THE CONVERGENCE OF THE PARTICLE METHOD FOR THE VLASOV–POISSON SYSTEM WITH EQUALLY SPACED INITIAL DATA POINTS

2001 ◽  
Vol 30 (1) ◽  
pp. 1-62 ◽  
Author(s):  
Stephen Wollman ◽  
Ercument Ozizmir ◽  
Revathi Narasimhan
Keyword(s):  
Initial Data ◽  
Particle Method ◽  
Poisson System ◽  
Data Points

scholarly journals Convergence from two-species Vlasov-Poisson-Boltzmann system to two-fluid incompressible Navier-Stokes-Fourier-Poisson system

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Zhendong Fang ◽  
Hao Wang
Keyword(s):  
Initial Data ◽  
Knudsen Number ◽  
Navier Stokes ◽  
Classical Solutions ◽  
Poisson System ◽  
Small Initial Data ◽  
Uniform Estimates ◽  
Poisson Boltzmann ◽  
Two Fluid

<p style='text-indent:20px;'>In this paper, we obtain the uniform estimates with respect to the Knudsen number <inline-formula><tex-math id="M1">\begin{document}$ \varepsilon $\end{document}</tex-math></inline-formula> for the fluctuations <inline-formula><tex-math id="M2">\begin{document}$ g^{\pm}_{\varepsilon} $\end{document}</tex-math></inline-formula> to the two-species Vlasov-Poisson-Boltzmann (in briefly, VPB) system. Then, we prove the existence of the global-in-time classical solutions for two-species VPB with all <inline-formula><tex-math id="M3">\begin{document}$ \varepsilon \in (0,1] $\end{document}</tex-math></inline-formula> on the torus under small initial data and rigorously derive the convergence to the two-fluid incompressible Navier-Stokes-Fourier-Poisson (in briefly, NSFP) system as <inline-formula><tex-math id="M4">\begin{document}$ \varepsilon $\end{document}</tex-math></inline-formula> go to 0.</p>

scholarly journals Asymptotic limit of nonlinear Schrödinger-Poisson system with general initial data

2011 ◽  
Vol 4 (3) ◽  
pp. 767-783
Author(s):  
Qiangchang Ju ◽  
◽  
Fucai Li ◽  
Hailiang Li ◽  
◽  
...  
Keyword(s):  
Initial Data ◽  
Asymptotic Limit ◽  
Poisson System ◽  
Nonlinear Schrödinger ◽  
General Initial Data

scholarly journals The luminosity function of quasars by the Principle of Maximum Entropy

2019 ◽  
Vol 488 (1) ◽  
pp. 183-190
Author(s):  
Alexandre Andrei ◽  
Bruno Coelho ◽  
Leandro L S Guedes ◽  
Alexandre Lyra
Keyword(s):  
Initial Data ◽  
Maximum Entropy ◽  
Observational Data ◽  
Input Data ◽  
Luminosity Function ◽  
Statistical Tests ◽  
Apparent Magnitude ◽  
Principle Of Maximum Entropy ◽  
Data Points ◽  
Principle Of Maximum

ABSTRACT We propose a different way to obtain the distribution of the luminosity function of quasars by using the Principle of Maximum Entropy. The input data come from Richard et al 2006 quasar counts, extending up to redshift 5 and limited from apparent magnitude i = 15–19.1 at z ≲ 3 to i = 20.2 for z ≳ 3. Using only few initial data points, the principle allows us to estimate probabilities and hence that luminosity curve. We carry out statistical tests to evaluate our results. The resulting luminosity function compares well to earlier determinations, and our results remain consistent either when the amount or choice of sampled sources is unbiasedly altered. Besides this, we estimate the distribution of the luminosity function for redshifts in which there is only observational data in the vicinity.

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