Concave Surface Research Articles

Combined internal resonances at crossover of slacked micromachined resonators

The dynamics of micro-/nanoelectromechanical systems (M/NEMS) curved beams have been thoroughly investigated in the literature, commonly for curved arch beams actuated with electrodes facing their concave surface. Except for few works on slacked carbon nanotubes, the literature lacks a deep understanding of the dynamics of slacked curved resonators, where the electrode is placed in front of the convex beam surface. This paper investigates the dynamics of slacked curved resonators as experiencing combined internal resonances. The curved slacked resonator is excited using an antisymmetric partial electrode while the electrostatic voltage load is driven to elevated excitations, which breaks the symmetry of the system and affects natural frequencies and corresponding mode shapes. The axial load is tuned to monitor the ratios between the natural frequencies of different vibration modes, which induces simultaneous 1:1 and 2:1 internal resonances between the first and second mode with the third. We observe the interaction of hardening and softening bending of the fundamental backbone curves triggering various patterns of the response scenario and the appearance of coexisting regions of irregular dynamics.

Graphical acoustic computing method incorporated with the shooting and bouncing ray: application to target strength prediction of concave objects with second-order reflection effects

The acoustic backscattering prediction of underwater targets has been drawing concerns from underwater vehicle designers. A graphical acoustic computing method combined with the shooting bouncing ray method (GRACO-SBR) is introduced to solve the acoustic target strength of complex underwater target with concave surfaces. The graphical acoustic computing (GRACO) is an asymptotic method based on physical acoustics. Aided with OpenGL 3D graphical rendering pipeline, this method can process the acoustic integration parallelly and efficiently. Since the traditional GRACO only considers the first-order scattering, the shooting and bouncing ray (SBR) is compounded with the GRACO to cope with the higher-order scattering of concave structures. The target strength of an impedance sphere is solved with several different methods including the GRACO. The results show that the GRACO has an outstanding advantage of the efficiency over the finite element method (FEM) and the traditional Kirchhoff approximation at minor cost of the accuracy in high frequency range. Besides, the prediction of the backscattering of a dihedral corner reflector tells that the GRACO-SBR which considers the second-order scattering can acquire much more accurate solutions than the traditional GRACO method. Further, a stern with cross rudders is considered by both GRACO and GRACO-SBR, and the solutions show that the second-order scattering cannot be overlook when predicting the backscattering of concave structures.

Microscopic mechanisms behind nucleate boiling heat transfer enhancement on large-aspect-ratio concave nanostructured surfaces for two-phase thermal management

• Aspect-ratio effects of nano-cavities on nanoscale boiling are quantitatively illustrated. • The incipient nucleation time and temperature are significantly enhanced for deeper cavities. • An optimal cavity depth for maximal nucleate boiling enhancement is obtained. • Thermal energy accumulation efficiency of liquid at the initial nucleation site are elaborated. • Microscopic mechanisms are elucidated thoroughly by molecular dynamics simulations. Enhancing boiling heat transfer and elaborating underlying mechanisms are of great significance to assist in improving the efficiency of energy systems and solving thermal management bottlenecks in advanced electronics. Numerous experimental studies have proved nanostructured surfaces enable boiling heat transfer to be enhanced strikingly. Nevertheless, it is a great challenge to perform more in-depth research due to the limitation of the observation accuracy of conventional experimental approaches. To optimize designs of nanostructured boiling surfaces and fully reveal the microscopic mechanisms, the aspect-ratio effects of rectangular nano-cavities on nucleate boiling heat transfer are investigated systematically by molecular dynamics simulations in this study. The nano-cavities have the same width of 3 nm and different depths of 2 nm to 8 nm, corresponding to aspect ratios from 2:3 to 8:3. The results illustrate that, compared with the plain surface, concave nanostructured surfaces can cause a significant heat accumulation effect, resulting in remarkable reinforcements in absorbed heat flux and bubble nucleation. The nucleate boiling heat transfer enhancements originating from large-aspect-ratio nano-cavities are fully verified by the notable reductions in the incipient nucleation time and boiling initiation temperature. Attractively, for cavities with the same width, an optimal depth for maximal nucleate boiling enhancement can be obtained, which is 7 nm in the present study. In this case, the incipient nucleation time is about eight times shorter than that for the plain substrate and the decrease in boiling initiation temperature is up to 53 K. Moreover, a novel and straightforward insight into the microscopic enhanced mechanism has been proposed. It is elucidated thoroughly from the perspective of the thermal energy accumulation of liquid at the initial nucleation site by taking into account the heat absorbed from the solid wall and the heat transferred to the adjacent cryogenic liquid comprehensively. These analysis and simulation results are in great agreement. This study provides significant guidance for state-of-the-art two-phase thermal management applications.

Simulation of Toolpaths Using 3D Method Strategies for Complex Shape in Milling Application

Several strategies can be used for machining complex 3D shapes on a 3-axis CNC vertical milling machine in Autodesk Inventor Professional software. However, it is challenging to determine suitable strategies without guidance. Among the strategies involved are Scallop, Radial, Spiral, and Morphed Spiral. The purpose of this study is to compare the toolpaths strategy in terms of machining time by using high-speed machining parameters. A hemisphere shape and a fillet feature in the part are considered complex shapes due to their convex and concave surfaces. There are two step machining processes involved, which are roughing and finishing. Comparison time is focused on finishing the process using those strategies. Actual fixed machining parameters like tool diameter, feed rate, spindle speed, stepover, and cutting depth are used to make simulations of the toolpaths. Based on the simulation, the radial strategy has the shortest machining time and cutting length by more than fifty percent (50%) compared to other strategies. This is due to the fact that this technique generates passes along the arc's radii, which are subsequently projected down on the surfaces. The passes can be linked in a zig-zag pattern between the outer and inner radius, either from inside to outside or outside to inside. However, collisions between the cutting tool and the workpiece must be closely monitored. As a result, cutting length must also be addressed when deciding to use this strategy. In conclusion, high-speed machining with the right machining strategy is essential for increased productivity.

New principles of shaping groove structures of high-aperture non-classical ruled toroidal diffraction gratings using pendulum-type ruling engines

Subject of study. Possible methods for increasing the range of optical parameters of fabricated high-aperture non-classical ruled toroidal diffraction gratings and new mathematical relations for describing the equations of curvilinear projections of grooves, laws of variation of the curvature radius of the closest vertex circle, and variable pitch for these groove projections are presented. Aim of study. The study aimed to improve the principles of designing pendulum-type ruling engines ensuring the implementation of a new method for fabricating high-aperture non-classical ruled concave toroidal diffraction gratings and derive analytical expressions for determining geometric parameters of curvilinear projections of the grooves of these gratings. Method of study. The investigation method was based on the theory of designing precision mechanisms, analytic geometry, and calculus. Main results. The possibility of solving the relevant issue of increasing the size, relative aperture, and relation between the curvature radii in meridional and sagittal cross-sections of high-aperture non-classical ruled toroidal diffraction gratings considering the optimization of their aberrations was demonstrated using pendulum-type ruling engines. In contrast to the available engines, pendulum-type ruling engines should be designed to ensure the intersection between the rotation axes of the diamond and blank carriages as well as alignment of the dimension chains of the structural parameters of the diamond and blank carriages according to the specified curvature radii in meridional and sagittal cross-sections of concave toroidal diffraction gratings. Considering that the cutting edge of the diamond tool must always be in contact with the concave toroidal surface of a substrate along the normal to the surface in all substrate points while ruling all grooves, we established that the system of curvilinear groove projections is described by a system of second-order curves, i.e., ellipse equations. With increasing discrete angle at which the grooves are ruled, the coordinates of the centers of the ellipses gradually shifted in the meridional cross-section from the origin of coordinates (grating vertex) in the direction of the edge light zone by a value directly proportional to the sine of the discrete angle and the difference between curvature radii in the meridional and sagittal cross-sections. Curvature radii of the closest vertex circles of the groove projections are variable parameters directly proportional to the product of curvature radii in the meridional and sagittal cross-sections of the grating and inversely proportional to the variable value of the specified coordinate. The variable pitch of the groove projections on the specified plane is a function that, to a first approximation, depends on the initial groove pitch at the grating vertex and the squared variable value of the specified coordinate and is inversely proportional to the squared curvature radius in the meridional cross-section of the grating. Practical significance. The proposed principles of shaping groove structures of the ruled toroidal diffraction gratings using pendulum-type ruling engines enable fabricating such gratings with extremely large relative aperture and optical size as well as increased range of ratios of their curvature radii in the meridional and sagittal cross-sections, which can be used to design novel advanced spectral instruments. The obtained analytical expressions describing the geometric parameters of the curvilinear groove projections enable correction of the first through third order aberrations of the gratings of the considered type.

Understanding the effects of electrode meso-macropore structure and solvent polarity on electric double layer capacitors based on a continuum model

The structures of electrode meso-macropore and the solvent polarity are the crucial factors dominating the performance of the electric double layer capacitors (EDLCs), but their impacts are usually tangled and difficult to decouple and quantitate. Here the effects of electrode meso-macropore structure and solvent polarity on the specific capacitance of an EDLC are quantitatively investigated using a steady-state continuum model. The simulation results indicate the specific capacitances are significantly affected by the meso-macropore surface structure. The specific capacitances significantly decrease for both convex surface structures but obviously increase for both concave surface structures, with the increase of curvature radius from 1 to 20 nm. As for solvents, the polar solvent with high saturated dielectric permittivity improves the capacitance performance. Moreover, the electrode meso-macropore structure is of more concern compared with solvent polarity when aiming at enhancing the specific capacitance. These results provide fundamentals for the rational design of porous electrodes and polar electrolytes for EDLCs. © 2020 The Chemical Industry and Engineering Society of China, and Chemical Industry Press Co., Ltd.. All rights reserved.

Effects of impacted dynamic hollows and extending dense drops on the concave surface with practical obstacles

In this study, the center of a concave surface was analytically studied using the volume of fluid approach to simulate hollow and dense droplets on a variety of solid obstacles. OpenFoam software was used to carry out the numerical simulations. The hollow droplet’s fluid phase, Glycerine, has an outer diameter of 5.25 mm and its gas phase, air, has a diameter of 4 mm. We looked at the laminar flow of an incompressible Newtonian fluid phase. Jet characteristics and droplet collision hydrodynamic behavior were investigated. Due to the interaction between droplets and shells on the obstacle’s surface and the concave surface, which causes a pressure difference and improves fluid movement, the largest jet size is consequently produced in rectangular obstacles. The sharp obstacle, on the other hand, molds the jet’s shortest length and height.

Crystal structures of FNIP/FGxxFN motif-containing leucine-rich repeat proteins

The Cafeteria roenbergensis virus (Crov), Dictyostelium, and other species encode a large family of leucine-rich repeat (LRR) proteins with FGxxFN motifs. We determined the structures of two of them and observed several unique structural features that set them aside from previously characterized LRR family members. Crov588 comprises 25 regular repeats with a LxxLxFGxxFNQxIxENVLPxx consensus, forming a unique closed circular repeat structure. Novel features include a repositioning of a conserved asparagine at the middle of the repeat, a double phenylalanine spine that generates an alternate core packing arrangement, and a histidine/tyrosine ladder on the concave surface. Crov539 is smaller, comprising 12 repeats of a similar LxxLxFGxxFNQPIExVxW/LPxx consensus and forming an unusual cap-swapped dimer structure. The phenylalanine spine of Crov539 is supplemented with a tryptophan spine, while a hydrophobic isoleucine-rich patch is found on the central concave surface. We present a detailed analysis of the structures of Crov588 and Crov539 and compare them to related repeat proteins and other LRR classes.

Effects of physicochemical properties and structural heterogeneity on mineral precipitation and dissolution in saturated porous media

Physicochemical properties, such as solute concentration, flow acidity and flow rate, regulate flow and reactive transport in porous media. Mineral precipitation – dissolution (PD) dynamically changes the pore structural heterogeneity and affects the physicochemical properties, yet the interplay between the PD process and structural heterogeneity remains unclear. This study took the precipitation of Ca2+ and CO32− (Ca2++CO32−⇌CaCO3) as an example to study the reactive transport behavior under different physicochemical conditions in saturated, heterogeneous-packed porous media. A series of column breakthrough experiments and numerical simulations of the coupled flow and PD processes were conducted. X-ray computed tomography (XCT) and pore morphology analysis were also applied to investigate the effects of calcite precipitation on pore structure. Results demonstrate that solute concentration, flow acidity, and flow rates in homogeneous columns significantly altered the time of the PD process to reach equilibrium, leading to immediate chemical environmental changes, and thus impact reactive transport behavior. Preferential flow paths in heterogeneous-packed columns could lead to early breakthroughs and thereby promoted the transport of calcium carbonate (CaCO3) in saturated porous media. XCT images revealed that surface roughness played an important role in Ca2+ precipitation, i.e., CaCO3 clustered more on concave surface than convex surface, reshaping a round coat outside grain particles. The CaCO3 precipitation could also narrow or even block the pore throats, and thus decrease the pore connectivity, which hinders the breakthrough behavior. Our study provided experimental evidence for a predictive understanding of Ca2+ reactive transport as well as new insights into the changes in soil structural heterogeneity and transport properties during the PD process.

The effect of nozzle geometry on the flow and heat transfer of pulsed impinging jet on the concave surface

The main aim of this paper is to investigate the effect of nozzle geometry on the flow and heat transfer from a pulsed jet into a concave surface. Experiments have been carried out for pulsed circular jet and numerical simulations were done for circular, elliptical, rectangular and square geometries. Numerical solution was performed for the frequency ranges of 25Hz to 100Hz, the jet Reynolds number of 7000, the dimensionless nozzle distance to concave surfaces of 2 and 5. Numerical results show a consistent agreement with experimental results and previous works. Accordingly, the geometry of nozzle directly affects the air entrainment ratio. In addition, with the increase of aspect ratio of the nozzle, average Nusselt number (Nuave) decreases. By pulsating the inlet jet with pulse frequency of 100Hz, the average Nu number for circular/square and elliptical/rectangular jets increases 22% and 15%, respectively. Generally, the pulsation causes a reduction and an increase of the Nuave at low and high frequencies, respectively, compared to that of the steady jet. At low frequencies, the Nuave of circular jet decreases significantly in comparison to that of the square and elliptical jets. However, at high frequencies, circular jet shows higher Nuave compared to other ones. As the distance between the jet and the concave surface increases, the effect of the nozzle shape on Nuave decreases.

Heat transfer characteristics of jet impingement onto the concave surface of a cone

ABSTRACT Heat transfer coefficient measurements for jet impingement onto the concave surface of a cone with apex angles equal to 30° and 70° are reported in this study. Static pressure measurements along the cone surface are also reported which aid in explaining the results from the heat transfer measurements. The conical geometry finds application for the heating of aircraft gas turbine engine nose bullet region which could experience ice formation whenever aircraft operates at higher altitudes. The concave surface of the cone is heated by impinging hot air tapped from the compressor. The heat transfer coefficients, which are significantly different compared to flat surface impingement, and are scarcely available, are reported in this study. The influence of the jet axis coincident with the cone axis and impinging into apex region was studied first. The methodology where a thin stainless-steel foil is heated with a known heat flux by passing electric current through it and then measuring the detailed surface temperature using an infrared thermal camera, was used to compute the wall Nusselt distribution. The Nusselt number variation is presented as a function of nondimensional apex to nozzle spacing (L/D) and the nondimensional axis displacement (O/D). Three different diameter (D equal to 10 mm,14 mm and 20 mm) pipes were used for the concentric impingement case and the Nusselt number distribution was observed not depend on the injection diameter. The jet Reynolds number was varied between 25000 and 82000. The peak Nusselt number values are similar to those for flat plate impingement and do not occur at the cone apex, but at a nondimensional distance between 3.2 and 3.9 for 4.25 < L/D < 10.25 for the 30° cone. The peak Nusselt number values increase by almost 30% with decrease in the L/D from 10.2 to 3.0. Wall static pressure measurements indicated that the peak Nusselt number values occur in regions where the interaction between the incoming and outgoing streams is strongest – these regions occur at distances downstream from the stagnation region toward cone exit. The peak heat transfer coefficient location could not be obtained for the 70° cone, but the measured maximum values are higher by 30–50% compared to those for the 30° case. The jet is able to penetrate further toward the apex of the cone for 70° cone compared to 30° cone shifting the peak heat transfer locations closer to the apex for larger apex angle case. There is insignificant influence of jet diameter on Nusselt number variation for the three diameter values investigated in this study. The influence of displacing the jet axis by a distance equal to half the jet diameter in a direction perpendicular to the cone axis was also studied but detailed measurements were possible only for the 30° cone. Two semi-circular regions, one close to the impingement tube and the other away from the tube, displaying similar heat transfer coefficient behavior were observed. A peak in the Nusselt number occurs in each semi-circular region and the magnitude of the peaks are nearly same and they lie on either side of the peak location observed for the concentric impingement case when the flow geometric parameters are similar for the two cases. The measurements for the 70° cone exhibited all features of the 30° cone but the maximum values were higher by nearly 40% for this case.

Technology of Manufacturing of ZC Cylindrical Worm.

Cylindrical worms are generally machined by the hobbing method using rotary tools, and they are formed in the finishing pass at the full profile height. In this case, the profile of the tool-action surface determines the profile of the machined surface, and for technological reasons, a rectilinear (less frequently circular) axial profile of the tool-action surface is generally assumed. In the currently known technology, machining takes place on special machine tools, and on tools that are specially prepared for a specific outline. The research objective of the article is to present the possibility of creating a helical surface with a circular concave profile on a CNC lathe with a universal tool: a ball-end mill cutter. In the case of the proposed processing method, the surface of the worm is shaped with a spherical-end mill cutter in many passes, and its shape depends on the setting of the tool. This machining method must be performed on CNC machines, and the tool is not geometrically related to the shape of the machined profile. The paper presents the mathematical apparatus for generating a concave helical surface. Based on the calculations, the worm was processed with a spherical-end mill on a CLX350 V4 DMG MORI turning machining center. The surface-quality analysis was carried out on a contact profilographometer, while the dimensional accuracy was verified on a coordinate-measuring machine, and the maximum tolerance field of the measurement was 13 μm. On the basis of the measurements made, the accuracy of the worm outline is consistent with the theoretical assumptions. Using the presented method of machining, we can shape helical surfaces with an assumed profile in the axial section on a CNC machine tool with the use of universal tools.

Flexible wearable hybrid nanogenerator to harvest solar energy and human kinetic energy

Solar energy is a clean energy and it is ubiquitous. The movement of people will generate kinetic energy and happened at any time. If solar energy and human kinetic energy could be harvest at the same time, it will be of great significance. In this paper, we used CNTs to fabricate a solar-thermal structure with special concave surface. The solar-thermal conversion ability of this solar-thermal structure is 14.3% higher than other CNTs surface. One side electrode of the pyroelectric nanogenerator was replaced with multi-strip conductive mesh, which can not only conduct electricity, but also cut the magnetic induction line many times to generate electricity. A compact hybrid nanogenerator was fabricated, the thickness is only 410 µm and the density is only 0.065 g/cm2. The hybrid nanogenerator is very light and thin, so it is very suitable for people wear. Experiments show that the output power density of hybrid nanogenerator can reach 2.78 mW/m2. When participants worn the hybrid nanogenerator during walking and running, it can harvest solar energy and human kinetic energy at the same time. The obtained electrical energy can drive a hygrothermograph to work. In a word, a flexible wearable hybrid nanogenerator to harvest solar energy and human kinetic energy is presented in this paper. This hybrid nanogenerator is suitable for people to wear during outdoor sports, and can realize power supply for outdoor electronic devices.

Asymmetric Jetting during the Impact of Liquid Drops on Superhydrophobic Concave Surfaces.

The impact of liquid drops on superhydrophobic solid surfaces is ubiquitous and of practical importance in many industrial processes. Here, we study the impingement of droplets on superhydrophobic surfaces with a macroscopic dimple structure, during which the droplet exhibits asymmetric jetting. Systematic experimental investigations and numerical simulations provide insight into the dynamics and underlying mechanisms of the observed phenomenon. The observation is a result of the interaction between the spreading droplet and the dimple. An upward internal flow is induced by the dimple, which is then superimposed on the horizontal flow inside the spreading droplet. As such, an inclined jet is issued asymmetrically into the air. This work would be conducive to the development of an open-space microfluidic platform for droplet manipulation and generation.

Enhanced electrochemical performance by structural design of electrolyte surface combining 3D printing technology with multi-physical modelling

Patterned electrolyte surfaces are considered an effective strategy to enhance the cell performance of solid oxide fuel cells by increasing the contact area between the electrode and electrolyte, and subsequently reducing the area specific resistance. In this study, the patterning of an 8 mol% yttria stabilised zirconia (8YSZ) electrolyte surface tailored using the stereolithography (SLA) 3D printing technology and the effects of the electrolyte surface geometry on the cell performance were investigated using multi-physical field simulation and quantitative analysis. Defect-free densified planar and concavo–convex electrolytes were successfully prepared by applying SLA, and the concavo–convex cell yielded a maximum output power density of 288.9 mW cm−2 at 850 °C, which was 46.2 % higher than that of the planar cell. The simulation results revealed significant consumption of reactants and strong electrochemical reactions at the concave surface. Moreover, the hydrogen and oxygen consumptions at the edges were greater than those at the centre of both the concave and convex surfaces, whereas the edges of the concavo–convex structure were more conducive to the electrochemical reaction. Finally, the quantitative correlation between cell performance and the influencing factors was obtained by conducting stepwise linear regression analysis. Reducing the ion transfer path length and providing a sufficiently large effective contact area proved to be a productive strategy for improving cell output performance.

High-order QED correction impacts on phase transition of the Euler-Heisenberg AdS black hole

Two-phase transition branches of the Euler-Heisenberg (EH) anti-de Sitter (AdS) black hole (BH) were derived from its phase transition critical behavior by Magos et al. [Phys. Rev. D. 102, 084011 (2020)]. We found that the phase transition is unstable. Considering the high-order quantum electrodynamics (QED) correction, we re-derive the EHAdS BH solution and investigate its critical thermodynamic quantities. It is found that the corrected EHAdS BH has only one stable phase transition branch, and its critical exponents are equivalent to that of the vdW system. From the microscopic point of view, we also derive its normalized scalar curvature based on the Ruppeiner geometry. Different from two concave surfaces of the scalar curvature without considering the high-order QED correction, we show that the corrected Ruppeiner geometry has only one concave surface. Our results indicate that the phase transition instability derived by Magos $et~al.$ is due to without considering the high-order QED correction.

Structural parameter variation working on the performance of anti-uplift multibell underreamed anchors

The structural parameters of multibell underreamed anchors play a crucial role in anchoring performance. The parameters of multibell underreamed anchor investigations are helpful when exploring optimized anchor structures. Based on the results of small-scale physical modelling tests, two types of multibell underreamed anchors were adopted under vertical uplifting loads. Numerical investigations were employed to study the effect of bell spacing, underream structure and bell dimension on the ultimate uplift bearing capacity. After an analysis of the anchorage mechanism, the anchoring efficiency was evaluated by the anchoring force provided by the unit concrete usage of the anchor, and the structural parameter λ equal to the surface area ratios of the expanded bell cone to the straight shaft between bells was defined. Then, the anchoring efficiency optimized structural parameters were presented. An analysis of model tests and simulation results showed that compared to concave bell surfaces, the convex shape could enhance the ultimate bearing capacity of a multibell underreamed anchor. There is an optimal value for the spacing of neighbouring bells, and there are three models of mechanisms for multibell anchors pulling out. When λ ∈ [1, 1.8], the multibell anchors can perform most efficiently to achieve their structural advantages.

Clinical efficacy of mandibular complete dentures with a resilient liner: study protocol for a multicenter randomized controlled trial

BackgroundDuring restoration of poorly fitting complete dentures (CDs) in edentulous patients, liners are used to reconstruct the concave surfaces of CDs with a new base material. These relining materials are classified into resilient liners (RLs) and non-resilient liners (NRLs), but the clinical effects of these liners and their selection criteria remain unclear. The purpose of this study is to evaluate the clinical efficacy of relining mandibular CDs using RL and NRL and to conduct a follow-up study.MethodsThe study is currently being conducted at eight centers, and a parallel-group randomized controlled trial (RCT) is underway. One hundred thirty-two edentulous patients with poorly fitting mandibular CDs will be assigned to two groups based on whether they will receive RL or NRL. Participants will have an RL or NRL applied for relining their CDs using an indirect method of dynamic impressions. Data will be recorded at 1 week and 3, 6, and 12 months after denture delivery. The primary outcome will be assessment of the patients’ general satisfaction by using a 100-mm visual analog scale (VAS). Secondary outcomes will be measured as patient-reported outcomes, including food intake status and oral hygiene-related quality of life. Masticatory performance and the number of sore spots on the oral mucosa will also be recorded. Comparisons between the two groups and within-subject comparisons of pre- and post-intervention measurements will be conducted.DiscussionFor dentists and prosthetic researchers in Japan, this RCT will provide information on the clinical efficacy of RL materials in comparison to RNL in CD wearers. The new evidence regarding the use of RL materials in an aging population will also be useful to dentists in other countries in their routine clinical practice.Trial registrationThis clinical trial has been registered at the University Hospital Medical Information Network (UMIN) Center (UMIN000041950).

On Finding Determinantal Equations Involving the Coordinates of the Object Point, Point of Incidence, Point of Observation and the Image Point in Cases of Reflection and Refraction

This paper is concerned with the procedure of finding determinantal equations, each of which involves the coordinates of the object point, point of incidence, point of observation, and the image point in cases of reflection and refraction of light. An algorithm has been presented for the said purpose and it has been subsequently employed for the generation of relevant determinantal equations by considering some particular cases of reflection and refraction, based on which the readers will be able to reach the desired goal for all other remaining cases of reflection and refraction. Overall, two sets of such determinantal equations have been found to prevail in the present study. One resulted from handling the following cases: (i) Reflection at a plane reflecting surface, (ii) Refraction at a plane surface of discontinuity regardless of whether light moves from a rarer medium to a denser medium or from a denser medium to a rarer medium. The second one has been found while going through the following cases: (i) Reflection at a concave spherical reflecting surface, (ii) Reflection at a convex spherical reflecting surface, (iii) Refraction at a concave spherical surface of discontinuity regardless of whether light passes from a rarer medium to a denser medium or from a denser medium to a rarer medium, (iv) Refraction at a convex spherical surface of discontinuity regardless of whether light moves from a rarer medium to a denser medium or from a denser medium to a rarer medium

Experimental and numerical investigation of the effects of the jet diameter and arrangement of effusion holes on the concave surface of an impingement/effusion cooling system

Experimental and numerical investigation of the effects of the jet diameter and arrangement of effusion holes on the concave surface of an impingement/effusion cooling system