Below is a paragraph from an academic paper. Polish the writing to meet the academic style, improve the spelling, grammar, clarity, concision and overall readability. When necessary, rewrite the whole sentence. Furthermore, list all modification and explain the reasons to do so in markdown table. Paragraph: This pressure difference between the two sides of the flame stabilizer will reduce the mixture flow rate, and thus cause causing a flow rate oscillation with 90° phase-lead relative the pressure oscillation. Conversely, the flowrate oscillation will be 90° phase-lag relative to the pressure oscillation under the condition of Equation (6). For the combustion under φ = 0.9, τ satisfies the Equation (7) (in which TM is the oscillation period), which indicates that the phase lag of heat release oscillation is less than 180° in relative to the flow rate oscillation. In this case, the phase difference between sound pressure oscillation and heat release oscillation would be less than 90° to promote the oscillation as long as the Equation (5) was also satisfied. When Equations (7) and (6) were satisfied at the same time, however, the sound pressure oscillation and heat re-lease oscillation would be out-of-phase and obtain a negative Rayleigh criterion to suppress oscillation. Under the combustion of φ = 0.7, however, Equation (8) was sat-isfied, and thus the condition of LP/λP meeting Equation (6) could result in an oscilla-tion promotion but Equation (5) leads to a oscillation suppression. With a symmetric supply structure, the two sides have the same effect that either promote or suppress oscillation. For the asymmetric supply system, however, the different LP may lead to the interaction between heat release oscillation and sound pressure oscillation pro-motes each other at one side but suppresses each other at the other side.The ratio of LP to λP at each side was calculated to analyze the mechanism for en-couraging or suppressing oscillation under asymmetric supply structure, as the results with combining the measured PRMS shown in Tables 2–4. Under an asymmetric supply system, the heat release oscillation could be in different phase between two sides and thus generating two sources (OS1 and OS2, respectively) with different effect on pres-sure oscillation. Take the results in Table 2 for example, for the symmetric supply sys-tem of L1 = L2 = 2.06 m, LP/λP is 0.439, under which both OS1 and OS2 promote oscilla-tion, and thus the result is a strong oscillation with PRMS being as high as 4108 Pa. With changing L2, however, OS2 may turn to suppress the oscillation, such as in case 29, 30, 31, and 38, and the overall result is a relatively weak oscillation. What’s more notable is that while OS1 still has a strong promotion effect in case 28, 36, and 37, these condi-tions present only a combustion noise without obvious oscillation.
For the results in Tables 3 and 4, most cases also show the same regularity that only when OS2 has a promotion effect could probably push the whole system into a strong oscillation. Exceptional circumstance occurs at case 58 and 59 that both OS1 and OS2 have promotion effect, but the whole system presents non-oscillation. This may be due to that the sound pressure antinode is too close to the stabilizer [24], causing a rel-atively weak flow rate oscillation, and thus muting the thermo-acoustic interaction. These observations indicate that for an asymmetric supply structure, a necessary but not sufficient condition required for strong oscillation is that both L1 and L2 satisfy os-cillation promotion.