Sentences with phrase «such nonlinear equations»

Not exact matches

For example, the classical equations used to predict the performance of such materials have indicated that the logarithm of the reaction rate should vary linearly as voltage is increased — but experiments have shown a nonlinear response, with the uptake of lithium flattening out at high voltage.

«A dynamical system such as the climate system, governed by nonlinear deterministic equations (see Nonlinearity), may exhibit erratic or chaotic behaviour in the sense that very small changes in the initial state of the system in time lead to large and apparently unpredictable changes in its temporal evolution.

In a system such as the climate, we can never include enough variables to describe the actual system on all relevant length scales (e.g. the butterfly effect — MICROSCOPIC perturbations grow exponentially in time to drive the system to completely different states over macroscopic time) so the best that we can often do is model it as a complex nonlinear set of ordinary differential equations with stochastic noise terms — a generalized Langevin equation or generalized Master equation, as it were — and average behaviors over what one hopes is a spanning set of butterfly - wing perturbations to assess whether or not the resulting system trajectories fill the available phase space uniformly or perhaps are restricted or constrained in some way.

As to offering up alternative «governing equations», check out the work by Ghil offered by Generalissimo Skippy and the book «Nonlinear Climate Dynamics» by Henk A. Dijkstra, offered up by me following a related recommendation by «Chief Hyrologist» for some hints at (a) work in progress to develop such governing equations and (b) how far the laborers in the field are from having one and getting it tested.