Sentences with phrase «of ergodicity»

Climate repeats because of ergodicity.

The standard argument that we can predict climate better than weather is certainly based on some kind of ergodicity, perhaps not for the full phase space but for a fraction of it at the minimum.

«The concepts of ergodicity and the ergodic hypothesis are central to applications of ergodic theory.

A central aspect here was to understand the processes in terms of the physical phenomenon of ergodicity.

A central aspect of the study was to investigate the atomic system on time scales that are relevant for the establishment of ergodicity.

Not exact matches

In any case the ergodicity has nothing to do with «perturbations» or variations of the external energy fluxes.

I think that Schmidt has the right answer even if it is for wrong reasons and therefore the question of climate ergodicity is for me the single most important question about the usefullness of the climate models.

Robert Brown: «But ergodicity is still expected, and the thermodynamics suggest that the functional shape of the phase space sampled by the molecules of even the very dilute gas high up in the vertical column is scale invariant, so that a true ergodic average will be similarly invariant.»

It presupposes that all thermal relaxation that can occur has occurred, unless you wish to work a system with broken ergodicity, or unless you can show that there is a vast separation of relaxation timescales, one large enough that equilibrium will not be reached in the particular times of interest in a particular problem.

But ergodicity is still expected, and the thermodynamics suggest that the functional shape of the phase space sampled by the molecules of even the very dilute gas high up in the vertical column is scale invariant, so that a true ergodic average will be similarly invariant.

It means that by taking some (any) initial condition and following the trajectory of the system for a (very) long time, you will obtain empirically ONE PDF but thanks to ergodicity you know that you don't need to redo it for the rest of the infinity of initial conditions because your PDf is the one unique for the whole system.

AGW doesn't explicity state that ergodicity is being assumed and thus the level of uncertainty to this hypothesis has been and now still is way understated.

The point of this short but rigorous introduction was to demonstrate that ergodicity is not some fog that could be interpreted by anybody as it suits his particular view.

Of course one can also talk about ergodicity but it takes considerably more skill and training and no easy analogies to statistical mechanics or thermodynamics work anymore.

There are no cycles as such — just patterns of chaotic change that repeat (ergodicity) over a long enough period.