Related papers: Variational Principles for Shock Dynamics in Compr…
We formulate a stochastic least-action principle for solutions of the incompressible Navier-Stokes equation, which formally reduces to Hamilton's principle for the incompressible Euler solutions in the case of zero viscosity. We use this…
An internal energy function of the mass density, the volumetric entropy and their gradients at n-order generates the representation of multi-gradient fluids. Thanks to Hamilton's principle, we obtain a thermodynamical form of the equation…
In this paper, we develop a Hamiltonian variational formulation for the nonequilibrium thermodynamics of simple adiabatically closed systems that is an extension of Hamilton's phase space principle in mechanics. We introduce the…
Variational principles for magnetohydrodynamics were introduced by previous authors both in Lagrangian and Eulerian form. In previous works [1] Yahalom & Lynden-Bell and later Yahalom [2] introduced a simpler Eulerian variational principle…
We establish the existence and stability of cylindrical transonic shock solutions under three dimensional perturbations of the incoming flows and the exit pressure without any further restrictions on the background transonic shock…
Stability conditions of magnetized plasma flows are obtained by exploiting the Hamiltonian structure of the magnetohydrodynamics (MHD) equations and, in particular, by using three kinds of energy principles. First, the Lagrangian variable…
The equations of reversible (inviscid, adiabatic) fluid dynamics have a well-known variational formulation based on Hamilton's principle and the Lagrangian, to which is associated a Hamiltonian formulation that involves a Poisson bracket…
The Navier-Stokes Hamiltonian is derived from first principles. Its Hamilton equations are shown to be equivalent to the continuity, Navier-Stokes, and energy conservation equations of a compressible viscous fluid. The derivations of the…
We consider Euler equations for potential flow of ideal incompressible fluid with a free surface and infinite depth in two dimensional geometry. Both gravity forces and surface tension are taken int account. A time-dependent conformal…
We present the variational action principle for initial value problems in classical, conservative-force point particle mechanics. We rigorously derive this formulation by taking the classical limit of the Schwinger-Keldysh expression for…
We present a comprehensive Eulerian (Hamiltonian) framework for relativistic fluid dynamics in curved spacetimes, with emphasis on Schwarzschild geometry. The key innovation lies in the consistent use of density and three-velocity fields,…
We consider the dominant equations for the motion of the non-Newtonian fluid in a domain from an energetic point of view. We apply our energetic variational approaches and the first law of thermodynamics to derive the generalized…
In the mechanics of inviscid conservative fluids, it is classical to generate the equations of dynamics by formulating with adequate variables, that the pressure integral calculated in the time-space domain corresponding to the motion of…
Variational principles for magnetohydrodynamics were introduced by previous authors both in Lagrangian and Eulerian form. In this paper we introduce simpler Eulerian variational principles from which all the relevant equations of…
The log-homotopy particle flow filter resolves the Bayesian update by transporting particles along a continuous trajectory in pseudo-time. However, the governing partial differential equation for the flow velocity is fundamentally…
The solution of a momentum conservation equation for the gas and liquid stream in the flowing element is obtained on the basis of the modern approach to a problem on contact interaction of bodies and mediums. A flowing element, system are:…
For binary mixtures of fluids without chemical reactions, but with components having different temperatures, the Hamilton principle of least action is able to produce the equation of motion for each component and a balance equation of the…
Many engineering and physiological applications deal with situations when a fluid is moving in flexible tubes with elastic walls. In the real-life applications like blood flow, there is often an additional complexity of vorticity being…
Causal variational principles, which are the analytic core of the physical theory of causal fermion systems, are found to have an underlying Hamiltonian structure, giving a formulation of the dynamics in terms of physical fields in…
The noncanonical Hamiltonian formulation of magnetohydrodynamics (MHD) is used to construct variational principles for symmetric equilibrium configurations of magnetized plasma including flow. In particular, helical symmetry is considered…