Memory in random bouncing ball dynamics

The bouncing of an inelastic ball on a vibrating plate is a popular model used in various fields, from granular gases to nanometer-sized mechanical contacts. For random plate motion, so far, the model has been studied using Poincar{\'e} maps in which the excitation by the plate at successive bounces is assumed to be a discrete Markovian (memoryless) process. Here, we investigate numerically the behaviour of the model for continuous random excitations with tunable correlation time. We show that the system dynamics are controlled by the ratio of the Markovian mean flight time of the ball and the mean time between successive peaks in the motion of the exciting plate. When this ratio, which depends on the bandwidth of the excitation signal, exceeds a certain value, the Markovian approach is appropriate; below, memory of preceding excitations arises, leading to a significant decrease of the jump duration; at the smallest values of the ratio, chattering occurs. Overall, our results open the way for uses of the model in the low excitation regime, which is still poorly understood.Comment: Final published version, 5 pages, 4 figure

Response of an impacting hertzian contact to an order-2 subharmonic excitation : theory and experiments

Response of a normally excited preloaded Hertzian contact is investigated in order to analyze the subharmonic resonance of order 2. The nonlinearity associated with contact losses is included. The method of multiple scales is used to obtain the non-trivial steady state solutions, their stability, and the frequency-response curves. To this end, a third order Taylor series of the elastic Hertzian contact force is introduced over the displacement interval where the system remains in contact. A classical time integration method is also used in conjunction with a shooting method to take into account losses of contact. The theoretical results show that the subharmonic resonance constitutes a precursor of dynamic responses characterised by loss of contact, and consequently, the resonance establishes over a wide frequency range. Finally, experimental validations are also presented in this paper. To this end, a specific test rig is used. It corresponds to a double sphere-plane contact preloaded by the weight of a moving mass. Experimental results show good agreements with theoretical ones

Decreased sAβPPβ, Aβ38, and Aβ40 Cerebrospinal Fluid Levels in Frontotemporal Dementia.

International audienceTo improve the etiological diagnosis of neurodegenerative dementias like Alzheimer's disease (AD) or frontotemporal dementia (FTD), we evaluated the value of individual and combined measurements of the following relevant cerebrospinal fluid (CSF) biomarkers: Tau, 181p-Tau, Aβ38, Aβ40, Aβ42, sAβPPα, and sAβPPβ. This study conducted in two centers included patients with FTD (n = 34), AD (n = 52), as well as a control group of persons without dementia (CTRL, n = 42). Identical clinical criteria and pre-analytical conditions were used while CSF biomarkers were measured using commercial single and multiplex quantitative immunoassays. Thorough statistical analyses, including ROC curves, logistic regressions, and decision trees, were performed. We validated in AD the specific increase of p-Tau levels and the decrease of Aβ42 levels, two biological hallmarks of this disease. Tau concentrations were highest in AD and intermediate in FTD when compared to CTRL. The most interesting results were obtained by focusing on amyloid biomarkers as we found out in FTD a significant decrease of sAβPPβ, Aβ38, and Aβ40 levels. Aβ38 in particular was the most useful biomarker to differentiate FTD subjects from the CTRL population. Combining p-Tau and Aβ38 led us to correctly classifying FTD patients with sensitivity at 85% and specificity at 82%. Significant changes in amyloid biomarkers, particularly for Aβ38, are therefore seen in FTD. This could be quite useful for diagnosis purposes and it might provide additional evidence on the interrelationship between Tau and AβPP biology which understanding is essential to progress towards optimal therapeutic and diagnostic approaches of dementia