Large Apex Angle Research Articles

Human-in-the-loop optimization of rocker shoe to reduce plantar pressure and collision work simultaneously

BackgroundRocker shoes can be used to reduce foot pressure and adjust lower limb kinetics for various patient population, such as people with diabetic peripheral neuropathy. Selecting adequate properties of the rocker sole is of great importance for its efficacy. This study investigated the capability of human-in-the-loop optimization (HILO) to individually optimize apex position and angle of rocker shoe to reduce peak pressure and collision work simultaneously. MethodsPeak pressure, kinetic, and kinematic data were recorded from 10 healthy participants while walking at preferred speed wearing rocker shoes with adjustable apex position and angle. An evolutionary algorithm was used to find optimal apex parameters to reduce both peak pressure in medial forefoot and collision work. The optimized shoe (HILO shoe) was compared with generic optimal rocker settings (Chapman settings) and normal shoe. FindingsCompared to normal shoe, the HILO shoe had lower plantar pressure (pHILO = 0.007; pChapman = 0.044) and Chapman shoe showed higher collision work (pHILO = 0.025; pChapman = 0.014). Both HILO and Chapman shoe had smaller push-off work than normal shoe (pHILO = 0.001; pChapman < 0.001) with the Chapman shoe exhibited earlier push-off onset (pHILO = 0.257; pChapman = 0.016). InterpretationThe Human-in-the-loop optimization approach resulted in individualized apex settings which performed on average similar to Chapman settings but, were superior in selected cases. In these cases, medial forefoot could be further offloaded with apex angles larger than generic settings. The larger apex angle might increase the external ankle moment arm and push-off work. However, there is limited room for improvement on collision work compared to generic settings.

Effects of heel apex position, apex angle and rocker radius on plantar pressure in the heel region

IntroductionRocker shoes and insoles are used to prevent diabetic foot ulcers in persons with diabetes mellitus and loss of protective sensation, by reducing the plantar pressure in regions with high pressure values (>200 kPa) (e.g., hallux, metatarsal heads and heel). However, forefoot rocker shoes that reduce pressure in the forefoot inadvertently increase pressure in the heel. No studies focused on mitigating the negative effects on heel pressure by optimizing the heel rocker midsole, yet. Therefore, we analyze the effect of different heel rocker parameters on the heel plantar pressure. MethodsIn-shoe pressure was measured, while 10 healthy participants walked with control shoe and 10 different heel rocker settings. Peak pressure was determined in 7 heel masks, for all shoes. Generalized estimating equations was performed to test the effect of the different shoes on the peak pressure in the different heel masks. ResultsIn the proximal heel, a rocker shoe with distal apex position, small rocker radius and large apex angle (100°), shows the largest significant decrease in peak pressure compared to rocker shoes with more proximally located apex positions. In the midheel and distal heel, the same rocker shoes or any other rocker shoes, analyzed in this study, do not reduce the PP more than 2 % compared to the control shoe. For the midheel and distal heel region with high pressure values (>200 kPa), rocker shoes alone are not the correct option to reduce the pressure to below 200 kPa. ConclusionWhen using rocker shoes to reduce the pressure in the forefoot, a heel rocker midsole with a distal apex position, small rocker radius and apex angle of 100°, mitigates the negative effects on proximal heel pressure. For the midheel and distal heel, other footwear options as an addition or instead of rocker shoes are needed to reduce the pressure.

Controllable fabrication of Au-nanoprotrusion arrays as a platform for the materials design and characterization

Au-nanoprotrusions (AuNPs) were fabricated on a gold substrate using obliquely incident Ar+ ions with a simultaneous supply of carbon at room temperature. The sputter erosion rate was kept almost constant at 49 nm/min, while the deposition rate of carbon ranged from 1.2 to 0.6 nm/min. Scanning electron microscopy (SEM) observation revealed the variation in the number density and shape of the AuNPs ranging from slender needles to cones with a large apex angle, depending on the carbon deposition rate. Transmission electron microscopy (TEM) demonstrated that the slender needles were characterized by the bi-metal like structure of the large Au grain-rich phase and amorphous carbon phase with a dispersion of fine Au nanoparticles, while the conical structures consisted of Au grains with an amorphous carbon cap region on top. Those structures were selectively prepared, depending on the application. Li-C nanocomposite films deposited on conical structures, for instance, were readily observed cross-sectionally by TEM without any post treatment, revealing the instantaneous formation of a solid electrolyte interphase (SEI) after only 2 charge-discharge cycles in the cyclic voltammetry (CV) measurement. Thus, AuNPs are promising as a platform for the materials design and characterization in atomic dimensions.

Simulation investigation of the spontaneous motion behaviors of underwater oil droplets on a conical surface.

A conical surface can realize the spontaneous transportation of micro-sized oil droplets in an aqueous environment without energy input, exhibiting great potential for applications in microfluidics, chemical micro-reactors, water remediation, etc. However, the precise manipulation of an oil droplet on a cone is still very challenging because the dynamic behavior of a droplet on a cone is not fully understood. Herein, the dynamic behavior of oil droplets on a cone is quantitively studied via numerical simulations, and the effects of wettability, apex angle, and droplet size on the droplet's dynamic behavior are systematically analyzed. The results show that the moving velocity and transport distance of the droplet on the cone are highly related to the droplet shape on the cone. It was found that a clamshell-shaped droplet moves faster than a barrel-shaped droplet. Besides, the clamshell-shaped droplet with a larger size, on the cone with a smaller apex angle and smaller contact angle tends to obtain a faster moving speed and a longer transportation distance. The droplet shape adopted on the cone was determined by the cone wettability and the size of the droplet relative to the local curvature of the cone. It was found that the oil droplet tends to form a barrel shape on the cone with a highly oleophilic and small apex angle, and tends to form a clamshell shape on cones with a highly oleophobic and large apex angle. In addition, the droplet might transit from a barrel shape to a clamshell shape when it moves from the cone tip to the cone base, and the trigger time of the transit is negatively correlated with the contact angle and apex angle of the cone. This work provides a microscale understanding of the dynamic behavior of an underwater oil droplet on a cone, and also offers theoretical guidance for manipulating the behavior of a droplet on a cone and for the rational design of cone surfaces for spontaneous droplet transport and droplet collection.

All-metal wideband metasurface for near-field transformation of medium-to-high gain electromagnetic sources

Electromagnetic (EM) metasurfaces are essential in a wide range of EM engineering applications, from incorporated into antenna designs to separate devices like radome. Near-field manipulators are a class of metasurfaces engineered to tailor an EM source’s radiation patterns by manipulating its near-field components. They can be made of all-dielectric, hybrid, or all-metal materials; however, simultaneously delivering a set of desired specifications by an all-metal structure is more challenging due to limitations of a substrate-less configuration. The existing near-field phase manipulators have at least one of the following limitations; expensive dielectric-based prototyping, subject to ray tracing approximation and conditions, narrowband performance, costly manufacturing, and polarization dependence. In contrast, we propose an all-metal wideband phase correcting structure (AWPCS) with none of these limitations and is designed based on the relative phase error extracted by post-processing the actual near-field distributions of any EM sources. Hence, it is applicable to any antennas, including those that cannot be accurately analyzed with ray-tracing, particularly for near-field analysis. To experimentally verify the wideband performance of the AWPCS, a shortened horn antenna with a large apex angle and a non-uniform near-field phase distribution is used as an EM source for the AWPCS. The measured results verify a significant improvement in the antenna’s aperture phase distribution in a large frequency band of 25%.

Smart Manipulation of Gas Bubbles in Harsh Environments Via a Fluorinert-Infused Shape-Gradient Slippery Surface

Fundamental research and practical applications have examined the manipulation of gas bubbles on open surfaces in low-surface-tension, high-pressure, and high-acidity, -alkalinity, or -salinity environments. However, to the best of our knowledge, efficient and general approaches to achieve the smart manipulation of gas bubbles in these harsh environments are limited. Herein, a Fluorinert-infused shape-gradient slippery surface (FSSS) that could effectively regulate the behavior of gas bubbles in harsh environments was successfully fabricated. The unique capability of FSSS was mainly attributed to the properties of Fluorinert, which include chemical inertness and incompressibility. The shape-gradient morphology of FSSS could induce asymmetric driving forces to move gas bubbles directionally on open surfaces. Factors influencing gas bubble transport on FSSS, such as the apex angle of the slippery surface and the surface tension of the aqueous environment, were carefully investigated, and large apex angles were found to result in large initial transport velocities and short transport distances. Lowering the surface tension of the aqueous environment is unfavorable to bubble transport. Nevertheless, FSSS could transport gas bubbles in aqueous environments with surface tensions as low as 28.5 ± 0.1 mN/m, which is lower than that of many organic solvents (e.g., formamide, ethylene glycol, and dimethylformamide). In addition, FSSS could also realize the facile manipulation of gas bubbles in various aqueous environments, e.g., high pressure (~ 6.8 atm), high acidity (1 mol/L H2SO4), high alkalinity (1 mol/L NaOH), and high salinity (1 mol/L NaCl). The current findings provide a source of knowledge and inspiration for studies on bubble-related interfacial phenomena and contribute to scientific and technological developments for controllable bubble manipulation in harsh environments.

Transport dynamics of droplet impact on the wedge-patterned biphilic surface

Droplet impact on biphilic surfaces with a wettability contrast has been intensively studied in recent years. In this work the effects of tilting and apex angles on droplet transport dynamics after impacting on a wedge-patterned biphilic surface at low Weber numbers were investigated experimentally. The biphilic surface was fabricated by applying a hydrophobic polymer coating on a bare silicon surface. According to the experimental results, a larger apex angle below 67.4° can accelerate the droplet effectively at first. Then the friction force controls the droplet movement and reduces the speed. The tilting angle along the hydrophilic direction activates the droplet. If the gravity component is opposite to the hydrophilic direction and the tilting angle is over 15°, the droplet can hardly move toward the hydrophilic area. By modeling the hydrodynamics of the droplet movement after impact on a biphilic surface with assumptions of no evaporation, no Marangoni effect, negligible dynamic contact angle variation and negligible rotation effect, the surface tension values versus the position at different apex angles are derived. The predicted position versus time trends agree well with the experimental data. This study aims to provide a better understanding of the mechanisms of droplet hydrodynamics on wedge-patterned biphilic surfaces at low Weber numbers.

Study on the effects of apex angle of the delta-type radiator on thermo-flow performance of natural draft dry cooling tower

A numerical model was established to reveal the effects of apex angle of the vertical arranged delta-type radiators on thermo-flow performance of natural draft dry cooling tower. When radiator number is fixed, a large apex angle along with the corresponding long tower base diameter contribute to tower performance improvement. The wide apex angle slightly mitigates air inflow deviation at radiator’s inlet and draws in more fresh air. The long base diameter alleviates the adverse impacts of internal vortex formed after air inflow convergence on heat transfer of the downstream radiators. The maximum increment of cooling capacity of the tower 15.6% is achieved under the medium wind speed of 8 m/s as apex angel increases from 48° to 60°. As wind speed further increases, sideward and leeward radiators suffer a sharp performance decline, and their performances achieve much smaller enhancement brought by apex angle increase, compared with windward radiators. So downwind deflection of internal rising airflows is more severe under a larger apex angle. When tower base diameter is fixed, larger apex angle results in fewer radiators. Although cooling capacity of the entire tower drops under this strategy, the greater heat dissipation capacity of windward radiators under a larger apex angle would gradually make up the defect of fewer radiators as wind speed increases. However, using larger apex angle but fewer radiators causes an aggravated air inflow rate imbalance among the radiators, which accelerates performance degradations of leeward radiators.

Spreading Dynamics of Droplet Impact on a Wedge-Patterned Biphilic Surface

The influence of apex angle and tilting angle on droplet spreading dynamics after impinging on wedge-patterned biphilic surface has been experimentally investigated. Once the droplet contacts the wedge-patterned biphilic surface, it spreads radially on the surface, with a tendency toward a more hydrophilic area. After reaching the maximum spreading diameter, the droplet contracts back. From the experimental results, the normalized diameter β ( β = D / D 0 ) was found to be related with the Weber number ( W e = ρ D V 2 / γ ) as β max ∼ W e 1 / 5 . during the first spreading process. Below 67.4°, a larger apex angle can help a droplet to spread on the surface more quickly. The maximum spreading diameter has a tendency to increase with the Weber number, and then decrease after the Weber number, beyond 2.7. Approximately, the critical Weber number is about 5, when the droplet lifts off the surface. Considering the effect of apex angle, the maximum normalized spreading diameter has a rough expression as β ∼ α τ

Quantum dot decorated nano-pyramid fiber tip for scanning near-field optical microscopy

We report a new type of nano-optical tip, the quantum dot decorated nano-pyramid fiber tip, for scanning near-field optical microscopy. The nano-pyramid tip has a large apex angle (70.5 degree), and consequently exhibits a significant improvement (17-fold) of the signal collection efficiency compared to conventional tapered fiber tips. Moreover, thanks to the template-based fabrication method and the surface treatment technique, the quantum-dot decorated nano-pyramid tip enjoys a clean and smooth surface, and can be produced with high accuracy and high reproducibility. Experimental results show that, with the nano-pyramid tip, the optical field distribution of a photonic nanostructure can be mapped with a 20 nm resolution (λ/20). It provides a powerful and reliable tool for near-field optical measurements.

Molecular Dynamics Study of Temperature Influence on Directional Motion of Gold Nanoparticle on Nanocone Surface

In this work, the directional motion and underlying mechanism of a circular gold nanoparticle (AuNP) on nanocone (NC) surface were studied with the aid of molecular dynamics simulation. Three specific sized AuNP(s) having particular number of atoms and three nanocones having distinct apex angle were utilized in this work. The simulation was run in a temperature range of 300–1300 K to observe the effect of temperature on the directional motion of AuNP located outside of NC surface. The results revealed that the AuNP tends to move toward the larger-diameter direction of the NC at higher temperature range, whereas it stayed intact on the area around the tip of NC at lower temperature range. It was observed that the average velocity of AuNP located outside the NC surface with large apex angle was comparatively lower than that on the NC surface having small apex angle. Furthermore, it was inspected that the interaction energy of the AuNP is reduced heavily as the temperature is increased, and it decayed more i...

Design of a Novel Linear Shaped Charge and Factors Influencing its Penetration Performance

In this paper, a novel linear shaped charge (LSC), called a bi-apex-angle linear shaped charge (BLSC), has been designed to investigate the improvement of penetration performance. Compared with a traditional single-apex-angle LSC, a BLSC, which consists of a small-apex-angle liner and a large-apex-angle liner, has been investigated by depth-of-penetration (DOP) test. The results show that the penetration depth of BLSC is 29.72% better than that of an ordinary LSC. An Eulerian method is applied to simulate the entire process of jet formation, as well as penetration on a #45 steel target. The effectiveness of the Eulerian model is demonstrated by the good agreement of the computational results with experimental observations. Furthermore, the numerical simulation is developed to investigate the influence of liner thickness, explosive type, combination of small and large apex angle, ratio of small to all apex angle liner, and standoff distance on the penetration performance of BLSCs. The suggested work and results can provide a guide and reference for the structural design of BLSC.

Directional Motion of Water Droplet on Nanocone Surface Driven by Curvature Gradient: A Molecular Dynamics Simulation Study

This research work focuses on the wetting behavior and directional motion of water droplet on the nanocone surface through molecular dynamics simulation approach. A total of five nanocones having different apex angle were utilized to observe the wetting characteristics. In addition, water droplets of different sizes based on containing number of molecules were also considered in this study. The results show that the water droplet spontaneously travels from the tip of the nanocone toward its larger diameter direction in all cases. The average velocity of water droplet on the nanocone surface with smaller apex angle was found to be higher than that with larger apex angle. Moreover, it was found that the energy parameter of the nanocone surface and the size of water droplet have a significant effect on the wetting characteristics and velocity of droplet. Furthermore, three different equilibrium states of the water droplet on the nanocone surface were observed; unwet, partially wet, and fully wet. The velocit...

Probing surface plasmons by bare V-shaped tips: modeling by geometrical optics and rigorous diffraction theory

We consider probing inhomogeneous waves in the near fields of metallic nanostructures with the aid of a dielectric V-shaped wedge connected to a waveguide. A geometrical model based on the local plane interface approach is proposed to describe the interaction of the wedge with the inhomogeneous field. The fundamental ideas behind the geometrical model are validated by comparison with the results given by rigorous diffraction analysis, and applied to probing plasmonic interference patterns generated by metallic gratings with very narrow slits. The model explains intuitively why a bare wedge with a large apex angle is capable of subwavelength resolution in the spirit of scanning near-field microscopy.

Decoding structural complexity in conical carbon nanofibers.

Conical carbon nanofibers (CNFs) exist primarily as graphitic ribbons that fold into a cylindrical structure with the formation of a hollow core. Structural analysis aided by molecular modeling proves useful for obtaining a full picture of how the size of the central channel varies from fiber to fiber. From a geometrical perspective, conical CNFs possibly have cone tips that are nearly closed. On the other hand, their fiber wall thickness can be reduced to a minimum possible value that is determined solely by the apex angle, regardless of the outer diameter. A formula has been developed to express the number of carbon atoms present in conical CNFs in terms of measurable structural parameters. It appears that the energetically preferred fiber wall thickness increases not only with the apex angle, but also with the number of atoms in the constituent graphitic cones. The origin of the empirical observation that conical CNFs with small apex angles tend to have a large hollow core lies in the fact that in graphene sheets that are more highly curved the curvature-induced strain energy rises more rapidly as the fiber wall thickens.

Study on subsurface-inclined crack propagation during machining of brittle crystal materials

There is an immense need to obtain high-quality surface and subsurface on brittle material owing to the advantage of its improved performance. Thus, in this paper, we proposed a mechanical and numerical study of fracture mechanics from the perspective of external loading and indentation geometry in brittle machining. Stress intensity factors are computed to analyze various impacts of external loading and indentation configuration on subsurface crack propagation. Results indicate that the main fracture mode for inclined crack is shear rather than opening and the apex angle of the indentation plays an important role in fracture behavior. As a certain external loading is exerted to the surface of the silicon, a large apex angle of indentation may lead to strong shielding effect on mode II crack propagation. A relationship between critical value of external loading to the crack propagation and the apex angle of the indentation is given in this paper that shows quantitative indication for suppression of crack growth.

Finite deformation of single-walled carbon nanocones under axial compression using a temperature-related multiscale quasi-continuum model

A temperature-related multiscale quasi-continuum (QC) model is presented herein for the investigation of the finite deformation behaviors, especially buckling and post-buckling, of open-tip single-walled carbon nanocones (SWCNCs) in thermal environments. The hyper-elastic constitutive model is established with the use of so-called temperature-related higher-order Cauchy–Born (THCB) rule as the kinematic description for the deformation of SWCNCs. The corresponding meshless computational scheme is developed to accomplish the numerical simulation of the deformation responses of SWCNCs. The numerical results reveal that the present approach is effective and efficient for the prediction of the buckling behaviors of SWCNCs at finite temperature. It is found that the buckling and post-buckling of SWCNCs are strongly dependent on the rotation angle of cutting lines, the top radius, the height and the apex angle. The mechanical properties and buckling of SWCNCs with large top radius and apex angle are close to those of graphene.

Controlling drop bouncing using surfaces with gradient features

Drop hitting on superhydrophobic surfaces usually undergoes spreading and retraction stages before its complete rebound and there exists a minimum amount of time for the spreading and retraction processes. Impressively, it was recently shown that the so-called contact time can be significantly reduced by engineering surfaces with millimeter-scale tapered post arrays that allow the impinging drop to leave the surfaces in a pancake shape at the end of lateral spreading (pancake bouncing). Despite exciting progress, it remains elusive to rationally control the contact time and quantitatively predict the critical Weber number for the occurrence of pancake bouncing. Here, we experimentally demonstrated that the drop bouncing is intricately modulated by the surface morphology. Under the same centre-to-centre post spacing, surfaces with a larger apex angle could give rise to more robust pancake bouncing, which is characterized by significant contact time reduction, smaller critical Weber number, and wider Weber number range. We also developed simple harmonic spring models and theoretically revealed the dependence of timescales associated with the impinging drop and the critical Weber number for pancake bouncing on the surface morphology. The insights learned from this work will allow us to rationally design various surfaces for many practical applications.

Predicting mechanical properties and buckling behavior of single-walled silicon carbide nanocones using a finite element method

In this paper, mechanical properties and buckling behavior of single-walled silicon carbide nanocones (SWSiCNCs) are studied using a finite element method. The elastic moduli of SWSiCNCs with different dimensions including different apex angles and lengths are presented. For large apex angles, it is shown that the effect of nanocone length on the elastic modulus can be neglected. Besides, the critical compressive forces of SWSiCNCs are computed. The influences of dimensions and boundary conditions on the buckling behavior of SWSiCNs are studied in detail. The results show that increasing the nanocone apex angle leads to decreasing the critical compressive force.

Approximate calculation of eigenfrequencies of biconical microwave cavities

Simplified expressions are obtained for the calculation of the eigenfrequencies of a biconical cavity with large apex angles with the use of two symmetrical points at the boundaries of overlapping partial regions in the form of a spherical sector. Using these expressions, the dependence of the cavity eigenfrequencies on the apex angles of the conical elements is studied, and the results are compared with those obtained by the classical finite-element method. The applicability range of the simplified expressions is identified, and recommendations on their use are given.