Related papers: Mechanics of Schrodinger mechanics
The substratum for physics can be seen microscopically as an ideal fluid pierced in all directions by the straight vortex filaments. Small disturbances of an isolated filament are considered. The Klein-Gordon equation without mass…
The small amplitude-to-thread ratio helical configuration of a vortex filament in the ideal fluid behaves exactly as de Broglie wave. The complex-valued algebra of quantum mechanics finds a simple mechanical interpretation in terms of…
An exact analogy of electromagnetic fields and particles can be found in mechanics of a turbulent ideal fluid with voids. The system is supposed to form a fine dispersion of voids in the fluid. This microscopically discontinuous medium is…
Quantum theory and relativity exhibit several formal analogies with fluid mechanics. This paper extends upon known analogies by showing that under specific assumptions, an Euler-Korteweg vortex model can be cast into equations that are…
By means of high-resolution numerical simulations, we compare the statistical properties of homogeneous and isotropic turbulence to those of the Navier-Stokes equation where small-scale vortex filaments are strongly depleted, thanks to a…
Quantum turbulence that exhibits vortex creation, annihilation and interactions is demonstrated as an exact solution of the time-dependent, free-particle Schr\"odinger equation evolved from a smooth random-phased initial condition. Relaxed…
The flow of an electrically conducting fluid in a thin disc under the action of an azimuthal Lorentz force is studied experimentally. At small forcing, the Lorentz force is balanced by either viscosity or inertia, yielding quasi-Keplerian…
We compute the angular dynamics of a neutrally buoyant nearly spherical particle immersed in an unsteady fluid. We assume that the particle is small, that its translational slip velocity is negligible, and that unsteady and convective…
Recent studies of turbulence in superfluid Helium indicate that turbulence in quantum fluids obeys a Kolmogorov scaling law. Such a law was previously attributed to classical solutions of the Navier-Stokes equations of motion. It is…
The Klein-Gordon equation describes the wave-like behavior of spinless particles since it is Lorentz invariant. While it seemed initially ripe for explaining the electronic structure of the hydrogen atom, the lack of a unconditional…
We study the statistical properties of coherent, small-scales, filamentary-like structures in Turbulence. In order to follow in time such complex spatial structures, we integrate Lagrangian and Eulerian measurements by seeding the flow with…
Exact analytic solutions of the time dependent Schrodinger equation are produced that exhibit a variety of vortex structures. The qualitative analysis of the motion of vortex lines is presented and various types of vortex behavior are…
We apply the modulation theory to study the vortex and radiation solution in the two-dimensional nonlinear Schr\"{o}dinger equation. The full modulation equations which describe the dynamics of the vortex and radiation separately are…
We theoretically investigate the phenomenon of modulation instability for systems obeying nonlinear Schr\"odinger equation, which are under the influence of an external homogeneous synthetic magnetic field. For an initial condition, the…
Through the Ginzburg-Landau and the Navier-Stokes equations, we study turbulence phenomena for viscous incompressible and compressible fluids by a second order phase transition. For this model, the velocity is defined by the sum of…
There exists a Klein-Gordon-like equation for a spin-1/2 particle in an electromagnetic field with 2-spinors as wave functions that is a direct consequence of the corresponding Dirac equation. Thus, it reproduces the same binding energies…
A superconducting rod with a magnetic moment on top develops vortices obtained here through 3D calculations of the Ginzburg-Landau theory. The inhomogeneity of the applied field brings new properties to the vortex patterns that vary…
The chaotic dynamics of small-scale vorticity plays a key role in understanding and controlling turbulence, with direct implications for energy transfer, mixing, and coherent structure evolution. However, measuring or controlling its…
It is shown that the Euler hydrodynamics for vortical flows of an ideal fluid coincides with the equations of motion of a charged {\it compressible} fluid moving due to a self-consistent electromagnetic field. Transition to the Lagrangian…
The dynamics of a two-dimensional vortex are analyzed within the framework of the nonlinear Schrodinger equation. Both a bare vortex and a vortex with an external mass trapped in a finite-sized core are considered. The bare vortex motion is…