Applied mathematics for the department of energy - Essay Example

? The following are specific topics of interest from one report, which include their significance, the underlying mathematics in them and some examples. A. Applied Mathematics for the Department of Energy Significance The world is increasingly sophisticated in its use of technology especially in the field of understanding the environment. The US Department of Energy continues its mission to be sustainable in its approach. Thus, various policies are recommended in order to promote its potentially good impact into the environment. In line with this, technology is also associated when it comes to computation and data analysis (Han et al., 2011). Mathematics is applied and statistics is most commonly used as the department continues to enhance its policies, procedures and its entire system in general. Policies require analysis of data and information. In most of the time, statistics is employed in this case as the basis of certain future decisions. The use of statistics in the US Department of Energy Science-based analyses are required in the Department of Energy and at some point statistical characterizations are needed especially in their need to come up with policies in line with the complex models of their processes or the entire system. Furthermore, in order to make everything simple out from complex data or information, mathematical modeling is substantially required at the Department of Energy. Examples At the Department of Energy, data analyses are necessary and in order to come up with significant information out from certain observation, mathematical analyses are required. Statistics is one of the most commonly used tools in order to obtain information on science-based approach. Inquiry of information is necessary because this could promote sound justification of policies and processes that need to be carried out. B. Mathematics and complex natural and human-made system Significance Predicting the behaviors of complex and natural human-made system is necessary especially in line with the creation of national policies in regards to the nation’s competitiveness and well being (Applied Mathematics Research Community, 2008). In this process, mathematics cannot be substantially overlooked because it plays an important role prior to achieving essential information that could help in the decision-making process (Shrader, 2009). Mathematics could serve as a significant tool in order to acquire information integrated with the environment and even in existing human-made system. This is a potential field where mathematics could have substantial value and high level of opportunity to be maximized to the fullest. Integration of mathematics and physics The application of mathematics within the complex natural and human-made system is evident in the Department of Energy. In this department, mathematics substantially combined with physics as the ultimate way to achieve potential uses for its applications. Computational-related activities within the field of physics are potential applications of mathematical theories. In fact, mathematics is the language of physics (Faddeev, 1995). Example One basic example that could show how mathematics and physics are integrated is observed within the field of fluid dynamics. There are various computations in this field that combined many concepts in physics and mathematical theories. The result of combining them is a substantial application of mathematics into physics. C. Experimental and computational techniques Significance Today’s complex systems eventually require experimental and computational techniques (Applied Mathematics Research Community, 2008). These two techniques should come together as each one of them is a substantial help to the other. If they are combined together, they could potentially come up with important information to help uncover and understand how complex exactly the system is. In today’s modern way of uncovering information, experiments are further justified by using computational tools (National Research Council (US), 2001). As a result, combined efforts for experiments and computations are necessary because each of them could contribute equal contribution in understanding system’s complexity. The role of mathematics in discovering information Various discoveries in this world are made out of observations. Scientific inquiries require careful observations of some certain issues or phenomena. Based on these observations, important inferences may be formulated or generated. These inferences are basically in quantitative forms that always aim to measure or quantify certain information. The role of mathematics in discovering information is of great importance considering that it could measure or quantify relevant issues (Schirn, 1998). For instance, in experimental and computational techniques, the role of mathematics in discovering information is very crucial because certain conclusions that will be generated should not only be dependent on the experimental design but it has to rely on the computational aspect. Example Applying the role of experimental and computational techniques at the Department of Energy is a clear and evident example how mathematics provides a specific contribution in improving complex systems. Mathematics is proven to be the language of physics and other related scientific inquiries that aim to quantify and measure certain information. In engineering discovery for instance, experimental and computational techniques are substantially used and maximized to the fullest in order to obtain useful ideas and information (Applied Mathematics Research Community, 2008). D. Modeling complex systems and the Department of Energy Significance At the Department of Energy, there are complex systems that need to be taken into account. In order to substantially eliminate these complexities involved in them, it is important to come up with a strategy that will ensure comprehensive understanding of certain things and information (Sokolowski and Banks, 2011). Modeling complex systems is common at the Department of Energy (Applied Mathematics Research Community, 2008). It is therefore important to consider that modeling complex systems is not an ordinary activity because of its ability to explain comprehensive information and allow someone to understand certain issues in great detail especially in the process of engineering discovery. Mathematics and modeling complex systems As usual, mathematics is commonly associated with modeling activities especially if there is involvement of complex data that are quantifiable. Data that are quantifiable could be analyzed in great detail and to the extent that they can potentially explain the prevailing trend of an actual situation. For instance, modeling is highly associated with predicting certain issues or situations (Velten, 2009). These issues or situations could only be predicted through the use of data that are then mathematically processed in order to create a working model. Example At the Department of Energy, there are certain issues that need to be addressed such as predicting the operating characteristics of a clean coal power plant, modifying chemical pathways in the production of biodiesel and more (Applied Mathematics Research Community, 2008). All of these require mathematical modeling of certain data and information. In the midst of information inquiry, researchers are faced with complex data and even more of them. This further resulted to the use of highly sophisticated approaches in understanding them. The use of mathematical models can substantially be integrated in the analysis leading to the discovery of significant information. E. Simulation of complex systems Significance The advancement of computation and programming paves the way for simulation of complex systems. This activity is a hybrid combination of different fields in the entire body of knowledge. In particular, simulation of complex systems ensures taking a look ahead of certain information or what is to come. Its principle is like modeling of complex system, but this approach is substantially more sophisticated than that. In other words, this activity requires inclusion of mathematics, intensive scientific inquiry and complex hybrid models (Applied Mathematics Research Community, 2008). Mathematics and simulation of complex systems It cannot be denied that simulation of complex systems today would require the use of various mathematical concepts. Programming and other modern computational tools make this activity achievable. In other words, mathematics played a significant role prior to coming up with a reliable simulation of complex systems. Example Today, environmental impacts of natural calamities such as hurricane, storm, earthquakes, tsunami and many more are events that need extra preparation. In order to at least have control over them, simulation of complex systems finds its way in computing, engineering and retrieval activities. References Applied Mathematics Research Community (2008) Applied Mathematics: At the US Department of Energy: Past, Present and a View to the Future [online]. Available from http://science.energy.gov/~/media/ascr/pdf/program-documents/docs/Brown_report_may_08.pdf [Accessed 22nd November 2011]. Han, J., Kamber, M., and Pei, J. (2011) Data Mining: Concepts and Techniques. 3rd ed. Waltham, MA: Elsevier. Faddeev, L. D. (1995). 40 years in mathematical physics, Volume 2. River Edge, NJ: World Scientific. National Research Council (US) 2001 An assessment of the Department of Energy’s Office of Fusion Energy Sciences program. NW, Washington, DC: National Academies Press. Schirn, M. (1998). The philosophy of mathematics today. New York, NY: Oxford University Press. Shrader, C. R. (2009). History of Operations Research in the United States Army, Volume 3; Volumes 1973-1995. NW, Washington: Government Printing Office. Sokolowski, J. A., and Banks, C. M. (2011). Principles of Modeling and Simulation: A Multidisciplinary Approach. Hoboken, NJ: John Wiley and Sons. Velten, K. (2009). Mathematical modeling and simulation: introduction for scientists and engineers. Weinheim: Wiley-VCH. Read More