Contact Length Research Articles

Characterisation of the Contact between Cross-Country Skis and Snow: A Macro-Scale Investigation of the Apparent Contact

In a cross-country skiing competition, the time difference between the winner and the skier coming in at second place is typically very small. Since the skier spends much of the energy on overcoming resistive forces, a relatively small reduction in these forces can have a significant impact on the results. The resistive forces come partly from the friction, at the tribological interface between the ski and the snow, and as with many tribological processes, the characterisation of its origin plays an important role in determining the frictional properties. Furthermore, in cross-country ski friction, there are several scales impacting the frictional performance, with the major contributors being the ski-camber profile and ski-base structure. Macro-scale measurements of the ski-camber profile under loading are often used to determine how adequate the ski is for use under specific conditions. The characteristic properties usually assessed are the force required to collapse the ski in order to obtain a certain camber height, the topography of the kick-wax zone, and the length (determined by simple means) of the frictional interfaces associated with the rear- and front glide zones, i.e., the apparent contact length. These measurements are, however, commonly performed by loading the ski against a much stiffer counter surface than snow and this affects the quantification of the characteristic properties. To date, some mathematical models have been proposed, but there is no reliable approach for determining the macro-scale properties of the contact between a cross-country ski and a counter surface using simulations. In the present paper, an Artificial Neural Network (ANN) has been trained to predict the ski-camber profile for various loads applied at different positions. A well-established deterministic approach has been employed to simulate the contact between the ANN-predicted ski-camber profile and a linearly elastic body with a flat upper surface, representing the snow. Our findings indicate that this method is feasible for the determination of relevant macro-scale contact characteristics of different skis with snow. Moreover, we show that the apparent contact area does not linearly depend on the load and that the material properties of the counter surface also exert a large impact when quantifying the apparent contact area and the average apparent contact pressure.

Monitoring Epoxy Coated Steel under Combined Mechanical Loads and Corrosion Using Fiber Bragg Grating Sensors.

Fiber Bragg grating (FBG) sensors have been applied to assess strains, stresses, loads, corrosion, and temperature for structural health monitoring (SHM) of steel infrastructure, such as buildings, bridges, and pipelines. Since a single FBG sensor measures a particular parameter at a local spot, it is challenging to detect different types of anomalies and interactions of anomalies. This paper presents an approach to assess interactive anomalies caused by mechanical loading and corrosion on epoxy coated steel substrates using FBG sensors in real time. Experiments were performed by comparing the monitored center wavelength changes in the conditions with loading only, corrosion only, and simultaneous loading and corrosion. The theoretical and experimental results indicated that there were significant interactive influences between loading and corrosion for steel substrates. Loading accelerated the progress of corrosion for the epoxy coated steel substrate, especially when delamination in the epoxy coating was noticed. Through the real-time monitoring from the FBG sensors, the interactions between the anomalies induced by the loading and corrosion can be quantitatively evaluated through the corrosion depth and the loading contact length. These fundamental understandings of the interactions of different anomalies on steel structures can provide valuable information to engineers for better management of steel structures.

Influence of loading and grafting on hard- and soft-tissue healing at immediately placed implants: An experimental study in minipigs.

To histologically evaluate the influence of (1) loading and (2) grafting on osseointegration and peri-implant soft-tissue healing at immediately placed, self-cutting progressive tissue-level implants (TLX) in a minipig model. TLX implants (n=56) were immediately placed following the extraction of the mandibular first and second premolars, bilaterally, in a total of n=14 minipigs. In each animal, the implant sites were allocated to the following four groups: (1) unloaded with simultaneous grafting using a bovine bone mineral; (2) unloaded without grafting; (3) loaded with simultaneous grafting; and (4) loaded without grafting. Histomorphometric assessments at 4 and 12 weeks (n=7 animals each) included primary (i.e., bone-to-implant contact [BIC]) and secondary outcome measures (e.g., first BIC [fBIC], junctional epithelium length [JE], connective tissue contact length [CTC], biological width [BW=JE + CTC]). At 4 weeks, mean BIC values ranged from 74.5± 11.6% in Group 2 to 83.8± 13.3% in Group 1, and, at 12 weeks, from 75.5%± 7.9% in Group 2 to 79.9± 8.6% in Group 1. Multivariate linear mixed regression did not reveal any associations between BIC and implant loading or grafting at 4 and 12 weeks. At 12 weeks, significantly higher fBIC values were noted in Group 2 when compared with Group 1. All groups showed comparable JE, CTC, and BW values. Implant loading and grafting had no major effects on osseointegration and peri-implant soft tissue healing at TLX implants.

Revealing the wetting mechanism of Li+-doped ionic liquids on the TiO2 surface

The sensible design of ionic liquid (IL)-based application relies on a thorough knowledge of the structure and characteristics of electrolyte–electrode interfaces. Here, the wetting processes of the Li+-doped ILs droplets on the TiO2-B(100) surface are investigated by molecular dynamics simulation. According to the spatial distributions of components, doped Li+ prefers to substitute the ILs and adsorb to the substrate, causing the orientation changes of the ILs, weakening the ILs-substrate interaction, and slowing down the wetting process significantly. As Li+ concentration rises from 0 to 80 %, the contact angle increases from 86.97 to 131.18°, inducing the hydrophilic-to-hydrophobic transition. On the contrary, heating up would reduce the contact angle by extending the contact length and enhancing the maximum density of Li+-doped ILs at the interface. These quantitative results prove that the dense adjacent layer in the interface induced by the strong adsorption of Li+ dominates the wetting process of Li+-doped ILs.

Determination of the Chip–Tool Contact Length in Orthogonal Cutting

Abstract This work presents an experimental–numerical approach aimed at determining the chip–tool contact length during orthogonal cutting of annealed AISI 4340 steel (223 HV) with TiN-coated tungsten carbide inserts. Initially, pin-on-disc tests were performed, followed by orthogonal cutting tests. The components of the cutting force were used to calculate the coefficient of friction in orthogonal cutting, and its value was compared with those obtained under sliding. Moreover, the cutting force components obtained experimentally were used to assess the reliability of the finite element model and estimate the temperature in the cutting zone. The contact length between chip and rake face was calculated based on the experimental feed force and shear strength of the work material and was compared with the results provided by an analytical model. The experimental–numerical approach can be considered more accurate due to the fact that it considers the effect of the tool–chip interface temperature on the shear strength of the work material. However, the analytical model is quite straightforward, since it only requires the values of chip thickness and undeformed chip thickness to estimate the tool–chip contact length.

Laminated bamboo lumber in compression perpendicular to the grain direction: Experimental investigation and the finite element analysis

ABSTRACT Localized damage may occur due to the fact that laminated bamboo lumber (LBL) has a lower compressive strength perpendicular to the grain direction than it does parallel to the grain. In this study, the transverse compressive performance of LBL under entire-surface compression and local-surface compression is investigated. Load–displacement curves, stress–strain relationship, detailed failure modes, and basic mechanical properties are obtained. The results show that despite the compressive strength and elastic modulus being nearly the same in the two transverse orientations, the failure patterns are distinct due to the layer structure. Ramberg-Osgood relation is utilized to fit the stress–strain curves. Proportional limit strength is determined indicating that specimens compressed locally have a greater load-bearing capability. Based on the finite element analysis and theoretical study, the mechanism of the enhancement in proportional limit strength is revealed. Equations for determining the bearing load of a specimen under local compression in the elastic stage are derived from the simulation data and logit model, considering the contact length and geometric size of the specimen. Additionally, parametric tests are conducted to determine the effect of bearing shape, bearing area, and loading mode on the stress distribution and bearing capacity.

On modelling coolant penetration into the microchannels at the tool-workpiece interface

A network of microchannels is formed at the interface between the cutting tool and the workpiece during machining due to their rough surface structures. The penetration of coolant into these microchannels has a great effect on the machined surface quality by changing the frictional behaviour and heat transfer characteristics of the interfaces. Most of the present studies focus on the macroscopic coolant delivery process but the mechanism of the microscopic penetration phenomena in the channels at the interface remains unclear. Thus, this study proposes a multi-scale and multi-phase comprehensive theoretical model by combining the machining process, coolant flowing in microchannels and lubrication process, to analyse the coolant transportation in the microchannels and investigate its lubrication effects and the friction mechanisms at the interface between the tool and the workpiece. Then, an orthogonal turning testing of Inconel 718 is designed to verify the proposed model. The cooling and lubrication effect of coolant in the microchannels on the reduction of tool wear, contact length, cutting force and temperature has been demonstrated. And the improvement of chip fragment and microstructure has also been revealed.

Influence of steel slag incorporation on internal skeletal contact characteristics within asphalt mixture

• Shape features of steel slag and limestone were calculated. • Meso-parameters of skeleton such as contact points and length were analyzed. • Gradations dominate the contact performance of steel slag in asphalt mixtures. • Potential interaction exists between gradation and slag content on skeleton contact. • Contact indicators of skeleton are remarkably influenced by aggregate angularity. This study employed X-ray computed tomography (CT) and image processing technology to characterize and quantify the internal skeleton composition within asphalt mixtures incorporating steel slag. The shape indices of steel slag and limestone including form and angularity features were calculated and meso-parameters of skeleton such as contact points, coordination number, and contact length were analysed, aiming to establish the relationship between aggregate shape and skeleton. The effect of gradations and slag contents were considered as well. Results denote gradations dominate the contact performance, the beneficial angularity of steel slag allows the promotion of contact originated by 4.75 mm-16.0 mm particles with surrounding ones in stone matrix asphalt (SMA-13), while encourages the contact from 2.36 mm to 4.75 mm particles in dense-graded asphalt concrete (AC-13). Instead of the common short contact lines in AC-13, the introduction of steel slag assures that SMA mixture creates plentiful longer contact lines among aggregates. Significance analysis indicates there is potential interaction between gradation and slag content on the skeleton contact. The skeleton of SMA mixture is more susceptible with slag content rather than AC one. Among overall meso-parameters, the average coordination number of 4.75 mm-9.5 mm particles and the sum of contact length are closely related to rut depth, and are remarkably influenced by the angularity of aggregate. These findings contribute to optimizing the skeleton design of steel slag asphalt mixture from the perspective of aggregate shape and possess enormous potential to reduce the dual environmental impacts of steel slag accumulation as well as resource mining.

Numerical study of mechanical clamps crack arresting efficiency in temporary repair solutions for cracked marine pipelines

ABSTRACT In this study, a typical gas pipeline exposed to environmental conditions is modeled through the finite element method to investigate the fracture response of the cracked pipeline and compare various mechanical clamps crack arresting efficiency. Comparing numerical simulation results with those available analytical data reveals a good agreement. The results show that tight-fit sleeves practically arrest longitudinal cracks and stop their growth entirely, as SIF values for cracks with the inclination angle of more than 30° are entirely negative. Furthermore, it is understood that cracks with inclination angles of up to about 30° are critical to arrest. It is found that friction between the clamp and the outer surface of pipeline and also clamps’ contact length may not consider as important options for increasing the clamp efficiency, while they have insignificant effect on arresting longitudinal cracks with the inclination angle of more than 30°.

MACHINE LEARNING-BASED MODELING AND OPTIMIZATION IN HARD TURNING OF AISI D6 STEEL WITH ADVANCED AlTiSiN-COATED CARBIDE INSERTS TO PREDICT SURFACE ROUGHNESS AND OTHER MACHINING CHARACTERISTICS

In recent times, mechanical and production industries are facing increasing challenges related to the shift towards sustainable manufacturing. In this work, the machining was performed in dry cutting condition with the newly developed AlTiSiN-coated carbide inserts coated through scalable pulsed power plasma technique, and a dataset was generated for different machining parameters and output responses. The machining parameters are speed, feed and depth of cut, while the output responses are surface roughness, cutting force, crater wear length, crater wear width and flank wear. Abrasion and adhesion were found to be the two dominant wear mechanisms. With speed, the tool wear was found to increase. Cutting force was found to increase rapidly for higher speed ranges (70, 80 and 90[Formula: see text]m/min). But reduction of cutting force was observed in both low and medium ranges of cutting speed (40, 50, 55 and 60[Formula: see text]m/min). With higher values of feed and depth of cut, higher cutting force was also noticed. With the variation of depth of cut, the machined surface morphology and machined surface roughness were found to deteriorate. With higher feed and depth of cut values, more surface damages were observed compared to low values of feed and depth of cut. Both the feed rate and tool–chip contact length contributed significantly to the formation of crater on the tool rake surface. At high speed, continuous chips were observed. Both chip sliding and sticking were observed on the tool rake face. The data collected from the machining operation was used for the development of machine learning (ML)-based surrogate models to test, evaluate and optimize various input machining parameters. Different ML approaches such as polynomial regression (PR), random forests (RF) regression, gradient boosted (GB) trees and adaptive boosting (AB)-based regression were used to model different output responses in the hard machining of AISI D6 steel. Out of the four ML methodologies, RF and PR performed better in comparison to the other two algorithms in terms of the [Formula: see text] values of predictions. The surrogate models for different output responses were used to prepare a complex objective function for the germinal center algorithm-based optimization of the machining parameters of the hard turning operation.

Indentation of a free beam resting on an elastic substrate with an internal lengthscale

The plane strain problem of a slender and weightless beam-plate loaded by a transversal point force in unilateral contact with a couple stress elastic foundation is investigated. The study aims to explore the consequences of the material internal lengthscale on the contact mechanics. In particular, compatibility between the beam and the foundation surface demands that both displacement and rotation match along the contact line. To this aim, couple tractions are exchanged besides the traditional contact pressure until separation between the beam and the foundation occurs. The problem is formulated making use of the Green's functions for a point force and a point couple acting atop of a couple stress elastic half-plane. A pair of coupled integral equations is thus derived, that governs the distribution of contact pressure and couple tractions, with one of them being immediately solved to provide an explicit relation between the two unknowns. In this sense, we retrieve the concept of a mechanically equivalent action, as it is the case of the Kirchhoff shear for plates. The remaining integral equation sets a cubic eigenvalue problem, whose linear term accounts for the microstructure. Its numerical solution is sought by expanding the equivalent contact pressure in series of Chebyshev polynomials vanishing at the contact region ends points, namely the lift-off points, and then applying a collocation strategy. The contact length, the distributions of contact pressure and couple tractions under the beam and the shearing force and bending moment along the beam are then obtained as a function of the material characteristic length. Results clearly indicate that accounting for the material internal lengthscale is mainly realized through exchange of the couple tractions, in the lack of which results much resemble those of the classical solution. Specifically, greater contact lengths and a stronger focusing effect about the loading point are encountered, which become very significant when the contact length approaches the internal lengthscale.

Effect of Coconut Oil-Based Cutting Fluid on Cutting Performance During Turning With Minimal Fluid Application

In the present work, an attempt was made to use vegetable oil as a cutting fluid during minimal fluid application to make the process more environmentally friendly. Coconut oil was selected as the vegetable oil in this study considering its availability, physical properties, and lubricating ability. The effect of newly formulated coconut oil-based emulsified cutting fluid on cutting performance during turning of hardened AISI 4340 steel with the minimal fluid application was investigated. It was observed that the coconut oil-based cutting fluid offered better cutting performance in terms of tool wear, surface roughness, cutting force, cutting temperature, and tool chip contact length when compared to mineral oil-based cutting fluid and raw coconut oil. It was also observed that the percentage of concentrate in the cutting fluid was to be maintained as 30% to achieve better cutting performance. The use of coconut oil-based cutting fluid holds promise as an environment friendly alternative for mineral oil-based cutting fluid.

Adaptability of hydraulic fracturing packers and optimization of their sealing performance for three common clastic rock reservoirs based on finite element analysis

In this paper, the adaptability characteristics of the packer to three types of common clastic rock reservoirs (mudstone, shale, sandstone) are analyzed systematically. Moreover, the identification and structural design of the packer in hydraulic fracturing are systematically conducted based on the finite element calculation. Finally, the nonlinear mathematical models of the packing safety factor and the pressure under the packer and the conditions of casing, mudstone, shale and sandstone are obtained. The results show that the maximum stress of the rubber cylinder in the three formation models of mudstone, shale and sandstone is lower than the compression set strength of the rubber cylinder, indicating that the rubber cylinder will not cause stress damage. At the same time, by analyzing the common rubber materials and constitutive models of the packers, the structure of the packer rubber cylinder and a new anti-shoulder protrusion device were redesigned. The Nitrile-butadiene rubber (NBR) meets the performance requirements of the rubber tube under the allowable pressure difference and temperature difference. The designed new anti-protrusion device can ensure the structural integrity and stress uniformity of the rubber tube, thereby ensuring good sealing performance. Under the three formation conditions of mudstone, shale and sandstone, the rubber cartridge can be in a safe working state, and its sealing width is close to the contact length of the rubber cartridge. In addition, the rubber cartridge is in a good elastic deformation range. The design of the packer in this study satisfies the third strength theory and the safety requirements. The deformation and sealing performance of the rubber cylinder are relatively stable, and the size of the rubber cylinder also meets the field requirements.

Effect of intermittent cutting behavior on the ultrasonic vibration-assisted grinding performance of Inconel718 nickel-based superalloy

Ultrasonic vibration-assisted grinding (UVG) is a promising precision machining method for difficult-to-cut materials. This study investigated the intermittent cutting behavior in UVG of Inconel718 nickel-based superalloy and its effect on the grinding temperature, grinding force and workpiece surface quality. A novel material removal probability model was established to analyze the impact depth and the contact length between the abrasive grain and the workpiece considering the interference of grinding trajectories in UVG. Results indicated that the intermittent cutting behavior in UVG caused a decrease in the contact length by 42%, resulting in a significant reduction of grinding temperature and grinding force by 40% and 41%, respectively. It was suggested that the increase in the cutting depth was better than the increase in the workpiece infeed speed for enabling the lager material removal rate in the tangential UVG due to the lower grinding force ratio and the less change of specific grinding energy. A specific surface texture was generated on the ground surface due to the phenomenon of frequent contact and separation, enabling the reduction of workpiece surface roughness by maximum 20%.

Prostate-specific antigen level, biopsy grade group, and tumor-capsular contact length on magnetic resonance imaging are independently associated with an extraprostatic extension.

To define the clinicopathological and radiological factors independently associated with the existence of an extraprostatic extension in radical prostatectomy specimens. A total of 202 patients who underwent robotic prostatectomy following biparametric magnetic resonance imaging were assessed. We evaluated the clinicopathological and magnetic resonance imaging variables. We performed receiver-operating characteristic curve analyses to identify factors associated with extraprostatic extension. We engaged in multivariate analysis to identify factors independently associated with such extension. Extraprostatic extensions were apparent in the final prostatectomy specimens of 62 patients (31%). The areas under the curves of the prostate-specific antigen level, the biopsy grade group, and the tumor-capsular contact length on magnetic resonance imaging were 0.76, 0.71, and 0.70, respectively, in receiver-operating characteristic analysis when used to predict extraprostatic extension; thus, higher than the areas under the curves of the other variables (0.61-0.68). The prostate-specific antigen level (odds ratio 1.090, p = 0.004), the biopsy grade group (odds ratios 2.678 and 6.358, p = 0.017 and p < 0.001 for grade group 3-4 and 5), and the tumor-capsular contact length (odds ratio 1.079, p = 0.001) were independently associated with extraprostatic extension. When the three factors were combined, the area under the receiver-operator characteristic curve increased to 0.79. The prostate-specific antigen level, the biopsy grade group, and the tumor-capsular contact length on magnetic resonance imaging were independently associated with extracapsular extension.

Atomic transistors based on seamless lateral metal-semiconductor junctions with a sub-1-nm transfer length

The edge-to-edge connected metal-semiconductor junction (MSJ) for two-dimensional (2D) transistors has the potential to reduce the contact length while improving the performance of the devices. However, typical 2D materials are thermally and chemically unstable, which impedes the reproducible achievement of high-quality edge contacts. Here we present a scalable synthetic strategy to fabricate low-resistance edge contacts to atomic transistors using a thermally stable 2D metal, PtTe2. The use of PtTe2 as an epitaxial template enables the lateral growth of monolayer MoS2 to achieve a PtTe2-MoS2 MSJ with the thinnest possible, seamless atomic interface. The synthesized lateral heterojunction enables the reduced dimensions of Schottky barriers and enhanced carrier injection compared to counterparts composed of a vertical 3D metal contact. Furthermore, facile position-selected growth of PtTe2-MoS2 MSJ arrays using conventional lithography can facilitate the design of device layouts with high processability, while providing low contact resistivity and ultrashort transfer length on wafer scales.

Surface profile and milling force prediction for milling thin-walled workpiece based on equivalent 3D undeformed chip thickness model

With the development of the aviation manufacturing industry, the application range of thin-walled parts is rapidly increasing. Accurate machining process and surface topography prediction are the keys to ensuring machining quality. This article is based on the relative geometric relationship between the real motion trajectory of the milling cutter and the workpiece; the undeformed chip thickness equation and the two-dimensional surface contour feature algorithm are established. By introducing the parameters of milling cutter critical height, milling cutter helix angle, and lag angle parameters, the three-dimensional surface profile prediction model and the equivalent three-dimensional model considering the chip formation process are derived. And the calculation equations of the instantaneous chip cross-sectional area and the blade-workpiece contact length of the three phases of chip formation are established, respectively. The multiple linear regression method was used to fit the orthogonal test results of titanium alloy Ti-6Al-4 V, so as to complete the dynamic milling force identification, and finally establish the milling force prediction model. The accuracy of the prediction model was verified by the single factor method, and the influence of different parameters on the milling process of thin-walled parts was observed. The results show that the established model has high accuracy in predicting the surface profile and milling force of thin-walled parts. This study provides guidance for efficient prediction of the milling process of thin-walled parts.

EP-241 Surgical virtual clinic (VC) practice: an audit of practice in the University Hospitals Sussex NHS Trust

Abstract Aims The aim of the study was to assess the appropriateness of surgical virtual clinic practice (VC) in the University of Sussex hospitals. Methods A retrospective assessment of Six consecutive clinics of three consultants, a total of 216 patients, was audited according to guidelines of the Royal College of Surgeons (1). Additionally, feedback forms were obtained from ten Consultants and matched against RCS guidelines. Ethical approval was obtained from the quality improvement department. Results The study cohort mean age was 67 (20–94) years with 1: 1.2 female to male ratio. VC site was 68% from home. The VC attendance rate was 97.5% (2.5% DNA rate) and 93% patients were suitable for VC appointment because 2.8% needed physical examination and remaining percentage was not suitable due to hearing impairment and language barrier. Telephone was the mode of virtual consultation in addition to 100% documentation and 100 conclusion documentations. Four blocks of RCS guidelines compliance based upon the opinion of the consultant surgeon was reported from 65% to 97.5%. Conclusion The attendance of VC clinics was 97.7% with suitability for VC up to 93%. There was a good compliance with RCS guidelines reaching up to 97.5%. However, few areas which needs improvement are obtaining consent (documentation if consent was taken), confirmation of alternative contact details, length and details of VC and reassurance that VC is equivalent to face to face clinic in terms of service provision.

Two-stream interaction problem and its application to mass transport

Classical boundary layer theory is effectively extended to study two-stream interaction problems. In particular, by proper scaling we invent a universal curve which relates the second-derivative initial condition of the normalized stream function to the first-derivative free-stream condition. This relationship is independent of any fluid property, and the Blasius flow profiles in respective streams are connected by matching at the interface. Accurate approximations to the universal curve are constructed by piecewise third-order polynomials. This technique finds an excellent application to mass transport problem of solvents from one immiscible fluid to another, namely, extraction of fluid as an interfacial problem. Analytical formula is obtained to show explicit dependence of mass flux on the nonlinear Blasius profiles, partition coefficient, Schmidt numbers, ratio of mass transfer coefficients, ratio of kinematic viscosities as well as the contact length of the two immiscible fluids. In other words, given these physical parameters, we directly obtain the mass flux simply by numerical quadrature of integrals involving the Blasius profiles.

Impact of Metal Hybridization on Contact Resistance and Leakage Current of Carbon Nanotube Transistors

Carbon nanotube field effect transistors (CNFETs) have potential applications in future logic technology as they display good electrostatic control and excellent transport properties. However, contact resistance and leakage currents could limit scaling of CNFETs. Non-equilibrium Green’s function (NEGF) simulation investigates that coupling between contact metal and CNT impacts both contact resistance and leakage current. The physical mechanisms underlying the effects are analyzed. A model with calibrated metal coupling strength from experimental data projects I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ON</sub> -I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">OFF</sub> design space to understand the trade-off between shrinking contact and extension lengths. For CNT with diameter of 1 nm, both contact and extension lengths greater than 8 nm are a good compromise between I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ON</sub> and I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">OFF</sub> for digital logic in advanced technology nodes.