Discrete phase-locked loop systems and spreadsheets

This paper demonstrates the use of a spreadsheet in exploring non-linear difference equations that describe digital control systems used in radio engineering, communication and computer architecture. These systems, being the focus of intensive studies of mathematicians and engineers over the last 40 years, may exhibit extremely complicated behaviour interpreted in contemporary terms as transition from global asymptotic stability to chaos through period-doubling bifurcations. The authors argue that embedding advanced mathematical ideas in the technological tool enables one to introduce fundamentals of discrete control systems in tertiary curricula without learners having to deal with complex machinery that rigorous mathematical methods of investigation require. In particular, in the appropriately designed spreadsheet environment, one can effectively visualize a qualitative difference in the behviour of systems with different types of non-linear characteristic.

Secular series and renormalization group for amplitude equations

We have developed a technique that circumvents the process of elimination of secular terms and reproduces the uniformly valid approximations, amplitude equations, and first integrals. The technique is based on a rearrangement of secular terms and their grouping into the secular series that multiplies the constants of the asymptotic expansion. We illustrate the technique by deriving amplitude equations for standard nonlinear oscillator and boundary-layer problems. © 2008 The American Physical Society.

Renormalization group interpretation of the Born and Rytov approximations

In this paper the method of renormalization group (RG) [Phys. Rev. E 54, 376 (1996)] is related to the well-known approximations of Rytov and Born used in wave propagation in deterministic and random media. Certain problems in linear and nonlinear media are examined from the viewpoint of RG and compared with the literature on Born and Rytov approximations. It is found that the Rytov approximation forms a special case of the asymptotic expansion generated by the RG, and as such it gives a superior approximation to the exact solution compared with its Born counterpart. Analogous conclusions are reached for nonlinear equations with an intensity-dependent index of refraction where the RG recovers the exact solution. © 2008 Optical Society of America.

Numerical analysis for the time distributed-order and Riesz space fractional diffusions on bounded domains

Subdiffusion equations with distributed-order fractional derivatives describe some important physical phenomena. In this paper, we consider the time distributed-order and Riesz space fractional diffusions on bounded domains with Dirichlet boundary conditions. Here, the time derivative is defined as the distributed-order fractional derivative in the Caputo sense, and the space derivative is defined as the Riesz fractional derivative. First, we discretize the integral term in the time distributed-order and Riesz space fractional diffusions using numerical approximation. Then the given equation can be written as a multi-term time–space fractional diffusion. Secondly, we propose an implicit difference method for the multi-term time–space fractional diffusion. Thirdly, using mathematical induction, we prove the implicit difference method is unconditionally stable and convergent. Also, the solvability for our method is discussed. Finally, two numerical examples are given to show that the numerical results are in good agreement with our theoretical analysis.

Examining the use of bid information in predicting the contractor’s performance

Purpose – The purpose of this paper is to examine the use of bid information, including both price and non-price factors in predicting the bidder’s performance. Design/methodology/approach – The practice of the industry was first reviewed. Data on bid evaluation and performance records of the successful bids were then obtained from the Hong Kong Housing Department, the largest housing provider in Hong Kong. This was followed by the development of a radial basis function (RBF) neural network based performance prediction model. Findings – It is found that public clients are more conscientious and include non-price factors in their bid evaluation equations. With the input variables used the information is available at the time of the bid and the output variable is the project performance score recorded during work in progress achieved by the successful bidder. It was found that past project performance score is the most sensitive input variable in predicting future performance. Research limitations/implications – The paper shows the inadequacy of using price alone for bid award criterion. The need for a systemic performance evaluation is also highlighted, as this information is highly instrumental for subsequent bid evaluations. The caveat for this study is that the prediction model was developed based on data obtained from one single source. Originality/value – The value of the paper is in the use of an RBF neural network as the prediction tool because it can model non-linear function. This capability avoids tedious ‘‘trial and error’’ in deciding the number of hidden layers to be used in the network model. Keywords Hong Kong, Construction industry, Neural nets, Modelling, Bid offer spreads Paper type Research paper

The effect of monocular and binocular cataract blur on postural stability among older adults

Purpose: First-eye cataract surgery can reduce the rate of falls among older adults, yet the effect of second-eye surgery on the rate of falling remains unclear. The present study investigated the effect of monocular and binocular simulated cataract blur on postural stability among older adults. Methods: Postural stability was assessed on 34 healthy older adults (mean 68.2 years, SD 3.5) with normal vision, using a portable force platform (BT4, HUR Labs, Finland) which collected data on centre of pressure (COP) displacement. Stability was assessed on firm and foam surfaces under four binocular viewing conditions using Vistech filters to simulate cataract blur: [1] best-corrected vision both eyes; [2] blur over non-dominant eye, [3] blur over dominant eye and [4] blur over both eyes. Binocular logMAR visual acuity, Pelli-Robson contrast sensitivity and stereoacuity were also measured under these viewing conditions and ocular dominance measured using the hole-in-card test. Generalized estimating equations with an exchangeable correlation structure examined the effect of the surface and vision conditions on postural stability. Results: Visual acuity and contrast sensitivity were significantly reduced under monocular and binocular cataract blur compared to normal viewing. All blur conditions resulted in loss of stereoacuity. Binocular cataract blur significantly reduced postural stability compared to normal vision on the firm (COP path length; p=0.013) and foam surface (anterior-posterior COP RMS, COP path length and COP area; p<0.01). However, no significant differences in postural stability were found between the monocular blur conditions compared to normal vision, or between the dominant and non-dominant monocular blur conditions on either the firm or foam surfaces. Conclusions: Findings indicate that binocular blur significantly impairs postural stability, and suggests that improvements in postural stability may justify first-eye cataract surgery, particularly during somatosensory disruption. Postural stability was not significantly impaired in the monocular cataract blur conditions compared to the normal vision condition, nor was there any effect of ocular dominance on postural stability in the presence of monocular cataract blur.

Spectroscopy of selected copper group minerals : chalcophyllite and chenevixite-implications for hydrogen bonding

NIR and IR spectroscopy has been applied for detection of chemical species and the nature of hydrogen bonding in arsenate complexes. The structure and spectral properties of copper(II) arsenate minerals chalcophyllite and chenevixite are compared with copper(II) sulphate minerals devilline, chalcoalumite and caledonite. Split NIR bands in the electronic spectrum of two ranges 11700-8500 cm-1 and 8500-7200 cm-1 confirm distortion of octahedral symmetry for Cu(II) in the arsenate complexes. The observed bands with maxima at 9860 and 7750 cm-1 are assigned to Cu(II) transitions 2B1g ® 2B2g and 2B1g ® 2A1g. Overlapping bands in the NIR region 4500-4000 cm-1 is the effect of multi anions OH-, (AsO4)3- and (SO4)2-. The observation of broad and diffuse bands in the range 3700-2900 cm-1 confirms strong hydrogen bonding in chalcophyllite relative to chenevixite. The position of the water bending vibrations indicates the water is strongly hydrogen bonded in the mineral structure. The strong absorption feature centred at 1644 cm-1 in chalcophyllite indicates water is strongly hydrogen bonded in the mineral structure. The H2O-bending vibrations shift to low wavenumbers in chenevixite and an additional band observed at 1390 cm-1 is related to carbonate impurity. The characterisation of IR spectra by ν3 antisymmetric stretching vibrations of (SO4)2- and (AsO4)3 ions near 1100 and 800 cm-1 respectively is the result of isomorphic substitution for arsenate by sulphate in both the minerals of chalcophyllite and chenevixite.

An analytical and experimental study of the vibration response of a clamped ribbed plate

An analytical solution is presented in this paper for the vibration response of a ribbed plate clamped on all its boundary edges by employing a travelling wave solution. A clamped ribbed plate test rig is also assembled in this study for the experimental investigation of the ribbed plate response and to provide verification results to the analytical solution. The dynamic characteristics and mode shapes of the ribbed plate are measured and compared to those obtained from the analytical solution and from finite element analysis (FEA). General good agreements are found between the results. Discrepancies between the computational and experimental results at low and high frequencies are also discussed. Explanations are offered in the study to disclose the mechanism causing the discrepancies. The dependency of the dynamic response of the ribbed plate on the distance between the excitation force and the rib is also investigated experimentally. It confirms the findings disclosed in a previous analytical study [T. R. Lin and J. Pan, A closed form solution for the dynamic response of finite ribbed plates. Journal of the Acoustical Society of America 119 (2006) 917-925] that the vibration response of a clamped ribbed plate due to a point force excitation is controlled by the plate stiffness when the source is more than a quarter plate bending wavelength away from the rib and from the plate boundary. The response is largely affected by the rib stiffness when the source location is less than a quarter bending wavelength away from the rib.

Binocular summation improves performance to defocus-induced blur

PURPOSE. To assess whether there are any advantages of binocular over monocular vision under blur conditions. METHODS. We measured the effect of defocus, induced by positive lenses, on the pattern reversal Visual Evoked Potential (VEP) and on visual acuity (VA). Monocular (dominant eye) and binocular VEPs were recorded from thirteen volunteers (average age: 28±5 years, average spherical equivalent: -0.25±0.73 D) for defocus up to 2.00 D using positive powered lenses. VEPs were elicited using reversing 10 arcmin checks at a rate of 4 reversals/second. The stimulus subtended a circular field of 7 degrees with 100% contrast and mean luminance 30 cd/m2. VA was measured under the same conditions using ETDRS charts. All measurements were performed at 1m viewing distance with best spectacle sphero-cylindrical correction and natural pupils. RESULTS. With binocular stimulation, amplitudes and implicit times of the P100 component of the VEPs were greater and shorter, respectively, in all cases than for monocular stimulation. Mean binocular enhancement ratio in the P100 amplitude was 2.1 in-focus, increasing linearly with defocus to be 3.1 at +2.00 D defocus. Mean peak latency was 2.9 ms shorter in-focus with binocular than for monocular stimulation, with the difference increasing with defocus to 8.8 ms at +2.00 D. As for the VEP amplitude, VA was always better with binocular than with monocular vision, with the difference being greater for higher retinal blur. CONCLUSIONS. Both subjective and electrophysiological results show that binocular vision ameliorates the effect of defocus. The increased binocular facilitation observed with retinal blur may be due to the activation of a larger population of neurons at close-to-threshold detection under binocular stimulation.

Normative influences across cultures : conceptual differences and potential confounders among drivers in Australia and China

Normative influences on road user behaviour have been well documented and include such things as personal, group, subjective and moral norms. Commonly, normative factors are examined within one cultural context, although a few examples of exploring the issue across cultures exist. Such examples add to our understanding of differences in perceptions of the normative factors that may exert influence on road users and can assist in determining whether successful road safety interventions in one location may be successful in another. Notably, the literature is relatively silent on such influences in countries experiencing rapidly escalating rates of motorization. China is one such country where new drivers are taking to the roads in unprecedented numbers and authorities are grappling with the associated challenges. This paper presents results from qualitative and quantitative research on self-reported driving speeds of car drivers and related issues in Australia and China. Focus group interviews and questionnaires conducted in each country examined normative factors that might influence driving in each cultural context. Qualitative findings indicated perceptions of community acceptance of speeding were present in both countries but appeared more widespread in China, yet quantitative results did not support this difference. Similarly, with regard to negative social feedback from speeding, qualitative findings suggested no embarrassment associated with speeding among Chinese participants and mixed results among Australian participants, yet quantitative results indicated greater embarrassment for Chinese drivers. This issue was also examined from the perspective of self-identity and findings were generally similar across both samples and appear related to whether it is important to be perceived as a skilled/safe driver by others. An interesting and important finding emerged with regard to how Chinese drivers may respond to questions about road safety issues if the answers might influence foreigners’ perceptions of China. In attempting to assess community norms associated with speeding, participants were asked to describe what they would tell a foreign visitor about the prevalence of speeding in China. Responses indicated that if asked by a foreigner, people may answer in a manner that portrayed China as a safe country (e.g., that drivers do not speed), irrespective of the actual situation. This ‘faking good for foreigners’ phenomenon highlights the importance of considering ‘face’ when conducting research in China – a concept absent from the road safety literature. An additional noteworthy finding that has been briefly described in the road safety literature is the importance and strength of the normative influence of social networks (guanxi) in China. The use of personal networks to assist in avoiding penalties for traffic violations was described by Chinese participants and is an area that could be addressed to strengthen the deterrent effect of traffic law enforcement. Overall, the findings suggest important considerations for developing and implementing road safety countermeasures in different cultural contexts.

Pulse dynamics in a three-component system : existence analysis

In this article, we analyze the three-component reaction-diffusion system originally developed by Schenk et al. (PRL 78:3781–3784, 1997). The system consists of bistable activator-inhibitor equations with an additional inhibitor that diffuses more rapidly than the standard inhibitor (or recovery variable). It has been used by several authors as a prototype three-component system that generates rich pulse dynamics and interactions, and this richness is the main motivation for the analysis we present. We demonstrate the existence of stationary one-pulse and two-pulse solutions, and travelling one-pulse solutions, on the real line, and we determine the parameter regimes in which they exist. Also, for one-pulse solutions, we analyze various bifurcations, including the saddle-node bifurcation in which they are created, as well as the bifurcation from a stationary to a travelling pulse, which we show can be either subcritical or supercritical. For two-pulse solutions, we show that the third component is essential, since the reduced bistable two-component system does not support them. We also analyze the saddle-node bifurcation in which two-pulse solutions are created. The analytical method used to construct all of these pulse solutions is geometric singular perturbation theory, which allows us to show that these solutions lie in the transverse intersections of invariant manifolds in the phase space of the associated six-dimensional travelling wave system. Finally, as we illustrate with numerical simulations, these solutions form the backbone of the rich pulse dynamics this system exhibits, including pulse replication, pulse annihilation, breathing pulses, and pulse scattering, among others.