Ignoring the volume change of solid grain and cement and combining the porosity strain relations (phi = 1 - frac{{1 - phi_{0} }}{{1 + varepsilon_{v} }}left( {1 + frac{{Delta V_{s} }}{{V_{s0} }}} right)), the bulk strain variation, its maximum value, and derivative over time under vibration or not could be derived (Li et al. 2003).
On the basis of the distribution of the experimental concentration curves at different lithiation times, we determined the normalized overall lithium content within the electrode and its derivative over time (i.e., the Li mass transport rate).
The Physioflow impedance cardiography (ICG) device that we employed differs from conventional ICG in that there is less reliance on the baseline thoracic impedance signal (resistance ZO) for transformation during exercise; instead, a pulsatile waveform representing the sensed impedance signal (delta Z) is processed and analyzed with its derivative over time.
Note that if the investigated property exhibits temporal variations (waves, circadian,...), the sampling method should be adequately adapted to accurately assess δρ/δt, the local partial time-derivative over time and space [equation (2)].
"People change over time.
Modeling the input delay as a transport Partial Differential Equation, we prove asymptotic stabilization of the system state, that is, robust delay compensation, providing that the average L2-norm of the delay time-derivative over some time-window is sufficiently small and that the average time between two discontinuities (average dwell time) is sufficiently large.
We calculated movement time as the time elapsed from movement onset to movement end, peak velocity, as the maximum peak of the first derivative of displacement over time, and time to peak velocity.
The amplitude of each spike was measured as a difference between peak potential during the spike and the potential at the kink point, defined as a point at which the 2nd derivative of potential over time went through a maximum.
Those sorts of derivatives pay out money over time, whereas derivatives tied to a country's debt pay out on one occasion: if a default occurs.
The AIC function essentially compares the information before and after a point in a time series (x), and a change in information between these two parts results in a peak in the first derivative of the function over time.
Using the derivative of the charge over time the capacitance change associated with the presteady-state current, was obtained (Fig. 3C inset, open circles).
