The wind power potential in Interior Alaska is evaluated from a micrometeorological perspective. Based on the local balance equation of momentum and the equation of continuity we derive the local balance equation of k...The wind power potential in Interior Alaska is evaluated from a micrometeorological perspective. Based on the local balance equation of momentum and the equation of continuity we derive the local balance equation of kinetic energy for macroscopic and turbulent systems, and in a further step, Bernoulli’s equation and integral equations that customarily serve as the key equations in momentum theory and blade-element analysis, where the Lanchester-Betz-Joukowsky limit, Glauert’s optimum actuator disk, and the results of the blade-element analysis by Okulov and Sorensen are exemplarily illustrated. The wind power potential at three different sites in Interior Alaska (Delta Junction, Eva Creek, and Poker Flat) is assessed by considering the results of wind field predictions for the winter period from October 1, 2008, to April 1, 2009 provided by the Weather Research and Forecasting (WRF) model to avoid time-consuming and expensive tall-tower observations in Interior Alaska which is characterized by a relatively low degree of infrastructure outside of the city of Fairbanks. To predict the average power output we use the Weibull distributions derived from the predicted wind fields for these three different sites and the power curves of five different propeller-type wind turbines with rated powers ranging from 2 MW to 2.5 MW. These power curves are represented by general logistic functions. The predicted power capacity for the Eva Creek site is compared with that of the Eva Creek wind farm established in 2012. The results of our predictions for the winter period 2008/2009 are nearly 20 percent lower than those of the Eva Creek wind farm for the period from January to September 2013.展开更多
The main design of this paper is to determine once and for all the true nature and status of the sequence of the prime numbers, or primes—that is, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and so on. The ma...The main design of this paper is to determine once and for all the true nature and status of the sequence of the prime numbers, or primes—that is, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and so on. The main conclusion revolves entirely around two points. First, on the one hand, it is shown that the prime sequence exhibits an extremely high level of organization. But second, on the other hand, it is also shown that the clearly detectable organization of the primes is ultimately beyond human comprehension. This conclusion runs radically counter and opposite—in regard to both points—to what may well be the default view held widely, if not universally, in current theoretical mathematics about the prime sequence, namely the following. First, on the one hand, the prime sequence is deemed by all appearance to be entirely random, not organized at all. Second, on the other hand, all hope has not been abandoned that the sequence may perhaps at some point be grasped by human cognition, even if no progress at all has been made in this regard. Current mathematical research seems to be entirely predicated on keeping this hope alive. In the present paper, it is proposed that there is no reason to hope, as it were. According to this point of view, theoretical mathematics needs to take a drastic 180-degree turn. The manner of demonstration that will be used is direct and empirical. Two key observations are adduced showing, 1), how the prime sequence is highly organized and, 2), how this organization transcends human intelligence because it plays out in the dimension of infinity and in relation to π. The present paper is part of a larger project whose design it is to present a complete and final mathematical and physical theory of rational human intelligence. Nothing seems more self-evident than that rational human intelligence is subject to absolute limitations. The brain is a material and physically finite tool. Everyone will therefore readily agree that, as far as reasoning is concerned, there are things that the brain can do and things that it cannot do. The search is therefore for the line that separates the two, or the limits beyond which rational human intelligence cannot go. It is proposed that the structure of the prime sequence lies beyond those limits. The contemplation of the prime sequence teaches us something deeply fundamental about the human condition. It is part of the quest to Know Thyself.展开更多
基金the National Science Foundation for funding the project work of Megan Hinzman and Samuel Smock in summer 2011Hannah K.Ross and John Cooney in summer 2012 through the Research Experience for Undergraduates(REU)Program,grant number AGS1005265the Alaska Department of Labor for funding Dr.Gary Sellhorst’s project work
文摘The wind power potential in Interior Alaska is evaluated from a micrometeorological perspective. Based on the local balance equation of momentum and the equation of continuity we derive the local balance equation of kinetic energy for macroscopic and turbulent systems, and in a further step, Bernoulli’s equation and integral equations that customarily serve as the key equations in momentum theory and blade-element analysis, where the Lanchester-Betz-Joukowsky limit, Glauert’s optimum actuator disk, and the results of the blade-element analysis by Okulov and Sorensen are exemplarily illustrated. The wind power potential at three different sites in Interior Alaska (Delta Junction, Eva Creek, and Poker Flat) is assessed by considering the results of wind field predictions for the winter period from October 1, 2008, to April 1, 2009 provided by the Weather Research and Forecasting (WRF) model to avoid time-consuming and expensive tall-tower observations in Interior Alaska which is characterized by a relatively low degree of infrastructure outside of the city of Fairbanks. To predict the average power output we use the Weibull distributions derived from the predicted wind fields for these three different sites and the power curves of five different propeller-type wind turbines with rated powers ranging from 2 MW to 2.5 MW. These power curves are represented by general logistic functions. The predicted power capacity for the Eva Creek site is compared with that of the Eva Creek wind farm established in 2012. The results of our predictions for the winter period 2008/2009 are nearly 20 percent lower than those of the Eva Creek wind farm for the period from January to September 2013.
文摘The main design of this paper is to determine once and for all the true nature and status of the sequence of the prime numbers, or primes—that is, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and so on. The main conclusion revolves entirely around two points. First, on the one hand, it is shown that the prime sequence exhibits an extremely high level of organization. But second, on the other hand, it is also shown that the clearly detectable organization of the primes is ultimately beyond human comprehension. This conclusion runs radically counter and opposite—in regard to both points—to what may well be the default view held widely, if not universally, in current theoretical mathematics about the prime sequence, namely the following. First, on the one hand, the prime sequence is deemed by all appearance to be entirely random, not organized at all. Second, on the other hand, all hope has not been abandoned that the sequence may perhaps at some point be grasped by human cognition, even if no progress at all has been made in this regard. Current mathematical research seems to be entirely predicated on keeping this hope alive. In the present paper, it is proposed that there is no reason to hope, as it were. According to this point of view, theoretical mathematics needs to take a drastic 180-degree turn. The manner of demonstration that will be used is direct and empirical. Two key observations are adduced showing, 1), how the prime sequence is highly organized and, 2), how this organization transcends human intelligence because it plays out in the dimension of infinity and in relation to π. The present paper is part of a larger project whose design it is to present a complete and final mathematical and physical theory of rational human intelligence. Nothing seems more self-evident than that rational human intelligence is subject to absolute limitations. The brain is a material and physically finite tool. Everyone will therefore readily agree that, as far as reasoning is concerned, there are things that the brain can do and things that it cannot do. The search is therefore for the line that separates the two, or the limits beyond which rational human intelligence cannot go. It is proposed that the structure of the prime sequence lies beyond those limits. The contemplation of the prime sequence teaches us something deeply fundamental about the human condition. It is part of the quest to Know Thyself.
