Multistability and localization in forced cyclic symmetric structures modelled by weakly-coupled Duffing oscillators

Many engineering structures are composed of weakly coupled sectors assembled in a cyclic and ideally symmetric configuration, which can be simplified as forced Duffing oscillators. In this paper, we study the emergence of localized states in the weakly nonlinear regime. We show that multiple spatially localized solutions may exist, and the resulting bifurcation diagram strongly resembles the snaking pattern observed in a variety of fields in physics, such as optics and fluid dynamics. Moreover, in the transition from the linear to the nonlinear behaviour isolated branches of solutions are identified. Localization is caused by the hardening effect introduced by the nonlinear stiffness, and occurs at large excitation levels. Contrary to the case of mistuning, the presented localization mechanism is triggered by the nonlinearities and arises in perfectly homogeneous systems

Early onset epilepsy and inherited metabolic disorders: Diagnosis and management

Epileptic encephalopathies presenting in early life present a diagnostic and therapeutic challenge. These disorders present with multiple seizure types that are treatment resistant and associated with significant abnormalities on electroencephalographic studies. The underlying etiology in many cases may be related to an inborn error of metabolism. Efforts to establish the specific diagnosis of a genetic defect or an inborn error of metabolism often results in requests for a vast array of biochemical and molecular tests leading to an expensive workup. In this review, we present the clinician with information that provides a rationale for a selective and nuanced approach to biochemical assays, and initial treatment strategies while waiting for a specific diagnosis to be established. A careful consideration of the presentation, identification of potentially treatable conditions, and consultation with the biochemical genetics laboratory can lead to a greater measure of success while limiting cost overruns. Such a targeted approach is hoped will lead to an early diagnosis and appropriate interventions

Direct measurement of molecular stiffness and damping in confined water layers

We present {\em direct} and {\em linear} measurements of the normal stiffness and damping of a confined, few molecule thick water layer. The measurements were obtained by use of a small amplitude (0.36 $\textrm{\AA}$), off-resonance Atomic Force Microscopy (AFM) technique. We measured stiffness and damping oscillations revealing up to 7 layers separated by 2.56 $\pm$ 0.20 $\textrm{\AA}$. Relaxation times could also be calculated and were found to indicate a significant slow-down of the dynamics of the system as the confining separation was reduced. We found that the dynamics of the system is determined not only by the interfacial pressure, but more significantly by solvation effects which depend on the exact separation of tip and surface. Thus ` solidification\rq seems to not be merely a result of pressure and confinement, but depends strongly on how commensurate the confining cavity is with the molecule size. We were able to model the results by starting from the simple assumption that the relaxation time depends linearly on the film stiffness.Comment: 7 pages, 6 figures, will be submitted to PR

Hybrid phase-space simulation method for interacting Bose fields

We introduce an approximate phase-space technique to simulate the quantum dynamics of interacting bosons. With the future goal of treating Bose-Einstein condensate systems, the method is designed for systems with a natural separation into highly occupied (condensed) modes and lightly occupied modes. The method self-consistently uses the Wigner representation to treat highly occupied modes and the positive-P representation for lightly occupied modes. In this method, truncation of higher-derivative terms from the Fokker-Planck equation is usually necessary. However, at least in the cases investigated here, the resulting systematic error, over a finite time, vanishes in the limit of large Wigner occupation numbers. We tested the method on a system of two interacting anharmonic oscillators, with high and low occupations, respectively. The Hybrid method successfully predicted atomic quadratures to a useful simulation time 60 times longer than that of the positive-P method. The truncated Wigner method also performed well in this test. For the prediction of the correlation in a quantum nondemolition measurement scheme, for this same system, the Hybrid method gave excellent agreement with the exact result, while the truncated Wigner method showed a large systematic error.Comment: 13 pages; 6 figures; references added; figures correcte

Travelling and standing envelope solitons in discrete non-linear cyclic structures

International audienceEnvelope solitons are demonstrated to exist in non-linear discrete structures with cyclic symmetry. The analysis is based on the Non-Linear Schrodinger Equation for the weakly non-linear limit, and on numerical simulation of the fully non-linear equations for larger amplitudes. Envelope solitons exist for parameters in which the wave equation is focussing and they have the form of shape-conserving wave packages propagating roughly with group velocity. For the limit of maximum wave number, where the group velocity vanishes, standing wave packages result and can be linked via a bifurcation to the non-localised non-linear normal modes. Numerical applications are carried out on a simple discrete system with cyclic symmetry which can be seen as a reduced model of a bladed disk as found in turbo-machinery

Multicenter-study of operative treatment of intraligamentous tears of the anterior cruciate ligament in children and adolescents: Comparison of four different techniques

Tears of the anterior cruciate ligament in skeletally immature patients were operated with four different methods and their outcome compared to each other. Sixty-eight patients (33 males, 35 females), mean 12.5years, were treated in four different centers from 1984 to 2001. Twenty-eight patients underwent the ACL-reconstruction with hamstring grafts, 16 patients with bone-patella-bone autografts, 12 patients with quadriceps grafts and 12 patients with facia lata. The mean follow-up was 32months. Postoperative evaluation included radiographs, KT-1000/2000 stability measurements, Lysholm score, The Tegner activity scale and IKDC score. Neither leg length discrepancy nor angular deformities were noted. Mean KT-1000 difference was 2.1mm, mean postoperative Lysholm knee score 93.3, IKDC 87% normal or nearly normal. The Tegner index decreased from 6.6 to 5.7. In total, six patients developed instability due to an adequate trauma 1year after the index operation. Two patients showed mild arthrotic changes. All but two patients were able to return to the same level of preoperative sports participation. None of the four methods studied showed major differences in outcome compared to the other. No growth disturbance could be note

Development of functional network architecture explains changes in children's altruistically motivated helping

Childhood is marked by profound changes in prosocial behaviour. The underlying motivational mechanisms remain poorly understood. We investigated the development of altruistically motivated helping in middle childhood and the neurocognitive and -affective mechanisms driving this development. One-hundred and twenty seven 6–12 year-old children performed a novel gustatory costly helping task designed to measure altruistic motivations of helping behaviour. Neurocognitive and -affective mechanisms including emotion regulation, emotional clarity and attentional reorienting were assessed experimentally through an extensive task-battery while functional brain activity and connectivity were measured during an empathy for taste paradigm and during rest. Altruistically motivated helping increased with age. Out of all mechanisms probed for, only emotional clarity increased with age and accounted for altruistically motivated helping. This was associated with greater functional integration of the empathy-related network with fronto-parietal brain regions at rest. We isolate a highly specific neuroaffective mechanism as the crucial driver of altruistically motivated helping during child development

Mini-garfagem: um novo metodo para a enxertia do mogno sul-americano (Swietenia macrophylla King).

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