This paper deals with the finite element solution of the convection diffusion equation in one and two dimensions. Two main techniques are adopted and compared. The first one includes Petrov-Galerkin based on Lagrangian tensor product elements in conjunction with streamlined upwinding. The second approach represents Bubnov/Petrov-Galerkin schemes based on a new group of exponential elements. It ...

It is shown that if the decoherence matrix corresponding to a qubit master equation has a block-diagonal real part, then the evolution is determined by a one-dimensional oscillator equation. Further, when the decoherence matrix itself is block-diagonal, then the necessary and sufficient conditions for completely positive evolution may be formulated in terms of the oscillator Hamiltonian or Lagr...

This paper derives a 2D, quasi-linear Schrödinger equation in Lagrangian coordinates that describes the effects of weak pressure gradients on large amplitude inertial oscillations in a rotating shallow fluid. The coefficients of the equation are singular at values of the gradient of the wave amplitude that correspond to the vanishing of the Jacobian of the transformation from Lagrangian to Eule...

A Lagrangian, for the slowly varying complex amplitude of an almost monocbromatio electrostatio plasma wave in an unmagnetized plasma, is derived. The method is a va,riant of the averaged Lagrangian technique of whitham, adoptod for uso in plasma pbysics by employing Low's Lagrangian, together with certain elimination procedures to simplify the Lagrangian to usable form. The erpansion in powers...

On the basis of the gauge principle of field theory, a new variational formulation is presented for flows of an ideal fluid. The fluid is defined thermodynamically by mass density and entropy density, and its flow fields are characterized by symmetries of translation and rotation. The rotational transformations are regarded as gauge transformations as well as the translational ones. In addition...

We discuss general incompressible inviscid models, including the Euler equations, the surface quasi-geostrophic equation, incompressible porous medium equation, and Boussinesq equations. All these models have classical unique solutions, at least for short time. We show that they have real analytic Lagrangian paths. More precisely, we show that as long as a solution of any of these equations is ...

Sunto. – In this note we survey some recent results on the well-posedness of the ordinary differential equation with non-Lipschitz vector fields. We introduce the notion of regular Lagrangian flow, which is the right concept of solution in this framework. We present two different approaches to the theory of regular Lagrangian flows. The first one is quite general and is based on the connection ...

In this paper we find a explicit moving frame along curves of Lagrangian planes invariant under the action of the symplectic group. We use the moving frame to find a family of independent and generating differential invariants. We then construct geometric Hamiltonian structures in the space of differential invariants and prove that, if we restrict them to a certain Poisson submanifold, they bec...

A lagrangian for relativistic fluid systems with matters inside is developed using gauge principle. In the model, the gauge boson represents the fluid field in a form Aμ ≡ ǫμ φ, where ǫμ contains the fluid kinematics and φ is an auxiliary field representing the fluid distribution. This leads to a new relativistic equation of motion for fluid, but which further coincides to the classical Euler e...

Direct Numerical Simulations (DNS) of the distribution function of conformation of small axisymmetric particles is considered from a numerical point of view. The mathematical modelling of microstructured uid has to take into account (i) the e ect of the surrounding uid onto the microstructure and (ii) the e ect of the microstructures on the uid. We consider (i) the simulation of the conformatio...