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For some special BOF blowing technologies, such as steelmaking with high phosphorus hot metal, post combustion oxygen lance, hot metal pretreatment, etc, the difference between working oxygen pressure and designed diffusion pressure which is related to Mach-number is necessary, so that the velocity of the oxygen jet will be decreased because of shock wave for expected metallurgical results.
This shift is believed to be driven by the diffusion pressure created by the imbalanced concentrations of c RGDfK -Bchl-D in the viable versus nec RGDfK -Bchl-Dmains.
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The fluid dynamics analogy is justified as their governing equations provide a more versatile modeling of physical processes using convection, diffusion, pressure-gradient terms compared to other commonly used equations in applied mathematics, such as Kirchhoff's law (Oldham 2008) or population model (Holmes et al. 1994).
are referred as self-diffusion pressures, and is cross-diffusion pressure.
ρ is a positive constant in the homogeneous case, which means a tendency for v to move to the low density region of u. (rho(x)) is referred to as the cross-diffusion pressure.
The constants d 1 and d 2 are the diffusion rates of the prey and predator respectively, δ and α are referred to as self-diffusion pressures, and the term d 2 Δ [ γ v / ( 1 + u l ) ] in the predator equation is cross-diffusion pressure, which expresses the population flux of the predator resulting from the presence of prey species.
and are cross-diffusion pressures.
are referred to as self-diffusion pressures.
The parameters d1, d2 are the diffusion rates, α ii (i = 1, 2) are referred as self-diffusion pressures, and α ij (i, j = 1, 2, i ≠ j) are cross-diffusion pressures.
The existence and uniqueness of nonnegative global solutions are given when one of the cross-diffusion pressures is zero.
However, few studies have considered the influences of pipe shape in the perspective of turbulent diffusion and pressure loss effects.
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