MODULE 14.2Solidification—Let’s Make It Crystal Clear!Prerequisite: Module 9.5, “Random Walk.”IntroductionWhat do snowflakes and steel have in common? At first glance, we probably would say, not much. However, if we could look closely enough, we would see that they both are crystall ine, possessing amazing structural similarities. Each is made of tree -like structures called dendrites , which are formed as substance cools during the process of solidification . Snowflakes are composed of one or more snow crystals . Each crystal is built of water molecules arranged in a very specific, hexagonal lattice . These crystals form. in the clouds by the condensatio n of water vapor into ice. At first, while very small, the crystals form. as hexagonall y shaped prisms, following the original, molecular symmetry. The edges of the facets of this prism grow out more rapidly than the fac -ets themselves, leading to the formation of “limbs.” These limbs may, and usually do, produce other branches, leading to the dendrite, or treelike, forms. A number of factors determine the precise shape of the crystal, but temperature is the primary influence. As snowflakes blow and fall through the clouds, they encoun -ter significant variations in temperature, humidity, and pressure. Each snowflake tends to have different environm ental “experiences,” which lead to the development of different shapes. Why snowflake shape is so temperature dependent is not com -pletely understood (Libbrecht).The solidification of snowflakes is fascinating, but the process of solidification has an impressive array of manufacturing applications. Despite the increased use of plastics, think of all the things we use everyday that are metal. Used to produce ev -erything from soda cans to car engines, these metals and alloys are formed from liquids that have “frozen,” or solidified. Solidification, therefore, is an important process for generating metal products as well as snowflakes. Dendrites form. within the molten metals/alloys as they solidify during the casting process. These dendrites vary greatly in shape, size, and orientation. Furthermore, In order to vie w this proof accurately , the Ov erprint Pre vie w Option must be check ed in Acrobat Professional or Adobe Reader . Please contact your Customer Service Rep-resentati v e if you ha v e questions about finding the option.Job Name: Cyan = PMS 300/356585t700 Module 14.2the individual dendrites interconnect in various ways to generate a series of intricate microstructures . These individual and collective variations greatly influence the structural qualit ies (e.g., strength and flexibility) of the product (Glicksman et al . 1991). There are numerous horror stories of castings that have broken apart from internal defects that originated from thermal stresses occurring during solidification (Seetharamu et al. 2001). According to scientists, we would be able to understand (and, therefore, control) the properties of materials that solidify dendritically better if we could develop effective computational models of the behavior. of individual dendrites.Under the influence of Earth’s gravity, liquid metal is subject to the influence of convective currents as it cools. These currents significantly alter the growth of the dendrites, which makes mode代做留学生Matlab作业、asp实验代写、代写留学生JSP实验作业、JSP实验代写留学生ling of “normal” dendritic growth and the effects of convective currents on such growth virtually impossible. Confronting this difficulty, the National Aeronautics and Space Administration (Glicksman et al . 1991) has teamed with scientists at Rensselaer Polytechnic Institute in the Isothermal Dendritic Growth Experiment (IDGE). Experiments in this program, conducted in conditions of low gravity that Earth orbit offers, have already shed tremendous light on den -dritic growth. For instance, scientists, using IDGE data, will be able to separate the effects of convection from other factors that impact solidificatio n of metals and al -loys. Such information will go far to improve computational models, which should guide us to improved industrial production of various metals/alloys.Projects1. a. We can use the technique of diffusion-limited aggregation ( DLA ) to build a dendritic structure. In one form. of the algorithm, a seed , or initial location for the developing dendritic structure, is in the middle of an m × m launching rectangle . This launching rectangle is a region in the middle of an n × n grid, where m rmax+ 4 from the seed, where rmaxis the radius of the struc -ture so far, then have step sizes of length r – rmax– 2; otherwise, have step sizes of length 1 (Gould and Tobochnik 1988).12. Repeat any of Projects 1 or 2, considering accumulation on a structure, such as the deposit of snow on a tree. Have the seed be a triangular tree-like struc -ture or other type of structure on the bottom of the grid. Release random walkers from the north end of the grid with a greater likelihood of traveling south (Panoff 2004).ReferencesGlicksman, Martin E., M. B. Koss, R. C. Hahn, Ana Cris R. Veloso, A. Rojas, and E. Winsa. 1991. “Scientific Basis for the Isothermal Dendritic Growth Experiment: A USMP-2 Space Flight Experiment.” In Materials Science Forum , 77: 51–60. Gould, Harvey, and Jan Tobochnik. 1988. An Introduction to Computer Simulation Methods, Applications to Physical Systems, Part 2 . Reading, MA: Addison-Wes -ley: 695.Libbrecht, Kenneth G. “Snowflake Primer—The Basic Facts About Snowflakes and Snow Crystals.” California Institute of Technology. http://www.its.caltech .edu/~atomic/snowcrystals/primer/primer.htm (accessed January 1, 2013)Panoff, Robert. 2004. “Diffusion Limited Aggregation.” Educational Materials for Undergraduate Compuational Science. Capital University. http://www.capital .edu/cs-computational-science/ (accessed January 1, 2013)Seetharamu, K. N., R. Paragasam, Ghulam A. Quadir, Z. A. Zaina l, P. Sthaya Prasad, and T. Sundararajan. 2001. “Finite Element Modeling of Solidification Phenom -ena.” Sadhana , 26 (Parts 1 and 2): 103–120.The Shodor Educational Foundation. 2002. “Software—Diffusion Limited Aggrega -tion Calculator.” Computational Science Education Reference Desk. http://www .shodor.org/refdesk/Resources/Models/DLA/ (accessed January 1, 2013)In order to vie w this proof accurately , the Ov erprint Pre vie w Option must be check ed in Acrobat Professional or Adobe Reader . Please contact your Customer Service Rep-resentati v e if you ha v e questions about finding the option.Job Name: Cyan = PMS 300/356585t转自：http://ass.3daixie.com/2018091823003147.html
