Chatter, sticking and chaotic impacting motion in a two-degree of freedom impact oscillator

We consider the dynamics of a two-degree of freedom impact oscillator subject to a motion limiting constraint. These systems exhibit a range of periodic and nonperiodic impact motions. For a particular set of parameters, we consider the bifurcations which occur between differing regimes of impacting motion and in particular those which occur due to a grazing bifurcation. Unexpected resonant behavior is also observed, due to the complexity of the dynamics. We consider both periodic and chaotic chatter motions and the regions of sticking which exist. Finally we consider the types of chaotic motion that occur within the parameter range. We discuss the possibility in relating successive low velocity impacts, especially with respect to possible low dimensional mappings for such a system

Simple model of bouncing ball dynamics. Displacement of the limiter assumed as a cubic function of time

Nonlinear dynamics of a bouncing ball moving vertically in a gravitational field and colliding with a moving limiter is considered and the Poincare map, describing evolution from an impact to the next impact, is described. Displacement of the limiter is assumed as periodic, cubic function of time. Due to simplicity of this function analytical computations are possible. Several dynamical modes, such as fixed points, 2 - cycles and chaotic bands are studied analytically and numerically. It is shown that chaotic bands are created from fixed points after first period doubling in a corner-type bifurcation. Equation for the time of the next impact is solved exactly for the case of two subsequent impacts occurring in the same period of limiter's motion making analysis of chattering possible.Comment: 8 pages, 1 figure, presented at the DSTA 2011 conference, Lodz, Polan

Multilayer Corrosion of Aluminum Activated by Lead

Segregation of Pb as a nanofilm between the thermal oxide and the metal substrate as a result of high temperature heat-treatment is known to activate aluminum alloys anodically in chloride solution. The relationship between the oxidation peaks in the polarization curve and corrosion morphology was investigated by the use of a video technique during electrochemical polarization. A model binary Al–Pb alloy containing 20 ppm Pb, which was annealed at 600°C, showed two oxidation peaks at −0.95 and −0.88 V_SCE. The video measurements revealed superficial etching of the surface by selective oxidation of the aluminum metal twice, followed each time by repassivation, as the two oxidation peaks were resolved during anodic potentiodynamic sweep. Ex situ scanning and transmission electron microscopy of the corroded specimens indicated that the first layer of etching followed the Pb film and undermined the thermal oxide, which remained attached to the metal surface at discrete locations, thereby forming a crevice. The second layer of attack was caused by crevice corrosion of the aluminum substrate in the crevice formed by the preceding oxidation process, which resulted in the removal of the attached thermal oxide film. The exposed aluminum substrate started to pit as the pitting potential was finally exceeded

Rotating strings

Analytical expressions are provided for the configurations of an inextensible, flexible, twistable inertial string rotating rigidly about a fixed axis. Solutions with trivial radial dependence are helices of arbitrary radius and pitch. Non-helical solutions are governed by a cubic equation whose roots delimit permissible values of the squared radial coordinate. Only curves coplanar with the axis of rotation make contact with it.Comment: added to discussion and made small revisions to tex

Researching "British [Muslim] Values": Vernacular politics, digital storytelling, and participant researchers

This article reflects on methodological decisions, strategies, and challenges from a recent interdisciplinary project on the relationship between ‘British values’ and Islam. The project employed digital storytelling to access ‘everyday’ conceptions and constructions of this contentious relationship. The research was undertaken by participant researchers recruited from Muslim communities in the UK’s East Anglia region, working with academics from media studies and political science. In this article we offer a detailed account of key moments relating especially to recruitment, retention, and the production of digital content. It offers two contributions. First, methodological guidance for researchers interested in combining participatory research with digital storytelling. And, second, rationale for so doing given the methodology’s scope for producing rich visual content with capacity (i) to deepen and disrupt established knowledge, and (ii) to change the views, ideas and aspirations of those involved in the content’s creation

Cerebral palsy in a total population of 4–11 year olds in southern Sweden. Prevalence and distribution according to different CP classification systems

<p>Abstract</p> <p>Background</p> <p>The aim of this study was to investigate the prevalence of cerebral palsy (CP) as well as to characterize the CP population, its participation in a secondary prevention programme (CPUP) and to validate the CPUP database.</p> <p>Methods</p> <p>The study population was born 1990–1997 and resident in Skåne/Blekinge on Jan 1^st2002. Multiple sources were used. Irrespective of earlier diagnoses, neuropaediatrician and other professional medical records were evaluated for all children at the child habilitation units. The CPUP database and diagnosis registers at hospital departments were searched for children with CP or psychomotor retardation, whose records were then evaluated. To enhance early prevention, CP/probable CP was searched for also in children below four years of age born 1998–2001.</p> <p>Results</p> <p>The prevalence of CP was 2.4/1,000 (95% CI 2.1–2.6) in children 4–11 years of age born in Sweden, excluding post-neonatally acquired CP. Children born abroad had a higher prevalence of CP with more severe functional limitations. In the total population, the prevalence of CP was 2.7/1,000 (95% CI 2.4–3.0) and 48% were GMFCS-level I (the mildest limitation of gross motor function).</p> <p>One third of the children with CP, who were born or had moved into the area after a previous study in 1998, were not in the CPUP database. The subtype classification in the CPUP database was adjusted in the case of every fifth child aged 4–7 years not previously reviewed.</p> <p>Conclusion</p> <p>The prevalence of CP and the subtype distribution did not differ from that reported in other studies, although the proportion of mild CP tended to be higher.</p> <p>The availability of a second opinion about the classification of CP/CP subtypes is necessary in order to keep a CP register valid, as well as an active search for undiagnosed CP among children with other impairments.</p

Long-term outcomes five years after selective dorsal rhizotomy

<p>Abstract</p> <p>Background</p> <p>Selective dorsal rhizotomy (SDR) is a well accepted neurosurgical procedure performed for the relief of spasticity interfering with motor function in children with spastic cerebral palsy (CP). The goal is to improve function, but long-term outcome studies are rare. The aims of this study were to evaluate long-term functional outcomes, safety and side effects during five postoperative years in all children with diplegia undergoing SDR combined with physiotherapy.</p> <p>Methods</p> <p>This study group consisted of 35 children, consecutively operated, with spastic diplegia, of which 26 were Gross Motor Function Classification System (GMFCS) levels III–V. Mean age was 4.5 years (range 2.5–6.6). They were all assessed by the same multidisciplinary team at pre- and at 6, 12, 18 months, 3 and 5 years postoperatively. Clinical and demographic data, complications and number of rootlets cut were prospectively registered. Deep tendon reflexes and muscle tone were examined, the latter graded with the modified Ashworth scale. Passive range of motion (PROM) was measured with a goniometer. Motor function was classified according to the GMFCS and measured with the Gross Motor Function Measure (GMFM-88) and derived into GMFM-66. Parent's opinions about the children's performance of skills and activities and the amount of caregiver assistance were measured with Pediatric Evaluation Disability Inventory (PEDI).</p> <p>Results</p> <p>The mean proportion of rootlets cut in S2-L2 was 40%. Muscle tone was immediately reduced in adductors, hamstrings and dorsiflexors (p < 0.001) with no recurrence of spasticity over the 5 years. For GMFCS-subgroups I–II, III and IV–V significant improvements during the five years were seen in PROM for hip abduction, popliteal angle and ankle dorsiflexion (p = 0.001), capacity of gross motor function (GMFM) (p = 0.001), performance of functional skills and independence in self-care and mobility (PEDI) (p = 0.001).</p> <p>Conclusion</p> <p>SDR is a safe and effective method for reducing spasticity permanently without major negative side effects. In combination with physiotherapy, in a group of carefully selected and systematically followed young children with spastic diplegia, it provides lasting functional benefits over a period of at least five years postoperatively.</p