In this paper we consider the transport–Stokes system, which describes sedimentation of a particles in viscous fluid inertialess regime. We show existence Lagrangian solutions to Cauchy problem with L1 initial data. prove uniqueness as corollary stability estimate respect 1-Wasserstein distance for data Yudovich-type refinement L3, finite first moment. Moreover, describe evolution starting from...

This paper deals with the Lagrangian analogue of symplectic or point reduction by stages. We develop Routh reduction as a reduction technique that preserves the Lagrangian nature of the dynamics. To do so we heavily rely on the relation between Routh reduction and cotangent symplectic reduction. The main results in this paper are: (i) we develop a class of so called magnetic Lagrangian systems ...

The Controlled Lagrangian method is a branch of energy shaping methods that is designed to control underactuated mechanical systems. The method emp...

A finite-volume dynamical core with a terrain-following Lagrangian control-volume discretization is described. The vertically Lagrangian discretization reduces the dimensionality of the physical problem from three to two with the resulting dynamical system closely resembling that of the shallow water system. The 2D horizontalto-Lagrangian-surface transport and dynamical processes are then discr...

the purpose of this paper is to investigate the egm method and the behavior of a solid particle suspended in a twodimensional rectangular cavity due to conjugate natural convection. a thermal lattice boltzmann bgk model is implemented to simulate the two dimensional natural convection and the particle phase was modeled using the lagrangian–lagrangian approach where the solid particles are treat...

An improved treatment of advection is essential for atmospheric transport and chemistry models. Eulerian treatments are generally plagued with instabilities, unrealistic negative constituent values, diffusion, and dispersion errors. A higher-order Eulerian model improves one error at significant cost but magnifies another error. The cost of semi-Lagrangian models is too high for many applicatio...

A derivative expansion technique is developed to compute functional determinants of quadratic operators, non diagonal in spacetime indices. This kind of operators arise in general ’t Hooft gauge fixed Lagrangians. Elaborate applications of the developed derivative expansion are presented. Typeset using REVTEX 1

We show that some very naturally occurring energymanifolds that are induced by second-order Lagrangians L = L(u, u′, u′′) are not, in general, of contact type in (R4, ω). We also comment on the more general question whether there exist any contact forms on these energy manifolds for which the associated Reeb vector field coincides with the Hamiltonian vector field.

We propose an algorithmic approach to stabilization of Lagrangian systems. The first step involves making admissible modifications to the Lagrangian for the uncontrolled system, thereby constructing what we call the controlled Lagrangian. The Euler-Lagrange equations derived from the controlled Lagrangian describe the closed-loop system where new terms are identified with control forces. Since ...

In order to obtain a framework in which both non-holonomic mechanical systems and non-holonomic mechanical systems with symmetry can be described, we introduce in this paper the notion of a Lagrangian system on a subbundle of a Lie algebroid.