Statistical physics of cerebral embolization leading to stroke

We discuss the physics of embolic stroke using a minimal model of emboli moving through the cerebral arteries. Our model of the blood flow network consists of a bifurcating tree, into which we introduce particles (emboli) that halt flow on reaching a node of similar size. Flow is weighted away from blocked arteries, inducing an effective interaction between emboli. We justify the form of the flow weighting using a steady flow (Poiseuille) analysis and a more complicated nonlinear analysis. We discuss free flowing and heavily congested limits and examine the transition from free flow to congestion using numerics. The correlation time is found to increase significantly at a critical value, and a finite size scaling is carried out. An order parameter for non-equilibrium critical behavior is identified as the overlap of blockages' flow shadows. Our work shows embolic stroke to be a feature of the cerebral blood flow network on the verge of a phase transition.Comment: 11 pages, 11 figures. Major rewrite including improved justification of the model and a finite size scalin

Optimal Strokes for Driftless Swimmers: A General Geometric Approach

Swimming consists by definition in propelling through a fluid by means of bodily movements. Thus, from a mathematical point of view, swimming turns into a control problem for which the controls are the deformations of the swimmer. The aim of this paper is to present a unified geometric approach for the optimization of the body deformations of so-called driftless swimmers. The class of driftless swimmers includes, among other, swimmers in a 3D Stokes flow (case of micro-swimmers in viscous fluids) or swimmers in a 2D or 3D potential flow. A general framework is introduced, allowing the complete analysis of five usual nonlinear optimization problems to be carried out. The results are illustrated with examples coming from the literature and with an in-depth study of a swimmer in a 2D potential flow. Numerical tests are also provided

On the parametrization of clapping

For a Reactive Virtual Trainer(RVT), subtle timing and lifelikeness\ud of motion is of primary importance. To allow for reactivity, movement\ud adaptation, like a change of tempo, is necessary. In this paper we\ud investigate the relation between movement tempo, its synchronization to\ud verbal counting, time distribution, amplitude, and left-right symmetry of\ud a clapping movement. We analyze motion capture data of two subjects\ud performing a clapping exercise, both freely and timed by a metronome.\ud Our findings are compared to existing gesture research and existing biomechanical models. We found that, for our subjects, verbal counting adheres\ud to the phonological synchrony rule. A linear relationship between\ud the movement path length and the tempo was found. The symmetry between\ud the left and the right hand can be described by the biomechanical\ud model of two coupled oscillators