FORGE
发表于 2025-3-21 17:35:14
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SPURN
发表于 2025-3-21 21:15:22
Phase and Test Function Spaces,The state of a flow can be represented as a point or a pathline in an appropriately set up function space, called phase space and denoted by ., which contains all possible flow states for all times.
negligence
发表于 2025-3-22 02:24:51
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Ischemia
发表于 2025-3-22 06:51:16
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Cultivate
发表于 2025-3-22 10:20:45
,Characteristic Functionals for Incompressible Turbulent Flows,The Fourier transform of a finite-dimensional Pdf is the characteristic function, hence contains probabilistic information equivalent to the Pdf/Cdf. The main difference to the Pdfs is its relation to statistical moments, which follow from the characteristic function by differentiation at the origin of the argument space ..
STYX
发表于 2025-3-22 15:45:15
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Decibel
发表于 2025-3-22 17:20:52
,Solution of Hopf-Type Equations in the Spatial Description,The assumption that the IBVP for the Navier–Stokes pdes governing the motion of incompressible fluids is well posed (.) leads to a formal solution of Hopf-type fdes, [.,.,.]. The assumption implies the existence of the solution operator .: . with unique inverse ..
埋葬
发表于 2025-3-22 22:09:17
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Gossamer
发表于 2025-3-23 01:31:44
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conquer
发表于 2025-3-23 06:14:41
,Equilibrium Theory of Kolmogorov and Onsager,Homogeneous turbulence cannot be in equilibrium since the kinetic energy . (kinetic energy is usually denoted by ., but the notation is changed to avoid confusion with the wavenumber) of turbulence can be shown to satisfy in this case.