Degree Of Taper Research Articles

SLM-printed lattice structures with tapered vertical struts: Design, simulation and experimentation

This study, designed new lattice structures using vertical struts that taper off. The degree of tapering was controlled using a parameter called “α”. To fabricate these structures, 3D-printing technology known as SLM (selected laser melting) was used. These lattice structures were also simulated using finite element analysis (FEA) and tested experimentally. The used material was 316L stainless steel. Stress–strain curves provided insights into their deformation behavior, revealing a noteworthy occurrence: the unloading modulus exceeded the loading modulus. The mechanical properties of these absolute and density-normalized lattice structures, demonstrated improvement with higher values of the shape parameter α. Yield stress increased by 31 %, loading modulus by 21 %, and energy absorption by 33 %. Specific yield stress improved by 24 %, and specific energy absorption increased by 27 %. While simulation and experimental results exhibited a correlation, they differed significantly in modulus estimation, with simulations overestimating it by more than 30 %.

Multi-objective optimization of custom implant abutment design for enhanced bone remodeling in single-crown implants using 3D finite element analysis

The optimal configuration of a customized implant abutment is crucial for bone remodeling and is influenced by various design parameters. This study introduces an optimization process for designing two-piece zirconia dental implant abutments. The aim is to enhance bone remodeling, increase bone density in the peri-implant region, and reduce the risk of late implant failure. A 12-month bone remodeling algorithm subroutine in finite element analysis to optimize three parameters: implant placement depth, abutment taper degree, and gingival height of the titanium base abutment. The response surface analysis shows that implant placement depth and gingival height significantly impact bone density and uniformity. The taper degree has a smaller effect on bone remodeling. The optimization identified optimal values of 1.5 mm for depth, 35° for taper, and 0.5 mm for gingival height. The optimum model significantly increased cortical bone density from 1.2 to 1.937 g/cm3 in 2 months, while the original model reached 1.91 g/cm3 in 11 months. The standard deviation of density showed more uniform bone apposition, with the optimum model showing values 2 to 6 times lower than the original over 12 months. The cancellous bone showed a similar trend. In conclusion, the depth and taper have a significant effect on bone remodeling. This optimized model significantly improves bone density uniformity.

Evaluation of Convergence Angles in Posterior Crown Preparations by Dental Students at Zawia University

Background and objectives: Achieving optimal axial taper and occlusal convergence in crown preparations is a crucial concern among dental students. Proper preparation design is essential for the long-term success of full-coverage restorations. This study aimed to evaluate the convergence angles and axial taper achieved by dental students in their crown preparations. Methods. A total of 80 posterior tooth preparations (40 mandibular first molars and 40 mandibular second molars) created by second-year dental students on a dental simulator were analyzed. The total occlusal convergence (TOC), bucco-lingual (BL) and mesio-distal (MD) convergence angles, as well as the degree of taper on the axial walls, were measured using the B&B dental software (Guide system, B&B, Italy). Statistical analysis was performed using SPSS version 27. Results. The overall mean of the total convergence angle was 21.88°, with a BL convergence angle mean value of 23.11° (standard deviation of 13.3°) and an MD convergence angle mean value of 20.66° (standard deviation of 11.0°). The results showed a statistically significant difference between the mesial axial taper and the distal axial taper (p-value < 0.001). However, no significant differences were observed between the buccal axial taper and lingual axial taper (p-value > 0.05), or between the BL convergence angle and MD convergence angle (p-value > 0.05). Conclusion. The study revealed variations in the convergence angles of full metal crown preparations created by dental students. The recommended convergence angle was difficult for these students to achieve.

Molecular characterization uncovering a novel genus of tapering-filamentous cyanobacteria from Thailand: Phayaothrix lacustris gen. & sp. nov. (Nostocales, Cyanophyta)

In this study, novel Calothrix-like strains NUACC09 and NUACC10 were isolated from the surfaces of rocks in Phayao Lake, Thailand. Morphological, molecular and ecological comparisons were investigated to characterize the taxonomic status of these novel strains. Under the light microscope, morphological studies indicated that these two strains were morphologically similar to Calothrix but could be differentiated by production of a non-hyaline hair at the terminal end, a low degree of tapering, twisted or loop-forming filaments, a knotted growth form, intertwined trichomes and presenting more than one trichome within the single sheath. In the 16S rRNA and rbcLX gene phylogenetic tree analyses, our strains formed a monophyletic clade with former freshwater/terrestrial Calothrix-like taxa separating distantly from other Calothrix-like genera. Furthermore, low 16S rRNA gene sequence similarity (<94.9%) to the closely related genera and species delimitation analyses (PTP/bPTP, GMYC, ABGD and ASAP methods) indicated that this clade should be considered as a different cyanobacterial lineage. The phylogenetic tree and secondary structures (D1–D1′, V2, Box-B and V3 helix) based on 16S–23S rRNA ITS regions suggested that multiple species might be contained in this clade. Therefore, here, Phayaothrix was proposed as a novel cyanobacterial genus with Phayaothrix lacustris sp. nov. as the type species following the International Code of Nomenclature for algae, fungi and plants.

Low-Friction and -Knocking Diesel Engine Cylindrical-Tapered Bore Profile Design

To reduce the friction loss and the piston-knocking noise from the perspective of the design of the cylinder bore profile, the piston-ring cylinder bore (PRCB) dynamic model of an L6 diesel engine was developed using AVL-Excite-Piston & Rings. Based on the full-scale test method, the effects of bore taper, starting height of tapered profile, and ellipticity on the friction power and knocking energy of the PRCB system were investigated, and the optimization of the design of the bore profile was carried out with the objectives of minimizing the system’s friction power and the peak knocking kinetic energy. The results showed that the taper of the cylinder bore has the greatest influence on the system’s friction power and the peak knocking kinetic energy, followed by the starting height of the conical profile. For the peak knocking kinetic energy of the piston, there was an obvious interaction between the taper and the starting height of the conical profile. When the taper was 35 μm and 45 μm, the peak knocking kinetic energy showed a decreasing and then increasing trend with the increase in the starting height of the profile, and when the taper was 55 μm the peak knocking kinetic energy monotonically was decreased with the increase in the starting height of the conical profile. The optimization results showed that the system’s friction power was decreased by 15.05% and the peak knocking kinetic energy was decreased by 21.41% for a taper degree of 55 μm, a tapered profile starting height of 31 mm, and an ellipticity of 50 μm compared to the initial cylindrical cylinder bore.

Experimental study on new structure teeth in a high-temperature environment.

In high-temperature drilling, especially in high-temperature geothermal drilling, cone bits often experience common and severe tooth loss. This issue significantly reduces the cone bit's service life and has a detrimental impact on drilling efficiency. The quality of the fixed teeth plays a crucial role in the performance of the cone bit. In high-temperature environments, conventional methods fail to meet the requirements for securing the cone bit's teeth. Therefore, to address the tooth loss problem in high-temperature drilling, a new tapered tooth structure is proposed. Laboratory experiments were conducted to secure teeth with varying tapers at both normal and high temperatures. The results revealed that the maximum fastening force increased progressively with the degree of taper, reaching its peak at C50. Compared to conventional cylindrical teeth, the maximum fastening force increased by approximately 88.6%-271.1% at different temperatures. The tapered structure demonstrated superior tooth-fixing strength. The maximum fastening force is the smallest at 300 °C, approximately 23.7%-61.2% lower than at normal temperature. Under the same interference conditions, the maximum fastening force increased with greater taper. With interference values of 0.075, 0.095, and 0.115, the maximum fastening force increased by 48.9%-175.1%, 14%-141.6%, and 53%-271.1%, respectively, when compared to cylindrical teeth with C300, C200, C100, and C50 tapers. The tapered structure exhibited superior tooth-fixing strength and significantly enhanced tooth retention strength at high temperatures.

Parametric optimization of hole taper control in ultraviolet nanosecond laser micro-drilling of copper foil

While hole taper is inevitably formed in the laser micro-drilling of through micro-holes, the formation propensity is largely determined by the interaction between laser processing parameters. In the present work, we perform numerical simulations and experiments to investigate the ultraviolet nanosecond laser micro-drilling of 1 mm diameter through micro-holes on copper foil with a thickness of 280 μm, with an emphasis on the coupled influence of laser processing parameters on both the hole taper and circularity. Firstly, the characteristics of formed micro-hole quality are experimentally characterized, and the formation mechanisms of hole taper are further revealed by finite element simulations of multi-pulse laser ablation. Then, the relational degree of individual laser processing parameters in determining the hole taper and circularity is discovered by experimental investigation based on the gray relational analysis model. Finally, the coupled effect between significant parameters of laser power and repeat scanning number on the hole taper and circularity is further investigated by utilizing the response surface methodology, which derives the optimum laser processing parameters for manufacturing 1 mm diameter through micro-hole with a taper degree of 2.556° and a circularity of 0.992 on the copper foil.

The Effect of Hot Wind on Needle and Stem Water Status: Response Strategies in Resprouting and Non-Resprouting Pine Species

High temperatures threaten tree survival and regeneration. A few pine species, such as Pinus oocarpa and Pinus canariensis, resprout after complete defoliation, a likely consequence of evolving in volcanic environments. Pinus pinea and Pinus pinaster rely on other mechanisms to survive wildfires. We hypothesized that the needle water potential (Ψ) and needle osmotic potential (Ψs) would decrease more under hot wind in resprouting species, a strategy of needle sacrifice in accordance with the hydraulic segmentation hypothesis. We submitted two-year-old seedlings to a two-phase hot wind treatment, consisting of one hour at 39 °C followed by five minutes at 70 °C. Phase 2 killed all needles. In non-resprouting species, Ψ decreased steeply at the beginning of Phase 1 and remained between −2 MPa and −4 MPa afterward, maintaining the loss of stem hydraulic conductance below the 50% threshold. On average, resprouting species had 15% lower wood densities and kept 51% higher stem water contents than non-resprouting species after Phase 2. The loss of hydraulic conductance did not affect resprouting. The increase in hydraulic conductance toward the base of the stem was lowest in P. canariensis, suggesting a lower degree of conduit tapering in the only species that had not undergone heteroblastic change. We measured the lowest Ψ and highest Ψs in the most xeric P. canariensis and the opposite in the most mesic P. oocarpa, highlighting the roles of xylary and extra-xylary hydraulic resistances in compartmentalizing the needle to preserve the stem. The measurement of both Ψ and Ψs allowed us to characterize the strategies of response to hot wind in resprouting and non-resprouting pine species.

Effect of customized abutment taper configuration on bone remodeling and peri-implant tissue around implant-supported single crown: A 3D nonlinear finite element study.

The optimal configuration of a customized implant abutment plays a crucial role in promoting bone remodeling and maintaining the peri-implant gingival contour. However, the biomechanical effects of abutment configuration on bone remodeling and peri-implant tissue remain unclear. This study aimed to evaluate the influence of abutment taper configurations on bone remodeling and peri-implant tissue. Five models with different abutment taper configurations (10°, 20°, 30°, 40°, and 50°) were analyzed using finite element analysis (FEA) to evaluate the biomechanical responses in peri-implant bone and the hydrostatic pressure in peri-implant tissue. The results demonstrated that the rate of increase in bone density was similar in all models. On the other hand, the hydrostatic pressure in peri-implant gingiva revealed significantly different results. Model 10° showed the highest maximum and volume-averaged hydrostatic pressures (69.31 and 4.5mmHg), whereas Model 30° demonstrated the lowest values (57.83 and 3.88mmHg) with the lowest excessive pressure area. The area of excessive hydrostatic pressure decreased in all models as the degree of abutment taper increased from 10° to 30°. In contrast, Models 40° and 50° exhibited greater hydrostatic pressure concentration at the cervical region. In conclusion, the abutment taper configuration had a slight effect on bone remodeling but exerted a significant effect on the peri-implant gingiva above the implant platform via hydrostatic pressure. Significant decreases in greatest and average hydrostatic pressures were observed in the peri-implant tissues of Model 30°. However, the results indicate that implant abutment tapering wider than 40° could result in a larger area of excessive hydrostatic pressure in peri-implant tissue, which could induce gingival recession.

The performance of tapered composite plate girders loaded in shear: An experimental and numerical investigation

Composite non-prismatic girders have been used in modern bridges worldwide. Experimental and theoretical studies were performed to investigate prismatic steel plate girders. However, research on evaluating the behavior of tapered composite plate girders is limited. This study examines the ultimate shear capacity of tapered composite plate girders. Five large-scale girders, one prismatic and four tapered, were tested under a single-point load at midspan to determine their ultimate shear capacity and shear failure mechanism. The taper angles (0°, 5°, 10°, and 15°) and web openings were considered. The failure mode of the tapered plates was also studied. In addition, a numerical simulation was performed to evaluate the influence of the shape and size of the web openings on the shear capacity of the tapered composite plate girders. The results indicated that the taper angles significantly affected the stiffness and ultimate load of the girders. The magnitude of the maximum drop in the shear capacity of the taper degree of 15° was approximately 18.7%. It was also observed that the web opening decreased the capacity of the girder because the rigidity of the web decreased. The decrease in strength of the girder with web opening was 27% compared with the strength of the sold web. Moreover, the validity of the developed finite element (FE) models was verified using corresponding experimental specimens. The results indicate that the FE model can predict the ultimate shear capacity of the tapered composite plate girders.

Root and branch hydraulic functioning and trait coordination across organs in drought-deciduous and evergreen tree species of a subtropical highland forest.

Vessel traits are key in understanding trees' hydraulic efficiency, and related characteristics like growth performance and drought tolerance. While most plant hydraulic studies have focused on aboveground organs, our understanding of root hydraulic functioning and trait coordination across organs remains limited. Furthermore, studies from seasonally dry (sub-)tropical ecosystems and mountain forests are virtually lacking and uncertainties remain regarding potentially different hydraulic strategies of plants differing in leaf habit. Here, we compared wood anatomical traits and specific hydraulic conductivities between coarse roots and small branches of five drought-deciduous and eight evergreen angiosperm tree species in a seasonally dry subtropical Afromontane forest in Ethiopia. We hypothesized that largest vessels and highest hydraulic conductivities are found in roots, with greater vessel tapering between roots and equally-sized branches in evergreen angiosperms due to their drought-tolerating strategy. We further hypothesized that the hydraulic efficiencies of root and branches cannot be predicted from wood density, but that wood densities across organs are generally related. Root-to-branch ratios of conduit diameters varied between 0.8 and 2.8, indicating considerable differences in tapering from coarse roots to small branches. While deciduous trees showed larger branch xylem vessels compared to evergreen angiosperms, root-to-branch ratios were highly variable within both leaf habit types, and evergreen species did not show a more pronounced degree of tapering. Empirically determined hydraulic conductivity and corresponding root-to-branch ratios were similar between both leaf habit types. Wood density of angiosperm roots was negatively related to hydraulic efficiency and vessel dimensions; weaker relationships were found in branches. Wood density of small branches was neither related to stem nor coarse root wood densities. We conclude that in seasonally dry subtropical forests, similar-sized coarse roots hold larger xylem vessels than small branches, but the degree of tapering from roots to branches is highly variable. Our results indicate that leaf habit does not necessarily influence the relationship between coarse root and branch hydraulic traits. However, larger conduits in branches and a low carbon investment in less dense wood may be a prerequisite for high growth rates of drought-deciduous trees during their shortened growing season. The correlation of stem and root wood densities with root hydraulic traits but not branch wood points toward large trade-offs in branch xylem towards mechanical properties.

Microbiological analysis of bacterial sealing of internal conical implants with different taper angles.

The present study evaluated the effect of the taper angle of different internal conical connection implants and cyclic loading on the implant-abutment bacterial seal. A total of 96 implant-abutment sets were divided into eight groups. Four groups of different taper degrees with cyclic mechanical loading of 500,000 cycles per sample, with a 120-N load at 2 Hz before analysis [16DC (16-degree, cycled), 11.5DC (11.5-degree, cycled), 3DC (3- degree, cycled) and 4DC (4- degree, cycled)] were compared to four control groups without cyclic loading [16D (16-degree), 11.5D (11.5-degree), 3D (3-degree), and 4D (4-degree)]. Microbiological analysis was performed by immersing all samples in a suspension containing Escherichia coli and incubating them at 37°C. After 14 days, the presence of bacterial seals was evaluated. Fisher-Freeman-Halton exact tests and binomial tests were performed (5% significance level). The groups showed significant differences in bacterial seal, and mechanical load cycling improved the bacterial seal in the 3DC group. In all other groups, no significant differences in bacterial seal were found between cycled and uncycled samples. To conclude, the internal conical connection with a 3-degree taper angle showed better results than the other connection with different angles when subjected to load cycling. However, none of the angles tested were fully effective in sealing the implant-abutment interface.

Objective assessment of tapering of the fingers in adults.

Mild proximal-to-distal tapering of the fingers is a relatively common trait in humans. When more extreme, finger tapering is a feature observed in many genetic syndromes. The range of variation for finger tapering in the general population is not well understood, and sex differences in the degree of tapering, while suspected, have not been documented. Part of the difficulty is a lack of objective methods to evaluate finger tapering. In the present report, we developed a tapering index based on linear measures derived from digital hand scans. We measured this index in a sample of 166 male and 166 age-matched female adults. We then looked at correlations both among fingers and with demographic and anthropometric variables, followed by tests for sex differences. We observed weak correlations between tapering and age, height and weight. Correlations between pairs of fingers tended to be more in the moderate range and were highest among the middle three fingers (ranging from 0.34 to 0.64). Tapering tended to increase slightly moving radially across the hand from the fifth finger to the second finger. Males showed less tapering than females for all fingers, with statistically significant differences involving the left second finger (p = 0.003), left fifth finger (p< 0.001), right second finger (p = 0.038), and right fourth finger (p = 0.021). Finally, we established baseline norms for both males and females out to three standard deviations. Our results indicate that finger tapering is present, to some degree, in most of the population and that the trait can be measured using a relatively simple and non-invasive method. These findings may have relevance for fields as diverse as medical genetics, forensics, and industrial design.

Electrolyte Channel Design By Physical Model and Machine Learning

Thick electrode is highly effective to increase the specific energy of a battery cell, but the associated increase in transport distance causes a major barrier for fast charging. We introduce a bio-inspired electrolyte channel design into thick electrodes to improve the cell performance, especially under fast charging conditions. The effects of channel length, width, tapering degree and active material width on the electrochemical performance and mechanical integrity are investigated. Machine learning by deep neural network (DNN) is developed to relate the geometrical parameters of channels to the overall cell performance. Integrating machine learning with the Markov chain Monte Carlo gradient descent optimization, we demonstrate that the complicated multivariable channel geometry optimization problem can be efficiently solved. The results show that within a certain range of geometrical parameters, the specific energy, specific capacity and specific power can be greatly improved. At the same time, the maximum first principal stress which is in the cathode region next to the separator can be significantly reduced, giving better mechanical integrity. Comparing to conventional designed cells without electrolyte channels, we show a 79% increase in specific energy using channel design optimization. This study provides a design strategy and optimization method to achieve significantly improved battery performance

Performance Analysis of the Self-Pumping Hydrodynamic Mechanical Seal with a Conical Convergent Diffuser Groove

Requirements such as high opening force, low leakage rate, and design without matching auxiliary flushing systems are expected of the modern fluid machinery shaft seals used in the process industry. A self-pumping hydrodynamic mechanical seal with a conical convergent diffuser groove is proposed and its sealing performance is studied by numerical simulation in this paper. Further, its sealing performance is compared to that of a flat-bottomed equal cross-sectional diffuser groove and the results have shown that the proposed seal has more superior sealing performance. The influence of structural and operating parameters on the sealing performance of the proposed seal is discussed and its working mechanism is explained. The results have shown that when the structural parameters of the spiral groove and the operating parameters are the same, the proposed design has a similar leakage rate and a higher opening force. The conical convergent diffuser groove has better wrapping properties, whereas the fluid energy is utilized more efficiently, improving the sealing interface opening force. The taper degree variation causes a slight change to the pressure at the root of the spiral groove, causing slight fluctuations in the seal leakage rate. The research results broaden the design of non-contact mechanical seals and provide a theoretical basis for the engineering application of the proposed self-pumping hydrodynamic mechanical seal with a conical convergent diffuser groove.

Assessment of the middle mesial canals of mandibular first molars using cone-beam computed tomography: an in vivo study.

For a successful root canal therapy, it is necessary to locate all the canals debride and seal them with an inert filling material. The clinician must be aware of the internal morphology and variations in a permanent tooth. Mandibular first molars are widely studied to identify variations in the anatomy of the pulp space. In this study, the primary objective was to measure the distance between the mesiobuccal (MB) and mesiolingual (ML) canals in patients with and without a middle mesial canal (MMC) using cone-beam computed tomography (CBCT). The secondary objectives were to assess the tapering degree of the mesial root and to measure the dentinal thickness in relation to the danger-zone area in patients with and without an MMC. A total of 200 CBCT scans were evaluated for the presence of an MMC. Two observers performed the observations, and the results obtained were subject to statistical analyses. The results revealed the prevalence of MMC was 5%. The average distance between the MB and ML canals was higher when there was an MMC [M(SD) = 3.61 (0.6) vs. 2.69 (0.66)]. However, there were no differences between the groups in the distance to the danger-zone area and the tapering degree of the mesial root. On CBCT images, the MMC was clearly visible 3 mm apical to the level of the cementoenamel junction; beyond 3 mm, the MMC could not be traced. Based upon the results of this study, the average distance between the MB and ML canals was higher when there was an MMC. A lesser degree of taper would be preferred to prepare the MMC than to prepare the other canals. It is recommended that careful examination of the canal 3 mm apical to the cementoenamel junction should be carried out when attempting to detect an MMC.

Anatomical variation of the aorta in the West of Scotland - A population with high cardiovascular disease burden. Implications for stent design and deployment.

The prevalence and complexity of cardiovascular disease (CVD) in the West of Scotland are high with the aortic arch and abdominal aorta, particularly at increased risk of cardiovascular pathology. Stent deployment can be key in preventing further cardiovascular events, however, current stent design does not account for complex advanced CVD in these areas. This cadaveric study aimed to provide anatomical measurements requested by manufacturers to improve stent design and deployment in this target population. Nine cadavers (six females and three males; age range=82.7±10.4years) from the West of Scotland were dissected to expose the aortic arch and abdominal aorta. Digital callipers and protractors were used to collect data on vessel diameters (including taper), branch spacing, angles and presence of collaterals. CVD was present in all cadavers and ranged from mild plaque presence to aortic dissections. One possessed a bovine aortic arch variation. Supra-aortic vessels were approximately equally spaced, but the left common carotid had the most acute branching angle. Angulation of the arch from the coronal plane positively correlated with a deviation of the left subclavian artery (LSA) from the sternal midline (Spearman's coefficient r=0.82, p=0.01) which may impact surgical access. The origin of the vertebral artery on the LSA was also highly variable. The diameter of the descending aorta decreased along its length from the aortic hiatus to superior mesenteric by 21±10% indicating a high degree of taper. The artery of Adamkiewicz was present in 33% and additional renal collaterals were present in 22%. 66% had tortuous vessels in the abdominal region. These results highlight the need for more data to aid the refinement of stent-graft design and deployment methods to ensure successful surgical intervention in this population.

Fabrication of 2 × 1 signal combiner for high power lasers based on D-shaped fiber pair

The all-fiber signal combiner based on incoherent beam combination is the key component to realize the power amplification of fiber laser. At present, the all-fiber combiner is generally fabricated by splicing a tapered fused fiber bundle with an output fiber. During the tapering process, the size of the cladding and core of the input fiber will become smaller at the same time, which will inevitably cause the core mode to change to the cladding mode. To reduce the degree of taper, the method of hydrofluoric acid corrosion is generally used to remove part of the cladding of the input fiber to make the diameter of the optical fiber smaller. Even so, the tapering process is still unavoidable. Therefore, we have proposed a new manufacturing method for the all-fiber signal combiner. This method uses a CO2 laser to ablate part of the cladding of the input optical fiber to produce a D-shaped fiber. Then, the planes of the two D-shaped optical fibers are pressed tightly and then heated to get fused. Finally, the D-shaped fiber pair is cut and spliced with an output fiber to form an all-fiber combiner. This novel method avoids the tapering process and hardly changes the core size of the input fiber. The relationship between the core distance of the input fiber and the beam quality of the signal combiner manufacturing by the new method is studied by the finite-difference beam propagation method. We also compared the combining ability and beam quality of the combiner made based on the D-shaped fiber and that made by the tapered fiber bundle. Both the simulation and experimental results showed that the beam quality of the combiner made based on the D-shaped fiber was better than that made by the traditional method.

Correction to: A trade-off between thickness and length in the zebra finch sperm mid-piece.

You have accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Mendonca Tania, Birkhead Tim R., Cadby Ashley J., Forstmeier Wolfgang and Hemmings Nicola 2021Correction to: A trade-off between thickness and length in the zebra finch sperm mid-pieceProc. R. Soc. B.2882021169520211695http://doi.org/10.1098/rspb.2021.1695SectionYou have accessCorrectionCorrection to: A trade-off between thickness and length in the zebra finch sperm mid-piece Tania Mendonca Tania Mendonca http://orcid.org/0000-0002-6232-4970 Google Scholar Find this author on PubMed Search for more papers by this author , Tim R. Birkhead Tim R. Birkhead Google Scholar Find this author on PubMed Search for more papers by this author , Ashley J. Cadby Ashley J. Cadby Google Scholar Find this author on PubMed Search for more papers by this author , Wolfgang Forstmeier Wolfgang Forstmeier http://orcid.org/0000-0002-5984-8925 Google Scholar Find this author on PubMed Search for more papers by this author and Nicola Hemmings Nicola Hemmings http://orcid.org/0000-0003-2418-3625 Google Scholar Find this author on PubMed Search for more papers by this author Tania Mendonca Tania Mendonca http://orcid.org/0000-0002-6232-4970 Google Scholar Find this author on PubMed Search for more papers by this author , Tim R. Birkhead Tim R. Birkhead Google Scholar Find this author on PubMed Search for more papers by this author , Ashley J. Cadby Ashley J. Cadby Google Scholar Find this author on PubMed Search for more papers by this author , Wolfgang Forstmeier Wolfgang Forstmeier http://orcid.org/0000-0002-5984-8925 Google Scholar Find this author on PubMed Search for more papers by this author and Nicola Hemmings Nicola Hemmings http://orcid.org/0000-0003-2418-3625 Google Scholar Find this author on PubMed Search for more papers by this author Published:08 September 2021https://doi.org/10.1098/rspb.2021.1695See original article.A trade-off between thickness and length in the zebra finch sperm mid-pieceProc. R. Soc. B285, 20180865. (Published online 25 July 2018) (doi:10.1098/rspb.2018.0865)The original article contains a typographical mistake in the formula notation for the volume of the sperm mitochondrial helix. In the discussion (paragraph 6), we refer to the formula as ‘v = (1/3)π(r2)T’; however, the formula used in our calculations was ‘v = π(r2)T’, where π(r2) is the mitochondrial cross-section area and T is the straightened helix length. The latter formula can be expanded to ‘v = (1/3)π(r12 + r1r2 + r22)T’ to describe a truncated cone, where r1 and r2 are the radii at either end of the truncated cone. We refer to this formula in our electronic supplementary material where we show that the trade-off between thickness and length persists irrespective of the degree of taper in the mitochondrial helix. This error does not impact any of the data, analyses, results or conclusions of our paper. Previous Article FiguresRelatedReferencesDetailsRelated articlesA trade-off between thickness and length in the zebra finch sperm mid-pieceJul 25, 2018, 12:00:00 AMProceedings of the Royal Society B: Biological Sciences This Issue08 September 2021Volume 288Issue 1958 Article InformationDOI:https://doi.org/10.1098/rspb.2021.1695PubMed:34493085Published by:Royal SocietyPrint ISSN:0962-8452Online ISSN:1471-2954History: Published online08/09/2021Published in print08/09/2021 License:© 2021 The Author(s)Published by the Royal Society. All rights reserved. Citations and impact Subjectsbehaviourevolutioncellular biology Large datasets are available through Proceedings B's partnership with Dryad

In Vitro Evaluation of the Effect of Different Luting Cements and Tooth Preparation Angle on the Microleakage of Zirconia Crowns

Introduction Discrepancy between the crown border and prepared tooth margin leads to a microleakage that eases the penetration of microorganisms and causes the dissolution of luting cement consequently. Several factors should be considered to achieve optimal fitness, including tooth preparation taper and type of cementing agent. The study aimed to determine the relation of tooth preparation taper and cement type on the microleakage of zirconia crowns. Materials and Methods Fifty-six freshly extracted premolars without caries and restorations were selected as the study sample and divided into two groups of different tapering degrees (6 and 12 degrees). Zirconia copings were designed and fabricated by the CAD/CAM system. The samples were divided into four subgroups for cementation, and each subgroup was cemented with a different luting cement (n = 7). After 5000 thermocycles at 5°C–55°C and dye penetration, the specimens were sectioned in the mid-buccolingual direction, and a digital photograph of each section was taken under a stereomicroscope. Data were analyzed by the Kruskal–Wallis and Mann–Whitney tests (α = 0.05). Results The results showed significant differences among the four types of luting cement in marginal permeability (PV < 0.001). Regardless of the type of cement, the 12-degree tapering resulted in a lower microleakage (46.4% without microleakage) with statistically significant differences from the 6-degree tapering (PV = 0.042). Conclusion Within the limitations of this study, increasing the tapering degree of the prepared tooth for CAD/CAM zirconia copings improved the marginal fit and decreased the microleakage score. In addition, total-etch resin cement indicated the least microleakage.