Stopping a Viscous Fluid by a Feedback Dissipative Field: Thermal Effects without Phase Changing -- Ultracontractive Bounds for Nonlinear Evolution Equations Governed by the Subcritical p-Laplacian -- Weighted L 2-spaces and Strong Solutions of the Navier-Stokes Equations in -- A Limit Model for Unidirectional Non-Newtonian Flows with Nonlocal Viscosity -- On the Problem of Thermocapillary Con…
Empirical Traffic Data -- Lane-Change Maneuvers Consuming Freeway Capacity -- Empirical Description of Car-Following -- Optimization Potential of a Highway Network: An Empirical Study -- Observation, Theory and Experiment for Freeway Traffic as Physics of Many-Body System -- Fluctuation in Expressway Traffic Flow -- Calibration and Validation of Microscopic Traffic Flow Models -- Real Highway T…
Random Closed Sets and Capacity Functionals -- Expectations of Random Sets -- Minkowski Addition -- Unions of Random Sets -- Random Sets and Random Functions. Appendices: Topological Spaces -- Linear Spaces -- Space of Closed Sets -- Compact Sets and the Hausdorff Metric -- Multifunctions and Continuity -- Measures and Probabilities -- Capacities -- Convex Sets -- Semigroups and Harmonic Analys…
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…
Geostatistics -- The genesis of geostatistics in gold and diamond industries -- Concepts and Methods of Geostatistics -- Prediction by conditional simulation: models and algorithms -- Flow in porous media: An attempt to outline Georges Matheron’s contributions -- Over Thirty Years of Petroleum Geostatistics -- The expansion of environmental geostatistics -- Random Sets -- Random Closed Sets -…
Basis Objects and Operations -- Functional Data Objects and Operations -- Linear Differential Operators and Smoothing -- Functional Registration -- Functional Linear Models -- Functional Generalized Linear Models -- Functional Principal Components -- Canonical Correlation -- Functional Cluster Analysis -- Principal Differential Analysis.S+Functional Data Analysis is the first commercial object …
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.