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Motivated by a design of a vertical axis wind turbine, we present a theory of dynamical similarity for mechanical systems consisting of interacting elastic solids, rigid bodies and incompress-ible fluids. Throughout, we focus on the geometrically nonlinear case. We approach the analysis by analyzing the equations of motion: we ask that a change of variables take these equations and mutual boundary conditions to themselves, while allowing a rescaling of space and time. While the disparity between the Eulerian and Lagrangian descriptions might seem to limit the possibilities, we find numerous cases that apparently have not been identified, especially for stiff nonlinear elastic materials (defined below). The results appear to be particularly adapted to structures made with origami design methods, where the tiles are allowed to deform isometrically. We collect the results in tables and discuss some particular numerical examples.

Motivated by a design of a vertical axis wind turbine, we present a theory of dynamical similarity for mechanical systems consisting of interacting elastic solids, rigid bodies and incompressible fluids. Throughout, we focus on the geometrically nonlinear case. We approach the analysis by analyzing the equations of motion: we ask that a change of variables take these equations and mutual boundary conditions to themselves, while allowing a rescaling of space and time. While the disparity between the Eulerian and Lagrangian descriptions might seem to limit the possibilities, we find numerous cases that apparently have not been identified, especially for stiff nonlinear elastic materials (defined below). The results appear to be particularly adapted to structures made with origami design methods, where the tiles are allowed to deform isometrically. We collect the results in tables and discuss some particular numerical examples.

People with drug addiction are more likely to suffer from sleep disorders than non-addicts. The roles that childhood adversity experiences and resilience play in the development of sleep disorders will be explored in this study. A total of 459 participants with drug addiction and 400 non-addicts were investigated with the Adverse Childhood Experiences (ACEs) Scale, Pittsburgh Sleep Quality Index (PSQI), and Connor–Davidson Resilience Scale from April 2019 to December 2020. Our results suggested that participants with drug addiction had worse sleep quality compared to non-addicts. Resilience acted as a mediator and significantly affected the relationship between ACEs and sleep quality. For all participants who experienced ACEs, individuals with high resilience reported lower PSQI score, the regulatory effect of medium and high resilience on sleep quality was better than that of low resilience. Moreover, comparing to the non-addicts who experienced mild ACEs, high resilience showed a good buffer effect on the sleep quality for people with drug addiction. And high resilience played a stronger regulatory role in females as compared to males. The results help to broaden the relevant research in the field of sleep and we should pay attention to the role of resilience in regulating sleep quality.

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