Research on Self-Aligning Flanges Based on Piezoelectric Actuators Applied to Precision Grinding Machines

Laser fusion research requires a large number of high-precision large-diameter aspherical components. To improve the grinding efficiency in the component production process, the manual operation time during the grinding process needs to be reduced. The grinding process requires the installation of the dressed grinding wheel onto the grinding machine spindle, and the off-line dressing results in installation errors during the loading and unloading process, which requires more time for manual alignment. To achieve self-aligning, the circumferential contour of the grinding wheel was first restored by the reversal method, then noise reduction and circle fitting were performed to obtain the eccentricity value and eccentricity position between the flange and the spindle, and finally, the flange was adjusted finely by three piezoelectric actuators installed inside the flange to reduce the eccentricity. Three repetitive experiments were conducted to verify that the self-aligning flange can reduce the eccentricity value by retracting the piezoelectric actuators so that the proper alignment between the flange and the spindle could meet the requirements; the average eccentricity value of the three experiments decreased by 74%, which greatly improved the efficiency of the grinding wheel alignment.

Visual numerosity estimation is based on anisotropic representations of visual space

Humans can estimate the number of visually displayed items without counting. This capacity of numerosity perception has often been attributed to a dedicated system to estimate numerosity, or alternatively to the exploitation of various stimulus features, such as density, convex hull, the size of items and occupancy area. The distribution of the presented items is usually not varied with eccentricity in the visual field. However, our visual fields are highly asymmetric, and to date, it is unclear how inhomogeneities of the visual field impact numerosity perception. Besides eccentricity, a pronounced asymmetry is the radial-tangential anisotropy. For example, in crowding, radially placed flankers interfere more strongly with target perception than tangentially placed flankers. Similarly, in redundancy masking, the number of perceived items in repeating patterns is reduced when the items are arranged radially but not when they are arranged tangentially. Here, we investigated whether numerosity perception is subject to the radial-tangential anisotropy of spatial vision to shed light on the underlying topology of numerosity perception. Observers were presented with varying numbers of discs and asked to report the perceived number. There were two conditions. Discs were predominantly arranged radially in the “radial” condition and tangentially in the “tangential” condition. Additionally, the spacing between discs was scaled with eccentricity. Physical properties, such as average eccentricity, average spacing, convex hull, and density were kept as similar as possible in the two conditions. Radial arrangements were expected to yield underestimation compared to tangential arrangements. Consistent with the hypothesis, numerosity estimates in the radial condition were lower compared to the tangential condition. Magnitudes of radial alignment (as well as predicted crowding strength) correlated with the observed numerosity estimates. Our results demonstrate a robust radial-tangential anisotropy, suggesting that the topology of spatial vision determines numerosity estimation. We suggest that asymmetries of spatial vision should be taken into account when investigating numerosity estimation.

Visual Effect on Brain Connectome That Scales Feedforward and Feedback Processes of Aged Postural System During Unstable Stance

Older adults with degenerative declines in sensory systems depend strongly on visual input for postural control. By connecting advanced neural imaging and a postural control model, this study investigated the visual effect on the brain functional network that regulates feedback and feedforward processes of the postural system in older adults under somatosensory perturbations. Thirty-six older adults conducted bilateral stance on a foam surface in the eyes-open (EO) and eyes-closed (EC) conditions while their center of pressure (COP) and scalp EEG were recorded. The stochastic COP trajectory was modeled with non-linear stabilogram diffusion analysis (SDA) to characterize shifts in postural control in a continuum of feedback and feedforward processes. The EEG network was analyzed with the phase-lag index (PLI) and minimum spanning tree (MST). The results indicated that visual input rebalanced feedforward and feedback processes for postural sway, resulting in a greater critical point of displacement (CD), short-term effective diffusion coefficients (Ds) and short-term exponent (Hs), but the smaller critical point of time (CT) and long-term exponent (Hl) for the EC state. The EC network demonstrated stronger frontoparietal-occipital connectivity but weaker fronto-tempo-motor connectivity of the theta (4–7 Hz), alpha (8–12 Hz), and beta (13–35 Hz) bands than did the EO network. MST analysis revealed generally greater leaf fraction and maximal betweenness centrality (BCmax) and kappa of the EC network, as compared with those of the EO network. In contrast, the EC network exhibited a smaller diameter and average eccentricity than those of the EO network. The modulation of long-term negative feedback gain of the aged postural system with visual occlusion was positively correlated with leaf fraction, BCmax, and kappa, but negatively correlated with the diameter and average eccentricity for all EEG sub-bands. In conclusion, the aged brain functional network in older adults is tuned to visual information for modulating long-term negative feedback of the postural system under somatosensory perturbations.

Ordering graphs with large eccentricity-based topological indices

For a connected graph, the first Zagreb eccentricity index $\xi _{1}$ ξ 1 is defined as the sum of the squares of the eccentricities of all vertices, and the second Zagreb eccentricity index $\xi _{2}$ ξ 2 is defined as the sum of the products of the eccentricities of pairs of adjacent vertices. In this paper, we mainly present a different and universal approach to determine the upper bounds respectively on the Zagreb eccentricity indices of trees, unicyclic graphs and bicyclic graphs, and characterize these corresponding extremal graphs, which extend the ordering results of trees, unicyclic graphs and bicyclic graphs in (Du et al. in Croat. Chem. Acta 85:359–362, 2012; Qi et al. in Discrete Appl. Math. 233:166–174, 2017; Li and Zhang in Appl. Math. Comput. 352:180–187, 2019). Specifically, we determine the n-vertex trees with the i-th largest indices $\xi _{1}$ ξ 1 and $\xi _{2}$ ξ 2 for i up to $\lfloor n/2+1 \rfloor $ ⌊ n / 2 + 1 ⌋ compared with the first three largest results of $\xi _{1}$ ξ 1 and $\xi _{2}$ ξ 2 in (Du et al. in Croat. Chem. Acta 85:359–362, 2012), the n-vertex unicyclic graphs with respectively the i-th and the j-th largest indices $\xi _{1}$ ξ 1 and $\xi _{2}$ ξ 2 for i up to $\lfloor n/2-1 \rfloor $ ⌊ n / 2 − 1 ⌋ and j up to $\lfloor 2n/5+1 \rfloor $ ⌊ 2 n / 5 + 1 ⌋ compared with respectively the first two and the first three largest results of $\xi _{1}$ ξ 1 and $\xi _{2}$ ξ 2 in (Qi et al. in Discrete Appl. Math. 233:166–174, 2017), and the n-vertex bicyclic graphs with respectively the i-th and the j-th largest indices $\xi _{1}$ ξ 1 and $\xi _{2}$ ξ 2 for i up to $\lfloor n/2-2\rfloor $ ⌊ n / 2 − 2 ⌋ and j up to $\lfloor 2n/15+1\rfloor $ ⌊ 2 n / 15 + 1 ⌋ compared with the first two largest results of $\xi _{2}$ ξ 2 in (Li and Zhang in Appl. Math. Comput. 352:180–187, 2019), where $n\ge 6$ n ≥ 6 . More importantly, we propose two kinds of index functions for the eccentricity-based topological indices, which can yield more general extremal results simultaneously for some classes of indices. As applications, we obtain and extend some ordering results about the average eccentricity of bicyclic graphs, and the eccentric connectivity index of trees, unicyclic graphs and bicyclic graphs.

Distance Measurements Related to Cartesian Product of Cycles

Graph theory and its wide applications in natural sciences and social sciences open a new era of research. Making the graph of computer networks and analyzing it with aid of graph theory are extensively studied and researched in the literature. An important discussion is based on distance between two nodes in a network which may include closeness of objects, centrality of objects, average path length between objects, and vertex eccentricity. For example, (1) disease transmission networks: closeness and centrality of objects are used to measure vulnerability to particular disease and its infectivity; (2) routing networks: eccentricity of objects is used to find vertices which form the periphery objects of the network. In this manuscript, we have discussed distance measurements including center, periphery, and average eccentricity for the Cartesian product of two cycles. The results are obtained using the definitions of eccentricity, radius, and diameter of a graph, and all possible cases (for different parity of length of cycles) have been proved.

Dynamic and stability performance improvement of the hydrodynamic bearing by using triangular-shaped textures

In the present study, the effect of triangular shape textured on the bearing dynamic and stability performance has been investigated. The triangular-shaped texture having variation in their depth size, number of textures, and location has been used in the study to find the stiffness, damping, and stability parameters and compared with un-textured bearing. The pressure and fluid-film thickness in the lubricant flow domain having characteristics of Newtonian and isothermal and which is governed with Reynold's equation have been computed by discretizing the domain into four-nodded quadrilateral isoparametric by using finite element method. Four different cases of texture distribution on the bearing surface have been studied. The study has been carried out considering the bearing operation only under average eccentricity ratios of 0.6. From obtained results, it is found that the value of direct stiffness coefficient and threshold speed is found maximum at lower texture depth and the direct damping coefficient is found maximum at higher value of texture depth corresponding to different texture distribution on the bearing surface. The optimum triangular-shaped textured parameters have been also finalized to get maximum dynamic performance and stability, which may be expected to be valuable for bearing designers. For the purpose of a better insight into the stability aspect of the optimal textured journal bearing, the journal center trajectories are also drawn and compared with un-textured bearing.