Morphing quantum mechanics and fluid dynamics
@article{Curtright2003MorphingQM, title={Morphing quantum mechanics and fluid dynamics}, author={Thomas L. Curtright and David B. Fairlie}, journal={Journal of Physics A}, year={2003}, volume={36}, pages={8885-8901} }
We investigate the effects of given pressure gradients on hydrodynamic flow equations. We obtain results in terms of implicit solutions and also in the framework of an extra-dimensional formalism involving the diffusion/Schrodinger equation.
4 Citations
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References
SHOWING 1-10 OF 35 REFERENCES
Turbulence without pressure
- Physics
- 1995
We develop exact field theoretic methods to treat turbulence when the effect of pressure is negligible. We find explicit forms of certain probability distributions, demonstrate that the breakdown of…
Noncommuting Gauge Fields as a Lagrange Fluid
- Mathematics
- 2002
Abstract The Lagrange description of an ideal fluid gives rise in a natural way to a gauge potential and a Poisson structure that are classical precursors of analogous noncommuting entities. With…
Integrable generalizations of the two-dimensional Born-Infeld equation
- Mathematics
- 1994
The Born-Infeld equation in two dimensions is generalized to higher dimensions. Lorentz invariance is retained, and the resulting system is completely integrable via linearization by Legendre…
Extra dimensions and nonlinear equations
- Mathematics
- 2003
Solutions of nonlinear multi-component Euler–Monge partial differential equations are constructed in n spatial dimensions by dimension-doubling, a method that completely linearizes the problem.…
Velocity and velocity-difference distributions in Burgers turbulence.
- PhysicsPhysical review letters
- 2004
We consider the one-dimensional Burgers equation randomly stirred at large scales by a Gaussian short-time correlated force. Using the method of dissipative anomalies, we obtain velocity and…
Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves
- Mathematics
- 1987
Quasi-linear Hyperbolic Equations Conservation Laws Single Conservation Laws The Decay of Solutions as t Tends to Infinity Hyperbolic Systems of Conservation Laws Pairs of Conservation Laws Notes…
The Geometric Origin of the Madelung Potential
- Physics
- 2002
Madelung's hydrodynamical forms of the Schrodinger equation and the Klein-Gordon equation are presented. The physical nature of the quantum potential is explored. It is demonstrated that the…
Multi‐Hamiltonian structure of the Born–Infeld equation
- Mathematics
- 1989
The multi‐Hamiltonian structure, conservation laws, and higher order symmetries for the Born–Infeld equation are exhibited. A new transformation of the Born‐Infeld equation to the equations of a…
Quantentheorie in hydrodynamischer Form
- Physics
- 1927
ZusammenfassungEs wird gezeigt, daß man die Schrödingersche Gleichung des Einelektronen-problems in die Form der hydrodynamischen Gleichungen transformieren kann.
Self-Dual Vortices in Chern–Simons Hydrodynamics
- Physics
- 2001
AbstractThe classical theory of a nonrelativistic charged particle interacting with a U(1) gauge field is reformulated as the Schrödinger wave equation modified by the de Broglie–Bohm nonlinear…