Impact dynamics of MEMS switches

During operation, a MEMS switch is activated by an applied voltage. This causes the switch, often a doped silicon microbeam, to be attracted toward (pulled-into) a substrate. The component–substrate contact completes a circuit and permits the flow of current. Calculations for the minimum voltage required to achieve quasi-static pull-in are well documented. But for these quasi-static pull-in voltages to be meaningful, the voltage would have to be increased gradually until the critical value V_pull-inV_{\mathrm{pull\mbox{-}in}} is reached and the switch closes. Of course, practical considerations might require the switch to cycle on and off quickly, i.e., dynamically. This is particularly true in the case of radio frequency (RF) MEMS switches. In this paper, a model is developed and used to consider the dynamic pull-in characteristics of a clamped-clamped microbeam. This model includes inertial effects, structural and air damping (squeeze-film damping), as well as the impact behavior of the microbeam with the substrate. Parameter combinations leading to various types of behavior (no pull-in, air-bounce, wall bounce, etc.) are clearly identified. In an attempt to ensure fast switch closure and limit bouncing, two new applied voltage profiles are considered.     

Simple Shearing of Incompressible and Slightly Compressible Isotropic Nonlinearly Elastic Materials

The classical problem of simple shear in nonlinear elasticity has played an important role as a basic pilot problem involving a homogeneous deformation that is rich enough to illustrate several key features of the nonlinear theory, most notably the presence of normal stress effects. Here our focus is on certain ambiguities in the formulation of simple shear arising from the determination of the arbitrary hydrostatic pressure term in the normal stresses for the case of an incompressible isotropic hyperelastic material. A new formulation in terms of the principal stretches is given. An alternative approach to the determination of the hydrostatic pressure is proposed here: it will be required that the stress distribution for a perfectly incompressible material be the same as that for a slightly compressible counterpart. The form of slight compressibility adopted here is that usually assumed in the finite element simulation of rubbers. For the particular case of a neo-Hookean material, the different stress distributions are compared and contrasted.     

Redetermination of fac‐tris­(benzo­hydrox­am­ato)­iron(III) tri­hydrate

Due to its importance as a model for naturally occurring iron(III) siderophores such as desferriox­amine B, the crystal structure of the title compound, [Fe(C₇H₆NO₂)₃]·3H₂O, which was reported previously (R = 0.12, one of water mol­ecules disordered), has been redetermined (R = 0.041 without disorder). The complex has pseudo‐octahedral geometry around the Fe^III atom, with Fe—O bond lengths ranging from 1.9689 (18) to 2.0585 (17) Å and O—Fe—O bond angles in the chelate rings of 78.01 (7), 78.83 (7) and 78.95 (7)°. There is extensive hydrogen bonding involving the water mol­ecules and the hydro­xamate ligands.     

The impact of environmental constraints on short term harvesting: Use of planning tools and mathematical models

Both in New Zealand and Chile there exist important forest industries based mostly on pine plantations. The management of harvesting requires a series of activities such as building access roads, harvesting with skidders on flat terrain and cable logging for steep terrain, transportation from forest origins to destinations, such as a port, pulp plant and sawmills.These harvesting activities imply some potentially harmful environmental impacts such as water sedimentation, erosion and loss of scenic beauty. This has led to the proposal of several mitigating actions, such as creating riparian strips along rivers, avoiding the use of heavy machinery on fragile soils and minimizing road building.The degree of implementation of these mitigating actions differs in Chile and New Zealand. In New Zealand, the 1991 Resource Management Act regulated the implementation of environmental protection measures. In Chile a series of such measures have been implemented, but a set of definite regulations has not been defined yet and there is a need to develop an economic evaluation of the implementation of environmental measures in terms of reduced timber production and high harvesting costs, together with the benefits to the environment. To support decisions at tactical and operational levels, mathematical models have been developed both in Chile and New Zealand and are being used successfully by the timber industries. These models can be modified to consider diverse environmental protection measures. We analyze the implementation of these modifications and how the new models can help evaluate the economic impact of the protection measures. We show some preliminary results.     

Modelling and control of natural convection in canned foods

In this paper we study mathematically an industrial problemrelated to sterilization processes involving heat transfer bynatural convection. We give results of existence and regularityfor the solution of this problem. We recast the whole problemas an optimal control problem with pointwise constraints onthe state and the control in order to ensure the reduction ofmicroorganism concentration and the retention of nutrients,and to save energy. Finally, we give results on existence ofthe optimal solution and optimality conditions for its characterization.     

Transport Coefficients of Hydrogen and Argon–Hydrogen Plasmas

Calculated values of the viscosity, thermal conductivity, and electrical conductivity of hydrogen and mixtures of argon and hydrogen at high temperatures are presented. Combined ordinary, pressure, temperature, and electric field diffusion coefficients are also given for the mixtures. The calculations, which assume local thermodynamic equilibrium, are performed for atmospheric pressure plasmas in the temperature range from 300 to 30,000 K. The results are compared with those of previously published studies. Generally, the agreement is reasonable; those discrepancies that exist are attributed to the improved values of some of the collision integrals used here in calculating the transport coefficients.     

Parallel pseudospectral electronic structure: II. Localized Møller–Plesset calculations

We have developed a parallel version of our pseudospectral localized Møller–Plesset electronic structure code. We present timings for molecules up to 1010 basis functions and parallel speedup for molecules in the range of 260–658 basis functions. We demonstrate that the code is scalable; that is, a larger number of nodes can be efficiently utilized as the size of the molecule increases. By taking advantage of the available distributed memory and disk space of a scalable parallel computer, the parallel code can calculate LMP2 energies of molecules too large to be done on workstations. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1030–1038, 1998