Sentence examples for behavior in the limit from inspiring English sources

For these cases we can say that the "limiting behavior" as ε→0 equals the "behavior in the limit" where ε = 0.

We might expect two-dimensional behavior in the limit a → 0 both from the difference of effective mass in the interface and from the interface potential.

On the other hand, if the behavior in the limit is of a fundamentally different character than the nearby solutions one obtains as ε→0, then the schema will fail.

The equation suffers a reduction in order when ε = 0. Thus, the character of the behavior in the limit ε = 0 differs fundamentally from the character of its limiting behavior.

If mass transfer is not possible, the dispersed phase exhibits non-Gaussian behavior in the limit of no coalescence or breakage.

The numerical solution for a scheme of polynomial order P is composed of P+1 eigenmodes, of which, one and exactly one is 'physical' such that it exhibits the analytical dispersion behavior in the limit of asymptotic grid resolution.

The Landau expansion allows us to express the phase behavior in the limiting cases of small and large coupling analytically.

At the other extreme, when r is very large compared with s, this behavior will, in the limit, approach Brownian motion.

We find that the high bias transport behavior in this limit can be described by hot electron scattered by the surface phonon emission, leading to a carrier velocity saturation.

Based on heuristic arguments and numerical experiments, we conjecture that these approximations exhibit divergent behavior in the continuum limit.

An additional movie file illustrates this shifting of the folded-saddle canard and its effect on spiking behavior in the singular limit [see Additional file 1].