A new curvature-controlled stacking-line method for optimization design of compressor cascade considering surface smoothness

The paper presents an advanced parametric method of blade stacking lines in terms of sweep and lean based on controlled curvature. To the knowledge of the authors, there is no related approach reported in open literature that uses Bezier spline as the radial curvature distribution to improve the smoothness of the blade surface; most previous studies ignored the discontinuous slopes of curvature of the parametric curves. The parametric method called curvature-controlled stacking-line method (CCSLM) is performed by changing the magnitude of the sweep or lean. A fourth Bezier spline is adopted to define the curvature of spanwise stacking line directly ensuring surface smoothness. Then, the redesign cascades are created by sectional profiles stacked along the radial stacking lines which are obtained by twice integrating the Bezier spline. Then, the advanced method is conducted to optimize a high-subsonic controlled diffusion airfoil at design point, where the blade shape is generated in terms of lean. A single-objective optimization is performed using Kriging model and genetic algorithm to optimize total pressure loss, and the optimized geometry is obtained. The optimization results show that the blade design CCSLM has significant effects on the endwall flow vortex as well as radial loading distribution. The reduction of total pressure loss and secondary flow is also observed, and the aerodynamic performance is well improved compared with the original cascade.

Bi-Radial Curvature Morphology of the Healthy Talus

Category: Ankle Introduction/Purpose: In order to design an implant for the ankle joint that mimics normal joint motion, the condylar geometry of the talus must be anatomically accurate. Previous attempts to describe the curvature of the talus have typically involved fitting single-radius arcs to the medial and lateral facets. The purpose of this investigation was to determine if the curvature of the medial and lateral sides of the talus can be more accurately described by dividing the condyles into anterior and posterior regions, thus creating bi-radial curves for both the medial and lateral sides of the talus. Methods: After IRB approval, 18 subjects (9 male, 9 female; mean age 34.5 years) underwent weight-bearing CT scans at mid- stance of simulated gait. All subjects were deemed to have a healthy right ankle by the surgeon investigator. CT images were used to generate 3D models of each talus. A coordinate system was defined and the articular surface of the talus was separated into four sections: medial-anterior (MA), medial-posterior (MP), lateral-anterior (LA) and lateral-posterior (LP). The curvature of each section was defined by selecting points on the articular surface at 10° intervals. The extent of each radius was 30° of arc and the magnitude of each radius was selected to minimize the gaps between the radii and the spline curve to define a best-fit bi-radial approximation to the spline curve using geometry that could be easily used to define the articular surface of the talus. Ratios of the aforementioned radii were calculated. Results: The average MA, MP, LA and LP radii were 18.3 mm, 26.6 mm, 21.5 mm and 25.1 mm, respectively. The medial (A/P), lateral (A/P), anterior (M/L) and posterior (M/L) radii ratios were 0.70, 0.87, 0.88 and 1.07, respectively. The anterior and posterior ratios were compared using a paired t-test and found to be statistically different (P=.019). Further, the data were compared against a hypothesized value of 1 using a one-tailed one-sample t-test. The anterior ratio was significantly lower than 1 (P=.014) while the posterior ratio was significantly greater (P=.037). On the lateral side, 83.3% of the subjects exhibited a larger posterior radius than anterior radius. Only one subject (5.6%) had a larger anterior radius than posterior radius on the medial side. Conclusion: This study shows that the radius increases in the sagittal plane from the anterior portion to the posterior portion of both the medial and lateral sides of the talus. Furthermore, the MA radius is smaller than the LA radius. Conversely, the MP radius is larger than the LP radius. These results substantiate the validity of an implant design that incorporates a condylar radius ratio that is smaller for the anterior dorsiflexion surface and greater for the posterior plantar flexion surface. Implants with more accurate anatomical geometry may allow for more normal kinematics and potentially prolong the life of the implant.

ANALYSIS THE THERMAL BEHAVIOR OF SOLAR CHIMNEY AT VARYING PARAMETERS

In this paper a computerized analysis of the fluid dynamics was conducted for a solar power plant stacked at collector height (H2 = 1.85 m, 3 m, 4 m and 5 m) with different solar irradiations such as 600 W / m2, 800 W / m2 m2, 900 W / m2 and 1000 W / m2. The slope of the roof and the radius of curvature of the manifold vary according to the height of the outlet manifold. The intake manifold height is set to H1 = 1.85 m from a solar cell power plant. The main objective of this work is to study the improvement of efficiency by modifying the design of the solar chimney system by diverging and radial curvature on the roof of the SCPP sensor. From the results, it was observed that the inclination and radius of curvature of the sensor roof had an effect on the efficiency of the sensor and that the efficiency of the sensor was at most 44.92% when the sensor height H2 = 5 m.

Applications of PDEs inpainting to magnetic particle imaging and corneal topography

In this work we propose a novel application of Partial Differential Equations (PDEs) inpainting techniques to two medical contexts. The first one concerning recovering of concentration maps for superparamagnetic nanoparticles, used as tracers in the framework of Magnetic Particle Imaging. The analysis is carried out by two set of simulations, with and without adding a source of noise, to show that the inpainted images preserve the main properties of the original ones. The second medical application is related to recovering data of corneal elevation maps in ophthalmology. A new procedure consisting in applying the PDEs inpainting techniques to the radial curvature image is proposed. The images of the anterior corneal surface are properly recovered to obtain an approximation error of the required precision. We compare inpainting methods based on second, third and fourth-order PDEs with standard approximation and interpolation techniques.

The amplitude in periodic neural state trajectories underlies the tempo of rhythmic tapping

Our motor commands can be exquisitely timed according to the demands of the environment, and the ability to generate rhythms of different tempos is a hallmark of musical cognition. Yet, the neuronal basis behind rhythmic tapping remains elusive. Here we found that the activity of hundreds of primate MPC neurons show a strong periodic pattern that becomes evident when their activity is projected into a lower dimensional state space. We show that different tempos are encoded by circular trajectories that travelled at a constant speed but with different radii, and that this neuronal code is highly resilient to the number of participating neurons. Crucially, the changes in the amplitude of the oscillatory dynamics in neuronal state space are a signature of beat-based timing, regardless of whether it is guided by an external metronome or is internally controlled and is not the result of repetitive motor commands. Furthermore, the increase in amplitude and variability of the neural trajectories accounted for the scalar property of interval timing. In addition, we found that the interval-dependent increments in the radius of periodic neural trajectories are the result of larger number of neurons engaged in the production of longer intervals. Our results support the notion that beat-based timing during rhythmic behaviors is encoded in the radial curvature of periodic MPC neural population trajectories.

Growth of the Eigensolutions of Laplacians on Riemannian Manifolds I: Construction of Energy Function

In this paper, we consider the eigensolutions of $-\Delta u+ Vu=\lambda u$, where $\Delta $ is the Laplacian on a non-compact complete Riemannian manifold. We develop Kato’s methods on manifold and establish the growth of the eigensolutions as r goes to infinity based on the asymptotical behaviors of $\Delta r$ and V (x), where r = r(x) is the distance function on the manifold. As applications, we prove several criteria of absence of eigenvalues of Laplacian, including a new proof of the absence of eigenvalues embedded into the essential spectra of free Laplacian if the radial curvature of the manifold satisfies $ K_{\textrm{rad}}(r)= -1+\frac{o(1)}{r}$.