Computer Simulations to test Projects

Computer Simulations to test Projects The idea of describing a physical phenomenon using mathematical models/computational tools is not a new one. About 430 years ago, Galileo Galilei exhorted that it is imperative to describe the results mathematically once a certain number of experiments sensate esperienze have been performed. If one succeeds in illustrating the physical phenomenon using the mathematical equations, then the response of the system of interest can be predicted for a broad range of conditions, including the ones for which conducting the experiments are very difficult, too costly, or not possible at all. In the recent years, the use of computational studies in materials research has been fueled by the drastic increase in the available computational power, resulting from the development of advanced computers with parallel architecture tuned for computationally intensive tasks. Nowadays, the leading engineering companies, such as GM, Ford, GE, Airbus and Boeing use computer simulations to model and test mechanical and aerodynamic characteristics of their products such as automobiles, jet engines and aircrafts before manufacturing the final product or even before testing a prototype in a wind tunnel or crashing them into a wall e.g. Figure 1. shows the deformed shape of the body of a truck body after it is crashed into a rigid wall simulated using a software. Among the numerous benefits of the simulation/computational tools in materials research, one is that if any problems are found in the design during modeling, it can be fixed before sending the technical drawings to the manufacturing unit of the company. Figure 1. 3D simulation of a truck crashing into a rigid virtual wall[1] Now, if we are going to predict the material behavior using the software/computational tools, then the accuracy of the software comes into limelight. The accuracy of these predictions depends on: 1. The accuracy of the adopted numerical solvers (e.g. a very popular scheme known as FEM), 2. The accuracy of the mathematical models that describe the materials behavior (i.e. constitutive laws). In addition to above, different mechanisms occur at different length scales that govern the macro behavior of the material. Therefore, in order to improve the accuracy of predictions of the software, information of these mechanisms happening at different length scales is also required, which lays down the need for a multi-scale model. In science and engineering, nearly all problems are multi-scale in nature. For example, multi-scale modeling of cancer cells is now being considered as an indispensable tool to enable more accurate predictions of growth of cancer cells (reference). Now, in context of modeling behavior of metals, different mathematical models that describe the physics of deformation at different length scales are used and are shown in Figure 2. Figure 2. Overview of length scales involved in metals[2] At atomic scale, the interaction forces between neighboring atoms are calculated using the First-Principles Density Functional Theory (DFT) but the computations are limited to a few hundred atoms, which is too small to study the macro behavior of a material. To model the mechanical behavior of a material using molecular statics / dynamics several million atoms must be considered that involves days / weeks of computations. (Reference)Moreover, characteristic length that is accessible using molecular statics / dynamics modeling is very small than the mean free path of the motion of dislocations (defects in regular atomic lattice). Dislocations are the critical elements in a microstructure of a polycrystalline solid to accommodate the plastic deformation and to analyze the behavior of a material at a length scale, where the material hardening is controlled by the interactions of dislocation, discrete dislocation framework is used. However, due to the large amount of degree of freedoms r equired to analyze interactions of dislocations, the discrete dislocation framework is limited to model a material with volume up to 10 microns. Continuum mechanics / Peridynamics employ the phenomenological laws of motion and of deformation energy to describe the mechanical behavior of a material at macroscopic length scale neglecting any phenomena that occur at smaller length scales which leads to a deficiency in the accuracy of the predictions. Nevertheless, there exists a framework at an intermediate scale (meso-scale) that models dislocations behavior in terms of slip and considers some vital microstructural features providing a very close estimate of real-word phenomena within reasonable computational time, known as crystal plasticity. Crystal plasticity-based models work at a length scale where the groups of crystals i.e. grain in a material becomes evident. In crystal plasticity models, usually a representative volume element (RVE) of the actual component is analyzed that yields a value which represents the behavior of the whole material. Hence, using crystal plasticity alone, one cannot simulate the actual lab scale (at macro-scale) component. Therefore, in order to accurately describe, to fundamentally understand, to reliably predict, and to eventually control the behavior of a material under different conditions, it is of tremendous importance to develop novel approaches that investigate the multiscale nature of met als. In this research work, a new multi-scale framework is proposed that incorporates physics of fine scale phenomena using crystal plasticity-based modeling approach with a Peridynamics-based coarse scale modeling approach. In addition, an attempt is made to enhance their existing modeling capabilities both in term of accuracy as well as computational speed with an interest to study effects of microstructure on: instability, localization and formability in aluminum sheets at meso-scale, crack initiation and crack propagation in a lab scale component made of aluminum. [1] http://www.mscsoftware.com/product/dytran [2] http://www.kochmann.caltech.edu/pics/scales0.gif      

Apush Supplemental Reading Notes- Early Settlements

APUSH SUPPLEMENTAL READING NOTES Early Settlements by James Horn |Please answer each question thoroughly and completely. If you have treated this assignment lightly, you will | |be at a disadvantage in writing essays that call for â€Å"substantial and appropriate outside information. † Read Early Settlements | |(http://www. gilderlehrman. org/history-by-era/early-settlements/essays/early-settlements ) by James Horn and complete the prompts below. |In two or three well thought out sentences, summarize the major point of this reading. (Please be thorough. This will be very important to| |you late in the year when reviewing for the AP test) In this reading, the author wrote about the early English settlers of | |the New World.He opens with a quote from a passage from the 16th century that speaks about the colonies in the new world, and how England| |should get involved and start to colonize as well. The author then goes into detail on the establishing of the 13 colonies of England in | |the New World and later on, the lifestyle in terms of immigrants, diversity, and population. The article ends talking about the expansion | |from the original 13 colonies to what would make Britain known as â€Å"the acknowledged master of North America†. |In a couple of sentences, what was the bias of the author? From what perspective does the author write–political, social, and economic? | |Why is this significant in the document you have read? Related article: Apush Taxation Without Representation DbqWhile most essays and articles seem to have some form of bias, I do not| |pick up in any way a sense of this at any time in the reading. He conveys his message of England’s rise to dominance of North America, | |maybe slightly hinting at bias in that sense, but nonetheless, in a writing style hat displays facts one by one, and gets straight to the| |point. This style of writing is clearly significant in the document simply because it is an easy way to limit bias, and shorten the | |article, therefore making it more reader-friendly for some- if not most readers. | Continued on the next page |Different from the â€Å"what is the main point† question above, list several things that you learned from this reading, things that you did | |not know before doing this reading. |Treaty of Utrecht (1713) gave Britain control of the areas of Hudson Bay, Acadia (Nova Scotia), and Newfoundland | |Spanish were involved in the Fr ench and Indian War | |The British 13 colonies grew in population (nearly 5 times size) over 60 years | |Surges into the backcountry (west of Appalachian) began so early (early 18th mainly) | |Black populations grew even more rapidly from about 20,000 in 1700 to 326,000 by 1760 | |Rice became the third great staple of Britain’s transatlantic commerce, alongside West Indian sugar and Chesapeake tobacco | |5,000 Algonquians who lived along the coastal plain of Virginia when the English first arrived, only about 1,000 remained by 1700 The purpose of this assignment is to help you be prepared to refer to historians or historically significant individuals in your AP test essays.In the space below, write down quotes from the document that you think might be useful. Try to be selective–choose those that are| |genuinely typical of the writer’s thinking or that highlight a major point in the writer's thinking or argument. Include page numbers so | |that you can find them again when we review. | |â€Å"English indentured ervants, Ulster Irish, Catholic Irish, Scots, French Huguenots, and tens of thousands of Germans from the Rhineland and Swiss cantons moved into the coastal plain; flocked to the burgeoning port cities of Boston, New York, and Philadelphia; trekked along fertile river valleys into the interior; and pressed on toward the Appalachian Mountains† â€Å"Together, Virginia, Maryland, and the Lower South accounted for fully 87 percent of all Africans and African Americans living in the | |mainland colonies in 1760† â€Å"The turn of the century witnessed a new direction in English colonizing activities. Peace with Spain in 1604 brought an end to | |privateering, plunder, and the need for a North American base from which to attack Spanish shipping† | | | |â€Å"Jamestown, founded on May 14, 1607, barely survived its first five years.A combination of disease, Indian attacks, faction, and the | |failure to make any signi ficant discoveries or profit brought the colony to the edge of collapse on several occasions and discouraged | |continuing investment. The discovery of a lucrative cash crop, tobacco, which could be cultivated extensively in Virginia and brought a | |handsome return in England, saved the colony but not the Virginia Company, whose exclusive charter was revoked in 1624. SOURCE: http://www. murrayschools. org/MHS/apus/ 10. 1. 2007

Investment policy statement Essay

Return Requirements: * Tax minimization – a continuing collateral goal * Inflation adjustment enhancement of investments- real growth of capital with possible extra return if possible. Risk Tolerance: * Investment risk – very low risk 1. The Muellers have been managing their own investments and are familiar with risk but may not understand volotiliity completely due to their high portion of volatile stocks within the portfolio 2. Want to provide for their daughter’s college education 3. Very high tax bracket (30% on income and 20% on net realized gains) Constraints: Time Horizon: The Muellers are relatively young and have still a lot of time to work and likely saving for retirement is in their agenda. The main goal is to provide for their daughter’s education and expenses associated with it. This goal would be considered long-term but is relatively short in comparison to possible saving for retirement. Liquidity Requirement: There is an ongoing stream of income available. Their may still be some liquidity needs in order to provide for the expenses of the college education along with life expenses associated with both The Muller’s and their daughter. Taxes: The family is in the highest of brackets. Future investments should take that into account on an indefinite basis. Tax-sheltered investments should be considered and will likely benefit the family more than high yields that are taxable. Legal and Regulatory: The Muellers would like to monitor their own investments, so their investments are generally only governed by state law. Unique Circumstances: Past unsuccessful investments of $100,000 can be used to offset tax distributions on net realized gains. Most important aspect and is unique to the saturation, Incoming expenses of $90,000 for the first year of college and then consistent four more years of $40,000 of college expenses.

Positive Impact Of Technology - 871 Words

Technology is always advancing, and people use it almost everywhere. Its used in jobs, homes, and everyday life. Recently technology also has made an immense impact on the way people learn. Many people have different opinions on how to use technology, and if it is a good tool for information. Some believe the use of the internet can help with creativity, and comprehensive. Other believe that through using internet imagination is lessened, and that it leaves students not understanding what was read. Technology can have positive, and negative results, it also had many different tests and studies done to see the impacts. When using technology for learning, many people have explained the positive outcome that is made. It was shown that†¦show more content†¦Although there was positive impacts from video games, there was negatives as well. Playing violent videos has lead to people becoming more aggressive in real life, and leading kids to be less sensitive to real life problems (Wolpert). When reading, and finding information is done online students wont read as fully as they need to. A university professor has explained that Google is not enough to find the information you need, and if the teachers dont help the kids slow down and read deeply, they wont comprehend what they are reading (Simpson). If students arent understanding what they are reading, because they have not read deeply enough, it will not benefit their learning. â€Å"Wiring classrooms for internet access does not enhance learning† (Wolpert). Another downside to technology is false information, and distraction. â€Å"With internet always at your fingertips, it is obvious that it can cause distractions keeping you from learning, and the information you receive may not be the most valuable either† (Skovira). Many believe that the internet is not going to have the resources you need, and that using technology isnt going to better anybodies learning. 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