Group approximation in Cayley topology and coarse geometry, Part III: Geometric property (T)

In this series of papers, we study correspondence between the following: (1) large scale structure of the metric space bigsqcup_m {Cay(G(m))} consisting of Cayley graphs of finite groups with k generators; (2) structure of groups which appear in the boundary of the set {G(m)}_m in the space of k-marked groups. In this third part of the series, we show the correspondence among the metric properties `geometric property (T),' `cohomological property (T),' and the group property `Kazhdan's property (T).' Geometric property (T) of Willett--Yu is stronger than being expander graphs. Cohomological property (T) is stronger than geometric property (T) for general coarse spaces.Comment: 20 pages, Appendix withdrawn due to the error in the proof of Theorem A.2 (v3); 24 pages, Appendix added (v2); 20 pages, no figur

A stress tensor discontinuity-based immersed boundary-lattice Boltzmann method

We propose an immersed boundary-lattice Boltzmann method using the discontinuity of the stress tensor. In the immersed boundary method, the body force which is applied to enforce the no-slip boundary condition is equivalent to the discontinuity of the stress tensor across the boundary. In the proposed method, the boundary is expressed by Lagrangian points independently of the background lattice points, and the discontinuity of the stress tensor is calculated on these points from desired particle distribution functions which satisfy the no-slip boundary condition based on the bounce-back scheme. By using this method, we can obtain the force locally acting on the boundary from the stress tensor of one side of the fluids divided by the boundary, and there is no need to consider the internal mass effect in calculating the total force and torque acting on the boundary. To our best knowledge, the present method is the first one which enables us to calculate the stress tensor on the boundary in the class of the diffusive interface method. In order to validate the present method, we apply it to simulations of typical moving-boundary problems, i.e., a Taylor-Couette flow, an oscillating circular cylinder in a stationary fluid, the sedimentation of an elliptical cylinder, and the sedimentation of a sphere. As a result, the present method has the first-order spatial accuracy and has a good agreement with other numerical and experimental results. In addition, we discuss two problems of the present method, i.e., penetration and spurious oscillation of local force, and a possible remedy for them. (C) 2018 Elsevier Ltd. All rights reserved.ArticleCOMPUTERS & FLUIDS.172: 593-608(2018)journal articl

A trapezoidal wing equivalent to a Janatella leucodesma's wing in terms of aerodynamic performance in the flapping flight of a butterfly model

Wing planform is one of the most important factors for lift and thrust generation and enhancement in flapping flight. In a previous study based on a simple numerical model of a butterfly, we found that the wing planform of an actual butterfly (Janatella leucodesma) is more efficient than any rectangular or trapezoidal wing planform. In the present study, we make a hypothesis that the efficient aerodynamic performance of a butterfly's wings can be reproduced by the following four geometrical parameters of wing planform: aspect ratio, taper ratio, position of the rotational axis for the geometric angle of attack, and sweepback angle. In order to test this hypothesis, we explore a trapezoidal wing planform equivalent to an actual butterfly's wing planform in terms of aerodynamic performance in a parameter space consisting of these four parameters. We use a simple butterfly model composed of two rigid thin wings and a rod-shaped body and calculate the aerodynamic performance of the model by an immersed boundary-lattice Boltzmann method to find such a trapezoidal wing planform. As a result, we find a trapezoidal wing planform which gives almost the same lift, thrust, pitching moment, power, and power-loading coefficients as an actual butterfly's wing planform. Furthermore, in the free flight of the butterfly model with pitching motion control, the flight behavior of the model with the resulting trapezoidal wing planform is almost the same as that with an actual butterfly's wing planform.ArticleBIOINSPIRATION & BIOMIMETICS.14(3):036003(2019)journal articl

Aerodynamic comparison of a butterfly-like flapping wing-body model and a revolving-wing model

The aerodynamic performance of flapping- and revolving-wing models is investigated by numerical simulations based on an immersed boundary-lattice Boltzmann method. As wing models, we use (i) a butterfly-like model with a body and flapping- rectangular wings and (ii) a revolving-wing model with the same wings as the flapping case. Firstly, we calculate aerodynamic performance factors such as the lift force, the power, and the power loading of the two models for Reynolds numbers in the range of 50-1000. For the flapping-wing model, the power loading is maximal for the maximum angle of attack of 90 degrees, a flapping amplitude of roughly 45 degrees, and a phase shift between the flapping angle and the angle of attack of roughly 90 degrees. For the revolving-wing model, the power loading peaks for an angle of attack of roughly 45 degrees. In addition, we examine the ground effect on the aerodynamic performance of the revolving-wing model. Secondly, we compare the aerodynamic performance of the flapping- and revolving-wing models at their respective maximal power loadings. It is found that the revolving-wing model is more efficient than the flapping- wing model both when the body of the latter is fixed and where it can move freely. Finally, we discuss the relative agilities of the flapping- and revolving-wing models.ArticleFLUID DYNAMICS RESEARCH.49(3):035512(2017)journal articl

Evaluation of the softness and its impression of visual stimuli in VR space

To examine the softness and impression of visual objects in VR (Virtual Reality) space, the impression of the visual stimuli in VR space was measured using the subjective evaluation of a seven-rank scale by changing with each the value of the deformation resistance of the stimuli, of shapes, and colors. The value of the deformation resistance of the stimuli expresses the degree of deformation to return to the original of the object when touching it in VR space. The lower value indicates the larger deformation like pudding and the higher one is the smaller one like thick rubber they were used three types of values lower and higher, and no-deformation of the objects. The shapes of objects as the stimuli were three shapes (sphere, cube, pyramid). The colors of the stimuli were selected from five colors (red, green, green, gray, and white) and they have used two types of the feeling of materials (matte and metallic) in each color. Ten participants were asked to subjectively evaluate the softness and impression of the stimulus. In the results, the evaluation changes from soft to hard by increasing the values of deformation resistance in all the stimuli in VR space. It is suggested that the degree of the deformation to return to the original can express the softness of objects when touching them in VR space even though the user does not touch them physically. It also discussed the relationship between softness and its impression of the stimuli in VR space