Sentence examples for time scale constraint from inspiring English sources

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.

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.

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

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

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

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.

The time-scale constraint, γ≤ γ0, implies that the set of scaling exponents α i 's and β k 's chosen is appropriate only up to time whose order of magnitude is equal to N γ 0. For the times larger than O(N γ 0), we need to choose a different set of values for the scaling exponents, α i 's.

Similarly to the time-scale constraint in the species balance condition, (18) implies that if maximal collective production and consumption rates for S23are not balanced, our choice of values for scaling exponents are valid up to times of order N u 23.

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.