Using Micro-Raman Spectroscopy to Assess MEMS Si/SiO2 Membranes Exhibiting Negative Spring Constant Behavior

We introduce a novel micro-mechanical structure that exhibits two regions of stable linear positive and negative stiffness. Springs, cantilevers, beams and any other geometry that display an increasing return force that is proportional to the displacement can be considered to have a “Hookean” positive spring constant, or stiffness. Less well known is the opposite characteristic of a reducing return force for a given deflection, or negative stiffness. Unfortunately many simple negative stiffness structures exhibit unstable buckling and require additional moving components during deflection to avoid deforming out of its useful shape. In Micro-Electro-Mechanical Systems (MEMS) devices, buckling caused by stress at the interface of silicon and thermally grown SiO₂ causes tensile and compressive forces that will warp structures if the silicon layer is thin enough. The 1 mm² membrane structures presented here utilizes this effect but overcome this limitation and empirically demonstrates linearity in both regions. The Si/SiO₂ membranes presented deflect ~17 μm from their pre-released position. The load deflection curves produced exhibit positive linear stiffness with an inflection point holding nearly constant with a slight negative stiffness. Depositing a 0.05 μm titanium and 0.3 μm layer of gold on top of the Si/SiO₂ membrane reduces the initial deflection to ~13.5 μm. However, the load deflection curve produced illustrates both a linear positive and negative spring constant with a fairly sharp inflection point. These results are potentially useful to selectively tune the spring constant of mechanical structures used in MEMS. The structures presented are manufactured using typical micromachining techniques and can be fabricated in-situ with other MEMS devices.     

Bifurcation Analysis of a Predator–Prey System with Generalised Holling Type III Functional Response

We consider a generalised Gause predator–prey system with a generalised Holling response function of type III: . We study the cases where b is positive or negative. We make a complete study of the bifurcation of the singular points including: the Hopf bifurcation of codimensions 1 and 2, the Bogdanov–Takens bifurcation of codimensions 2 and 3. Numerical simulations are given to calculate the homoclinic orbit of the system. Based on the results obtained, a bifurcation diagram is conjectured and a biological interpretation is given.      

Facile Construction of Medium-Sized Carbocycles,Total Synthesis of (±)-Parvifoline

Abstract

A new synthetic approach to medium-sized rings has been accomplished via intramolecular cyclization of a sulfone-stabilized carbanion. This strategy was applied to the total synthesis of (±)-parvifoline.