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.

Nonlinear dynamics of a periodically driven Duffing resonator coupled to a Van der Pol oscillator

We explore the dynamics of a periodically driven Duffing resonator coupled elastically to a van der Pol oscillator in the case of 1?:?1 internal resonance in the cases of weak and strong coupling. Whilst strong coupling leads to dominating synchronization, the weak coupling case leads to a multitude of complex behaviours. A two-time scales method is used to obtain the frequency-amplitude modulation. The internal resonance leads to an antiresonance response of the Duffing resonator and a stagnant response (a small shoulder in the curve) of the van der Pol oscillator. The stability of the dynamic motions is also analyzed. The coupled system shows a hysteretic response pattern and symmetry-breaking facets. Chaotic behaviour of the coupled system is also observed and the dependence of the system dynamics on the parameters are also studied using bifurcation analysis.

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.

The separation of secondary oil-water dispersions in particulate beds

The literature relating to haze formation, methods of separation, coalescence mechanisms, and models by which droplets <100 μm are collected, coalesced and transferred, have been reviewed with particular reference to particulate bed coalescers. The separation of secondary oil-water dispersions was studied experimentally using packed beds of monosized glass ballotini particles. The variables investigated were superficial velocity, bed depth, particle size, and the phase ratio and drop size distribution of inlet secondary dispersion. A modified pump loop was used to generate secondary dispersions of toluene or Clairsol 350 in water with phase ratios between 0.5-6.0 v/v%.Inlet drop size distributions were determined using a Malvern Particle Size Analyser;effluent, coalesced droplets were sized by photography. Single phase flow pressure drop data were correlated by means of a Carman-Kozeny type equation. Correlations were obtained relating single and two phase pressure drops, as (ΔP2/μc)/ΔP1/μd) = kp Ua Lb dcc dpd Cine A flow equation was derived to correlate the two phase pressure drop data as, ΔP2/(ρcU2) = 8.64*107 [dc/D]-0.27 [L/D]0.71 [dp/D]-0.17 [NRe]1.5 [e1]-0.14 [Cin]0.26  In a comparison between functions to characterise the inlet drop size distributions a modification of the Weibull function provided the best fit of experimental data. The general mean drop diameter was correlated by: q_p q_p p_q /β      Γ ((q-3/β) +1) d qp = d fr  .α        Γ ((P-3/β +1 The measured and predicted mean inlet drop diameters agreed within ±15%. Secondary dispersion separation depends largely upon drop capture within a bed. A theoretical analysis of drop capture mechanisms in this work indicated that indirect interception and London-van der Waal's mechanisms predominate. Mathematical models of dispersed phase concentration m the bed were developed by considering drop motion to be analogous to molecular diffusion.The number of possible channels in a bed was predicted from a model in which the pores comprised randomly-interconnected passage-ways between adjacent packing elements and axial flow occured in cylinders on an equilateral triangular pitch. An expression was derived for length of service channels in a queuing system leading to the prediction of filter coefficients. The insight provided into the mechanisms of drop collection and travel, and the correlations of operating parameters, should assist design of industrial particulate bed coalescers.