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Bifurcations --- Discontinuous systems --- Nonlinear dynamics --- Stick and slip --- Vibrations

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Differential geometry. Global analysis --- Nonlinear Dynamics --- Evolution --- Chaotic behavior in systems --- Evolution (Biology) --- Philosophers --- Scientists --- Chaos --- Evolution (Biologie) --- Philosophes --- Scientifiques --- Interviews --- Entretiens --- Chaotic behavior in systems. --- Evolution (Biology). --- Interviews. --- Nonlinear Dynamics.

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The drive towards reducing aircraft engines' aerodynamic losses has led engineers to reduce the clearances between blade tips and their surrounding casing, thereby increasing the risk of blade/casing contact interactions. Tools to accurately predict subsequent nonlinear dynamics are thus essential at design stage. Design of Experiments and the construction of surrogate models are very effective in studying complex and costly experimental blade/casing devices. Nonetheless, the convergence of surrogate models is linked to the smoothness of the response, evidencing the requirement of new approximation approaches for discontinuous responses. In this context, this report proposes a methodology to localize discontinuities in a 2D Design of Experiments inputs space in order to apply approximation methods on the smooth subdomains subsequently. First, a mesh is constructed on the inputs parameter space using a Delaunay triangulation and gradient-based indicators along with polynomial annihilation are then used as refinement indicators. The proposed methodology makes use of the Support Vector Machine to create a smooth approximation of the discontinuity location. Local improvement of the solution is finally completed. The applicability and the robustness of the proposed discontinuity localization tool are then tested on a variety of analytical models. The test cases have demonstrated satisfactory localization of closed discontinuities, multiple discontinuities in the same model, and discontinuities running partially through the domain. The numerically costly engineering model of blade/casing contact interactions is then considered and the proposed methodology is used to localize a jump in the response.

Discontinuities localization --- Blade/casing contact interactions --- Nonlinear dynamics --- Design of Experiments --- Machine learning --- Ingénierie, informatique & technologie > Ingénierie aérospatiale

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Nonlinear Dynamics --- Chaos (théorie des systèmes) --- climatologie --- fractales --- Philosophie et sciences --- Science --- Philosophy --- Systems Theory --- Chaotic behavior in systems. --- Chaos. --- Chaos (théorie des systèmes)

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The basal ganglia constitute a group of subcortical structures, highly interconnected among themselves, as well as with the cerebral cortex, thalamus and other brain areas. These nuclei play a central role in the control of voluntary movement, and their specific pathology comprises the group of diseases known as movement disorders, including Parkinson's disease, Huntington's disease, dystonia and Gilles de la Tourette syndrome, among others. Additionally, the presence of a number of circuits within the basal ganglia related to non-motor functions has been acknowledged. Currently, the basal ganglia are thought to participate in cognitive, limbic and learning functions. Moreover, disorders related to the basal ganglia are known to involve a number of complex, non-motor symptoms and syndromes (e.g. compulsive and addictive behavior). In the light of this evidence, it is becoming clear that our knowledge about the basal ganglia needs to be revised, and that new pathophysiological models of movement disorders are needed. In this context, the study of the pathophysiology of the basal ganglia and the treatment of their pathology is becoming increasingly interdisciplinary. Nowadays, an appropriate approach to the study of these problems must necessarily involve the use of complex mathematical modeling, computer simulations, basic research (ranging from biomolecular studies to animal experimentation), and clinical research. This research topic aims to bring together the most recent advances related to the pathophysiology of the basal ganglia and movement disorders.

Braak's hypothesis --- basal ganglia --- Parkinson's disease --- cycling --- movement disorders --- computational modeling --- Huntington's disease --- non-motor symptoms --- nonlinear dynamics --- deep brain stimulation