Sentence examples for time scale constraints from inspiring English sources

Due to time scale constraints in experiments, it is rather difficult to measure the deformation process with the strain rate below 10−9 s−1, in Figs. 2 and 3 we put two creep equations not only for comparison but also as an extrapolation of the data which were observed in experiments.

Note that the second set of scaling exponents is valid when γ≤1 based on the time scale constraints given in Table 4.

The enthalpy landscape approach has proven to be successful in overcoming this time scale constraint and providing insights into the fundamental physics governing glass transition and relaxation behavior.

8. Plugging the chosen values for α i 's and β k 's in the time-scale constraints obtained in Steps 4 and 6, compute an upper bound (denoted as γ0) for a time-scale exponent.

If some of the balance equations are not satisfied, corresponding time-scale constraints give a range of γ where the chosen α i 's and β k 's are valid.

In case the kth reaction is second-order with reactants of the same species, λ k (x ) = κ k ′ x p (x p − 1 ) is replaced by λ ^ k (z ) = κ k z p (z p − N − α p ). 4. Write a set of species balance equations and their time-scale constraints.

Comparing ρ k 's for k ∈ Γ i + and those for k ∈ Γ i −, set the balance equations as max k ∈ Γ i + ρ k = max k ∈ Γ i − ρ k, i = 1, ⋯, s 0. (b) Time-scale constraints are given as γ ≤ max k ∈ Γ i + ∪ Γ i − ρ k, i = 1, ⋯, s 0. 5. Find a minimum set of linear combinations of species whose maximum of collective production (or consumption) rates may be different from that of one of any species.

In each case, either the balance equation or the time-scale constraint must hold.

We call the balance equation and the time-scale constraint for each species as the species balance condition.

For each selected linear combination of species, write a collective species balance equation and its time-scale constraint.

With chosen values for the scaling exponents, we check whether each balance equation is satisfied and give a time-scale constraint in the Additional file 1: Table S6 in case the balance equation is not satisfied.