Yubredahl4409

Plane Poiseuille flow and plane Couette flow are shown to behave similarly in this context. © 2020 The Author(s).Multiferroic materials, with their combined and coupled magnetism and ferroelectricity, provide a playground for studying new physics and chemistry as well as a platform for the development of novel devices and technologies. Based on my July 2017 Royal Society Inaugural Lecture, I review recent progress and propose future directions in the fundamentals and applications of multiferroics, with a focus on initially unanticipated developments outside of the core activity of electric-field control of magnetism. © 2020 The Author(s).In biological systems, the growth of cells, tissues and organs is influenced by mechanical cues. Locally, cell growth leads to a mechanically heterogeneous environment as cells pull and push their neighbours in a cell network. Despite this local heterogeneity, at the tissue level, the cell network is remarkably robust, as it is not easily perturbed by changes in the mechanical environment or the network connectivity. Through a network model, we relate global tissue structure (i.e. the cell network topology) and local growth mechanisms (growth laws) to the overall tissue response. Within this framework, we investigate the two main mechanical growth laws that have been proposed stress-driven or strain-driven growth. We show that in order to create a robust and stable tissue environment, networks with predominantly series connections are naturally driven by stress-driven growth, whereas networks with predominantly parallel connections are associated with strain-driven growth. © 2020 The Author(s).Adhesive contact of the Hertzian indenter with an incompressible elastic substrate bi-directionally stretched along the indenter principal planes of curvature is considered in the Johnson-Kendall-Roberts theoretical framework. An approximate model is constructed by examining energy release rate conditions only on the edges of the minor and major axes of the contact ellipse. The effect of weak coupling between fracture modes I and II is introduced using a phenomenological mode-mixity function. This study was motivated by the need to model a passive-adhesive mechanism in cell mechanics on stretchable substrates. © 2020 The Author(s).Vibration energy is becoming a significant alternative solution for energy generation. Recently, a great deal of research has been conducted on how to harvest energy from vibration sources ranging from ocean waves to human motion to microsystems. selleck products In this paper, a theoretical model of a piecewise-linear (PWL) nonlinear vibration harvester that has potential applications in variety of fields is proposed and numerically investigated. This new technique enables automatic frequency tunability in the energy harvester by controlling the gap size in the PWL oscillator so that it is able to adapt to changes in excitations. To optimize the performance of the proposed system, a control method combining the response prediction, signal measurement and gap adjustment mechanism is proposed in this paper. This new energy harvester not only overcomes the limitation of traditional linear energy harvesters that can only provide the maximum power generation efficiency over a narrow frequency range but also improves the performance of current nonlinear energy harvesters that are not as efficient as linear energy harvesters at resonance. The proposed system is demonstrated in several case studies to illustrate its effectiveness for a number of different excitations. © 2020 The Author(s).Social groups such as schools of fish or flocks of birds display collective dynamics that can be modulated by group leaders, which facilitate decision-making toward a consensus state beneficial to the entire group. For instance, leaders could alert the group about attacking predators or the presence of food sources. Motivated by biological insight on social groups, we examine a stochastic leader-follower consensus problem where information sharing among agents is affected by perceptual constraints and each individual has a different tendency to form social connections. Leveraging tools from stochastic stability and eigenvalue perturbation theories, we study the consensus protocol in a mean-square sense, offering necessary-and-sufficient conditions for asymptotic stability and closed-form estimates of the convergence rate. Surprisingly, the prediction of our minimalistic model share similarities with observed traits of animal and human groups. Our analysis anticipates the counterintuitive result that heterogeneity can be beneficial to group decision-making by improving the convergence rate of the consensus protocol. This observation finds support in theoretical and empirical studies on social insects such as spider or honeybee colonies, as well as human teams, where inter-individual variability enhances the group performance. © 2020 The Author(s).We consider the simplest model of a passive biped walking down a slope given by the equations of switched coupled pendula (McGeer T. 1990 Passive dynamic walking. Int. J. Robot. Res. 9, 62-82. (doi10.1177/027836499000900206)). Following the fundamental work by Garcia (Garcia et al. 1998 J. Biomech. Eng. 120, 281. (doi10.1115/1.2798313)), we view the slope of the ground as a small parameter γ ≥ 0. When γ = 0, the system can be solved in closed form and the existence of a family of cycles (i.e. potential walking cycles) can be computed in closed form. As observed in Garcia et al. (Garcia et al. 1998 J. Biomech. Eng. 120, 281. (doi10.1115/1.2798313)), the family of cycles disappears when γ increases and only isolated asymptotically stable cycles (walking cycles) persist. However, no mathematically complete proofs of the existence and stability of walking cycles have been reported in the literature to date. The present paper proves the existence and stability of a walking cycle (long-period gait cycle, as termed by McGeer) by using the methods of perturbation theory for maps. In particular, we derive a perturbation theorem for the occurrence of stable fixed points from 1-parameter families in two-dimensional maps that can be of independent interest in applied sciences. © 2020 The Author(s).