Collective behaviour in a square lattice of driven Duffing resonators coupled to van der Pol oscillators

The global and local synchronisation of a square lattice composed of alternating Duffing resonators and van der Pol oscillators coupled through displacement is studied. The lattice acts as a sensing device in which the input signal is characterised by an external driving force that is injected into the system through a subset of the Duffing resonators. The parameters of the system are taken from MEMS devices. The effects of the system parameters, the lattice architecture and size are discussed.

Electromechanical resonators as measuring transducers

With the increasing use of digital computers for data acquisition and digital process control, frequency domain transducers have become very attractive due to their virtual digital output. Essentially they are electrically maintained oscillators where the sensor is the controlling resonator.They are designed to make the frequency a function of the physical parameter being measured. Because of their high quality factor, mechanical resonators give very good frequency stability and are widely used as sensors. For this work symmetrical mechanical resonators such as the tuning fork were considered, to be the most promising. These are dynamically clamped and can be designed to have extensive regions where no vibrations occur.This enables the resonators to be robustly mounted in a way convenient for various applications. Designs for the measurement of fluid density and tension have been produced. The principle of the design of the resonator for fluid density measurement is a thin gap (trapping a lamina of fluid) between its two members which vibrate in antiphase.An analysis of the inter­ action between this resonator and the fluid lamina has carried out.In gases narrow gaps are needed for a good sensitivity and the use of the material fused quartz, because of its low density and very low temperature coefficient, is ideally suitable. In liquids an adequate sensitivity is achieved even with a wide lamina gap. Practical designs of such transducers have been evolved. The accuracy for liquid measurements is better than 1%. For gases it was found that, in air, a change of atmospheric pressure of 0.3% could be detected. In constructing a tension transducer using such a mechanical sensor as a wire or a beam, major difficulties are encountered in making an efficient clamping arrangement for the sensor. The use of dynamically clamped beams has been found to overcome the problem and this is the basis of the transducer investigated.

Statnote 7: chi-square contingency tables

When the data are counts or the frequencies of particular events and can be expressed as a contingency table, then they can be analysed using the chi-square distribution. When applied to a 2 x 2 table, the test is approximate and care needs to be taken in analysing tables when the expected frequencies are small either by applying Yate’s correction or by using Fisher’s exact test. Larger contingency tables can also be analysed using this method. Note that it is a serious statistical error to use any of these tests on measurement data!

A preliminary study into emergent behaviours in a lattice of interacting nonlinear resonators and oscillators

Future sensor arrays will be composed of interacting nonlinear components with complex behaviours with no known analytic solutions. This paper provides a preliminary insight into the expected behaviour through numerical and analytical analysis. Specically, the complex behaviour of a periodically driven nonlinear Duffing resonator coupled elastically to a van der Pol oscillator is investigated as a building block in a 2D lattice of such units with local connectivity. An analytic treatment of the 2-device unit is provided through a two-time-scales approach and the stability of the complex dynamic motion is analysed. The pattern formation characteristics of a 2D lattice composed of these units coupled together through nearest neighbour interactions is analysed numerically for parameters appropriate to a physical realisation through MEMS devices. The emergent patterns of global and cluster synchronisation are investigated with respect to system parameters and lattice size.

Basic elements for microfiber photonics : micro/nanofibers and microfiber coil resonators

The basic functional element of microfiber photonics is a microfiber coil resonator (MCR), which potentially can perform filtering, time delay, and nonlinear transformations of electromagnetic waves, as well as sensing of the ambient medium. The first experimental demonstration of an MCR has been recently performed by researchers of the OFS Laboratories (Optical Fiber Communication Conference 2007, Postdeadline paper PDP46). This paper follows up on the later publication presenting a brief introduction to the theory, transmission properties and applications of optical micro/nanofibers and MCRs. Fabrication of MCRs in air and in liquid is reported. For the MCR immersed in liquid, the Q-factor exceeding 60 000 is achieved. © 2008 IEEE.

Study of synchronisation in chains of coupled non-linear oscillators and resonators

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Basic elements for microfiber photonics:micro/nanofibers and microfiber coil resonators

The basic functional element of microfiber photonics is a microfiber coil resonator (MCR), which potentially can perform filtering, time delay, and nonlinear transformations of electromagnetic waves, as well as sensing of the ambient medium. The first experimental demonstration of an MCR has been recently performed by researchers of the OFS Laboratories (Optical Fiber Communication Conference 2007, Postdeadline paper PDP46). This paper follows up on the later publication presenting a brief introduction to the theory, transmission properties and applications of optical micro/nanofibers and MCRs. Fabrication of MCRs in air and in liquid is reported. For the MCR immersed in liquid, the Q-factor exceeding 60 000 is achieved. © 2008 IEEE.

Vortex shedding from a row of square bars

Interactions of wakes in a flow past a row of square bars, which is placed across a uniform flow, are investigated by numerical simulations and experiments on the tassumption that the flow is two-dimensional and incompressible. At small Reynolds numbers the flow is steady and symmetric with respect not only to streamwise lines through the center of each square bar but also to streamwise centerlines between adjacent square bars. However, the steady symmetric flow becomes unstable at larger Reynolds numbers and make a transition to a steady asymmetric flow with respect to the centerlines between adjacent square bars in some cases or to an oscillatory flow in other cases. It is found that vortices are shed synchronously from adjacent square bars in the same phase or in anti-phase depending upon the distance between the bars when the flow is oscillatory. The origin of the transition to the steady asymmetric flow is identified as a pitchfork bifurcation, while the oscillatory flows with synchronous shedding of vortices are clarified to originate from a Hopf bifurcation. The critical Reynolds numbers of the transitions are evaluated numerically and the bifurcation diagram of the flow is obtained.

Tunable coaxial resonators based on silicon optical fibers

Thermal tuning of a coaxial fiber resonator with a silica cladding surrounding an inner silicon core is investigated. By pumping the silicon with below bandgap light, it is possible to redshift the WGM resonances. © 2014 OSA.

Management of slow light dispersion and delay time characteristics with SNAP bottle resonators

The nanoscale radius variation of a bottle microresonator with the required dispersion characteristics is determined theoretically. Experimentally, a microresonator with the footprint 0.08 mm2 exhibiting 20 ns/nm dispersion compensation of 100 ps pulses is demonstrated. © 2014 OSA.

A geometrical model for surface roughness prediction when face milling Al 7075-T7351 with square insert tools

Surface quality is important in engineering and a vital aspect of it is surface roughness, since it plays an important role in wear resistance, ductility, tensile, and fatigue strength for machined parts. This paper reports on a research study on the development of a geometrical model for surface roughness prediction when face milling with square inserts. The model is based on a geometrical analysis of the recreation of the tool trail left on the machined surface. The model has been validated with experimental data obtained for high speed milling of aluminum alloy (Al 7075-T7351) when using a wide range of cutting speed, feed per tooth, axial depth of cut and different values of tool nose radius (0.8. mm and 2.5. mm), using the Taguchi method as the design of experiments. The experimental roughness was obtained by measuring the surface roughness of the milled surfaces with a non-contact profilometer. The developed model can be used for any combination of material workpiece and tool, when tool flank wear is not considered and is suitable for using any tool diameter with any number of teeth and tool nose radius. The results show that the developed model achieved an excellent performance with almost 98% accuracy in terms of predicting the surface roughness when compared to the experimental data. © 2014 The Society of Manufacturing Engineers.

Reflectionless potentials for slow whispering gallery modes in surface nanoscale axial photonic fiber resonators

We consider an optical fiber with a nanoscale variation of the effective fiber radius that supports whispering gallery modes slowly propagating along the fiber, and reveal that the radius variation can be designed to support the reflectionless propagation of these modes. We show that reflectionless modulations can realize control of the transmission amplitude and temporal delay, while enabling close packing due to the absence of cross talk, in contrast to the conventional potentials.

Permanent matching of coupled optical bottle resonators with better than 0.16 GHz precision

The fabrication precision is one of the most critical challenges to the creation of practical photonic circuits composed of coupled high Q-factor microresonators. While very accurate transient tuning of microresonators based on local heating has been reported, the record precision of permanent resonance positioning achieved by post-processing is still within 1 and 5 GHz. Here we demonstrate two coupled bottle microresonators fabricated at the fiber surface with resonances that are matched with a better than 0.16 GHz precision. This corresponds to a better than 0.17 Å precision in the effective fiber radius variation. The achieved fabrication precision is only limited by the resolution of our optical spectrum analyzer and can be potentially improved by an order of magnitude.