Modèles micro-macro pour les solides -- Techniques d’homogénéisation -- Simulation moléculaire -- Modèles micro-macro pour les fluides -- Cinétique chimique -- Vers une unité des approches.Systèmes multi-échelles est une introduction à la problématique des systémes multi-échelles du point de vue du mathématicien appliqué. Il se compose d'une mosaique d'exemples dont le seul lie…
Kinetic theory -- Related Markov processes -- Stochastic weighted particle method -- Numerical experiments.Stochastic numerical methods play an important role in large scale computations in the applied sciences. The first goal of this book is to give a mathematical description of classical direct simulation Monte Carlo (DSMC) procedures for rarefied gases, using the theory of Markov processes a…
Inverse Problems and Interpretation of Measurements -- Classical Regularization Methods -- Statistical Inversion Theory -- Nonstationary Inverse Problems -- Classical Methods Revisited -- Model Problems -- Case Studies.The book develops the statistical approach to inverse problems with an emphasis on modeling and computations. The framework is the Bayesian paradigm, where all variables are mode…
Methods of Solving Ill-Posed Problems -- One-Dimensional Inverse Scattering and Spectral Problems -- Inverse Obstacle Scattering -- Stability of the Solutions to 3D Inverse Scattering Problems with Fixed-Energy Data -- Non-Uniqueness and Uniqueness Results -- Inverse Problems of Potential Theory and Other Inverse Source Problems -- Non-Overdetermined Inverse Problems -- Low-Frequency Inversion …
Foundational Material -- De Rham Cohomology and Harmonic Differential Forms -- Parallel Transport, Connections, and Covariant Derivatives -- Geodesics and Jacobi Fields -- Symmetric Spaces and Kähler Manifolds -- Morse Theory and Floer Homology -- Variational Problems from Quantum Field Theory -- Harmonic Maps.
Lévy Processes in Euclidean Spaces and Groups -- Locally Compact Quantum Groups -- Quantum Stochastic Analysis - an Introduction -- Dilations, Cocycles and Product Systems.This volume is the first of two volumes containing the revised and completed notes lectures given at the school "Quantum Independent Increment Processes: Structure and Applications to Physics". This school was held at the Al…
to Quantum Trajectories -- The Bohmian Route to the Hydrodynamic Equations -- The Phase Space Route to the Hydrodynamic Equations -- The Dynamics and Properties of Quantum Trajectories -- Function and Derivative Approximation on Unstructured Grids -- Applications of the Quantum Trajectory Method -- Adaptive Methods for Trajectory Dynamics -- Quantum Trajectories for Multidimensional Dynamics --…
What is a Quadrature Domain? -- Recent Progress and Open Problems in the Bergman Space -- The Bergman Kernel and Quadrature Domains in the Plane -- The Cauchy Transform -- Quadrature Domains and Fluid Dynamics -- On Uniformly Discrete Sequences in the Disk -- Algebraic Aspects of the Dirichlet Problem -- Linear Analysis of Quadrature Domains. IV -- Restriction, Localization and Microlocalizatio…
Surveys -- An Introduction to Lattice Chiral Fermions -- Computing f(A)b for Matrix Functions f -- Computational Methods for the Fermion Determinant and the Link Between Overlap and Domain Wall Fermions -- Monte Carlo Simulations of Lattice QCD -- Lattice QCD -- Determinant and Order Statistics -- Monte Carlo Overrelaxation for SU(N) Gauge Theories -- Improved Staggered Fermions -- Perturbative…
Introduction -- 1. Quantities and Measures -- 2. Variables and Functions -- 3. Trigonometry, Geometry of Plane and Space -- 4. Cartography -- 5. Derivation -- Integration and Differential Equations.This undergraduate textbook presents a unique comprehensive overview on Mathematics in Earth Sciences and Geography. It deals with fundamental theoretical and applied mathematics, needed by bachelor …