Related papers: Quaternion wavefunction theory bridges quantum for…

It is the matter of fact that quantum mechanics operates with notions that are not determined in the frame of the mechanics' formalism. Among them we can call the notion of "wave-particle" (that, however, does not appear in both classical…

We discuss the implications of a wave function for quantum gravity, which involves nothing but 3-dimensional geometries as arguments and is invariant under general coordinate transformations. We derive an analytic wave function from the…

There were many attempts to geometrize electromagnetic field and find out new interpretation for quantum mechanics formalism. The distinctive feature of this work is that it combines geometrization of electromagnetic field and…

This paper develops a geometric mechanics framework for the reduction of general relativistic hydrodynamic variational principles, from the variation of worldlines approach in 4D spacetime to 3-dimensional Eulerian descriptions. We consider…

The existence of frictionless flow below a critical velocity for obstacles moving in a superfluid is well established in the context of the mean-field Gross-Pitaevskii theory. We calculate the next order correction due to quantum and…

In the standard formulation of quantum mechanics, one starts by proposing a potential function that models the physical system. The potential is then inserted into the Schr\"odinger equation, which is solved for the wave function, bound…

There is a remarkable and canonical problem in 3D geometry and topology: To understand existing models of 3D fluid motion or to create new ones that may be useful. We discuss from an algebraic viewpoint the PDE called Euler's equation for…

Inspired from the idea of minimally coupling of a real scalar field to geometry, we investigate the classical and quantum models of a flat energy-dependent FRW cosmology coupled to a perfect fluid in the framework of the scalar-rainbow…

The paper considers the Euler system of PDE on a smooth compact Riemannian manifold of positive curvature without boundary, and the sphere ${\mathbb{S}}^2$ in particular. The paper interprets the Euler equations as a transport problem for…

In earlier papers [3,4,5,6] Gursey et al. showed development of a bilocal baryon-meson field from two quark-antiquark fields. The Hamiltonian in the case of vanishing quark masses was shown to have a very good agreement with experiments…

A fluid described by an Abelian Chern-Simons action principle in 4+1 dimensions is considered. Letting 3+1 dimensions correspond to the usual space and time, and assuming the fields to be independent of the fifth coordinate, the free theory…

We are concerned with the stability of steady multi-wave configurations for the full Euler equations of compressible fluid flow. In this paper, we focus on the stability of steady four-wave configurations that are the solutions of the…

From a columnar approximation of the Euler equations of an incompressible fluid with surface tension, we derive in the short-wave approximation a new integrable classical 1+1 dimensional field theory for the motion of the surface. Together…

We consider the vorticity formulation of the Euler equations describing the flow of a two-dimensional incompressible ideal fluid on the sphere. Zeitlin's model provides a finite-dimensional approximation of the vorticity formulation that…

Flows of one-dimensional continuum in Lagrangian coordinates are studied in the paper. Equations describing these flows are reduced to a single Euler-Lagrange equation which contains two undefined functions. Particular choices of the…

We present an alternative Eulerian hydrodynamic model for the electromagnetic field in which the discrete vector indices in Maxwell\s equations are replaced by continuous angular freedoms, and develop the corresponding Lagrangian picture in…

In 1966, Arnold [1] showed that the Lagrangian flow of ideal incompressible fluids (described by Euler equations) coincide with the geodesic flow on the manifold of volume preserving diffeomorphisms of the fluid domain. Arnold's proof and…

We present a geometrical way of understanding the dynamics of wavefunctions in a free space, using the phase-space formulation of quantum mechanics. By visualizing the Wigner function, the spreading, shearing, the so-called "negative…

In this paper, we study the global Cauchy problem for a two-phase fluid model consisting of the pressureless Euler equations and the incompressible Navier-Stokes equations where the coupling of two equations is through the drag force. We…

This paper develops the geometry and analysis of the averaged Euler equations for ideal incompressible flow in domains in Euclidean space and on Riemannian manifolds, possibly with boundary. The averaged Euler equations involve a parameter…