Introduction: Basic Notions and Methods -- Heterogeneous Rod -- Heterogeneous Plate -- Finite Rod Structures -- Lattice Structures -- The Multi-Scale Domain Decomposition.Numerous applications of rod structures in civil engineering, aircraft and spacecraft confirm the importance of the topic. On the other hand the majority of books on structural mechanics use some simplifying hypotheses; these …
Atomistic Models -- Lattice Gas Models and Kinetic Monte Carlo Simulations of Epitaxial Growth -- Cluster Diffusion and Island Formation on fcc(111) Metal Surfaces Studied by Atomic Scale Computer Simulations -- A Multiscale Study of the Epitaxial CVD of Si from Chlorosilanes -- Off-lattice Kinetic Monte Carlo Simulations of Strained Heteroepitaxial Growth -- Quasicontinuum Monte Carlo Simulati…
Nonlinear Inverse Problems: Theoretical Aspects and Some Industrial Applications -- Numerical Methods for the Simulation of Incompressible Viscous Flow: An Introduction -- Computational Techniques for the Verification and Control of Hybrid Systems -- Data Assimilation Methods for an Oceanographic Problem -- Ant Colonies: a Nature inspired Paradigm for the Mathematical Modelling of Self-Organizi…
Linearization -- Fixed-Point Theorems -- Degree Theory and Applications -- Minimization Methods -- Topological and Variational Methods.Nonlinear analysis has developed rapidly in the last three decades. Theories, techniques and results in many different branches of mathematics have been combined in solving nonlinear problems. This book collects and reorganizes up-to-date materials scattered thr…
Basic Material -- Approximation of Integrals -- Boundary Layer Behaviour -- Two-Point Boundary Value Problems -- Nonlinear Boundary Value Problems -- Elliptic Boundary Value Problems -- Boundary Layers in Time -- Evolution Equations with Boundary Layers -- The Continuation Method -- Averaging and Timescales -- Advanced Averaging -- Averaging for Evolution Equations -- Wave Equations on Unbounde…
Three-Dimensional Differential Geometry -- Differential Geometry of Surfaces -- Applications to Three-Dimensional Elasticity in Curvilinear Coordinates -- Applications to Shell Theory.curvilinear coordinates. This treatment includes in particular a direct proof of the three-dimensional Korn inequality in curvilinear coordinates. The fourth and last chapter, which heavily relies on Chapter 2, be…
This volume contains two of the three lectures that were given at the 33rd Probability Summer School in Saint-Flour (July 6-23, 2003). Amir Dembo’s course is devoted to recent studies of the fractal nature of random sets, focusing on some fine properties of the sample path of random walk and Brownian motion. In particular, the cover time for Markov chains, the dimension of discrete limsup ran…
Setting the Scene -- Two-Point Boundary Value Problems -- The Heat Equation -- Finite Difference Schemes for the Heat Equation -- The Wave Equation -- Maximum Principles -- Poisson's Equation in Two Space Dimensions -- Orthogonality and General Fourier Series -- Convergence of Fourier Series -- The Heat Equation Revisited -- Reaction-Diffusion Equations -- Applications of the Fourier Transform.…
and Outline -- Indefinite Inner Products -- Orthogonalization and Orthogonal Polynomials -- Classes of Linear Transformations -- Canonical Forms -- Real H-Selfadjoint Matrices -- Functions of H-Selfadjoint Matrices -- H-Normal Matrices -- General Perturbations. Stability of Diagonalizable Matrices -- Definite Invariant Subspaces -- Differential Equations of First Order -- Matrix Polynomials -- …
Kohn's Proof of the Hypoellipticity of the Hörmander Operators -- Compactness Criteria for the Resolvent of Schrödinger Operators -- Global Pseudo-differential Calculus -- Analysis of some Fokker-Planck Operator -- Return to Equillibrium for the Fokker-Planck Operator -- Hypoellipticity and Nilpotent Groups -- Maximal Hypoellipticity for Polynomial of Vector Fields and Spectral Byproducts -- …