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A delayed diffusion model has been proposed for a complex gas-solid reaction exemplified by the disproportionation of potassium benzoate, a practically important reaction.
We consider a family of stochastic differential equations with a drift depending on the past history and a delayed diffusion term perturbed by a small parameter ε>0.
Sustained drug delivery by biocompatible pristine PU and its nanocomposites has been demonstrated either by controlling the crystallite size of the polyurethane through alteration of the aliphatic chain length of the extender or by incorporating disc-like nanoclay, creating a tortuous path that results in delayed diffusion.
These expressions for the hindrance effects would be useful to depict delayed diffusion rate which is occurred in consequence of narrow pore diameter and collision of oxygen gas with each others.
Injury progression in NT pups is rapid perhaps due to evolving vasogenic edema that is not only reduced in HT pups but its appearance was delayed too, as reflected in delayed diffusion reversal in ADC data.
Interestingly, delayed diffusion reversal was observed in the HT-treated pups where ADC hypo-intensity was present even at 72 hr post-HII, while such hypo-intensity was not noted in the NT pups.
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Recently, studies have been done researching the effects of crosslinking density and its effects on protein diffusion; increased density delayed protein diffusion through the polymer membrane [43].
The presence of CaCl2 led to lower initial and after-fermentation pHs, delayed sugar diffusion into the brine, its maximum concentration and titratable acidity formation.
In [3], the authors established the existence of positive travelling fronts for N-dimensional delayed reaction diffusion systems.
Then, model (1.1) can be naturally extended to the following delayed reaction diffusion equation: ∂ u ( t, x ) ∂ t = d Δ u ( t, x ) − δ u ( t, x ) + p u ( t − τ, x ) e − a u ( t − τ, x ), x ∈ Ω ⊂ R n. (1.2).
The difference in the peak values between moist/compacted and moist/loose manure might be due to the larger wet bulk density of the moist/compacted manure (Table 1), which could have delayed gas diffusion from the substrates to their surface/air interface.
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