These are related through the Lorentz transformation using the local plasma flow velocity, (u(x mathbf {e}_x), where (u(x)=u_i =const).) for the three regions, (i=1, 2, 3), and (mathbf {e}_x) is the unit vector in the x direction.
For the solution of the model equations, the essential parameters such as the junction loss coefficients in Equation 23 are given by Equations 11, 15, 16, and 17 using the local Reynolds number Re and flow ratio Q s /Q c. Figure 10 illustrates the flow network in the form of junction and frictional resistances through a parallel piping connected in Z-configuration.
The method used to derive the probability density function (PDF) equations in a pure gaseous medium was extended to two-phase flows by using the local equations written in terms of distribution functions.
We, therefore, applied soft clipping to the 3′-end of each read using bowtie2 (using the local parameter) and re-estimated the per-flow error rates.
Importantly, such multiscale flow behaviors cannot be represented using the local Darcy law.
CFD simulation based on 3D luminal reconstructions can be used to analyse the local flow fields and flow profiling due to changes of coronary artery geometry, thus, identifying risk factors for development and progression of coronary artery disease.
Despite its remarkably simplicity, the analytical approximation La can then be used to compute the local flow component L in the Green function, in the entire flow region, within the framework of the NM linear potential flow theory and the related Hogner approximation.
Attempts were made to characterize the local flow properties by using the fractal dimension.
Moreover, the sinkage, the trim angle and the wave drag predicted by the Neumann Michell (NM) theory, with the local flow potential evaluated using L or La, are in very close agreement.
Previous numerical simulations of the hydro-dynamic response in the various bioreactor designs were mostly concentrated on the local flow field analysis using computational fluid dynamics, which cannot provide the global hydro-dynamics information to assist the bioreactor design.
