A simple variational Lagrangian is proposed for the time development of an arbitrary density matrix, employing the ”factorization” of the density. Only the ”kinetic energy” appears in the Lagrangian. The formalism applies to pure and mixed state cases, the NavierStokes equations of hydrodynamics, transport theory, etc. It recaptures the Least Dissipation Function condition of Rayleigh-Onsager a...

In this paper, we construct a lagrangian subspace of the space of representations Mg,l := HomC(πg,l, U)/U of the fundamental group πg,l of a punctured Riemann surface into an arbitrary compact connected Lie group U . This lagrangian subspace is obtained as the fixed-point set of an anti-symplectic involution β̂ defined on Mg,l. We show that the involution β̂ is induced by a form-reversing involut...

We propose a new approach to describe baryonic structure in terms of an effective chiral Lagrangian. The state vector of a baryon is defined on the light front of general position ω·x = 0, where ω is an arbitrary light-like four vector. It is then decomposed in Fock components including an increasing number of pions. The maximal number of particles in the state vector is mapped out to the order...

In end milling, cutting forces and residual stresses need to be precisely predicted in order to improve the quality of the workpiece. Numerical simulation has however not been very successful using the Lagrangian formulation in Finite Element Analysis. This is partly because there is no satisfactory and accurate separation criterion used in the modelling procedure. The results are found to be h...

We show how to orient moduli spaces of holomorphic disks with boundary on an exact Lagrangian immersion of a spin manifold into complex n-space in a coherent manner. This allows us to lift the coefficients of the contact homology of Legendrian spin submanifolds of standard contact (2n + 1)-space from Z2 to Z. We demonstrate how the Z-lift provides a more refined invariant of Legendrian isotopy....

In this article, we prove the local well-posedness, for arbitrary initial data with certain regularity assumptions, of the equations of a Viscoelastic Fluid of Johnson-Segalman type with a free surface. More general constitutive laws can be easily managed in the same way. The geometry is defined by a solid fixed bottom and an upper free boundary submitted to surface tension. The proof relies on...