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A three-dimensional double distribution function thermal lattice Boltzmann model has been developed for simulation of thermal compressible flows in the low Mach number limit.
In this paper, a newly developed 3D thermal Lattice Boltzmann method (LBM), incorporating double distribution functions (DDF), pseudo-potential model and equation of state (EOS) of a real gas, is used to simulate dynamic evaporation along the vapor/liquid interface and boiling in the liquid thin film on a microstructured surface consisting of micro pillars.
In this study, we develop new 3D lattice Boltzmann (LB) methods based on central moments and using multiple relaxation times for the three-dimensional, fifteen velocity (D3Q15) lattice, as well as it subset, i.e. the three-dimensional, seven velocity (D3Q7) lattice to solve the 3D CDE for the temperature field in a double distribution function framework.
The double distribution (not including the first tailing peak) is the result of a high temporal jitter in droplet arrival at the ICP (>10 ms) and unsynchronized signal acquisition.
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There exist interesting general results showing that families of single and double distributions are the marginals of a single multiple distribution if and only if some corresponding Bell-type inequalities hold (Pitowsky 1989).
Some so-called double-distribution machines permit two magazines to be used at once by pressing a supplementary key.
It shows that, for the double Pareto distribution and Inverse Gamma distribution respectively, when sample size gets around 150 and 350, there will be half a chance that the estimated V a has a relative error of 50%%.
For both the double Pareto distribution and the Inverse Gamma distribution, as sample size gets smaller, the mean of the estimated parameters gets more deviated from the theoretical value (Fig. 3a, b) while the standard deviation gets larger (Fig. 3c, d).
For example, with regard to a sample size of 100 and a subdividing ratio of 5, the regions of acceptance for γ estimated using the double Pareto distribution and the Inverse Gamma distribution are [−14.69, 13.75] and [−18.22, 15.24], respectively.
The model for Bayesian Lasso assumes that the marker effects follow a double exponential distribution [ 12, 17], which is a thick-tailed distribution.
Therefore, the performance of the double Pareto distribution on estimating the exponent is relatively better than the Inverse Gamma distribution (Fig. 3e).
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Justyna Jupowicz-Kozak
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