Related papers: Action Principle for Hydrodynamics and Thermodynam…
Some features of hydro- and thermodynamics, as applied to atmospheres and to stellar structures, are puzzling: 1. The suggestion, first made by Laplace, that our atmosphere has an adiabatic temperature distribution, is confirmed for the…
The formulation of a dynamical theory of General Relativity, including matter, is viewed as a problem of coupling Einstein's theory of pure gravity, formulated as an action principle, to an independently chosen and well defined field theory…
Variational formulations for viscous flows which lead to the Navier-Stokes equation are examined. Since viscosity leads to dissipation and, therefore, to the irreversible transfer of mechanical energy to heat, thermal degrees of freedom…
A general set of fluid equations that allow for energy-conserving momentum transport by gyroscopic motion of fluid elements is obtained. The equations are produced by a class of action principles that yield a large subset of the known fluid…
The action principle is introduced to describe the thermodynamic processes of the state functions from the initial equilibrium state to the final equilibrium state. To capture the path-independent property of the state functions through the…
Hamilton's principle plays a central role in fluid mechanics as a fundamental tool for deriving governing equations, analyzing conservation laws, and designing structure-preserving numerical schemes. However, its classical formulation is…
A simple procedure is presented to study the conservation of energy equation with dissipation in continuum mechanics in 1D. This procedure is used to transform this nonlinear evolution-diffusion equation into a hyperbolic PDE; specifically,…
In this article, a suite of physically inconsistent properties of the Navier-Stokes equations, associated with the lack of mass diffusion and the definition of velocity, are presented. We show that these inconsistencies are consequences of…
Hydrodynamic equations for a one-component plasma are derived as a generalization of the Euler equations to include the effects of the long-range Coulomb interaction. By using a variational principle, these equations self-consistently unify…
In the present work we redefine and generalize the action principle for dissipative systems proposed by Riewe by fixing the mathematical inconsistencies present in the original approach. In order to formulate a quadratic Lagrangian for…
Fluid dynamics accompanies with the entropy production thus increases the local temperature, which plays an important role in charged systems such as the ion channel in biological environment and electrodiffusion in capacitors/batteries. In…
We propose a novel action principle for two dimensional incompressible fluid dynamics that naturally incorporates both vorticity and viscous dissipation via gauge field couplings. The action features a Chern Simons like term,…
In the variational principle leading to the Euler equation for a perfect fluid, we can use the method of undetermined multiplier for holonomic constraints representing mass conservation and adiabatic condition. For a dissipative fluid, the…
Variational principles play a fundamental role in deriving evolution equations of physics. They are working well in case of nondissipative evolution but for dissipative systems they are not unique, not predictive and not constructive. With…
The variational principle for the special and general relativistic hydrodynamics are discussed in view of its application to obtain approximate solutions to these problems. We show that effective Lagrangians can be obtained for suitable…
This paper proposes a new thermodynamic hypothesis that states that a nonlinear natural system that is not isolated and involves positive feedbacks tends to minimize its resistance to the flow process through it that is imposed by its…
Hydrodynamics is a general theoretical framework for describing the long-time large-distance behaviors of various macroscopic physical systems, with its equations based on conservation laws such as energy-momentum conservation and charge…
Extended irreversible thermodynamics is a theory that expands the classical framework of nonequilibrium thermodynamics by going beyond the local-equilibrium assumption. A notable example of this is the Maxwell-Cattaneo heat flux model,…
A variational principle is derived for two-dimensional incompressible rotational fluid flow with a free surface in a moving vessel when both the vessel and fluid motion are to be determined. The fluid is represented by a stream function and…
We present some novel thermodynamic ideas based on the Maupertuis principle. By considering Hamiltonians written in terms of appropriate action-angle variables we show that thermal states can be characterized by the action variables and by…