LEADER 04309nam 22006255 450 001 9910149488003321 005 20200705095649.0 010 $a9783319457260 024 7 $a10.1007/978-3-319-45726-0 035 $a(CKB)3710000000928173 035 $a(DE-He213)978-3-319-45726-0 035 $a(MiAaPQ)EBC4731740 035 $a(PPN)197141005 035 $a(EXLCZ)993710000000928173 100 $a20161102d2017 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aDimensional Analysis Beyond the Pi Theorem /$fby Bahman Zohuri 205 $a1st ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017. 215 $a1 online resource (XIX, 266 p. 78 illus., 36 illus. in color.) 311 $a3-319-45725-X 311 $a3-319-45726-8 320 $aIncludes bibliographical references at the end of each chapters and index. 327 $aPrinciples of the Dimensional Analysis -- Dimensional Analysis: Similarity and Self-Similarity -- Shock Wave and High Pressure Phenomena -- Similarity Methods for Nonlinear Problems -- Appendix A: Simple Harmonic Motion -- Appendix B: Pendulum Problem -- Appendix C: Similarity Solutions Methods for Partial Differential Equations (PDEs) -- Index. 330 $aDimensional Analysis and Physical Similarity are well understood subjects, and the general concepts of dynamical similarity are explained in this book. Our exposition is essentially different from those available in the literature, although it follows the general ideas known as Pi Theorem. There are many excellent books that one can refer to; however, dimensional analysis goes beyond Pi theorem, which is also known as Buckingham?s Pi Theorem. Many techniques via self-similar solutions can bound solutions to problems that seem intractable. A time-developing phenomenon is called self-similar if the spatial distributions of its properties at different points in time can be obtained from one another by a similarity transformation, and identifying one of the independent variables as time. However, this is where Dimensional Analysis goes beyond Pi Theorem into self-similarity, which has represented progress for researchers. In recent years there has been a surge of interest in self-similar solutions of the First and Second kind. Such solutions are not newly discovered; they have been identified and named by Zel?dovich, a famous Russian Mathematician in 1956. They have been used in the context of a variety of problems, such as shock waves in gas dynamics, and filtration through elasto-plastic materials. Self-Similarity has simplified computations and the representation of the properties of phenomena under investigation. It handles experimental data, reduces what would be a random cloud of empirical points to lie on a single curve or surface, and constructs procedures that are self-similar. Variables can be specifically chosen for the calculations. 606 $aApplied mathematics 606 $aEngineering mathematics 606 $aThermodynamics 606 $aHeat engineering 606 $aHeat transfer 606 $aMass transfer 606 $aFluid mechanics 606 $aMathematical and Computational Engineering$3https://scigraph.springernature.com/ontologies/product-market-codes/T11006 606 $aEngineering Thermodynamics, Heat and Mass Transfer$3https://scigraph.springernature.com/ontologies/product-market-codes/T14000 606 $aEngineering Fluid Dynamics$3https://scigraph.springernature.com/ontologies/product-market-codes/T15044 615 0$aApplied mathematics. 615 0$aEngineering mathematics. 615 0$aThermodynamics. 615 0$aHeat engineering. 615 0$aHeat transfer. 615 0$aMass transfer. 615 0$aFluid mechanics. 615 14$aMathematical and Computational Engineering. 615 24$aEngineering Thermodynamics, Heat and Mass Transfer. 615 24$aEngineering Fluid Dynamics. 676 $a519 700 $aZohuri$b Bahman$4aut$4http://id.loc.gov/vocabulary/relators/aut$0720918 906 $aBOOK 912 $a9910149488003321 996 $aDimensional Analysis Beyond the Pi Theorem$91982041 997 $aUNINA