We minimize elastic energies on framed curves which penalize both curvature and torsion. also discuss critical points using the infinite dimensional version of Lagrange multipliers' method. Finally, some examples arising from applications are discussed numerical experiments presented.

Table of contents Chapter 1 ‘Incremental formulation of 3D/4D variational assimilation—an overview’ Chapter 2 ‘3D variational assimilation’ Chapter 3 ‘4D variational assimilation’ Chapter 4 ‘Background term’ Chapter 5 ‘Conventional observational constraints’ Chapter 6 ‘Satellite observational constraints’ Chapter 7 ‘Background, analysis and forecast errors’ Chapter 8 ‘Gravity-wave control’ Chap...

Table of contents Chapter 1 ‘Incremental formulation of 3D/4D variational assimilation—an overview’ Chapter 2 ‘3D variational assimilation’ Chapter 3 ‘4D variational assimilation’ Chapter 4 ‘Background term’ Chapter 5 ‘Conventional observational constraints’ Chapter 6 ‘Satellite observational constraints’ Chapter 7 ‘Background, analysis and forecast errors’ Chapter 8 ‘Gravity-wave control’ Chap...

We discuss a smooth variational principle for partially smooth viscosity subdiierentials and explore its applications in nonsmooth analysis. Short Title: Partially smooth variational principles.