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Schroedinger vs. Navier–Stokes
2016
Entropy
Preserved Fulltext
Here we support this view by establishing a map between certain solutions of the Schroedinger equation, and the corresponding solutions of the irrotational Navier-Stokes equation for viscous fluid flow ...
On the other hand, the nonzero viscosity of nonstationary states provides an information-loss mechanism whereby a deterministic theory (a classical fluid governed by the Navier-Stokes equation) gives rise ...
The Physics of Navier-Stokes from Schroedinger
Computation of the Viscosity Our starting point is Madelung's rewriting of the Schroedinger equation for a mass m subject to a static potential V = V(x) ...
doi:10.3390/e18010034
fatcat:szy4mf23yjdypbvcm6kcs7frqq
Schroedinger vs. Navier-Stokes
[article]
2014
arXiv
pre-print
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Here we support this view by establishing a map between certain solutions of the Schroedinger equation, and the corresponding solutions of the irrotational Navier-Stokes equation for viscous fluid flow ...
On the other hand, the nonzero viscosity of nonstationary states provides an information-loss mechanism whereby a deterministic theory (a classical fluid governed by the Navier-Stokes equation) gives rise ...
The physics of Navier-Stokes from Schroedinger
Computation of the viscosity Our starting point is Madelung's rewriting of the Schroedinger equation for a mass m subject to a static potential V = V (x ...
arXiv:1409.7036v1
fatcat:e2supgrhuvb7lcr5m3qojk27di
Vortex Heating in Superfluid Helium at Low Temperatures
1998
Physical Review Letters
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. + q, 67.40.Vs Current experiments on the turbulence of helium II have produced some surprising results and opened a number of interesting questions about the relation between traditional classical Navier-Stokes ...
Nore et al. [6] used the nonlinear Schroedinger equation (NLSE) model, which naturally describes a pure superflow (T 0) and nonsingular quantized vortex lines. ...
. + q, 67.40.Vs Current experiments on the turbulence of helium II have produced some surprising results and opened a number of interesting questions about the relation between traditional classical Navier-Stokes ...
doi:10.1103/physrevlett.81.4381
fatcat:5q6yn42sv5b2tp7r2cwbemiceq
On the controllability of distributed systems
1997
Proceedings of the National Academy of Sciences of the United States of America
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When the PDEs are the Navier-Stokes equations, it leads to conjectures, which are presented and explained. ...
Conjectures for Navier-Stokes Equations After proper scaling, we write the Navier-Stokes equations in the form Ѩy Ѩt ϩ yٌy Ϫ ⌬y ϭ Ϫٌp ϩ v in ⍀ ϫ ͑0, T͒, [3.1] div y ϭ 0 in ⍀ ϫ ͑0, T͒, [3.
2] subject ...
Ѩy Ѩt Ϫ ⌬y Ϫ ␣y 3 ϭ v in ⍀ ϫ ͑0, T͒, ␣ Ͼ 0, We are now ready to proceed with Navier-Stokes equations. ...
doi:10.1073/pnas.94.10.4828
pmid:11038539
pmcid:PMC24591
fatcat:dct7caedv5htnbsbc5rzek2ytu
Adaptive unstructured volume remeshing – I: The method
2005
Journal of Computational Physics
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Recent applications of AMR include hyperbolic conservation laws [20, 21] , the Stokes and Navier-Stokes equations [1, 4, 5, 12, 22, 31] and thermal and reactive flows [5, 23] . ...
Initial (h) and final (·) edge lengths (e) vs radial position; prescribed length scale L R (--) from Eq. (7) ...
doi:10.1016/j.jcp.2005.02.023
fatcat:2sosyunbtzdn3bjaubk6rifoou
Hyperbolic Conservation Laws
2008
Oberwolfach Reports
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Geometrical Solutions Vs. ...
Recently, it is shown that the Navier-Stokes equations can be approximated with the hyperbolic systems in the diffusive limit. ...
doi:10.4171/owr/2008/56
fatcat:vwgkrt2egzgr3krlmfhngtxm4i
Analytical and Numerical Treatments of Conservative Diffusions and the Burgers Equation
2018
Entropy
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Later, Constantin and Iyer derived a probabilistic representation of the deterministic three-dimensional Navier-Stokes equations [17, 18] . ...
It can be derived from the full Navier-Stokes equations under some simplifying assumptions. It was later studied extensively by Burgers as a cartoon model of turbulence [13] . ...
doi:10.3390/e20070492
pmid:33265582
fatcat:6fhqlu7pqvh7jnsvwvrzkd3oui
ANALOGY BETWEEN TURBULENCE AND QUANTUM GRAVITY: BEYOND KOLMOGOROV'S 1941 THEORY
2012
International Journal of Modern Physics C
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2011 pre-print arXiv:1111.3207v1 fatcat:lptzegzv3bhe3oonrgpjq2i52e
For instance, the recent analogies between Navier-Stokes and Einstein equations shed some hope that concepts and methods from the celebrated AdS/CFT duality [1, 2] , can be used to attack fluid turbulence ...
Unfortunately, ψ(x) is generally not known a-priori, and consequently ESS cannot be used to deduce the exponent by log-plotting y vs ψ(x) from numerical data. ...
doi:10.1142/s0129183112500015
fatcat:6tg5ydwhmzetnkil7vojbguria
New Foundation in the Sciences: Physics without Sweeping Infinities under the Rug
[article]
2020
Figshare
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The model is also governed by Navier-Stokes equations. [10] 6. ...
Another possible solution of Navier-Stokes equations comes in the form of vortex. For example, it is known that Serrin's swirling vortex is a solution of Navier-Stokes equations. ...
Kiehn has also shown that the Navier-Stokes equation corresponds exactly to Schroedinger equation [27] , which seems to support the idea of quantization of celestial motion [1] [2] [3] . ...
doi:10.6084/m9.figshare.12387260
fatcat:6qqvy3zxrfgebm6ctt5jkakqz4
Relativistic Heavy Ion Collisions: Viscous Hydrodynamic Simulations and Final State Interactions
[article]
2009
arXiv
pre-print
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Upon plugging into the conservation equations, this results in what are termed the relativistic Navier-Stokes equations, since they reduce to Navier-Stokes in the non-relativistic limit. η is then identified ...
Initial Conditions: Glauber Model vs. ...
arXiv:0908.4100v1
fatcat:sv5p5c7r2jh7vbbpa3mvooxppi
Implicitly Restarted Arnoldi/Lanczos Methods for Large Scale Eigenvalue Calculations
[chapter]
1997
ICASE/LaRC Interdisciplinary Series in Science and Engineering
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Here the matrices are obtained through discretization of the Navier-Stokes equations. ...
"Krylov
Methods for the Incompressible
Navier-Stokes
Equations,"
Journal of Computational
Physics 110, pp. 82-102.
Ericsson,
T., and Ruhe, A., 1980. ...
doi:10.1007/978-94-011-5412-3_5
fatcat:mz6qewb43zguhnpy2t5v2g46cu
On ionospheric aerodynamics
1975
Progress in Aerospace Sciences
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Should the constitutive relation be linear and the fluid isotropic, the Navier-Stokes eqlaation will be recovered from the momentum conservation eqn. (5.23) for neutral species provided the Stokes viscosity ...
In comparison to the continuityequation and the Navier-Stokes equation of the classical fluid dynamics, °~' which are the counterpart to eqns. (5.22) and (5
( b ) b Locally Maxwellian hypothesis• If ...
doi:10.1016/0376-0421(75)90017-2
fatcat:scb6clr6r5bqxkltkhvzzoouwa
Self-similarity in Laplacian Growth
2007
Physica D : Non-linear phenomena
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2006 accepted arXiv:nlin/0606068v2 fatcat:efeor4m6y5hidi2m53egqoxjbyOther Versions
It is shown that solutions to the integral equation obey also a second order differential equation which is the one dimensional Schroedinger equation with the sinh inverse square potential. ...
For a quasistatic motion of a viscous fluid between two closely spaced parallel surfaces, the Navier-Stokes equation is reduced to the Darcy's Law [25] which states that the 2D velocity v of the fluid ...
Together with the previous equation this gives v + vS ′ = 0. (13) Using equation (10) and (9) (with Q = π) we then finḋ S = 2v = 2∂ z W = ∂ z log w (14) After analytical continuation from the boundary ...
doi:10.1016/j.physd.2007.04.012
fatcat:67yesryqwzdgtppunpvmvhf5li
Anomalous scaling laws in multifractal objects
1987
Physics reports
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The opposite situation is fully-developed turbulence where a theory on the structure of the Navier Stokes equation singularities is still far from being formulated. ...
The approaches to the statistical description of turbulence (K41, fractal, multifractal, lognormal) do not directly use the dynamics given by the Navier-Stokes (and Euler) equations. ...
doi:10.1016/0370-1573(87)90110-4
fatcat:ibruxgsiq5dcvakeqlow7ip3hi
Page 1222 of Mathematical Reviews Vol. , Issue Index
[page]
Mathematical Reviews
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(Summary) 89m:68071 68Q35 (68Q25)
Varnhorn, Werner Energy conserving Lagrangian approximation for the equations of Navier-Stokes. J. Differential Equations 76 (1988), no. 2, 256-268. (P. L. ...
Opfer) 89m:30054 30D10 (11Y35, 65E05)
— (with Ruttan, Arden) A unified theory for real vs. complex rational Chebyshev approxi- mation on an interval. Trans. Amer. Math. ...
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