Related papers: Vortex Dynamics: A Variational Approach Using the …
A kinetic model is proposed for rarefied flows of molecular gas with rotational and temperature-dependent vibrational degrees of freedom. The model reduces to the Boltzmann equation for monatomic gas when the energy exchange between the…
Many applications of porous media research involves high pressures and, correspondingly, exchange of thermal energy between the fluid and the matrix. While the system is relatively well understood for the case of non-moving porous media,…
The Letter considers dynamics of helical vortices and helical-vortex rings either solving directly the equations of motions of a vortex line or using canonical relations following from the Hamiltonian equations of motion. An analytical…
A longstanding open question in classical mechanics is to formulate the least action principle for dissipative systems. In this work, we give a general formulation of this principle by considering a whole conservative system including the…
We critically compare thermodynamic and kinetic approaches, that have been recently used to study relations between the spin polarization and fluid vorticity in systems consisting of spin-one-half particles. The thermodynamic approach…
The relativistic hydrodynamical equations are being examined with the aim of extracting the quantum-mechanical equations (the relativistic Klein-Gordon equation and the Schr\"odinger equation in the non-relativistic limit). In both cases it…
A conventional derivation of motion equations in mechanics and field equations in field theory is based on the principle of least action with a proper Lagrangian. With a time-independent Lagrangian, a function of coordinates and velocities…
We introduce a three independent functions variational formalism for stationary and non-stationary barotropic flows. This is less than the four variables which appear in the standard equations of fluid dynamics which are the velocity field…
The principles of behavior of the system with discrete interactions are applied to description of motion of the relativistic particle. Applying the concept of non-local behavior both to position in space and to time, the apparently…
Holm (Proc. Roy. Soc 2015) introduced a variational framework for stochastically parametrising unresolved scales of hydrodynamic motion. This variational framework preserves fundamental features of fluid dynamics, such as Kelvin's…
The general local, nondissipative equations of motion for a quantized vortex moving in an uncharged laboratory superfluid are derived from a relativistic, co-ordinate invariant framework, having vortices as its elementary objects in the…
The Hamiltonian equation of motion is studied for a vortex occuring in 2-dimensional Heisenberg ferromagnet of anisotropic type by starting with the effective action for the spin field formulated by the Bloch (or spin) coherent state. The…
The two-dimensional Navier-Stokes equations are rewritten as a system of coupled nonlinear ordinary differential equations. These equations describe the evolution of the moments of an expansion of the vorticity with respect to Hermite…
In this work, a second order smoothed particle hydrodynamics is derived for the study of relativistic heavy ion collisions. The hydrodynamical equation of motion is formulated in terms of the variational principle. In order to describe the…
We write a Ginzburg-Landau Hamiltonian for a charged order parameter interacting with a background electromagnetic field in 2+1 dimensions. Using the method of Lund we derive a collective coordinate action for vortex defects in the order…
We investigate the dynamics of quantized vortices in a model two-dimensional supersolid. Starting from an effective action that captures the dynamics of the superfluid condensate and its coupling to the lattice displacements, we integrate…
In spirit of the principle of least action, which means that when a perturbation is applied to a physical system its reaction is such that it modifies its state to "agree" with the perturbation by "minimal" change of its initial state. In…
We review the development and practical uses of a generalized Maupertuis least action principle in classical mechanics, in which the action is varied under the constraint of fixed mean energy for the trial trajectory. The original…
A rigorous method for introducing the variational principle describing relativistic ideal hydrodynamic flows with all possible types of breaks (including shocks) is presented in the framework of an exact Clebsch type representation of the…
In this work, a methodology is proposed for formulating general dynamical equations in mechanics under the umbrella of the principle of energy conservation. It is shown that Lagrange's equation, Hamilton's canonical equations, and…