Stochastic Geometric Mechanics

1. Noise and Dissipation in Rigid Body Motion
Alexis Arnaudon, Alex L. De Castro, Darryl D. Holm

2. An Open Problem in the Theory of Regularization by Noise for Nonlinear PDEs
Franco Flandoli

3. Surface Integrals in Hilbert Spaces for General Measures and Applications
Giuseppe Da Prato

4. Geometric Analysis of Noisy Perturbations to Nonholonomic Constraints
François Gay-Balmaz, Vakhtang Putkaradze

5. Degenerate Diffusions and Harmonic Analysis on SE(3): A Tutorial
Gregory S. Chirikjian

6. Covariant Central Extensions of Gauge Lie Algebras
Bas Janssens, Karl-Hermann Neeb

7. Four Chapters on Low-Dimensional Gauge Theories
Thierry Lévy, Ambar Sengupta

8. Some Variational and Stochastic Methods for the Euler Equations of Incompressible Fluid Dynamics and Related Models
Yann Brenier

9. Introduction to Homogenization Theory
Gregory A. Chechkin

10. Modeling, Minimizing and Managing the Risk of Fatigue for Mechanical Components
L. Bittner, H. Gottschalk, M. Gröger, N. Moch, M. Saadi, S. Schmitz

Keywords: Mathematics, Geometry, Probability Theory and Stochastic Processes, Calculus of Variations and Optimal Control; Optimization, Mathematical Applications in the Physical Sciences, Partial Differential Equations