Mathematical Models and Methods for Real World Systems

This volume centers on the links between mathematics and the physical world. It first explores future challenges of mathematical technology, offers a wide-ranging definition of industrial mathematics, and explains the mathematics of type-II superconductors. After lucid discussions on theoretical and applied aspects of wavelets, the book presents classical and fractal methods for physical problems, including a fractal approach to porous media textures and using MATLAB to model chaos in the motion of a satellite. The final section surveys recent trends in variational methods, focusing on areas such as elliptic inverse problems, sweeping processes, and the BBKY hierarchy of quantum kinetic equations.

Mathematics does not exist in isolation but is linked inextricably to the physical world. At the 2003 International Congress of Industrial and Applied Mathematics, leading mathematicians from around the globe gathered for a symposium on the "Mathematics of Real World Problems," which focused on furthering the establishment and dissemination of those links.Presented in four parts, Mathematical Models and Methods for Real World Systems comprises chapters by those invited to this symposium. The first part examines mathematics for technology, exploring future challenges of mathematical technology, offering a wide-ranging definition of industrial mathematics, and explaining the mathematics of type-II superconductors. After lucid discussions on theoretical and applied aspects of wavelets, the book presents classical and fractal methods for physical problems, including a fractal approach to porous media textures and using MATLAB® to model chaos in the motion of a satellite. The final section surveys recent trends in variational methods, focusing on areas such as elliptic inverse problems, sweeping processes, and the BBKY hierarchy of quantum kinetic equations.By virtue of its abstraction, mathematics allows the transfer of ideas between fields of applications. Mathematical Models and Methods for Real World Systems clearly demonstrates this and promotes the kind of cross-thinking that nurtures creativity and leads to further innovation.

MATHEMATICS FOR TECHNOLOGYMathematics as a Technology-Challenges for the Next Ten YearsH. NeunzertIndustrial Mathematics-What Is It?N.G. BartonMathematical Models and Algorithms for Type-II SuperconductorsK.M. Furati and A.H. SiddiqiWAVELET METHODS FOR REAL-WORLD PROBLEMSWavelet Frames and Multiresolution AnalysisO. ChristensenComparison of a Wavelet-Galerkin Procedure with a Crank-Nicolson-Galerkin Procedure for the Diffusion Equation Subject to the Specification of MassS.H. Behiry, J.R. Cannon, H. Hashish, and A.I. ZayedTrends in Wavelet ApplicationsK.M. Furati, P. Manchanda, M.K. Ahmad, and A.H. SiddiqiWavelet Methods for Indian Rainfall DataJ. Kumar, P. Manchanda, and N.A. SontakkeWavelet Analysis of Tropospheric and Lower Stratospheric Gravity WavesO. O?guz, Z. Can, Z. Aslan, and A.H. SiddiqiAdvanced Data Processes of Some Meteorological ParametersA. Tokgozlu and Z. AslanWavelet Methods for Seismic Data Analysis and ProcessingF.M. Kh`eneCLASSICAL AND FRACTAL METHODS FOR PHYSICAL PROBLEMSGradient Catastrophe in Heat Propagation with Second SoundS.A. Messaoudi and A.S. Al ShehriAcoustic Waves in a Perturbed Layered OceanF.D. Zaman and A.M. Al-MarzougNon-Linear Planar Oscillation of a Satellite Leading to Chaos under the Influence of Third-Body TorqueR. Bhardwaj and R. TuliChaos Using MATLAB in the Motion of a Satellite under the Influence of Magnetic TorqueR. Bhardwaj and P. KaurA New Analysis Approach to Porous Media Texture-Mathematical Tools for Signal Analysis in a Context of Increasing ComplexityF. Nekka and J. LiTRENDS IN VARIATIONAL METHODSA Convex Objective Functional for Elliptic Inverse ProblemsM.S. Gockenbach and A.A. KhanThe Solutions of BBGKY Hierarchy of Quantum Kinetic Equations for Dense SystemsM. Yu. Rasulova, A.H. Siddiqi, U. Avazov, and M. RahmatullaevConvergence and the Optimal Choice of the Relation Parameter for a Class of Iterative MethodsM.A. El-Gebeily and M.B.M. ElgindiOn a Special Class of Sweeping ProcessM. Brokate and P. Manchanda