes this type of treatment is a beneficial, cost effective, and sustainable solution for mining facilities that generate high concentrations of fluoride in their water

Removal of Fluoride from Mine Water via Adsorption for Land-Applied Soil Amendment

The process of mining minerals and elements from ores and rocks creates acid rock drainage (ARD). This drainage is water that contains heavy metals and minerals that can be dangerous for human consumption or damaging to the environment. The mining industry has employed various water treatment methods to prevent these metals and minerals from being discharged into water sources such as ponds, lakes, and streams. Currently, the most used treatment process in the mining industry is a cost-effective highdensity sludge (HDS) process. This method reduces the concentration of metals and elements with the use of lime/limestone. However, the concentration of fluoride is not reduced to Environmental Protection Agency (EPA) standards, and so it is necessary to design a fluoride removal system. Reverse osmosis (RO) was considered as well as precipitation, ion exchange, and adsorption by media such as biochars, bone char, and activated alumina. Although RO is perhaps the most obvious solution to reducing fluoride concentrations, this method was eliminated due to expensive overhead and maintenance costs. Many metals and compounds present in the mine water will lead to severe scaling and precipitates collecting in the membrane, requiring constant upkeep and high maintenance costs. Precipitation was eliminated because it produced a byproduct only suitable for landfilling, and ion exchange was eliminated due to its high cost and complications with competitive ions. Adsorption was chosen as a viable option for fluoride removal because of its low cost and environmentally friendly byproduct generation. The adsorption media was chosen based on a ranking system designed by our team. This system provided a way for our team to compare the adsorption capacity, rate of adsorption, byproduct application, and price per ton for each adsorbent. From this ranking system, Moo Pig Sooie is presenting a solution of cow bone char as a fluoride adsorbent. This type of biochar can be bought pre-charred and can be land applied as a fertilizer once the char is spent. A full-scale facility was designed to treat 1000 gallons per minute (GPM) of mine water 24 hours a day, seven days a week, for eight months out of the year. To achieve this flowrate and timeline, two packed beds with volumes of 8,900 ft3 each were designed to run in parallel to ensure loading does not occur until the 168-hour mark, the end of the work week. Once the bone char is loaded, the spent bone char will be hauled offsite to be land applied in soil that is naturally slightly acidic. Our experimental results indicate that minimal amounts of fluoride are stripped from bone char in acidic environments. Applying spent bone char to soil presented a desirable environmentally friendly solution for our byproduct. The overall capital cost of a full-scale facility is approximately $750,894 with a yearly operating cost of$4,778,840. Although this is high, the proposed solution will reduce the concentration of fluoride to EPA standards of 2ppm and the process will generate a land-applicable byproduct. Since consuming fluoride in excessive amounts can lead to health issues, public awareness is a necessary aspect of this solution. Citizens affected by the application of fluoride to their soil and water sources should be regularly involved in and aware of the fluoride levels in their environment. From our analysis of bone char adsorption, Moo Pig Sooie believes this type of treatment is a beneficial, cost effective, and sustainable solution for mining facilities that generate high concentrations of fluoride in their water