Bifurcations to travelling planar spots in a three-component FitzHugh-Nagumo system

In this article, we analyse bifurcations from stationary stable spots to travelling spots in a planar three-component FitzHugh-Nagumo system that was proposed previously as a phenomenological model of gas-discharge systems. By combining formal analyses, center-manifold reductions, and detailed numerical continuation studies, we show that, in the parameter regime under consideration, the stationary spot destabilizes either through its zeroth Fourier mode in a Hopf bifurcation or through its first Fourier mode in a pitchfork or drift bifurcation, whilst the remaining Fourier modes appear to create only secondary bifurcations. Pitchfork bifurcations result in travelling spots, and we derive criteria for the criticality of these bifurcations. Our main finding is that supercritical drift bifurcations, leading to stable travelling spots, arise in this model, which does not seem possible for its two-component version.

Existence of travelling wave solutions for a model of tumour invasion

The existence of travelling wave solutions to a haptotaxis dominated model is analysed. A version of this model has been derived in Perumpanani et al. (1999) to describe tumour invasion, where diffusion is neglected as it is assumed to play only a small role in the cell migration. By instead allowing diffusion to be small, we reformulate the model as a singular perturbation problem, which can then be analysed using geometric singular perturbation theory. We prove the existence of three types of physically realistic travelling wave solutions in the case of small diffusion. These solutions reduce to the no diffusion solutions in the singular limit as diffusion as is taken to zero. A fourth travelling wave solution is also shown to exist, but that is physically unrealistic as it has a component with negative cell population. The numerical stability, in particular the wavespeed of the travelling wave solutions is also discussed.

A geometric construction of travelling wave solutions to the Keller–Segel model

We study a version of the Keller–Segel model for bacterial chemotaxis, for which exact travelling wave solutions are explicitly known in the zero attractant diffusion limit. Using geometric singular perturbation theory, we construct travelling wave solutions in the small diffusion case that converge to these exact solutions in the singular limit.

Desorption electrospray ionisation mass spectrometry of stabilised polyesters reveals activation of hindered amine light stabilisers

The use of hindered amine light stabilizers (HALS) to retard thermo- and photo-degradation of polymers has become increasingly common. Proposed mechanisms of polymer stabilisation involve significant changes to the HALS chemical structure; however, reports of the characterisation of these modified chemical species are limited. To better understand the fate of HALS and determine their in situ modifications, desorption electrospray ionisation mass spectrometry (DESI-MS) was employed to characterise ten commercially available HALS present in polyester-based coil coatings. TINUVIN® 770, 292, 144, 123, 152, and NOR371; HOSTAVIN® 3052, 3055, 3050, and 3058 were separately formulated with a pigmented, thermosetting polyester resin, cured on metal at 262 C and analysed directly by DESI-MS. High-level ab initio molecular orbital theory calculations were also undertaken to aid the mechanistic interpretation of the results. For HALS containing N-substituted piperidines (i.e., N-CH3, N-C(O)CH3, and N-OR) a secondary piperidine (N-H) analogue was detected in all cases. The formation of these intermediates can be explained either through hydrogen abstraction based mechanisms or direct N-OR homolysis with the former dominant under normal service temperatures (ca. 25-80 C), and the latter potentially becoming competitive under the high temperatures associated with curing (ca. 230-260 C). © 2013 Elsevier Ltd. All rights reserved.

Understanding the abnormal brain activity in epilepsy as a potential predictor of the onset of an epileptic seizure

The Brain Research Institute (BRI) uses various types of indirect measurements, including EEG and fMRI, to understand and assess brain activity and function. As well as the recovery of generic information about brain function, research also focuses on the utilisation of such data and understanding to study the initiation, dynamics, spread and suppression of epileptic seizures. To assist with the future focussing of this aspect of their research, the BRI asked the MISG 2010 participants to examine how the available EEG and fMRI data and current knowledge about epilepsy should be analysed and interpreted to yield an enhanced understanding about brain activity occurring before, at commencement of, during, and after a seizure. Though the deliberations of the study group were wide ranging in terms of the related matters considered and discussed, considerable progress was made with the following three aspects. (1) The science behind brain activity investigations depends crucially on the quality of the analysis and interpretation of, as well as the recovery of information from, EEG and fMRI measurements. A number of specific methodologies were discussed and formalised, including independent component analysis, principal component analysis, profile monitoring and change point analysis (hidden Markov modelling, time series analysis, discontinuity identification). (2) Even though EEG measurements accurately and very sensitively record the onset of an epileptic event or seizure, they are, from the perspective of understanding the internal initiation and localisation, of limited utility. They only record neuronal activity in the cortical (surface layer) neurons of the brain, which is a direct reflection of the type of electrical activity they have been designed to record. Because fMRI records, through the monitoring of blood flow activity, the location of localised brain activity within the brain, the possibility of combining fMRI measurements with EEG, as a joint inversion activity, was discussed and examined in detail. (3) A major goal for the BRI is to improve understanding about ``when'' (at what time) an epileptic seizure actually commenced before it is identified on an eeg recording, ``where'' the source of this initiation is located in the brain, and ``what'' is the initiator. Because of the general agreement in the literature that, in one way or another, epileptic events and seizures represent abnormal synchronisations of localised and/or global brain activity the modelling of synchronisations was examined in some detail. References C. M. Michel, G. Thut, S. Morand, A. Khateb, A. J. Pegna, R. Grave de Peralta, S. Gonzalez, M. Seeck and T. Landis, Electric source imaging of human brain functions, Brain Res. Rev. , 36 (2--3), 2001, 108--118. doi:10.1016/S0165-0173(01)00086-8 S. Ogawa, R. S. Menon, S. G. Kim and K. Ugurbil, On the characteristics of functional magnetic resonance imaging of the brain, Annu. Rev. Bioph. Biom. , 27 , 1998, 447--474. doi:10.1146/annurev.biophys.27.1.447 C. D. Binnie and H. Stefan, Modern electroencephalography: its role in epilepsy management, Clin. Neurophysiol. , 110 (10), 1999, 1671--1697. doi:10.1016/S1388-2457(99)00125-X J. X. Tao, A. Ray, S. Hawes-Ebersole and J. S. Ebersole, Intracranial eeg substrates of scalp eeg interictal spikes, Epilepsia , 46 (5), 2005, 669--76. doi:10.1111/j.1528-1167.2005.11404.x S. Ogawa, D. W. Tank, R. Menon, J. M. Ellermann, S. G. Kim, H. Merkle and K. Ugurbil, Intrinsic signal changes accompanying sensory stimulation: Functional brain mapping with magnetic resonance imaging, P. Natl. Acad. Sci. USA , 89 (13), 1992, 5951--5955. doi:10.1073/pnas.89.13.5951 J. Engel Jr., Report of the ilae classification core group, Epilepsia , 47 (9), 2006, 1558--1568. doi:10.1111/j.1528-1167.2006.00215.x L. Lemieux, A. Salek-Haddadi, O. Josephs, P. Allen, N. Toms, C. Scott, K. Krakow, R. Turner and D. R. Fish, Event-related fmri with simultaneous and continuous eeg: description of the method and initial case r port, NeuroImage , 14 (3), 2001, 780--7. doi:10.1006/nimg.2001.0853 P. Federico, D. F. Abbott, R. S. Briellmann, A. S. Harvey and G. D. Jackson, Functional mri of the pre-ictal state, Brain , 128 (8), 2005, 1811-7. doi:10.1093/brain/awh533 C. S. Hawco, A. P. Bagshaw, Y. Lu, F. Dubeau and J. Gotman, bold changes occur prior to epileptic spikes seen on scalp eeg, NeuroImage , 35 (4), 2007, 1450--1458. doi:10.1016/j.neuroimage.2006.12.042 F. Moeller, H. R. Siebner, S. Wolff, H. Muhle, R. Boor, O. Granert, O. Jansen, U. Stephani and M. Siniatchkin, Changes in activity of striato-thalamo-cortical network precede generalized spike wave discharges, NeuroImage , 39 (4), 2008, 1839--1849. doi:10.1016/j.neuroimage.2007.10.058 V. Osharina, E. Ponchel, A. Aarabi, R. Grebe and F. Wallois, Local haemodynamic changes preceding interictal spikes: A simultaneous electrocorticography (ecog) and near-infrared spectroscopy (nirs) analysis in rats, NeuroImage , 50 (2), 2010, 600--607. doi:10.1016/j.neuroimage.2010.01.009 R. S. Fisher, W. Boas, W. Blume, C. Elger, P. Genton, P. Lee and J. Engel, Epileptic seizures and epilepsy: Definitions proposed by the international league against epilepsy (ilae) and the international bureau for epilepsy (ibe), Epilepsia , 46 (4), 2005, 470--472. doi:10.1111/j.0013-9580.2005.66104.x H. Berger, Electroencephalogram in humans, Arch. Psychiat. Nerven. , 87 , 1929, 527--570. C. M. Michel, M. M. Murray, G. Lantz, S. Gonzalez, L. Spinelli and R. G. de Peralta, eeg source imaging, Clin. Neurophysiol. , 115 (10), 2004, 2195--2222. doi:10.1016/j.clinph.2004.06.001 P. L. Nunez and R. B. Silberstein, On the relationship of synaptic activity to macroscopic measurements: Does co-registration of eeg with fmri make sense?, Brain Topogr. , 13 (2), 2000, 79--96. doi:10.1023/A:1026683200895 S. Ogawa, T. M. Lee, A. R. Kay and D. W. Tank, Brain magnetic resonance imaging with contrast dependent on blood oxygenation, P. Natl. Acad. Sci. USA , 87 (24), 1990, 9868--9872. doi:10.1073/pnas.87.24.9868 J. S. Gati, R. S. Menon, K. Ugurbil and B. K. Rutt, Experimental determination of the bold field strength dependence in vessels and tissue, Magn. Reson. Med. , 38 (2), 1997, 296--302. doi:10.1002/mrm.1910380220 P. A. Bandettini, E. C. Wong, R. S. Hinks, R. S. Tikofsky and J. S. Hyde, Time course EPI of human brain function during task activation, Magn. Reson. Med. , 25 (2), 1992, 390--397. K. K. Kwong, J. W. Belliveau, D. A. Chesler, I. E. Goldberg, R. M. Weisskoff, B. P. Poncelet, D. N. Kennedy, B. E. Hoppelm, M. S. Cohen and R. Turner, Dynamic magnetic resonance imaging of human brain activity during primary sensory stimulation, P. Natl. Acad. Sci. USA , 89 (12), 1992, 5675--5679. doi:10.1073/pnas.89.12.5675 J. Frahm, K. D. Merboldt and W. Hnicke, Functional mri of human brain activation at high spatial resolution, Magn. Reson. Med. , 29 (1), 1993, 139--144. P. A. Bandettini, A. Jesmanowicz, E. C. Wong and J. S. Hyde, Processing strategies for time-course data sets in functional MRI of the human brain, Magn. Reson. Med. , 30 (2), 1993, 161--173. K. J. Friston, P. Jezzard and R. Turner, Analysis of functional MRI time-series, Hum. Brain Mapp. , 1 (2), 1994, 153--171. B. Biswal, F. Z. Yetkin, V. M. Haughton and J. S. Hyde, Functional connectivity in the motor cortex of resting human brain using echo-planar mri, Mag. Reson. Med. , 34 (4), 1995, 537--541. doi:10.1002/mrm.1910340409 K. J. Friston, J. Ashburner, C. D. Frith, J. Poline, J. D. Heather and R. S. J. Frackowiak, Spatial registration and normalization of images, Hum. Brain Mapp. , 3 (3), 1995, 165--189. K. J. Friston, S. Williams, R. Howard, R. S. Frackowiak and R. Turner, Movement-related effects in fmri time-series, Magn. Reson. Med. , 35 (3), 1996, 346--355. G. H. Glover, T. Q. Li and D. Ress, Image-based method for retrospective correction of physiological motion effects in fmri: Retroicor, Magn. Reson. Med. , 44 (1), 2000, 162--167. doi:10.1002/1522-2594(200007)44:13.0.CO;2-E K. J. Friston, O. Josephs, G. Rees and R. Turner, Nonlinear event-related responses in fmri, Magn. Reson. Med. , 39 (1), 1998, 41--52. doi:10.1002/mrm.1910390109 K. Ugurbil, L. Toth and D. Kim, How accurate is magnetic resonance imaging of brain function?, Trends Neurosci. , 26 (2), 2003, 108--114. doi:10.1016/S0166-2236(02)00039-5 D. S. Kim, I. Ronen, C. Olman, S. G. Kim, K. Ugurbil and L. J. Toth, Spatial relationship between neuronal activity and bold functional mri, NeuroImage , 21 (3), 2004, 876--885. doi:10.1016/j.neuroimage.2003.10.018 A. Connelly, G. D. Jackson, R. S. Frackowiak, J. W. Belliveau, F. Vargha-Khadem and D. G. Gadian, Functional mapping of activated human primary cortex with a clinical mr imaging system, Radiology , 188 (1), 1993, 125--130. L. Allison, Hidden Markov Models, Technical Report , School of Computer and Software Engineering, Monash University, 2000. R. J. Elliott, L. Aggoun and J.B. Moore, Hidden Markov Models: Estimation and Control, Appl. Math.-Czech. , 2004. B. Bhavnagri, Discontinuities of plane functions projected from a surface with methods for finding these , Technical Report, 2009. B. Bhavnagri, Computer Vision using Shape Spaces , Technical Report,1996, University of Adelaide. B. Bhavnagri, A method for representing shape based on an equivalence relation on polygons, Pattern Recogn. , 27 (2), 1994, 247--260. doi:10.1016/0031-3203(94)90057-4 D. F. Abbott, A. B. Waites, A. S. Harvey and G. D. Jackson, Exploring epileptic seizure onset with fmri, NeuroImage , 36(S1) (344TH-PM), 2007. M. C. Mackey and L. Glass, Oscillation and chaos in physiological control systems, Science , 197 , 1977, 287--289. S. H. Strogatz, SYNC - The Emerging Science of Spontaneous Order , Theia, New York, 2003. J. W. Kim, J. A. Roberts and P. A. Robinson, Dynamics of epileptic seizures: Evolution, spreading, and suppression, J. Theor. Biol. , 257 (4), 2009, 527--532. doi:10.1016/j.jtbi.2008.12.009 Y. Kuramoto, T. Aoyagi, I. Nishikawa, T. Chawanya T and K. Okuda, Neural network model carrying phase information with application to collective dynamics, J. Theor. Phys. , 87 (5), 1992, 1119--1126. V. B. Mountcastle, The columnar organization of the neocortex, Brain , 120 (4), 1997, 701. doi:10.1093/brain/120.4.701 F. L. Silva, W. Blanes, S. N. Kalitzin, J. Parra, P. Suffczynski and D. N. Velis, Epilepsies as dynamical diseases of brain systems: Basic models of the transition between normal and epileptic activity, Epilepsia , 44 (12), 2003, 72--83. F. H. Lopes da Silva, W. Blanes, S. N. Kalitzin, J. Parra, P. Suffczynski and D. N. Velis, Dynamical diseases of brain systems: different routes to epileptic seizures, ieee T. Bio-Med. Eng. , 50 (5), 2003, 540. L.D. Iasemidis, Epileptic seizure prediction and control, ieee T. Bio-Med. Eng. , 50 (5), 2003, 549--558. L. D. Iasemidis, D. S. Shiau, W. Chaovalitwongse, J. C. Sackellares, P. M. Pardalos, J. C. Principe, P. R. Carney, A. Prasad, B. Veeramani, and K. Tsakalis, Adaptive epileptic seizure prediction system, ieee T. Bio-Med. Eng. , 50 (5), 2003, 616--627. K. Lehnertz, F. Mormann, T. Kreuz, R.G. Andrzejak, C. Rieke, P. David and C. E. Elger, Seizure prediction by nonlinear eeg analysis, ieee Eng. Med. Biol. , 22 (1), 2003, 57--63. doi:10.1109/MEMB.2003.1191451 K. Lehnertz, R. G. Andrzejak, J. Arnhold, T. Kreuz, F. Mormann, C. Rieke, G. Widman and C. E. Elger, Nonlinear eeg analysis in epilepsy: Its possible use for interictal focus localization, seizure anticipation, and prevention, J. Clin. Neurophysiol. , 18 (3), 2001, 209. B. Litt and K. Lehnertz, Seizure prediction and the preseizure period, Curr. Opin. Neurol. , 15 (2), 2002, 173. doi:10.1097/00019052-200204000-00008 B. Litt and J. Echauz, Prediction of epileptic seizures, Lancet Neurol. , 1 (1), 2002, 22--30. doi:10.1016/S1474-4422(02)00003-0 M. M{a}kiranta, J. Ruohonen, K Suominen, J. Niinim{a}ki, E. Sonkaj{a}rvi, V. Kiviniemi, T. Sepp{a}nen, S. Alahuhta, V. J{a}ntti and O. Tervonen, {bold} signal increase preceeds eeg spike activity--a dynamic penicillin induced focal epilepsy in deep anesthesia, NeuroImage , 27 (4), 2005, 715--724. doi:10.1016/j.neuroimage.2005.05.025 K. Lehnertz, F. Mormann, H. Osterhage, A. M{u}ller, J. Prusseit, A. Chernihovskyi, M. Staniek, D. Krug, S. Bialonski and C. E. Elger, State-of-the-art of seizure prediction, J. Clin. Neurophysiol. , 24 (2), 2007, 147. doi:10.1097/WNP.0b013e3180336f16 F. Mormann, T. Kreuz, C. Rieke, R. G. Andrzejak, A. Kraskov, P. David, C. E. Elger and K. Lehnertz, On the predictability of epileptic seizures, Clin. Neurophysiol. , 116 (3), 2005, 569--587. doi:10.1016/j.clinph.2004.08.025 F. Mormann, R. G. Andrzejak, C. E. Elger and K. Lehnertz, Seizure prediction: the long and winding road, Brain , 130 (2), 2007, 314--333. doi:10.1093/brain/awl241 Z. Rogowski, I. Gath and E. Bental, On the prediction of epileptic seizures, Biol. Cybern. , 42 (1), 1981, 9--15. Y. Salant, I. Gath, O. Henriksen, Prediction of epileptic seizures from two-channel eeg, Med. Biol. Eng. Comput. , 36 (5), 1998, 549--556. doi:10.1007/BF02524422 J. Gotman and D.J. Koffler, Interictal spiking increases after seizures but does not after decrease in medication, Evoked Potential , 72 (1), 1989, 7--15. J. Gotman and M. G. Marciani, Electroencephalographic spiking activity, drug levels, and seizure occurence in epileptic patients, Ann. Neurol. , 17 (6), 1985, 59--603. A. Katz, D. A. Marks, G. McCarthy and S. S. Spencer, Does interictal spiking change prior to seizures?, Electroen. Clin. Neuro. , 79 (2), 1991, 153--156. A. Granada, R. M. Hennig, B. Ronacher, A. Kramer and H. Herzel, Phase Response Curves: Elucidating the dynamics of couples oscillators, Method Enzymol. , 454 (A), 2009, 1--27. doi:10.1016/S0076-6879(08)03801-9 doi:10.1016/S0076-6879(08)03801-9 H. Kantz and T. Schreiber, Nonlinear time series analysis , 2004, Cambridge Univ Press. M. V. L. Bennett and R. S Zukin, Electrical coupling and neuronal synchronization in the mammalian brain, Neuron , 41 (4), 2004, 495 --511. doi:10.1016/S0896-6273(04)00043-1 L.D. Iasemidis, J. Chris Sackellares, H. P. Zaveri and W. J. Williams, Phase space topography and the Lyapunov exponent of electrocorticograms in partial seizures, Brain Topogr. , 2 (3), 1990, 187--201. doi:10.1007/BF01140588 M. Le Van Quyen, J. Martinerie, V. Navarro, M. Baulac and F. J. Varela, Characterizing neurodynamic changes before seizures, J. Clin. Neurophysiol. , 18 (3), 2001, 191. J. Martinerie, C. Adam, M. Le Van Quyen, M. Baulac, S. Clemenceau, B. Renault and F. J. Varela, Epileptic seizures can be anticipated by non-linear analysis, Nat. Med. , 4 (10), 1998, 1173--1176. doi:10.1038/2667 A. Pikovsky, M. Rosenblum, J. Kurths and R. C. Hilborn, Synchronization: A universal concept in nonlinear science, Amer. J. Phys. , 70 , 2002, 655. H. R. Wilson and J. D. Cowan, Excitatory and inhibitory interactions in localized populations of model neurons, Biophys. J. , 12 (1), 1972, 1--24. D. Cumin and C. P. Unsworth, Generalising the Kuramoto model for the study of neuronal synchronisation in the brain, Physica D , 226 (2), 2007, 181--196. doi:10.1016/j.physd.2006.12.004 F. K. Skinner, H. Bazzazi and S. A. Campbell, Two-cell to N-cell heterogeneous, inhibitory networks: Precise linking of multistable and coherent properties, J. Comput. Neurosci. , 18 (3), 2005, 343--352. doi:10.1007/s10827-005-0331-1 W. W. Lytton, Computer modelling of epilepsy, Nat. Rev. Neurosci. , 9 (8), 2008, 626--637. doi:10.1038/nrn2416 R. D. Traub, A. Bibbig, F. E. N. LeBeau, E. H. Buhl and M. A. Whittington, Cellular mechanisms of neuronal population oscillations in the hippocampus in vitro, Ann. Rev. , 2004. R. D. Traub, A. Draguhn, M. A. Whittington, T. Baldeweg, A. Bibbig, E. H. Buhl and D. Schmitz, Axonal gap junc ions between principal neurons: A novel source of network oscillations, and perhaps epileptogenesis., Rev. Neuroscience , 13 (1), 2002, 1. doi:10.1146/annurev.neuro.27.070203.144303 M. Scheffer, J. Bascompte, W. A. Brock, V. Brovkin, S. R. Carpenter, V. Dakos, H. Held, E. H. van Nes, M. Rietkerk and G. Sugihara, Early-warning signals for critical transitions, Nature , 461 (7260), 2009, 53--59. doi:10.1038/nature08227 K. Murphy, A Brief Introduction to Graphical Models and Bayesian Networks , 2008, http://www.cs.ubc.ca/murphyk/Bayes/bnintro.html . R. C. Bradley, An elementary

The SCRAMSPACE I scramjet flight design and construction

The design activities of the development of the SCRAMSPACE I scramjet-powered free-flight experiment are described in this paper. The objectives of this flight are first described together with the definition of the primary, secondary and tertiary experiments. The Scramjet configuration studied is first discussed together with the rocket motor system selected for this flight. The different flight sequences are then explained, highlighting the SCRAMSPACE I free-flyer separation and re-orientation procedures. A design trade-off study is then described considering vehicle stability, packaging, thermo-structural analysis and trajectory, discussing the alignment of the predicted performance with the mission scientific requirements. The global system architecture and instrumentation of the vehicle are then explained. The conclusions of this design phase are that a vehicle design has been produced which is able to meet the mission scientific goals and the procurement & construction of the vehicle are ongoing.

Residual stresses in rail-ends from the in-service insulated rail joints using neutron diffraction

Insulated rail joints (IRJs) are an integral part of the rail track signaling system and pose significant maintenance and replacement costs due to their low and fluctuating service lives. Failure occurs mainly in rail head region, bolt- holes of fishplates and web-holes of the rails. Propagation of cracks is influenced by the evolution of internal residual stresses in rails during rail manufacturing (hot-rolling, roller-straightening, and head-hardening process), and during service, particularly in heavy rail haul freight systems where loads are high. In this investigation, rail head accumulated residual stresses were analysed using neutron diffraction at the Australian Nuclear Science and Technology Organisation (ANSTO). Two ex-service two head-hardened rail joints damaged under different loading were examined and results were compared with those obtained from an unused rail joint reference sample in order to differentiate the stresses developed during rail manufacturing and stresses accumulated during rail service. Neutron diffraction analyses were carried out on the samples in longitudinal, transverse and vertical directions, and on 5mm thick sliceed samples cut by Electric Discharge Machining (EDM). For the rail joints from the service line, irrespective of loading conditions and in-service times, results revealed similar depth profiles of stress distribution. Evolution of residual stress fields in rails due to service was also accompanied by evidence of larger material flow based on reflected light and scanning electron microscopy studies. Stress evolution in the vicinity of rail ends was characterised by a compressive layer, approximately 5 mm deep, and a tension zone located approximately 5- 15mm below the surfaces. A significant variation of d0 with depth near the top surface was detected and was attributed to decarburization in the top layer induced by cold work. Stress distributions observed in longitudinal slices of the two different deformed rail samples were found to be similar. For the undeformed rail, the stress distributions obtained could be attributed to variations associated with thermo-mechanical history of the rail.

A model of workplace safety incorporating worker interactions and simple interventions

Although there was substantial research into the occupational health and safety sector over the past forty years, this generally focused on statistical analyses of data related to costs and/or fatalities and injuries. There is a lack of mathematical modelling of the interactions between workers and the resulting safety dynamics of the workplace. There is also little work investigating the potential impact of different safety intervention programs prior to their implementation. In this article, we present a fundamental, differential equation-based model of workplace safety that treats worker safety habits similarly to an infectious disease in an epidemic model. Analytical results for the model, derived via phase plane and stability analysis, are discussed. The model is coupled with a model of a generic safety strategy aimed at minimising unsafe work habits, to produce an optimal control problem. The optimal control model is solved using the forward-backward sweep numerical scheme implemented in Matlab.

CFD simulations of flow and heat transfer through the porous interface of a metal foam heat exchanger

This paper offers numerical modelling of a waste heat recovery system. A thin layer of metal foam is attached to a cold plate to absorb heat from hot gases leaving the system. The heat transferred from the exhaust gas is then transferred to a cold liquid flowing in a secondary loop. Two different foam PPI (Pores Per Inch) values are examined over a range of fluid velocities. Numerical results are then compared to both experimental data and theoretical results available in the literature. Challenges in getting the simulation results to match those of the experiments are addressed and discussed in detail. In particular, interface boundary conditions specified between a porous layer and a fluid layer are investigated. While physically one expects much lower fluid velocity in the pores compared to that of free flow, capturing this sharp gradient at the interface can add to the difficulties of numerical simulation. The existing models in the literature are modified by considering the pressure gradient inside and outside the foam. Comparisons against the numerical modelling are presented. Finally, based on experimentally-validated numerical results, thermo-hydraulic performance of foam heat exchangers as waste heat recovery units is discussed with the main goal of reducing the excess pressure drop and maximising the amount of heat that can be recovered from the hot gas stream.

Scaling laws for localised states in a nonlocal amplitude equation

It is well known that, although a uniform magnetic field inhibits the onset of small amplitude thermal convection in a layer of fluid heated from below, isolated convection cells may persist if the fluid motion within them is sufficiently vigorous to expel magnetic flux. Such fully nonlinear(‘‘convecton’’) solutions for magnetoconvection have been investigated by several authors. Here we explore a model amplitude equation describing this separation of a fluid layer into a vigorously convecting part and a magnetically-dominated part at rest. Our analysis elucidates the origin of the scaling laws observed numerically to form the boundaries in parameter space of the region of existence of these localised states, and importantly, for the lowest thermal forcing required to sustain them.

The dynamics of cellular automata on 2-manifolds is affected by topology

In this paper, we demonstrate that the distribution of Wolfram classes within a cellular automata rule space in the triangular tessellation is not consistent across different topological general. Using a statistical mechanics approach, cellular automata dynamical classes were approximated for cellular automata defined on genus-0, genus-1 and genus-2 2-manifolds. A distribution-free equality test for empirical distributions was applied to identify cases in which Wolfram classes were distributed differently across topologies. This result implies that global structure and local dynamics contribute to the long term evolution of cellular automata.

On the effect of topology on cellular automata rule spaces

This thesis presents an empirical study of the effects of topology on cellular automata rule spaces. The classical definition of a cellular automaton is restricted to that of a regular lattice, often with periodic boundary conditions. This definition is extended to allow for arbitrary topologies. The dynamics of cellular automata within the triangular tessellation were analysed when transformed to 2-manifolds of topological genus 0, genus 1 and genus 2. Cellular automata dynamics were analysed from a statistical mechanics perspective. The sample sizes required to obtain accurate entropy calculations were determined by an entropy error analysis which observed the error in the computed entropy against increasing sample sizes. Each cellular automata rule space was sampled repeatedly and the selected cellular automata were simulated over many thousands of trials for each topology. This resulted in an entropy distribution for each rule space. The computed entropy distributions are indicative of the cellular automata dynamical class distribution. Through the comparison of these dynamical class distributions using the E-statistic, it was identified that such topological changes cause these distributions to alter. This is a significant result which implies that both global structure and local dynamics play a important role in defining long term behaviour of cellular automata.

Characterization of the tail-specific protease (Tsp) from Legionella

Bacterial tail-specific proteases (Tsps) have been attributed a wide variety of functions including intracellular virulence, cell wall morphology, proteolytic signal cascades and stress response. This study tested the hypothesis that Tsp has a key function for the transmissive form of Legionella pneumophila. A tsp mutant was generated in Legionella pneumophila 130b and the characteristics of this strain and the isogenic wild-type were examined using a range of growth and proteomic analyses. Recombinant Tsp protein was also produced and analyzed. The L. pneumophila tsp mutant showed no defect in growth on rich media or during thermo-osmotic stress conditions. In addition, no defects in cellular morphology were observed when the cells were examined using transmission electron microscopy. Purified recombinant Tsp was found to be an active protease with a narrow substrate range. Proteome analysis using iTRAQ (5% coverage of the proteome) found that, of those proteins detected, only 5 had different levels in the tsp mutant compared to the wild type. ACP (Acyl Carrier Protein), which has a key role for Legionella differentiation to the infectious form, was reduced in the tsp mutant; however, tsp(-) was able to infect and replicate inside macrophages to the same extent as the wild type. Combined, these data demonstrate that Tsp is a protease but is not essential for Legionella growth or cell infection. Thus, Tsp may have functional redundancy in Legionella.

Coherent phonon decay and the boron isotope effect for MgB2

Ab-initio DFT calculations for the phonon dispersion (PD) and the Phonon Density Of States (PDOS) of the two isotopic forms (10B and 11B) of MgB2 demonstrate that use of a reduced symmetry super-lattice provides an improved approximation to the dynamical, phonon-distorted P6/mmm crystal structure. Construction of phonon frequency plots using calculated values for these isotopic forms gives linear trends with integer multiples of a base frequency that change in slope in a manner consistent with the isotope effect (IE). Spectral parameters inferred from this method are similar to that determined experimentally for the pure isotopic forms of MgB2. Comparison with AlB2 demonstrates that a coherent phonon decay down to acoustic modes is not possible for this metal. Coherent acoustic phonon decay may be an important contributor to superconductivity for MgB2.