Fluid browser extension5/20/2023 ![]() Programming language: C (with Fortran subroutines) Licensing provisions: GNU General Public License version 3 The main code can be downloaded from Dai et al. It includes all of the black-hole gray-body factors known to date and incorporates the effects of black-hole rotation, splitting between the fermions, non-zero brane tension and black-hole recoil due to Hawking radiation (although not all simultaneously). The generator is based on phenomenologically realistic models free of serious problems that plague low-scale gravity. This is the users manual of the black-hole event generator BlackMax (Dai et al., 2008), which simulates the experimental signatures of microscopic and Planckian black-hole production and evolution at proton–proton, proton–antiproton and electron–positron colliders in the context of brane world models with low-scale quantum gravity. 201606010047) and the National Natural Science Foundations of China (Grant Nos. DE-AC52-7NA27344 and is supported by the ITER-China Program (Grant Nos. This work was performed under the auspices of the U.S. Umansky for their constructive comments on the Landau resonance closures. The spectrum shift parameter k 0 and the number of Lorentzians N are the Acknowledgements For k 0 = 1, the k ∥ m i n ≃ 20 and k ∥ m a x depends on N in scaling law (11). 0275 were constructed which gives less than 1.16% relative error in the resolved wavenumber range. The further studies about collisionless LF closure with α = 5. The invention of the fast and efficient non-Fourier method (SMHS) makes it possible to implement the Landau fluid closure in the two fluid simulation framework BOUT++. In this non-Fourier method, the Lorentzian approximation is employed in k ∥ | k ∥ | ≃ ∑ n = 0 N − 1 α n β k ∥ ∕ k 0 ( k ∥ ∕ k 0 ) 2 + ( α n ) 2 = ∑ n = 0 N − 1 β 2 + 1, (a) k ∥ | k ∥ | + ζ 0 = k ∥ ∕ ζ 0 | k ∥ ∕ ζ 0 | + 1 ≃ ∑ n = 0 N − 1 α n k ∥ ∕ ζ 0 ( k ∥ ∕ ζ 0 ) 2 + β n 2 (b) Summary and discussions The innovation of an efficient and practical non-Fourier method for the Landau-Fluid (LF) operators make it possible and more applicable to implement the LF closure in the fluid simulations Numerical studies and benchmarks Even worse, the particular geometry or the boundary conditions make the implementation of the models difficult or impossible considering both the complex representation and the computational resources. When there are large spatial inhomogeneities, evaluation using Fourier methods becomes very inefficient. The typical dimensionless neoclassical collisionality ν e ∗ in pedestal region ranges from 0.01 to 10 according to the world multi-tokamak experimental data , Non-Fourier method for Landau-fluid operators ![]() Although the untruncated fluid moment equation hierarchy includes all the kinetic information and is equivalent to the basic Landau fluid closuresĪs the kinetic effects (e.g. the Landau wave-particle resonance effects, magnetic drift resonance effects, etc.) provide access to new free-energy source (sink) for microinstabilities and microturbulence, they play a very important role in plasma physics and can be key factors in determining plasma transport . The fluid moment equations can be derived mathematically by taking velocity moments of the Boltzmann Equation or Vlasov Equation. The fluid description of plasma has been long used to study plasma dynamics and plasma turbulence because of its simplicity and has provided much insight into the understanding of plasma systems, ,, ,, ,. Section snippets Classical fluid descriptions for parallel thermal conductions This work will make it more applicable and possible to include the Landau damping kinetic effect in the fluid simulation of tokamak plasma. The test cases also obviously demonstrate the nonlocal effects from LF closures and responding to different boundary conditions in open surface region. The collisional LF closure recovers the classical Spitzer–Härm result q ∥ e SH in collisional limit and is same as the collisionless LF closure in collisionless limit. The flux limited expression q ∥ e FL is reduced to free streaming expression q ∥ e FS in collisionless limit and gives classical Spitzer–Härm result q ∥ e SH in collisional limit as we expected. The scaling for upper limit of wavenumber resolved in collisionless LF operator and the fitting coefficients for the collisional LF operator, the later is extended to weakly collisional regime ( ν e ∗ ∼ 0. The spectral range of good fit can be conveniently extended to larger domain by adding more Lorentzians. Both collisionless and collisional Landau fluid (LF) closure have been developed and implemented in two-fluid plasma simulation framework BOUT++, taking full advantage of the fast non-Fourier method (Dimits, 2014).
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