Sentence examples for macroscopic concentration of from inspiring English sources

Although the macroscopic concentration of Tb3+/Eu3+ activators is fixed at 4 at.% in this work, concentration difference exists among different crystal planes.

Equation (30) essentially states that the integrated micromixing rate is proportional to the mean (macroscopic) concentration of the limiting reactant divided by the time scale of the large eddies ( k ε = τ mix ).

Note that X i in the macroscopic rate functions denotes the macroscopic concentration of species i.

The starting point of this method is to write the absolute number of molecules of species i in the CME, equation (2), as (3) n i Ω = X i + Ω − 1 / 2 ε i, where X i is the macroscopic concentration of species i and ε i is proportional to the noise about this concentration.

Deterministic approach dealing with macroscopic concentrations of molecules (such as ordinary differential equations of classical chemical kinetics) is then inappropriate.

Note that the time-dependence of the matrices in the above equations comes from that of the macroscopic concentrations of fast and slow species.

This new FPE is the legitimate mesoscopic description of intrinsic noise about the macroscopic concentrations of the coarse-grained network as obtained by the deterministic QSSA.

The effective REs have information about the macroscopic concentrations of the slow species only, while the effective CME has information about the fluctuations of the slow species only.

On such timescales, transients in the macroscopic concentrations of fast species have decayed, a quasi-steady-state is achieved and by the deterministic QSSA, we know that the fast-species concentrations can be expressed in terms of those of the slow-species concentrations.

This leads to a linear FPE of the form (8) ∂P η →, t ∂t = − ∇ T J F η → + 1 2 ∇ T D F ∇ P η →, t, where η → = η → s, η → f and η → s and η → f are, respectively, the vectors of concentration fluctuations about the macroscopic concentrations of the slow and fast species.

Such a reaction scheme is compatible with the reduced REs: defining [ X → s ] as the macroscopic concentration vector of the slow species, we have d [ X → s ] / d t = S ′ f → ([ X → s ] ) = S s f → ([ X → s ] ) since S f f → = 0 as required by the deterministic QSSA.