Pull-in dynamics of overdamped microbeams

We study the dynamics of MEMS microbeams undergoing electrostatic pull-in. At DC voltages close to the pull-in voltage, experiments and numerical simulations have reported `bottleneck' behaviour in which the transient dynamics slow down considerably. This slowing down is highly sensitive to external forces, and so has widespread potential for applications that use pull-in time as a sensing mechanism, including high-resolution accelerometers and pressure sensors. Previously, the bottleneck phenomenon has only been understood using lumped mass-spring models that do not account for effects such as variable residual stress and different boundary conditions. We extend these studies to incorporate the beam geometry, developing an asymptotic method to analyse the pull-in dynamics. We attribute bottleneck behaviour to critical slowing down near the pull-in transition, and we obtain a simple expression for the pull-in time in terms of the beam parameters and external damping coefficient. This expression is found to agree well with previous experiments and numerical simulations that incorporate more realistic models of squeeze film damping, and so provides a useful design rule for sensing applications. We also consider the accuracy of a single-mode approximation of the microbeam equations --- an approach that is commonly used to make analytical progress, without systematic investigation of its accuracy. By comparing to our bottleneck analysis, we identify the factors that control the error of this approach, and we demonstrate that this error can indeed be very small.Comment: 18 page

Dynamics of viscoelastic snap-through

We study the dynamics of snap-through when viscoelastic effects are present. To gain analytical insight we analyse a modified form of the Mises truss, a single-degree-of-freedom structure, which features an `inverted' shape that snaps to a `natural' shape. Motivated by the anomalously slow snap-through shown by spherical elastic caps, we consider a thought experiment in which the truss is first indented to an inverted state and allowed to relax while a specified displacement is maintained; the constraint of an imposed displacement is then removed. Focussing on the dynamics for the limit in which the timescale of viscous relaxation is much larger than the characteristic elastic timescale, we show that two types of snap-through are possible: the truss either immediately snaps back over the elastic timescale or it displays `pseudo-bistability', in which it undergoes a slow creeping motion before rapidly accelerating. In particular, we demonstrate that accurately determining when pseudo-bistability occurs requires the consideration of inertial effects immediately after the indentation force is removed. Our analysis also explains many basic features of pseudo-bistability that have been observed previously in experiments and numerical simulations; for example, we show that pseudo-bistability occurs in a narrow parameter range at the bifurcation between bistability and monostability, so that the dynamics is naturally susceptible to critical slowing down. We then study an analogous thought experiment performed on a continuous arch, showing that the qualitative features of the snap-through dynamics are well captured by the truss model. In addition, we analyse experimental and numerical data of viscoelastic snap-through times reported in the literature. Combining these approaches suggests that our conclusions may also extend to more complex viscoelastic structures used in morphing applications.Comment: Main text 37 pages, Appendices 13 page

Passive control of viscous flow via elastic snap-through

We demonstrate the passive control of viscous flow in a channel by using an elastic arch embedded in the flow. Depending on the fluid flux, the arch may `snap' between two states --- constricting and unconstricting --- that differ in hydraulic conductivity by up to an order of magnitude. We use a combination of experiments at a macroscopic scale and theory to study the constricting and unconstricting states, and determine the critical flux required to transition between them. We show that such a device may be precisely tuned for use in a range of applications, and in particular has potential as a passive microfluidic fuse to prevent excessive fluxes in rigid-walled channels.Comment: Main text 5 pages, Supplementary Information 14 page

Delayed pull-in transitions in overdamped MEMS devices

We consider the dynamics of overdamped MEMS devices undergoing the pull-in instability. Numerous previous experiments and numerical simulations have shown a significant increase in the pull-in time under DC voltages close to the pull-in voltage. Here the transient dynamics slow down as the device passes through a meta-stable or bottleneck phase, but this slowing down is not well understood quantitatively. Using a lumped parallel-plate model, we perform a detailed analysis of the pull-in dynamics in this regime. We show that the bottleneck phenomenon is a type of critical slowing down arising from the pull-in transition. This allows us to show that the pull-in time obeys an inverse square-root scaling law as the transition is approached; moreover we determine an analytical expression for this pull-in time. We then compare our prediction to a wide range of pull-in time data reported in the literature, showing that the observed slowing down is well captured by our scaling law, which appears to be generic for overdamped pull-in under DC loads. This realization provides a useful design rule with which to tune dynamic response in applications, including state-of-the-art accelerometers and pressure sensors that use pull-in time as a sensing mechanism. We also propose a method to estimate the pull-in voltage based only on data of the pull-in times.Comment: 17 page

In-flight Evaluation of Aerodynamic Predictions of an Air-launched Space Booster

Several analytical aerodynamic design tools that were applied to the Pegasus (registered trademark) air-launched space booster were evaluated using flight measurements. The study was limited to existing codes and was conducted with limited computational resources. The flight instrumentation was constrained to have minimal impact on the primary Pegasus missions. Where appropriate, the flight measurements were compared with computational data. Aerodynamic performance and trim data from the first two flights were correlated with predictions. Local measurements in the wing and wing-body interference region were correlated with analytical data. This complex flow region includes the effect of aerothermal heating magnification caused by the presence of a corner vortex and interaction of the wing leading edge shock and fuselage boundary layer. The operation of the first two missions indicates that the aerodynamic design approach for Pegasus was adequate, and data show that acceptable margins were available. Additionally, the correlations provide insight into the capabilities of these analytical tools for more complex vehicles in which the design margins may be more stringent

Semantic Interoperability in the Fixed Income Securities Industry: A Knowledge Representation Architecture for Dynamic Integration of Web-Based Information

We examine a knowledge representation architecture to support context interchange mediation. For autonomous receivers and sources sharing a common subject domain, the mediator's reasoning engine can devise query plans integrating multiple sources and resolving semantic heterogeneity. Receiver applications obtain the data they need in the form they need it without imposing changes on sources. The KR architecture includes: 1) data models for each source and receiver, 2) subject domain ontologies, containing abstract subject matter conceptualizations that would be known to experienced practitioners in the industry, and 3) context models for each source and receiver that explain how each source or receiver data model implements the abstract concepts from a subject domain ontology. Examples drawn from the fixed income securities industry illustrate problems and solutions enabled by the proposed architecture

Novel Distances for Dollo Data

We investigate distances on binary (presence/absence) data in the context of a Dollo process, where a trait can only arise once on a phylogenetic tree but may be lost many times. We introduce a novel distance, the Additive Dollo Distance (ADD), which is consistent for data generated under a Dollo model, and show that it has some useful theoretical properties including an intriguing link to the LogDet distance. Simulations of Dollo data are used to compare a number of binary distances including ADD, LogDet, Nei Li and some simple, but to our knowledge previously unstudied, variations on common binary distances. The simulations suggest that ADD outperforms other distances on Dollo data. Interestingly, we found that the LogDet distance performs poorly in the context of a Dollo process, which may have implications for its use in connection with conditioned genome reconstruction. We apply the ADD to two Diversity Arrays Technology (DArT) datasets, one that broadly covers Eucalyptus species and one that focuses on the Eucalyptus series Adnataria. We also reanalyse gene family presence/absence data on bacteria from the COG database and compare the results to previous phylogenies estimated using the conditioned genome reconstruction approach

A comparison of success rates of introduced passeriform birds in New Zealand, Australia and the United States

In this study, we compiled lists of successful and unsuccessful passeriform introductions to nine sites in New Zealand, Australia and the United States. We limited our analysis to introductions during the 19th century to minimize potential variation in transport modes and habitat quality changes, such as those due to increasing urbanization. We compared introduction success rates at three levels. First we included all passeriforms introduced to any of the sites in the three locations, then we compared the fates of just those species with a European origin and finally we compared success rates of just the 13 species released into all three locations. We found that the pattern of success or failure differed significantly across the three locations: Passeriforms introduced by acclimatization organizations to the United States were significantly more likely to fail than those introduced to New Zealand or Australia. Several species that succeeded in either New Zealand or Australia failed in the United States, even after the introduction of seemingly sufficient numbers