Nitrogen (N) and silicon (Si) are two important nutritional elements required for plant growth, and both impact host plant resistance toward insect herbivores. The interaction between the two elements may therefore play a significant role in determining host plant resistance. We investigated this interaction in rice (Oryza sativa L.) and its effect on resistance to the herbivore brown planthopper Nilaparvata lugens (BPH). Our results indicate that high-level (5.76 mM) N fertilization reduced Si accumulation in rice leaves, and furthermore, this decrease was likely due to decreased expression of Si transporters OsLsi1 and OsLsi2. Conversely, reduced N accumulation was observed at high N fertilization levels when Si was exogenously provided, and this was associated with down-regulation of OsAMT1;1 and OsGS1;1, which are involved in ammonium uptake and assimilation, respectively. Under lower N fertilization levels (0.72 and/or 1.44 mM), Si amendment resulted in increased OsNRT1:1, OsGS2, OsFd-GOGAT, OsNADH-GOGAT2, and OsGDH2 expression. Additionally, bioassays revealed that high N fertilization level significantly decreased rice resistance to BPH, and the opposite effect was observed when Si was provided. These results provide additional insight into the antagonistic interaction between Si and N accumulation in rice, and the effects on plant growth and susceptibility to herbivores.
A semi-analytical method is presented in this paper for stability analysis of milling with a variable spindle speed (VSS), periodically modulated around a nominal spindle speed. Taking the regenerative effect into account, the dynamics of the VSS milling is governed by a delay-differential equation (DDE) with time-periodic coefficients and a time-varying delay. By reformulating the original DDE in an integral-equation form, one time period is divided into a series of subintervals. With the aid of numerical integrations, the transition matrix over one time period is then obtained to determine the milling stability by using Floquet theory. On this basis, the stability lobes consisting of critical machining parameters can be calculated. Unlike the constant spindle speed (CSS) milling, the time delay for the VSS is determined by an integral transcendental equation which is accurately calculated with an ordinary differential equation (ODE) based method instead of the formerly adopted approximation expressions. The proposed numerical integration method is verified with high computational efficiency and accuracy by comparing with other methods via a two-degree-of-freedom milling example. With the proposed method, this paper details the influence of modulation parameters on stability diagrams for the VSS milling.
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