Turbulent transition in a truncated one-dimensional model for shear flow

We present a reduced model for the transition to turbulence in shear flow that is simple enough to admit a thorough numerical investigation while allowing spatio-temporal dynamics that are substantially more complex than those allowed in previous modal truncations. Our model allows a comparison of the dynamics resulting from initial perturbations that are localised in the spanwise direction with those resulting from sinusoidal perturbations. For spanwise-localised initial conditions the subcritical transition to a `turbulent' state (i) takes place more abruptly, with a boundary between laminar and `turbulent' flow that is appears to be much less `structured' and (ii) results in a spatiotemporally chaotic regime within which the lifetimes of spatiotemporally complicated transients are longer, and are even more sensitive to initial conditions. The minimum initial energy $E_0$ required for a spanwise-localised initial perturbation to excite a chaotic transient has a power-law scaling with Reynolds number $E_0 \sim Re^p$ with $p \approx -4.3$. The exponent $p$ depends only weakly on the width of the localised perturbation and is lower than that commonly observed in previous low-dimensional models where typically $p \approx -2$. The distributions of lifetimes of chaotic transients at fixed Reynolds number are found to be consistent with exponential distributions.Comment: 22 pages. 11 figures. To appear in Proc. Roy. Soc.

The meandering instability of a viscous thread

A viscous thread falling from a nozzle onto a surface exhibits the famous rope-coiling effect, in which the thread buckles to form loops. If the surface is replaced by a belt moving with speed $U$, the rotational symmetry of the buckling instability is broken and a wealth of interesting states are observed [See S. Chiu-Webster and J. R. Lister, J. Fluid Mech., {\bf 569}, 89 (2006)]. We experimentally studied this "fluid mechanical sewing machine" in a new, more precise apparatus. As $U$ is reduced, the steady catenary thread bifurcates into a meandering state in which the thread displacements are only transverse to the motion of the belt. We measured the amplitude and frequency $\omega$ of the meandering close to the bifurcation. For smaller $U$, single-frequency meandering bifurcates to a two-frequency "figure eight" state, which contains a significant $2\omega$ component and parallel as well as transverse displacements. This eventually reverts to single-frequency coiling at still smaller $U$. More complex, highly hysteretic states with additional frequencies are observed for larger nozzle heights. We propose to understand this zoology in terms of the generic amplitude equations appropriate for resonant interactions between two oscillatory modes with frequencies $\omega$ and $2\omega$. The form of the amplitude equations captures both the axisymmetry of the U=0 coiling state and the symmetry-breaking effects induced by the moving belt.Comment: 12 pages, 9 figures, revised, resubmitted to Physical Review

Ion-Beam Induced Current in High-Resistance Materials

The peculiarities of electric current in high-resistance materials, such as semiconductors or semimetals, irradiated by ion beams are considered. It is shown that after ion--beam irradiation an unusual electric current may arise directed against the applied voltage. Such a negative current is a transient effect appearing at the initial stage of the process. The possibility of using this effect for studying the characteristics of irradiated materials is discussed. A new method for defining the mean projected range of ions is suggested.Comment: 1 file, 7 pages, RevTex, no figure

Resonance bifurcations from robust homoclinic cycles

We present two calculations for a class of robust homoclinic cycles with symmetry Z_n x Z_2^n, for which the sufficient conditions for asymptotic stability given by Krupa and Melbourne are not optimal. Firstly, we compute optimal conditions for asymptotic stability using transition matrix techniques which make explicit use of the geometry of the group action. Secondly, through an explicit computation of the global parts of the Poincare map near the cycle we show that, generically, the resonance bifurcations from the cycles are supercritical: a unique branch of asymptotically stable period orbits emerges from the resonance bifurcation and exists for coefficient values where the cycle has lost stability. This calculation is the first to explicitly compute the criticality of a resonance bifurcation, and answers a conjecture of Field and Swift in a particular limiting case. Moreover, we are able to obtain an asymptotically-correct analytic expression for the period of the bifurcating orbit, with no adjustable parameters, which has not proved possible previously. We show that the asymptotic analysis compares very favourably with numerical results.Comment: 24 pages, 3 figures, submitted to Nonlinearit

Improving access to exercise for people with neurological conditions

The pioneering research carried out by Brookes’ Movement Science Group (under the umbrella of the Centre for Rehabilitation) into the barriers and benefits of safe community led exercise for people with long-term neurological conditions, has significantly improved quality of life for many sufferers. Their research has raised awareness amongst healthcare and fitness professionals, and led to specific measures being put in place to facilitate and encourage exercise. These measures include the development of: clinical exercise and rehabilitation units, web-based physical activity support system, national occupational standards, and the only level 4 accredited exercise training course in the UK. The research has also led to the establishment of a registered charity that aims to increase exercise participation of people with long-term neurological conditions across the UK

Novel Generic Models for Differentiating Stem Cells Reveal Oscillatory Mechanisms

Understanding cell fate selection remains a central challenge in developmental biology. We present a class of simple yet biologically-motivated mathematical models for cell differentiation that generically generate oscillations and hence suggest alternatives to the standard framework based on Waddington's epigenetic landscape. The models allow us to suggest two generic dynamical scenarios that describe the differentiation process. In the first scenario gradual variation of a single control parameter is responsible for both entering and exiting the oscillatory regime. In the second scenario two control parameters vary: one responsible for entering, and the other for exiting the oscillatory regime. We analyse the standard repressilator and four variants of it and show the dynamical behaviours associated with each scenario. We present a thorough analysis of the associated bifurcations and argue that gene regulatory networks with these repressilator-like characteristics are promising candidates to describe cell fate selection through an oscillatory process

Wearable accelerometry-based technology capable of assessing functional activities in neurological populations in community settings: a systematic review

Background: Integrating rehabilitation services through wearable systems has the potential to accurately assess the type, intensity, duration, and quality of movement necessary for procuring key outcome measures. Objectives: This review aims to explore wearable accelerometry-based technology (ABT) capable of assessing mobility-related functional activities intended for rehabilitation purposes in community settings for neurological populations. In this review, we focus on the accuracy of ABT-based methods, types of outcome measures, and the implementation of ABT in non-clinical settings for rehabilitation purposes. Data sources: Cochrane, PubMed, Web of Knowledge, EMBASE, and IEEE Xplore. The search strategy covered three main areas, namely wearable technology, rehabilitation, and setting. Study selection: Potentially relevant studies were categorized as systems either evaluating methods or outcome parameters. Methods: Methodological qualities of studies were assessed by two customized checklists, depending on their categorization and rated independently by three blinded reviewers. Results: Twelve studies involving ABT met the eligibility criteria, of which three studies were identified as having implemented ABT for rehabilitation purposes in non-clinical settings. From the twelve studies, seven studies achieved high methodological quality scores. These studies were not only capable of assessing the type, quantity, and quality measures of functional activities, but could also distinguish healthy from non-healthy subjects and/or address disease severity levels. Conclusion: While many studies support ABT’s potential for telerehabilitation, few actually utilized it to assess mobility-related functional activities outside laboratory settings. To generate more appropriate outcome measures, there is a clear need to translate research findings and novel methods into practice