Running is an essential mode of human locomotion, during which ballistic aerial phases alternate with phases when a single foot contacts the ground. The spring-loaded inverted pendulum (SLIP) provides a starting point for modelling running, and generates ground reaction forces that resemble those of the centre of mass (CoM) of a human runner. Here, we show that while SLIP reproduces within-step...

We define and study an equivariant E-theory with respect to coactions of Hopf C-algebras; we prove the Baaj-Skandalis duality in this setting. We show that the corresponding equivariant KK-theory of Baaj and Skandalis enjoys an universal property. In the appendix, we look at the different ways of expressing equivariant stability for a functor, and prove an equivariant BrownGreen-Rieffel stabili...

The exit time and the exit location of a non-Markovian diffusion is analyzed. More particularly, we focus on the so-called self-stabilizing process. The question has been studied by Herrmann, Imkeller and Peithmann in [6] with results similar to those by Freidlin and Wentzell. We aim to provide the same results by a more intuitive approach and without reconstructing the proofs of Freidlin and W...

We generalize the Randall Sundrum warped braneworld model in six and higher dimension and propose a resolution to the mass hierarchy among the standard model fermions. The fine tuning problem in connection with the scalar mass however is shown to reappear in a new guise in five dimensional warped model when the two form antisymmetric tensor fields, a massless string mode, propagates in the bulk...

We derive two classes of brane-world solutions arising in the presence of a bulk scalar field. For static field configurations, we adopt a time-dependent, factorizable metric ansatz that allows for radion stabilization. The solutions are characterized by a non-trivial warping along the extra dimension, even in the case of a vanishing bulk cosmological constant, and lead to a variety of inflatio...

We prove a sharp decay rate for the total energy of two classes of systems of weakly coupled hyperbolic equations. We show that we can stabilize the full system through a single damping term, acting on one component only of the system (indirect stabilization). The energy estimate is achieved by means of suitable estimates of the resolvent operator norm. We apply this technique to a system of wa...

Using a nonlocal macroscopic LWR-type traffic flow model, we present an approach to control the velocity towards given equilibrium velocity. Therefore, Lyapunov function measuring L2 distance between these velocities. We compute explicit rate at which system tends stationary speed. The is controlled by leading vehicle. Numerical examples demonstrate theoretical results and possible extensions o...

The biomechanical performance of a locking compression plate system was compared to an intramedullary photodynamic bone stabilization system in a femur and humerus osteotomy model. The photodynamic bone stabilization system utilizes an angioplasty-like balloon that is introduced into the intramedullary canal of a fractured bone, filled with monomer that is then polymerized and hardened by visib...