Statistics of noise-driven coupled nonlinear oscillators:applications to systems with Kerr nonlinearity

We present exact analytical results for the statistics of nonlinear coupled oscillators under the influence of additive white noise. We suggest a perturbative approach for analysing the statistics of such systems under the action of a deterministic perturbation, based on the exact expressions for probability density functions for noise-driven oscillators. Using our perturbation technique we show that our results can be applied to studying the optical signal propagation in noisy fibres at (nearly) zero dispersion as well as to weakly nonlinear lattice models with additive noise. The approach proposed can account for a wide spectrum of physically meaningful perturbations and is applicable to the case of large noise strength. © 2005 Elsevier B.V. All rights reserved.

Design and fabrication of a nonlinear micro impact oscillator

In this paper we describe the design and fabrication of a mechanical autonomous impact oscillator with a MEMS resonator as the frequency control element. The design has been developed with scalability to large 2-D arrays of coupled oscillators in mind. The dynamic behaviour of the impact oscillator was numerically studied and it was found that the geometry nonlinearity has an effect on the static pull-in voltage and equilibrium position. The external driving power can alter the frequency of the impact oscillator. The autonomous nature of the oscillator simplifies the complexity of the drive circuitry and is essential for large 2-D arrays.

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.

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

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Emergent behaviour in arrays of coupled nonlinear oscillators

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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.

Family resemblances? Ligand binding and activation of family A and B G-protein-coupled receptors

In April 2007, the Biochemical Society held a meeting to compare and contrast ligand binding and activation of Family A and B GPCRs (G-protein-coupled receptors). Being the largest class, Family A GPCRs usually receive the most attention, although a previous Biochemical Society meeting has focused on Family B GPCRs. The aim of the present meeting was to bring researchers of both families together in order to identify commonalities between the two. The present article introduces the proceedings of the meeting, briefly commenting on the focus of each of the following articles. ©The Authors.

A key role for transmembrane prolines in calcitonin receptor-like receptor agonist binding and signalling:implications for family B G-protein-coupled receptors

Calcitonin receptor like-receptor is a family B G-protein coupled receptor (GPCR). It requires receptor activity modifying protein (RAMP) 1 to give a calcitonin gene-related peptide (CGRP) receptor. Little is known of how members of this receptor family function. Proline residues often form important kinks in alpha-helices. Therefore, all proline residues within the transmembrane helices of the receptor (Pro241, Pro244 in helix 4, Pro275 in helix 5, Pro321 and Pro331 in helix 6) were mutated to alanine. Pro241 Pro275, and Pro321 are highly conserved throughout all family B GPCRs. The binding of CGRP and its ability to stimulate cAMP production were investigated in mutant and wild-type receptors after transient transfection into COS-7 cells with RAMP1. The P321A mutation significantly decreased the pEC(50) for CGRP and reduced its affinity but did not change cell-surface expression. Antagonist binding [CGRP(8-37) and 1-piperidinecarboxamide N-[2-[[5amino-1-[[4-(4-pyridinyl)-1-piperazinyl]carbonyl]pentyl]amino]-1-[(3 5-dibromo-4-hydroxyphenyl)methyl]-2-oxoethyl]-4-(1,4-dihydro-2-oxo-3(2H)-quina zolinyl) (BIBN4096BS)] was little altered by the mutation. Adrenomedullin-mediated signaling was disrupted when P321A was coexpressed with RAMP1, RAMP2, or RAMP3. The P331A mutant produced a moderate reduction in CGRP binding and receptor activation. Mutation of the other residues had no effect on receptor function. Thus, Pro321 and Pro331 are required for agonist binding and receptor activation. Modeling suggested that Pro321 induces a bend in helix 6, bringing its C terminus near that of helix 3, as seen in many family A GPCRs. This is abolished in P321A. P321A-I325P predicted to restore this conformation, showed wild-type activation. Modeling can also rationalize the effects of transmembrane proline mutants previously reported for another family B GPCR, the VPAC(1) receptor.

Quantitative risk assessment of groundwater quality utilizing GIS technology and coupled groundwater models

The thesis presents a two-dimensional Risk Assessment Method (RAM) where the assessment of risk to the groundwater resources incorporates both the quantification of the probability of the occurrence of contaminant source terms, as well as the assessment of the resultant impacts. The approach emphasizes the need for a greater dependency on the potential pollution sources, rather than the traditional approach where assessment is based mainly on the intrinsic geo-hydrologic parameters. The risk is calculated using Monte Carlo simulation methods whereby random pollution events were generated to the same distribution as historically occurring events or a priori potential probability distribution. Integrated mathematical models then simulate contaminant concentrations at the predefined monitoring points within the aquifer. The spatial and temporal distributions of the concentrations were calculated from repeated realisations, and the number of times when a user defined concentration magnitude was exceeded is quantified as a risk. The method was setup by integrating MODFLOW-2000, MT3DMS and a FORTRAN coded risk model, and automated, using a DOS batch processing file. GIS software was employed in producing the input files and for the presentation of the results. The functionalities of the method, as well as its sensitivities to the model grid sizes, contaminant loading rates, length of stress periods, and the historical frequencies of occurrence of pollution events were evaluated using hypothetical scenarios and a case study. Chloride-related pollution sources were compiled and used as indicative potential contaminant sources for the case study. At any active model cell, if a random generated number is less than the probability of pollution occurrence, then the risk model will generate synthetic contaminant source term as an input into the transport model. The results of the applications of the method are presented in the form of tables, graphs and spatial maps. Varying the model grid sizes indicates no significant effects on the simulated groundwater head. The simulated frequency of daily occurrence of pollution incidents is also independent of the model dimensions. However, the simulated total contaminant mass generated within the aquifer, and the associated volumetric numerical error appear to increase with the increasing grid sizes. Also, the migration of contaminant plume advances faster with the coarse grid sizes as compared to the finer grid sizes. The number of daily contaminant source terms generated and consequently the total mass of contaminant within the aquifer increases in a non linear proportion to the increasing frequency of occurrence of pollution events. The risk of pollution from a number of sources all occurring by chance together was evaluated, and quantitatively presented as risk maps. This capability to combine the risk to a groundwater feature from numerous potential sources of pollution proved to be a great asset to the method, and a large benefit over the contemporary risk and vulnerability methods.

RAMPs and the modulation of G-protein coupled receptors

Receptor activity modifying proteins (RAMPs) are a family of three proteins that can interact with G-protein coupled receptors (GPCRs) to create new receptors and also alter the signalling and trafficing of existing receptors. There are frequently changes in RAMP expression in cardiovascular disease RAMPs represent important drug targets.

Independent neuronal oscillators of the rat globus pallidus

In vivo, neurons of the globus pallidus (GP) and subthalamic nucleus (STN) resonate independently around 70 Hz. However, on the loss of dopamine as in Parkinson's disease, there is a switch to a lower frequency of firing with increased bursting and synchronization of activity. In vitro, type A neurons of the GP, identified by the presence of Ih and rebound depolarizations, fire at frequencies (≤80 Hz) in response to glutamate pressure ejection, designed to mimic STN input. The profile of this frequency response was unaltered by bath application of the GABAA antagonist bicuculline (10 μM), indicating the lack of involvement of a local GABA neuronal network, while cross-correlations of neuronal pairs revealed uncorrelated activity or phase-locked activity with a variable phase delay, consistent with each GP neuron acting as an independent oscillator. This autonomy of firing appears to arise due to the presence of intrinsic voltage- and sodium-dependent subthreshold membrane oscillations. GABAA inhibitory postsynaptic potentials are able to disrupt this tonic activity while promoting a rebound depolarization and action potential firing. This rebound is able to reset the phase of the intrinsic oscillation and provides a mechanism for promoting coherent firing activity in ensembles of GP neurons that may ultimately lead to abnormal and pathological disorders of movement.

Surface:plasma interactions in GaAs subjected to capacitively coupled RF plasmas

Surface compositional changes in GaAs due to RF plasmas of different gases have been investigated by XPS and etch rates were measured using AFM. Angular Resolved XPS (ARXPS) was also employed for depth analysis of the composition of the surface layers. An important role in this study was determination of oxide thickness using XPS data. The study of surface - plasma interaction was undertaken by correlating results of surface analysis with plasma diagnosis. Different experiments were designed to accurately measure the BEs associated with the Ga 3d, Ga 2P3/2 and LMM peaks using XPS analysis and propose identification in terms of the oxides of GaAs. Along with GaAs wafers, some reference compounds such as metallic Ga and Ga2O3 powder were used. A separate study aiming the identification of the GaAs surface oxides formed on the GaAs surface during and after plasma processing was undertaken. Surface compositional changes after plasma treatment, prior to surface analysis are considered, with particular reference to the oxides formed in the air on the activated surface. Samples exposed to ambient air for different periods of time and also to pure oxygen were analysed. Models of surface processes were proposed for explanation of the stoichiometry changes observed with the inert and reactive plasmas used. In order to help with the understanding of the mechanisms responsible for surface effects during plasma treatment, computer simulation using SRIM code was also undertaken. Based on simulation and experimental results, models of surface phenomena are proposed. Discussion of the experimental and simulated results is made in accordance with current theories and published results of different authors. The experimental errors introduced by impurities and also by data acquisition and processing are also evaluated.