The effect of aneurismal-wall mechanical properties on patient-specific hemodynamic simulations： two clinical case reports

Hemodynamic factors such as the wall shear stress play an important role in the pathogenesis and treatment of cerebral aneurysms. In present study, we apply computational fluid-structure interaction analyses on cerebral aneurysms with two different constitutive relations for aneurismal wall in order to investigate the effect of the aneurismal wall mechanical properties on the simulation results. We carry out these analyses by using two patient-specific models of cerebral aneurysms of different sizes located in different branches of the circle of Willis. The models are constructed from 3D rotational angiography image data and blood flow dynamics is studied under physiologically representative waveform of inflow. From the patient models analyzed in this investigation, we find that the deformations of cerebral aneurysms are very small. But due to the nonlinear character of the Navier-Stokes equations, these small deformations could have significant influences on the flow characteristics. In addition, we find that the aneurismal-wall mechanical properties have great effects on the deformation distribution of the aneurysm, which also affects the wall shear stress distribution and flow patterns. Therefore, how to define a proper constitutive relation for aneurismal wall should be considered carefully in the hemodynamic simulation.     

Acoustic stop bands in almost-periodic and weakly randomized stratified media： perturbation analysis

In this paper, we analyze the effect of both deter- ministic and random perturbations of a regular multi-layered elastic structure on its stop band properties. The tool of choice is the transfer matrix method, which is both versatile and easy to implement. In both cases, we find that the stop-bands widen. We observe the appearance of very narrow pass-bands within the stop-bands, which can be observed in other instances in optics.     

Passive elasto-magnetic suspensions: nonlinear models and experimental outcomes

The paper presents a passive elasto-magnetic suspension based on rare-earth permanent magnets: the dynamical system is described with theoretical and numerical nonlinear models, whose results are validated through experimental comparison. The goal is to minimize the dependence on mass of the natural frequency of a single degree of freedom system. For a system with variable mass, static configuration and dynamical behaviour are compared for classic linear elastic systems, for purely magnetic suspensions and for a combination of the two. In particular the dynamics of the magneto-mechanic interaction is predicted by use of nonlinear and linearised models and experimentally observed through a suitable single degree of freedom test rig.     

Detecting unstable periodic orbits and unstable quasiperiodic orbits in vibro-impact systems

In this paper, unstable dynamics is considered for the models of vibro-impact systems with linear differential equations coupled to an impact map. To provide a skeleton for the organization of chaotic attractors, we propose a method for detecting unstable periodic orbits embedded in chaotic attractors through a combination of unconstrained optimization technique and Poincaré map. Three numerical examples from different vibro-impact models demonstrate that the strategy can efficiently detect unstable periodic orbits in chaotic attractors. In order to explore the mechanism responsible for the creation of multi-dimensional tori attractors, we also present another method to detect unstable quasiperiodic orbits embedded multi-dimensional tori attractors by examining a specially transient time series. The upper bound and lower bound of the transient time series (in the Poincaré map) can be obtained by analyzing transient Lyapunov exponent and transient Lyapunov dimension. Some examples verify the effectiveness of the numerical algorithm.