Related papers: Dynamics of distributed sources
This paper studies the continuous-time dynamics generated by control-theoretic Lagrangian methods for equality-constrained optimization. In particular, we consider dynamics induced by proportional-integral and feedback linearization…
In this article, we generalize the theory of discrete Lagrangian mechanics and variational integrators in two principal directions. First, we show that Lagrangian submanifolds of symplectic groupoids give rise to discrete dynamical systems,…
The formulation of combinatorial differential forms, proposed by Forman for analysis of topological properties of discrete complexes, is extended by defining the operators required for analysis of physical processes dependent on scalar…
We study the cosmological dynamics of non-minimally coupled matter models using the Brown's variational approach to relativistic fluids in General Relativity. After decomposing the Ricci scalar into a bulk and a boundary term, we construct…
The statistical nature of discrete fluid molecules with random thermal motion so far has not been considered in mainstream fluid mechanics based on Navier-Stokes equations, wherein fluids have been treated as a continuum breaking into many…
The purpose of this paper is to examine the Lagrangian stochastic modeling of the fluid velocity seen by inertial particles in a nonhomogeneous turbulent flow. A new Langevin-type model, compatible with the transport equation of the drift…
An alternative approach - nonequilibrium evolution thermodynamics, is compared with classical Landau approach. A statistical justification of the approach is carried out with help of probability distribution function on an example of a…
Non-Gaussian shapes, despite a linear form of the mean-squared displacement, have been observed for the displacement distribution in a large range of diffusive systems. Stochastic models for such "Brownian yet non-Gaussian" diffusion will…
Thermodynamic relations are derived from first principles of mechanics for non-equilibrium processes. Since the key role herein is played by the law of increase of entropy, the latter is analyzed at first. It is shown that its derivation…
In this survey, we address mixing from the point of view of partial differential equations, motivated by applications that arise in fluid dynamics. We give an account of optimal mixing, loss of regularity for transport equations, enhanced…
Linear diffusions are used to model a large number of stochastic processes in physics, including small mechanical and electrical systems perturbed by thermal noise, as well as Brownian particles controlled by electrical and optical forces.…
A gaussian distribution of binding energies, but conditioned to exploit generally available information on packing in liquids, provides a statistical-thermodynamic theory of liquid water that is structurally non-committal, molecularly…
Nonlinear systems with model uncertainty are often described by stochastic differential equations. Some techniques from random dynamical systems are discussed. They are relevant to better understanding of solution processes of stochastic…
This work aims at introducing model methodology and numerical studies related to a Lagrangian stochastic approach applied to the computation of the wind circulation around mills. We adapt the Lagrangian stochastic downscaling method that we…
The suggested approach makes it possible to produce a consistent description of motions of a physical system. It is shown that the concept of force fields defining the systems dynamics is equivalent to the choice of the corresponding metric…
The General Lagrangian Mean (GLM) theory uses a set of averaged equations of fluid dynamics to describe interactions between mean flows and waves. These equations are formulated in coordinates that follow the fluid's average velocity and…
We consider hydrodynamics with non conserved number of particles and show that it can be modeled with effective fluid Lagrangians which explicitly depend on the velocity potentials. For such theories, the {}``shift symetry''…
We present a new formalism which allows to derive the general Lagrangian dynamical equations for the motion of gravitating particles in a non--flat Friedmann universe with arbitrary density parameter $\Omega$ and no cosmological constant.…
Applications of variational methods are typically restricted to conservative systems. Some extensions to dissipative systems have been reported too but require ad hoc techniques such as the artificial doubling of the dynamical variables.…
This paper exposes a novel exploratory formalism, which end goal is the numerical simulation of the dynamics of a cloud of particles weakly or strongly coupled with a turbulent fluid. Giventhe large panel of expertise of the list of…