4 resultados para Eigenfunctions and fundamental solution

em Digital Commons - Michigan Tech


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Water resource depletion and sanitation are growing problems around the world. A solution to both of these problems is the use of composting latrines, as it requires no water and has been recommended by the World Health Organization as an improved sanitation technology. However, little analysis has been done on the decomposition process occurring inside the latrine, including what temperatures are reached and what variables most affect the composting process. Having better knowledge of how outside variables affect composting latrines can aid development workers on the choice of implementing such technology, and to better educate the users on the appropriate methods of maintenance. This report presents a full, detailed construction manual and temperature data analysis of a double vault composting latrine. During the author’s two year Peace Corps service in rural Paraguay he was involved with building twenty one composting latrines, and took detailed temperature readings and visual observations of his personal latrine for ten months. The author also took limited temperature readings of fourteen community member’s latrines over a three month period. These data points were analyzed to find correlations between compost temperatures and several variables. The two main variables found to affect the compost temperatures were the seasonal trends of the outside temperatures, and the mixing and addition of moisture to the compost. Outside seasonal temperature changes were compared to those of the compost and a linear regression was performed resulting in a R2-value of 0.89. Mixing the compost and adding water, or a water/urine mixture, resulted in temperature increases of the compost 100% of the time, with seasonal temperatures determining the rate and duration of the temperature increases. The temperature readings were also used to find events when certain temperatures were held for sufficient amounts of time to reach total pathogen destruction in the compost. Four different events were recorded when a temperature of 122°F (50°C) was held for at least 24 hours, ensuring total pathogen destruction in that area of the compost. One event of 114.8°F (46°C) held for one week was also recorded, again ensuring total pathogen destruction. Through the analysis of the temperature data, however, it was found that the compost only reached total pathogen destruction levels during ten percent of the data points. Because of this the storage time recommendation outlined by the World Health Organization should be complied with. The WHO recommends storing compost for 1.5-2 years in climates with ambient temperatures of 2-20°C (35-68°F), and for at least 1 year with ambient temperatures of 20-35°C (68-95°F). If these storage durations are obtainable the use of the double vault composting latrine is an economical and achievable solution to sanitation while conserving water resources.

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With the development and capabilities of the Smart Home system, people today are entering an era in which household appliances are no longer just controlled by people, but also operated by a Smart System. This results in a more efficient, convenient, comfortable, and environmentally friendly living environment. A critical part of the Smart Home system is Home Automation, which means that there is a Micro-Controller Unit (MCU) to control all the household appliances and schedule their operating times. This reduces electricity bills by shifting amounts of power consumption from the on-peak hour consumption to the off-peak hour consumption, in terms of different “hour price”. In this paper, we propose an algorithm for scheduling multi-user power consumption and implement it on an FPGA board, using it as the MCU. This algorithm for discrete power level tasks scheduling is based on dynamic programming, which could find a scheduling solution close to the optimal one. We chose FPGA as our system’s controller because FPGA has low complexity, parallel processing capability, a large amount of I/O interface for further development and is programmable on both software and hardware. In conclusion, it costs little time running on FPGA board and the solution obtained is good enough for the consumers.

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Linear programs, or LPs, are often used in optimization problems, such as improving manufacturing efficiency of maximizing the yield from limited resources. The most common method for solving LPs is the Simplex Method, which will yield a solution, if one exists, but over the real numbers. From a purely numerical standpoint, it will be an optimal solution, but quite often we desire an optimal integer solution. A linear program in which the variables are also constrained to be integers is called an integer linear program or ILP. It is the focus of this report to present a parallel algorithm for solving ILPs. We discuss a serial algorithm using a breadth-first branch-and-bound search to check the feasible solution space, and then extend it into a parallel algorithm using a client-server model. In the parallel mode, the search may not be truly breadth-first, depending on the solution time for each node in the solution tree. Our search takes advantage of pruning, often resulting in super-linear improvements in solution time. Finally, we present results from sample ILPs, describe a few modifications to enhance the algorithm and improve solution time, and offer suggestions for future work.

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This dissertation presents the competitive control methodologies for small-scale power system (SSPS). A SSPS is a collection of sources and loads that shares a common network which can be isolated during terrestrial disturbances. Micro-grids, naval ship electric power systems (NSEPS), aircraft power systems and telecommunication system power systems are typical examples of SSPS. The analysis and development of control systems for small-scale power systems (SSPS) lacks a defined slack bus. In addition, a change of a load or source will influence the real time system parameters of the system. Therefore, the control system should provide the required flexibility, to ensure operation as a single aggregated system. In most of the cases of a SSPS the sources and loads must be equipped with power electronic interfaces which can be modeled as a dynamic controllable quantity. The mathematical formulation of the micro-grid is carried out with the help of game theory, optimal control and fundamental theory of electrical power systems. Then the micro-grid can be viewed as a dynamical multi-objective optimization problem with nonlinear objectives and variables. Basically detailed analysis was done with optimal solutions with regards to start up transient modeling, bus selection modeling and level of communication within the micro-grids. In each approach a detail mathematical model is formed to observe the system response. The differential game theoretic approach was also used for modeling and optimization of startup transients. The startup transient controller was implemented with open loop, PI and feedback control methodologies. Then the hardware implementation was carried out to validate the theoretical results. The proposed game theoretic controller shows higher performances over traditional the PI controller during startup. In addition, the optimal transient surface is necessary while implementing the feedback controller for startup transient. Further, the experimental results are in agreement with the theoretical simulation. The bus selection and team communication was modeled with discrete and continuous game theory models. Although players have multiple choices, this controller is capable of choosing the optimum bus. Next the team communication structures are able to optimize the players’ Nash equilibrium point. All mathematical models are based on the local information of the load or source. As a result, these models are the keys to developing accurate distributed controllers.