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Schroedinger vs. Navier–Stokes

P. Fernández de Córdoba, J. Isidro, J. Vázquez Molina
2016 Entropy  
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]

P. Fernandez de Cordoba, J.M. Isidro, J. Vazquez Molina
2014 arXiv   pre-print
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

David C. Samuels, Carlo F. Barenghi
1998 Physical Review Letters  
. + 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

J. L. Lions
1997 Proceedings of the National Academy of Sciences of the United States of America  
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

Anthony Anderson, Xiaoming Zheng, Vittorio Cristini
2005 Journal of Computational Physics  
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

Constantine Dafermos, Dietmar Kröner, Randall LeVeque
2008 Oberwolfach Reports  
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

Dimiter Prodanov
2018 Entropy  
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

SAURO SUCCI
2012 International Journal of Modern Physics C  
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]

Victor Christianto, Florentin Smarandache, Robert Neil Boyd
2020 Figshare  
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]

Matthew Luzum
2009 arXiv   pre-print
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]

Danny C. Sorensen
1997 ICASE/LaRC Interdisciplinary Series in Science and Engineering  
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

V.C. Liu
1975 Progress in Aerospace Sciences  
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

Ar. Abanov, M. Mineev-Weinstein, A. Zabrodin
2007 Physica D : Non-linear phenomena  
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

Giovanni Paladin, Angelo Vulpiani
1987 Physics reports  
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  
(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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