LEADER 06998nam 2200745 a 450 001 9910438142403321 005 20200520144314.0 010 $a1-283-90974-X 010 $a1-4614-5389-5 024 7 $a10.1007/978-1-4614-5389-5 035 $a(CKB)3400000000085993 035 $a(EBL)1081909 035 $a(OCoLC)811773008 035 $a(SSID)ssj0000766926 035 $a(PQKBManifestationID)11511276 035 $a(PQKBTitleCode)TC0000766926 035 $a(PQKBWorkID)10740506 035 $a(PQKB)10901138 035 $a(DE-He213)978-1-4614-5389-5 035 $a(MiAaPQ)EBC1081909 035 $a(PPN)16830290X 035 $a(EXLCZ)993400000000085993 100 $a20120918d2013 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aAdvances in applied mathematics, modeling, and computational science /$fRoderick Melnik, Ilias Kotsireas, editors 205 $a1st ed. 210 $aNew York $cFields Institute for Research in the Mathematical Sciences $cSpringer$d2013 215 $a1 online resource (247 p.) 225 0$aFields Institute communications,$x1069-5265 ;$vv. 66 300 $aDescription based upon print version of record. 311 $a1-4899-8987-0 311 $a1-4614-5388-7 320 $aIncludes bibliographical references and index. 327 $aAdvances in Applied Mathematics, Modeling, and Computational Science; Preface; Contents; Interconnected Challenges and New Perspectives in Applied Mathematical and Computational Sciences; 1 Mathematical Models and Algorithms; 2 Mathematical Modeling and Computational Experiments; 3 What Is Next; 4 What This Book Is About; 5 Concluding Remarks; References; Dynamic Blocking Problems for a Model of Fire Propagation; 1 Introduction; 1.1 A Model for Fire Propagation; 1.2 Barriers; 1.3 Blocking and Optimization Problems; 2 An Equivalent Formulation; 3 Existence of Blocking Strategies 327 $a3.1 The Isotropic Case3.2 The Non-isotropic Case; 4 Existence of Optimal Strategies; 5 Necessary Conditions for Optimality; 5.1 Free Arcs; 5.2 A Single Boundary Arc; 5.3 Several Boundary Arcs Constructed Simultaneously; 5.4 Necessary Conditions at Junctions; 6 Sufficient Conditions for Optimality; 7 Numerical Computation of Optimal Barriers; 8 Open Problems; 8.1 Isotropic Blocking Problem; 8.2 Existence of Optimal Strategies; 8.3 Sufficient Conditions for Optimality; 8.4 Regularity; References 327 $aInverse Lax-Wendroff Procedure for Numerical Boundary Conditions of Hyperbolic Equations: Survey and New Developments1 Introduction; 2 Interior Finite Difference Schemes; 3 1D Scalar Conservation Laws; 3.1 Robust and High Order Extrapolation for Outflow Boundary Conditions; 3.2 The ILW Procedure for Inflow Boundary Conditions; 3.3 Computational Results; 4 2D Euler Equations in Static Geometries; 4.1 General Framework; 4.2 No-Penetration Boundary Condition; 4.3 Algorithm Flow Chart; 4.4 Computational Results; 5 2D Euler Equations in Moving Geometries; 6 Concluding Remarks; References 327 $aElliptic Curves over Finite Fields: Number Theoretic and Cryptographic Aspects1 Introduction; 1.1 Motivation; 1.2 Arranging a Group Structure on Elliptic Curves; 1.3 General Notation; 1.4 Basic Facts on Elliptic Curves; 2 Structure of Elliptic Curves over Finite Fields; 2.1 Isogeny and Isomorphism Classes in Various Families; 2.2 Finding the Group Structure; 2.3 Groups Represented by Elliptic Curves; 2.4 Exponent; 2.5 Prime Cardinalities; 2.6 Smooth and Easily Factorable Cardinalities; 2.7 Endomorphism Rings; 2.8 Ranks; 3 Cryptographic Applications of Elliptic Curves over Finite Fields 327 $a3.1 Embedding Degree3.2 Pairing-Friendly Curves; 3.3 Elliptic Twins; 3.4 Pseudorandom Number Generators and Hash Functions; 4 Concluding Remarks; References; Random Matrix Theory and Its Innovative Applications; 1 Random Matrix Theory in the Press; 2 Famous Laws in RMT with MATLAB Experiments; 2.1 The Most Famous Semi-circle Law; 2.2 Marcenko-Pastur Law (Special Case: Quarter Circle Law); 2.3 Circular Law; 2.4 Tracy-Widom Distribution (Law); 3 Random Matrix Factorization; 3.1 The Chi-Distribution and Orthogonal Invariance; 3.2 The QR Decomposition of randn(n) 327 $a3.2.1 Haar Measure on Orthogonal Matrices 330 $aThis volume presents a selection of in-depth studies and state-of-the-art surveys of several challenging topics that are at the forefront of modern applied mathematics, mathematical modeling, and computational science.  These three areas represent the foundation upon which the methodology of mathematical modeling and computational experiment is built as a tool in all areas of applications of mathematics. The articles cover both fundamental and applied research, and provide the reader with state-of-the-art achievements in the development and application of new theories at the interfaces of applied mathematics, modeling, and computational science. The book can serve as a reference on several important current topics in modern applied mathematics and modeling, including random matrix theory with its innovative applications, and dynamic blocking problems. Other important areas covered include: energy stable weighted essentially non-oscillatory schemes with applications in fluid dynamics and aerospace sciences; elliptic curves over finite fields and their applications in cryptography; multiple scale methods coupling network and continuum models and their applications in various areas involving porous media; new and efficient finite difference schemes for hyperbolic equations; statistical geometric  and topological techniques and their applications in the life sciences; optimal control applications combining discrete and continuous features. The material presented in this book aims at fostering interdisciplinary collaborations required to meet the modern challenges of applied mathematics, modeling and computational science. At the same time, the contributions combine rigorous mathematical and computational procedures and examples from a variety of applications ranging from engineering to life sciences, and provide a rich source for graduate student projects. 410 0$aFields Institute Communications,$x1069-5265 ;$v66 606 $aMathematics 606 $aComputer simulation 606 $aMathematical models 606 $aComputer science 606 $aComputer science$xMathematics 615 0$aMathematics. 615 0$aComputer simulation. 615 0$aMathematical models. 615 0$aComputer science. 615 0$aComputer science$xMathematics. 676 $a510 701 $aMelnik$b Roderick$01721471 701 $aKotsireas$b Ilias$0950774 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910438142403321 996 $aAdvances in applied mathematics, modeling, and computational science$94198139 997 $aUNINA