Sentence examples for upper and lower branches from inspiring English sources

Thus, the upper and lower branches of Im Ωb) pertain to the first and second longitudinal modes, respectively.

In this low mass-damping regime, two separate regions of the high amplitude response curve were identified, which we label "upper" and "lower" branches of response.

There is bistability between upper and lower branches of the z-curve which is typically a necessary condition for bursting with this type of analysis.

It is shown that the transition between resonant and divergent vibrations begins when the horizontal tangents of the upper and lower branches of the response curve merge, while the maximal value of the characteristic polynomial of horizontal tangents becomes zero.

Even if the amplitude and phase are perfectly adjusted in both loops, a delay difference between the upper and lower branches of a cancellation circuit causes a reduction of the effective bandwidth.

These figures show that there are regions of unique solutions for ε ≥ − 1, dual (upper and lower branches) solutions for ε c ≤ ε < − 1 and no solutions for ε < ε c < 0, where ε c is the critical value of ε ( < ε c < 0 ) beyond which Eqs. (7) and (8) have no solutions.

Velocity profiles for upper and lower branch solutions are shown in Fig. 4a, b, respectively.

It is found that, the slip parameter has a reducing impact on the skin friction coefficient for both upper and lower branch solutions.

In the case of shrinking sheet (both upper and lower branch), the reduced Nusselt number increases with γ, |δ| and Pr, and it decreases with φ.

Figure 7a c illustrates the effects of γ and φ on temperature profile of Au-water in case of stretching sheet, shrinking sheet upper and lower branch solutions, respectively.

The temperature profile decreases with the increasing values of |δ| and increases with the increase of φ in both upper and lower branch solutions (Fig. 8b, c).